Axiomatic Model

A Sky without veils

Premise:

1) With this work, I set out (using only mathematical tools and without any experimental observations) to explore the possibility and feasibility of working out, through a coherent formal theory[1], a ‘cosmological model’, according to a procedure akin to that of a theorem[2] that                                                                                         

– Identifies axioms/postulates;                                                                                                                              

– Draws, through reasoning, deductions, inferences (logical implications), demonstrations, … certain conclusions.                                                                                                                                                      

The conclusions, which are reached, do not have a subjective character, of the type: ‘I think that …‘, ‘it seems to me that …‘ but, in the rigor of the formal coherence of the arguments made, they draw their reasons from what are the direct and indirect consequences of the two axioms used.

2)Theoretical physicists and all that galaxy of specialists in the various fields of experimental physics and beyond, wherever they operate in this infinite Universe of ours, carry out an important part of their work around those boundaries that separate the known from the unknown. of these boundaries we find, respectively: in the direction of the infinitely large and in the opposite direction, of the infinitely small. Every time science takes a step forward and makes new discoveries, wherever this happens, that specific ‘red thread’ that, there, separates the known from the unknown is moved a little further into that endless, borderless field of awareness and knowledge. It must be said, however, that this quest evokes the intriguing and fascinating concept of the limit which, applied to our scientific investigation, reminds us that there is and always will be an insurmountable boundary. In steps, ever smaller and smaller, we can relentlessly approach this tantalizing boundary that is and will always remain unreachable. Sean Carroll in Copyright C 2012, writes: «…thousands of person-years of effort by good scientists who sacrifice their lives to dig just a little deeper into the mysteries of nature. »

3) As one enters the world of the extremely small, the size of what is used for research and observation (photon of light, for example) tends to approximate to the size of what is being researched. This situation inevitably complicates things because the observation process tends to modify what is observed and thus distort the results of that observation. Heisenberg’s “uncertainty principle” essentially says this and states that we cannot know, with precision, simultaneously the position and the momentum of a particle.   Heisenberg’s “uncertainty principle” essentially says this and establishes that we cannot know, with precision, simultaneously the position and the momentum of a particle. Research, in the field of the extremely small, can only resort to “probability functions“, which allow, in some way, to compensate for the impossibility of knowing all the variables, the object of the research.

[1] David Hilbert: ‘Mathematics is the mediating tool between theory and practice, between thought and observation…’

[2] A theorem is a proposition or set of several propositions that, starting from arbitrarily established initial conditions (axioms/postulates), draws conclusions, using a finite sequence of deductive steps (inferences), ending with the thesis of the theorem to be proved (the conclusions).

Subjects treated:

- First axiom: 'the law of conservation of energy';

- Second axiom: 'the law of universal gravitation';

- Observations regarding other cosmological models;

- Some considerations;

- The starting point;

- The axiomatic model;

– Effects foreseen by the same.

First axiom: ‘ the principle of conservation of energy or mass ‘

[Nothing is created; nothing is destroyed.] [3]

This principle only confirms what Titus Lucretius Carus (*98/94 BC †50/55 BC) already claimed in the first century BC, namely that:

  ‘Nothing is ever born out of nothing by divine virtue and nothing is reduced to nothing, …’.

This principle attributes to our Universe the character of an endless entity: an ‘infinite Universe‘.

The concept of ‘infinity’, with its infinite levels of infinity, its paradoxes and singularities, is one of the most intriguing, most vertiginous and at the same time most fascinating concepts developed by the human mind. Order, disorder, simplicity and complexity in this  Universe infinite of ours do not detract from the fascination of this concept of infinity; on the contrary, they enrich, enhance and characterize it!

The fact that this ‘infinite Universe‘ does not take the form of an endless repetition of successive and alternating ‘Big Bang‘ and ‘Big Crunch[4]’ finds its justification in the reflection relating to the subject ‘Universe‘ on page 8 and following, of this work and is confirmed (by observational / experimental way) by the discovery, made in 1998, which confirms that the expansion of our cosmos is accelerating and, consequently, the phenomenon called ‘Big Crunch‘ would be excluded.

Regarding this ‘principle of conservation of energy‘, see the chapter concerning: ‘The law/principle of conservation of mass/energy in a non-closed infinite system, but with the characteristics of a ‘perfectly and completely isolated‘

[3] This is actually the principle of conservation of energy, the first principle of thermodynamics.

In: 'The physics of Feynman' (Richard Feynman, Nobel Prize in Physics 1965, for the elaboration of quantum electrodynamics), Vol. 1, we read: 'There is a fact, or if you like, a law, which governs the natural phenomena known so far. There are no exceptions to this law, as far as we know it is correct. The law is called 'conservation of energy', and it is really a very abstract idea, because it is a mathematical principle: it says that there is a numerical quantity, which does not change whatever happens. It doesn't describe a mechanism, or anything concrete: it's just a bit strange: we can calculate a certain number, and when we finish observing nature playing its games, and recalculate the number, we find that it hasn't changed… '. With his  famous end revolutionary formula E = m · c2, Albert Einstein establishes the equivalence between mass and energy and, consequently, the 'principle of conservation of energy' becomes: the 'principle of conservation of mass / energy'.

[4] The ‘Big Crunch‘ is a hypothesis that was formulated a few decades ago and that concerns the fate of our cosmos. This hypothesis argued that, once the expansion phase was over, our Cosmos would begin to contract until it collapsed on itself, symmetrically at the initial Big Bang.

Second axiom: ‘the law of universal gravitation‘

Of this law, used as an axiom, the 'Axiomatic Model' essentially exploits the aspect concerning the peculiarity of each body (endowed with mass/energy) to attract (through their respective gravitational fields) another body or bodies (endowed with mass/energy). It invokes neither the Newtonian principle (of gravity), since general relativity corrects Newton, for velocities close to that of light, nor the Einsteinian principle (of gravity), since ε0 (dielectric constant of the vacuum), μ0 (magnetic permeability of the vacuum), C (speed of light in a 'vacuum'), …  cannot be considered, with certainty, as constants in the totality of the immense infinite Universe and, consequently, the speed of light would also lose its current status as a universal constant. It is useful to remember that the speed of light depends on the values ​​of the dielectric constant and the magnetic permeability because these two constants describe the properties of the medium through which light propagates and the value of 'C ' is inversely proportional to the square root of  (ε0 x μ0).

The peculiarity invoked refers to that necessity and need for an increase in the quantity of mass/energy (see the chapter 'Universal, archaic and ever-present law'). To this archaic and ever-present law should be attributed the main responsibility for the fact that our infinite Universe is not only not static and lifeless, but possesses that dynamism capable of endlessly generating cosmos and then destroying them to generate others, in a sequence with no beginning and no end. The force of gravity, also called the weight force[5], is a force perceived by man and not only by man, since always.

It is a force that acts on every object, endowed with mass, of the world in which we are immersed[6] and constitutes the basis of all cosmic dynamics and beyond.

In the 17th century, the English mathematician, physicist and philosopher Isaac Newton defined it as follows[7]: 'Two bodies endowed with matter attract each other with a force that is directly proportional to the product of the masses and inversely proportional to the square of the distance that separates them'[8].

This is the 'force / curvature of space-time (according to General Relativity)' which:

a.           regulates the fall to the ground of an object, left free in the air;

b.           it is co-responsible for the balance of our solar system;

c.           it is mainly responsible for the birth of celestial bodies, galaxies, clusters of galaxies, black holes,… (matter attracts matter);

d.           is co-responsible for that concentration of mass, with a temperature and pressure such as to trigger a deflagration, followed by a very rapid expansion [9]. It is the one that about 13.8 billion years ago allowed the birth of our Cosmos;

e.           is jointly responsible for the progressive decrease in speed, once the initial propulsive effect is exhausted. Volume has increased; the amount of energy did not change;

f.            is responsible for the subsequent acceleration of this escape velocity[10] when the masses that make up our Cosmos have begun to feel the attraction force of those celestial bodies, not involved in the 'brushing[11]' operation, which are out there, compared to our Cosmos, and whose distance is decreasing more and more rapidly from our galaxies that go towards them, at ever higher speeds[12];

g.        it is jointly responsible for those infinite concentrations of matter (following a gravitational collapse).

Concerning this ‘principle of conservation of energy’, see the chapter ‘The law/principle of conservation of mass/energy in a non-enclosed infinite system, but with the characteristics of a ‘perfectly and completely isolated system‘.

The arguments developed in this chapter allow us to state that this ‘axiomatic model’ could also make use of the second axiom (the law of universal gravitation) exclusively.

This conclusion would authorize the assumption that this law, or at least part of it, is the fundamental law of our entire infinite Universe.

[5] The Latin term 'gravis' means: weight, heavy, grave.

[6] A more complete interpretation of this force has been given in the box on page 54. According to Einstein’s theory of general relativity, even photons of light are affected by the space-time deformations generated by a mass. The ‘gravitational lens’ effect would be a confirmation of this.

[7] In the work: 'Philosophiae Naturalis Principia Mathematica', published July 5, 1687.

[8] This law of gravitation will later be reformulated, in some respects, in Albert Einstein's theory of general relativity. See also note 51, relating to the 'MOND' issue (MOdified Newtonian Dynamics).

[9] The expansion, predicted by this axiomatic model, is confirmed by the work of Hubble, and Milton Humason, who in 1929 announced the discovery of the empirical law concerning the 'redshift' suffered by the light coming from other galaxies. This 'redshift' was the greater the greater the distance of a galaxy from us. This discovery has finally provided confirmation that our cosmos is not static, but undergoing continuous expansion.

[10] This prediction of the 'axiomatic model' is confirmed in the discovery made by some American astronomers in 1998. See chapter 'dark energy'.

[11] For the clarification of what is stated in this point and what is meant by 'brushing', see the chapter 'Black holes'.

[12] The approach to this thinking is developed in the following chapters. However, it is a direct consequence of the axioms on which this work is based.

Observations regarding other cosmological models

Over the past decades, numerous models have been proposed in addition to the 'model (Λ CDM) of cosmology '[13]. None of these, however, was able to satisfactorily answer my 'why' and my 'how'.

In this paper, some considerations/observations will be made, but they will essentially refer to this 'cosmological model (Λ CDM )'.

Some considerations:

a.      The first and second axioms together allow us to affirm that a sustainable and coherent cosmological model cannot in any way do without the component that refers to the concept of 'infinity';

b.      Einstein was convinced that our Cosmos was static (this was a generalized belief at the beginning of the last century) and, for this reason, he included a cosmological constant in its field equations, called: lambda (Λ). However, when the discoveries of Hubble in 1929 (in the wake of what Georges Lemaître predicted in 1927, and even earlier by the mathematician and physicist Aleksandr Aleksandrovich Fridman) allow us to understand that our cosmos is not static but expanding, Einstein rejects this cosmological constant, declaring that it was the greatest error of he.

c.       A large part of current cosmology, in order to justify the escape acceleration of our galaxies, has dusted off the old idea of Einstein's cosmological constant lambda (Λ) (with negative pressure), arguing that it is a 'property of space' and calling it: 'dark energy '.

[13] This model is called: 'Lambda CDM', where Lambda (Λ) stands for cosmological constant, 'C' stands for Cold, 'D' stands for Dark and 'M' stands for Matter. Therefore: 'Lambda-Matter-Dark-Cold'.

It is a cosmological model that describes the universe as an expanding system dominated by cold dark matter (CDM) and a cosmological constant Lambda (Λ), which would correspond to the one used by Einstein (rejected afterwards by him) and which is supposed to represent what is now called 'dark energy'. This model explains, in its own way, the evolution of the universe, from its origin, through the Big Bang, to its current structure.

It is useful to remember that none of the ‘Cosmological Models’ known today has a status of ‘Theorem’; they are configured as theories, as hypotheses and, at most, (like the Model Λ CDM) founded according to the criterion of ‘logical economy’ (novacula Occami).

Creation

Resorting to the idea of creation is incompatible with one of the axioms on which this work is based, which is the principle of conservation of energy. 

It is also unthinkable to argue that we can make a 'sufficient but not necessary condition' (that of propulsion from within our cosmos), a 'necessary condition', given that the existence of another condition that can be considered 'sufficient' cannot be ruled out: namely a force of attraction, exerted from outside. This assumption is confirmed by the fact that the Universe, of which our Cosmos constitutes a subset proper, is not only infinite in time, but is endowed with an infinite 'mass/energy'.

Our ‘physical laws’ are considered valid and are declared unquestionable by present-day science, but science must necessarily take note that these laws are those of a specific subset of the infinite Universe, that of our Cosmos and more precisely of what is called the ‘observable universe’ (a proper subset of our own Cosmos, with a diameter of approximately 93 billion light years). In fact, many laws are based on observations and measurements made within a given cosmological framework. Some theoretical models, such as eternal inflation, suggest that there may be multiple universes with different physical laws. For this ‘axiomatic model / theorem‘, this proper subset can only represent an infinitesimal of the infinite Universe.

Since a certain number of physical laws, formulae and equations devised in and for this subset of our own cannot but depend on the specific value of the energy that gave rise to our Big Bang, it is certainly neither licit nor permissible to attribute a universal value to these laws. These may be valid for an infinite number of their own proper subsets and not be valid for others, of our infinite Universe.

A proper and finite subset of the infinite Universe, therefore of the size of an infinitesimal, cannot claim to erect itself as the model and rule of the infinite entity of which it is a part, i.e. of our entire infinite Universe.

The starting point

The attempt to remedy the critical issues contained in the 'model (Λ CDM) of cosmology' and beyond led to the exploration of the possibility of developing a model based essentially on logical-mathematical principles.

Introduction

Since ancient times, humanity has felt the need to find answers to the various 'whys' and 'how' concerning its habitat. At first, the focus was probably on the surrounding environment and then, gradually, the horizons widened to encompass ever larger spaces and subjects, both in the direction of the infinitely large and in the direction of the infinitely small.

The various civilizations that have followed have developed beliefs, superstitions and convictions, often very different from each other.

The literature, available today, which addresses the problems of ‘whys‘ and ‘how‘ concerning cosmology, is indeed very vast. The theories and models that aim to shed light on the how and why of this Cosmos of ours are numerous and perhaps even more.

Every serious study and every coherent and sensible idea undoubtedly brings a contribution to knowledge and nothing should be overlooked in the search for some more truth, regarding current knowledge.

Since I have not been able or have not been able to find, in the literature cited, what has been floating in my head for years, I have made the decision to put, in black and white, some reflections.

Preview:

[The first part of this chapter, in wisteria color, shows a particularly pleasant memory of mine from my life path, which certainly marked my thoughts for the following years. It is not an essential element of this work and can be ignored.]

My great-aunt Émilie (Meulîe), sister of Pierre, my maternal grandfather, was a cultured person.

She was an elementary school teacher in Combes, a village in the municipality of Introd (Vallée d'Aoste), a place of vacation and rest, for years, of the popes: St. John Paul II and his successor Benedict XVI.

With a cheerful and very witty character, Émilie loved to read and, in particular, she loved to meditate. When I went to see her, on long winter evenings, I often found her in the dark. She wasn't sleeping, she greeted me and said: 'arta mòque la leumii' (turn on the light). Often he justified himself by saying that electricity should be saved, when possible.

She was very happy to have me with her for a moment and took the opportunity to tell me something, taken from her great wealth of memories.

I listened to her, sometimes very interested, sometimes a little less. However, I knew that his stories always ended with a small and particularly welcome gift for me. It was a teaspoon of condensed milk, taken from a cylindrical metal can.

Sometimes she took advantage of it too… a teaspoon each.

Then he placed with great care and always with the same slow and neat gestures, that precious (for me and perhaps not only for me) jar in his ancient and sober fir wood cabinet, which I still cherish today.

I tried to make this moment of tasting so appreciated and yummy last as long as possible.

Meulîe was a practicing Catholic Christian, although at times she expressed some perplexity regarding certain dogmas of the Church.

He often asked himself, without making it a question of principle, why that 'god' wanted or had to wait so long before manifesting himself (he showed up only 2,000 years ago for our religion) and to give indications and prescriptions for the redemption of only a small part of humanity. He added: 'Didn't all those who lived before the coming of our Christ really deserve it?'

Today I think of eras (but not only those) that saw the work of the figures of Thales (* 640/625 † 548/545), of Pythagoras (* 625 † 546), of Plato of Euclid (who lived around 300 BC), of Aristotle (fourth century BC) of Archimedes (* 288 BC † 212 BC), of Lucretius (first century BC), …

However, he ended up concluding: ‘believing hurts no one and if that someone is not up there, the world does not fall apart….’.

In this vision of the world, Meulîe took up and made her own a thought already expressed, at the time, by the mathematician, physicist and philosopher Blaise Pascal.

In her will, in addition to leaving what she possessed to her niece Simonne (my mother) and her husband Mario (my father), Meulîe left a plot of land, intended for the cultivation of rye, in the locality of 'Combagola' (Cumba-Galla, in documents from the late Middle Ages, meaning an area inhabited by people from Gaul) to the parish of Introd, so that every year and 'à perpétuité' (forever)[14], a mass in its suffrage was celebrated. 

She took out insurance for eternity.

Meulîe was also known and appreciated as a 'healer' and, a few months before leaving us, she gave me her 'lîvro dî seucret' (book of secrets). This was actually a notebook, which contained formulas, prayers and procedures necessary to obtain the healing of the patients who came to her.

It had been written entirely in her own hand (in French), after having received it from her godmother, who had explained to her to copy what was given to her and then to burn the text that had been sent to her, so that this gesture could produce the desired effects. I should have done the same.

In reality, I never copied the contents of that notebook, because I intended to keep what my great-aunt wrote.

That 'lîvro dî seucret' was then burned in the fire that, in October 2003, devastated our house and completely destroyed the contents of our accommodation.

Meulîe knew how to make a correct and discreet use of irony and also made self-irony.

Of herself, she said she was 'àn lûpa' (a she-wolf).When, one day, I asked what he meant by that statement. She replied that she too (Meulîe) collected everything, absolutely everything, just as she had done, a few millennia earlier, that Roman she-wolf who had also collected and then nursed Romulus and Remus.

As my 'lanta Meulîe' (aunt Émilie), I too have some doubts about some dogmas of the church and not only of the church.

I have, since many years, put aside the idea that the world in which we live could be the work of some 'Divinity' who, at a certain moment, decided to give rise to his own 'Cosmos'.

However, I must admit that I have just as much, and perhaps even greater, difficulty in accepting a rather widespread and generalized idea today, according to which this 'Cosmos' of ours, and everything (including space and time), would have been born in this way, from a certain initial ' gravitational singularity[15]', at a given moment, billions of years ago, following an event, the 'Big Bang', responsible for a very rapid expansion.

[14] Last glimpses of an idea and a conviction that everything was like this, that it is and it will be. In his work: 'Physics', Aristotle (fourth century BC) argued that the universe is static, eternal and unique, with its 55 rotating spheres.

[15] A point where the curvature of space-time should tend towards an infinite value (??). It is called this, because current physics cannot explain this event. Many hypotheses have been formulated.
One of these presupposes that the sum of the energy present today is equal to 'absolute zero' and that our cosmos was born from this 'absolute zero'. Perhaps one day, taking a step that requires a bit of 'courage', our scientific community, or at least part of it, will dare to replace this concept of 'absolute zero' with another, no less demanding but more consistent, sensible and finally inevitable, that of the 'infinite'.

The Universe and our Cosmos

Before going into the details of the topic that I want to address, I want to clarify what is meant, in this model, by ‘Universe‘ and what is meant by ‘Our Cosmos‘.

- Universe: infinite entity, not limited in 'space-time', a whole that includes everything, including itself as an improper subset;

The Universe can only occupy an unlimited  'space-time'  and, at the same time, can only contain an infinite  'mass / energy'.

- Our Cosmos[16]: space-time entity, proper (non-empty) subset of the set 'Universe.'

This ‘our Cosmos‘ must therefore be identified with what today is commonly called ‘universe‘.

According to what is suggested by the 'model Λ CDM ' of cosmology, and beyond, the 'Big Bang' would have given rise to this Cosmos of ours, to everything and it would have taken place about 13.8 billion years ago. He would be responsible for the origin of matter, space and time.

There are no elements to doubt the fact that this 'Big Bang' really took place (this axiomatic model foresees it) and on the date indicated[17], however, it should be noted that, if we want to avoid having recourse to some form of  'creationism' (current science rejects it), one cannot help but conclude that the entity that generated it must necessarily contain in itself all the necessary (energy/mass, momentum and whatnot …) for the birth and development of this 'our Cosmos'.

On the other hand, the forecasts of this 'axiomatic model' do not include the possibility that, at that moment, everything was born, including space and time[18]. This model predicts this very rapid expansion, due to the 'Big Bang', is nothing more than the effect of a situation that developed in a space-time[19] preceding that explosion. 

This situation finds, in turn, its reason and the origin of its 'being' in yet another earlier one. A principle is evoked here, that of causality, that is: of 'cause-effect'.

The mathematician, physicist, astronomer and politician Pierre-Simon Laplace, in ‘Essai philosophique sur les probabilités’ (1814), writes:

«Nous devons donc envisager l'état présent de l'univers comme l'effet de son état antérieur et comme la cause de celui qui va suivre ...' that is: 'We must therefore consider the current state of the universe as the effect of its previous state and as the cause of the next one ... »[20]

[16] Term deriving from the Greek κόσμος (kósmos) which means 'order'.

[17] I am not able to express a judgment on the correctness of this value. What is known is that not all 'insiders' agree on this date.

[18] See the arguments, regarding the infinite entity characteristic of 'Universe', on page 2.

[19] I realize that what is meant by 'previous space-time' should be defined. In the following pages this concept will be clarified, for now I would suggest to take it like this, in an intuitive way.
[20] [Einstein] If, in its eternal path around the Earth, the moon was able to be aware of this movement, it would certainly be persuaded that it is turning according to its will along its path, Similarly, a being endowed with superior intuition and absolute intelligence, who observed man and his behavior, would be amazed at the human illusion that leads him to think that he can act according to his own free will.'

In this ‘axiomatic model / theorem‘, it is shown that it is neither thinkable nor possible to deny this principle (cause-effect) [21], since the only alternative would be to have recourse, necessarily, to the idea of some creation (in contradiction with the first axiom).

Therefore, each 'state / effect [22]' depends on at least one or a plurality of 'state / effect '.

Possible 'entanglement' effects cannot be excluded. Quantum entanglement {quantum correlation} does not violate or deny the principle of causality. A 'state' {state, temperature, energy, relative position, …} depends on an 'other state' or 'other states'. 

According to quantum mechanics, physical systems evolve deterministically within 'Hilbert spaces'.

Hilbert spaces are a set of "vectors" that can be used to represent functions or signals (e.g., sound waves) of various kinds. They are a mathematical structure used primarily in signal theory and functional analysis.

In quantum entanglement, the 'effect' and the 'cause' would be interchangeable.

The use of the conditional is a must because, for the 'Axiomatic Model' there, exhaustive, experimental verification would be problematic, indeed, even impossible in an infinite Universe.

The physical experiment is known (see study published in Physical Review Letters, by Kaumudibikash Goswami of the University of Queensland) which would have shown the fact that, in a quantum system, A can be the cause of  B and, at the same time, B the cause of A. Such an experiment would not violate the principle of ‘cause-and-effect’ at all, indeed.

Every effect can only be determined by one or a plurality of causes. To deny this principle, to deny this concept, would put us in the position of having to invoke, necessarily and without any alternative, some form of ‘creation’ and this is ‘false science’, since it is not absolutely and scientifically conceivable. To assert that: ‘event A is the cause of event B and that event B is the cause of event A‘ means to state that: ‘event A precedes event B (being the cause) and that event B precedes event A (being the cause)‘.

[21] Its denial would necessarily imply the rejection and disavowal of one of the axioms at the basis of this work, which states: ('nothing from absolute nothing ...') which is 'the principle of conservation of energy '. The theories of 'hidden variables' are being developed that seek alternative solutions to some assumptions of quantum mechanics, considered by many to be incomplete. I have always been deeply surprised by the claims of Richard Phillips Feynman, Nobel laureate in 1965, for his contribution to the development of quantum electrodynamics. In fact, he declared: 'If you think you understand quantum theory, it means you don't understand it!' and again: 'I think I can say that nobody understands quantum mechanics'.

[22] Proper subset, not null, of the infinite Universe, even if small as desired.

The laws of physics (1)

Physical laws express, in a mathematical language, the regularities found in natural or physical phenomena and describe these regularities through a series of formulas/equations. These can initially be sketched on a hypothetical basis, but must then find confirmation through observation and experimentation.

For this axiomatic model, it makes sense to talk about two types of laws:

1. the local ones that find specific application in our Cosmos, that is, that relate specifically to it and, many of which, may depend on the energetic conditions that generated our Big Bang;

2. the universal ones that have validity outside this Cosmos. The latter are evidently fewer in number. This axiomatic model has identified two and used them as axioms in this work. As for the second, it limits itself to taking into consideration the aspect relating to the mutual attraction, due to the interaction of gravitational fields, of bodies endowed with mass/energy.

Creation  ?

If an event, taken as small as we like, let's call it: 'epsilon' (ε), were able to violate the principle of 'causality', then it would mean that (ε) would lack that complete link with its past[23].

Therefore (ε) would be devoid of a complete origin, but this would mean that (ε) would necessarily have a characteristic that evokes some creation. This 'creation':

1.      On the one hand, it is in contradiction with the first axiom used in this work; therefore it cannot be taken into account in the present axiomatic model.

2.      On the other hand, if we imagine that we can question this first axiom, we cannot help but accept the idea of ​​some creation. 

But, this brings with it inevitable consequences.

If one admits that 'a cosmos' or even 'a simple event' (taken as small as desired) can be born from absolute nothingness, then one is authorized to imagine that from that absolute nothingness can spring: 'quodlibet' ('anything').

But, if  ‘anything’ is also to be understood as ‘everything and the opposite of everything’, since it is neither possible nor permissible to exclude anything,then one cannot deny the fact that this assumption leads to an ‘absurdity’, to a ‘contradiction’: ‘T ∧ ¬T’ (to be read: ‘T and not T’) is a proposition that is always false.

So ?

Denying the cause-effect principle means admitting some creation, but ...

[23] By past, we mean what triggered the event (possible 'entanglement' effect included. See what has been written in some previous lines). What emerges is in tune with the 'locality principle'. In physics, this principle states that distant objects cannot have instant influence on each other: an object is directly affected only by its immediate vicinity. By 'immediate vicinity', of course, we also mean those signals / impulses sent from distant sources and reaching the object.

10

This hypothesis would contradict one of the two axioms, inserted at the foundation of this ‘model‘, for which it cannot, understandably, claim citizenship rights in this work.

In this principle/law (cause-effect), there are the roots of the concept of infinity, of something that has always existed[24] and that, for Lucretius, takes place in: 'nothing is ever born out of nothing by divine will and nothing is reduces to nothing… '.

In this perspective, the subject 'space' can only constitute an entity of another level, endowed with a specific peculiarity: that of being infinite, without limits, because the quantity of mass / energy is infinite and limitless.

In its dimensions, our 'Universe' would therefore not have, for this 'model', a limit, it would not have an origin or even an end. [25]

Our cosmos

The idea that humanity has made, over the millennia, about our Cosmos and its origins, is the most varied and multifaceted one can imagine, limited only by human imagination.

Leaving aside what the various religions affirm or have sustained, in this regard, we must remember the profound and anticipatory thought of a Roman philosopher who lived in the first century BC.

A follower of Epicureanism, Titus Lucretius Carus, in the first book of his work 'De rerum natura'[26] states: 'Ex nihilo nihil fit…',  'never anything is born from nothing by divine virtue and nothing is reduced to nothing, only it is transformed.'

A few millennia later, this statement will be made its own by our physics and will become: ‘ the principle of conservation of energy ‘, also known as: ‘first law of thermodynamics‘, which constitutes the generalization of the principle of conservation of energy.

It does not appear that this 'first principle of thermodynamics' has ever been contested by the scientific community. Any attempt would clash with the need to have recourse to some 'creation' and this would lead to inevitable contradictions and therefore to an absurdity.

Lucretius' philosophy can be seen as an attempt to explain the world through rational reasoning, partly anticipating the scientific method. Often, the most profound questions about the reality that surrounds us require an interdisciplinary approach that embraces both philosophical and scientific investigation.

This 'first principle of thermodynamics' is in sharp contrast to the idea that our Cosmos, time, space and everything else were born about 13.8 billion years ago. We must then ask ourselves: 'But why exactly 13.8 billion years ago?'.

[24] See demonstration page 2 and following and, in particular, the chapter "Typologies of Universe".

[25] I realize that, for some, the idea of ​​an infinite Universe that did not have an origin and will not even have an end, that has always existed and will always exist, could be difficult to digest, and yet (...).

In many religions, this feature of eternity is present and has been attributed to a 'God'. In fact, Giordano Bruno's thought revolved around an idea: 'the infinite, understood as the infinite universe, the effect of an infinite God, made up of infinite worlds, to be loved. '

[26] The nature of things.

Expansion of our cosmos

In summary: in 1929 Edwin Hubble, and Milton Lasell Humason announced the discovery of the empirical law concerning the red shift: the 'red-shift' undergone by the light coming from other galaxies. This 'red-shift' was the greater the greater the distance of a galaxy from us.

This discovery confirmed what was anticipated, in 1925, by Alexander Alexandrovich Fridman and, later, by Georges Lemaître and allowed everyone to understand that our Cosmos is not static, as many have believed and claimed, but undergoing continuous expansion.

Since, therefore, our Cosmos expands, the conclusion was drawn that, going backwards in space-time, it was possible to hypothesize, gradually, a grouping of increasingly compressed matter. Continuing this journey further back, one would have arrived at a time when all the mass/energy of this Cosmos of ours is concentrated in a single and perhaps (doubt is in order) tiny 'place'[27].

Upon reaching a certain level of energy/temperature/pressure/…, accumulated in this 'place', the Big Bang[28] would take place, which would then generate the expansion, at a very high speed, of everything contained in it. 

This reconstruction of the facts, which starts from the observation of an expanding cosmos and, going back in time, arrives by deduction at the Big Bang, leads to the same conclusion foreseen by this 'axiomatic model'. The latter however does not require a procedure that goes back in time. (See chapter 'black holes').

Some important stages, from antiquity to the beginning of the 20th century:

Below, only some dates or centuries and the related subject / personage are given that contributed, significantly, to shedding light on the mysteries concerning the birth, development and complexity of our Cosmos. 

This list makes no claim to be exhaustive and could perhaps even have been avoided.

I did not consider it appropriate to go into the points listed in detail, as it would have made this work unnecessarily heavy, and because the literature on them is easily available and detailed.

- Sixth century a. C. - Parmenides states: 'what is and what is not cannot be'. The term 'Ex nihilo nihil fit' is attributed to him (nothing can come from nothing);

- fifth century a. C.- Anaxagoras was a Greek philosopher who lived in a period ranging from 496 to 428 a. C.;

  He is convinced that the primordial elements are infinite, irreducible and can be divided indefinitely. For him: everything is in everything; a complex, no matter how infinitely it can be divided, always remains the same.

  To my knowledge, Anaxagoras is the first to evoke the concept of infinity and to try to illustrate its properties;

- fifth century a. C.- Plato (* Athens, 428/427 BC - † Athens, 348/347 BC)

In his work 'The Philebus', he states: 'in a certain way the infinite is multiple' therefore 'indeterminate'. It is always susceptible to a 'plus' and a 'minus'. It escapes knowledge which is determination. Plato challenges Democritus' atomism and is, in some respects, the muse of Heisenberg and Schrödinger;

[27] In support of the 'Big Bang' hypothesis there would also be other results obtained by observation, which concern the cosmic background radiation (CMBR) and the cosmic abundance of elements that were confirmed by the observations made. Predicted in 1948 by George Gamow, Ralph Alpher and Robert Herman, existence of the cosmic background radiation  was experimentally confirmed in 1964 by the US astronomers Arno Penzias and Robert Woodrow Wilson who, for this discovery, were awarded the Nobel prize for physics in 1978.

[28] Expression coined by the British physicist Fred Hoyle (* 1915 – † 2001).

– first century a. C. – Lucretius, in De rerum natura (first book): ‘Nothing is ever born from nothing by divine virtue and nothing is reduced to nothing, it only transforms itself. Life is composed of a set of first bodies, the atoms, corporeal , indivisible and indestructible; when one dies they disintegrate and move in the void of an infinite universe. ‘.

About Lucretius, of whom little or nothing is known, see the excellent book, entitled: 'How are things ...' by the mathematician and scientist Piergiorgio Odifreddi. It is a very particular and unusual work, which analyzes in depth the Latin didactic poem 'De rerum natura', which is said to have been written by Tito Lucretius Caro;

– second century – Ptolemy, born in Egypt, was a geographer, astronomer and astrologer. He is the author of important scientific works. The main one is undoubtedly the astronomical treatise known as ‘Almagest‘ (the great one). The geocentric model is due to him. ;

- XIVth century - Ockam (* 1285 - † 1347) - First admits the paradox of a cosmological infinite: 'The part is equal to the whole, being like it infinite[29]';

- 15th century: Prosdocimo de Beldemandis (Padua, * 1370-1380 - † 1428) was a mathematician, astronomer and music theorist. He is known for his musical treatises and for having inaugurated the chair of astronomy at the University of Padua. His is the 'Brevis tractatulus de electionibus secundum situm lune in suis 28 mansionibus, Montagnana, 1413';

- 15th century: Paolo dal Pozzo Toscanelli (*Florence, 21 April 1397 - †Pisa, 10 May 1482)

His observations of comets are the first to be known: he determined many positions of the comets of 1433, 1449-1450, 1456, 1457 and 1472, tracing their orbits on star maps prepared by him;

- 15th century: Nicola Cusano (* Kues, 1401 - † Todi, 11 August 1464). Cusano argued, precisely against Ptolemy and Aristotle, that the Earth is not immobile, but rotates around its own axis and that it is not possible to determine the center of the universe, this being infinite. In his work 'docta ignorantia', Cusano affirms that the world has no center and an external limit, as Aristotle believed, but its center is everywhere and its circumference nowhere. It is the attitude of the philosopher who, aware of how narrow the band of the known is compared to the immensity of the unknown, assumes as his sole title of privilege the 'knowing of not knowing', in the manner of Socrates and other sages of antiquity. Cusano believes that human knowledge is modeled on mathematical knowledge[30];

- 16th century - Copernicus (* 1473- † 1543) - Polish presbyter, he was a mathematician and an astronomer. He is best known for having developed the astronomical model, known as 'heliocentric theory' or 'heliostatic';

- 17th century - Giordano Bruno (*1548 –  †1600) represented, in the centuries following his death[31], the symbol of free thought and the intellectual capable of challenging established authority. His thought revolved around an idea: the infinite, understood as the infinite universe, the effect of an infinite God, made up of infinite worlds, to be loved infinitely. In 'Il Calendaio', a work (comedy) published in 1582, Giordano Bruno states: 'Time takes everything away and gives everything; all things are transformed, none are annihilated; only one is immutable, only one is eternal and can last forever …';

- 17th century - Galileo (* 1564 - † 1642) - mathematician, physicist, philosopher and astronomer, he contributed to the scientific development and diffusion of the heliocentric system. He proposed a new philosophy of nature in which science and mathematics become the fundamental tools for knowing reality in an objective way. He was able to scan the sky not only with his telescope but, above all, with his mind's eye;

[29] In set theory, a definition of an infinite set can be the following: 'a set is called infinite if there is a one-to-one correspondence between each element of this set and each element of its subset proper'. The part is numerically equal to the whole, as stated by Ockam. In this case, the proper subset also has the characteristic of being infinite.

[30] It is precisely in this mathematics that the ‘Axiomatic model / theorem‘ has sought and found its roots and it is through mathematics that its conclusions have been elaborated and formulated.

[31] For his ideas, he was burned alive in Campo dei Fiori, Rome, on February 17, 1600.

– 17th century – Newton (* 1642 J.c. [32] – † 1727 J.c.) – founder of modern science, he elaborated the law of universal gravitation and provided laws of dynamics and optics. He dealt with mathematics and, together with Leibnitz, contributed to the birth of infinitesimal calculus.

- 1915 - Einstein publishes the theory of general relativity which extends the basic concepts of special relativity to non-inertial frames of reference, that is, they are in motion at a non-constant speed and therefore subject to acceleration;

- 1917 - Einstein published the theory of general relativity, which extends the basic concepts of special relativity to non-inertial reference systems, i.e. those that are in motion at non-constant velocity and therefore subject to possible acceleration;

- 1929 – Hubble, in collaboration with other astrophysicists, makes a series of observations that will allow us to understand that our cosmos is expanding. He discovers, in fact, thanks to the Doppler effect, that many galaxies move away from us with a speed directly proportional to their distance;

- Einstein, following the discovery of Hubble, will declare, regarding the cosmological constant he introduced: 'It was my biggest mistake.';

• …

Black holes

Black holes (for more details, see the 'no-hair theorem' and annexes) are celestial bodies that occupy space-time in the 'infinite Universe'[33].

They are, according to this "axiomatic model", proper subsets of the latter and, thanks to their intense gravitational fields, they interact with any "body" with mass (and not only) that is in their "vicinity". They represent the furnaces of our "infinite Universe", since they play an important role:

They are, according to this 'axiomatic model', subsets of the latter and interact with any 'body' with mass (and not only) that is in their 'vicinity'. They represent the furnaces of this 'infinite Universe' of ours, as they play an important role:

- in the birth and formation of new 'cosmoses', following the transformation of 'energy' into 'matter', consequent to the Big Bang;

- in their subsequent disintegration;

- in the formation of other cosmoses, through a continuous, endless cycle.

Possible scenario

In a space-time (proper subset of the 'infinite Universe'), due to the mutual gravitational interaction, matter/… attracts matter/…

When the mass of a celestial body exceeds certain values ​​of pressure, temperature, energy, ..., the latter collapses. If the concentration of matter becomes sufficiently high, the gravitational attraction force becomes so strong that it even prevents the escape of light, giving rise to what we call a "black hole[34] ". The limit of this region is known as the "event horizon".

[32] Julian calendar.

[33] Physicist Roger Penrose was awarded the Nobel Prize in Physics in October 2020 thanks to a work published in 1965. Using Einstein's theory of general relativity, he was able to demonstrate that black holes are celestial bodies that can form under very common conditions. Exceptional conditions are not necessary.

The experimental data, which emerged later, confirmed what was expected and announced by Penrose.

[34] This term was coined by the US physicist John Archibald Wheeler (* 1911 † 2007), in 1967. Previously, the term was used: ‘dark star‘ or ‘black star‘.

The increased intensity of its gravitational field[35] and perhaps not only: (x-rays?, radio waves?, …) is propagated into the surrounding space[36].

Again as a result of these gravitational fields, black holes and others end up attracting each other and forming celestial bodies with ever greater mass, energy, temperature and pressure. 

They perform a 'brushing' work, of what is brush able, in a given 'space-time', i.e. in a proper (non-empty) subset of the infinite Universe.

This process (accumulation of matter and energy) cannot last forever [37] because, once a 'critical threshold' is reached or exceeded, an deflagration[38] occurs and that phase called 'cosmic inflation' takes place. It can be the beginning of a new 'cosmos'.

Many laws of this 'cosmos' (not all) should probably depend on the value of the energy developed at the time of the 'Big Bang', caused by the last and fatal encounter / collision between black hole and other surrounding matter (black holes , galaxies, clusters of galaxies, stars, ...).

This energy, the result of this last collision, will not necessarily be the same for all the infinite 'cosmoses', on the contrary ...

This 'model' predicts the existence of infinite subsets proper composed of infinite 'cosmoses' born from an equivalent energetic impulse[39].

Since it is not possible to set an arbitrary limit to this energetic value, it follows that it is legitimate to suppose the existence of infinite ‘cosmoses‘ born from an energy impulse much higher than the minimum threshold necessary for their development and therefore for their existence. In some of these ‘cosmos‘ there may be the case that, within them, other cosmos develop, and ‘matriosca‘ effects cannot be ruled out.

Dark energy

Following the observation of some 'Type Ia'[40] Supernovae, in distant galaxies, some American astronomers, in 1998, made a sensational and surprising revelation: 'The expansion of our Cosmos did not correspond to what was hypothesized by the cosmological models of the 'epoch,

because it was accelerating '[41].

This discovery, the result of careful observational activity, is in agreement with what is predicted by this 'axiomatic model', namely that after a prolonged phase of deceleration, following the initial Big Bang, the galaxies in our Cosmos cannot but begin to feel the effect of gravitational fields, of masses outside our Cosmos. 

This 'force' / 'space-time deformation (for Einstein)' therefore produces the effect of an acceleration of escape of the masses constituting our Cosmos. The Standard Model of physics (theory describing elementary particles and the fundamental forces acting on them) does not contemplate the existence of dark energy.

[35] It would perhaps be more correct to speak of a ‘gravitational potential field’. A gravitational field and the mass/energy it is linked to are a unified entity. So, we can say that there is an intrinsic relationship between mass/energy and its relative gravitational field. This is a fundamental concept to understand the behavior of celestial bodies and the dynamics of the universe.

[36] This continuous emanation of energy can only be at the expense of the overall mass/energy of each black hole. This sacrifice is not free, however, as it is rewarded (with interest) as surrounding matter, drawn by its gravitational field, is added to its mass/energy.  It would seem to suggest the idea of an archaic form of the 'survival capacity'.

[37] This process of growth of matter has a limit, in 'space-time'. See the evolution of 'supernovae'.

[38] See the explosion process leading to the birth of 'supernovae'.

[39] know that it would be necessary to define precisely what is meant by 'equivalent'. For now, I just take it that way, intuitively.

[40] Supernovae of 'Type Ia' (first a / one a) originate from the explosion of a white dwarf, which is what remains of a small-medium mass star, which has completed its life cycle and, in the interior of which, nuclear fusion has ceased. The brightness generated by its explosion is such as to exceed, for us distant observers, that of the entire galaxy to which it belongs.

[41] This announcement could be worth a Nobel Prize for the authors of this discovery.

The cosmological model (Lambda CDM[42]):

The accelerated expansion of our Cosmos would find its explanation, according to this model that is currently widely used, in the existence of a mysterious form of energy (dark energy), not directly detectable, but which should be homogeneously diffused in space and which should have a negative pressure (pushed from within).

This energy, imagined along the lines of Einstein's cosmological constant lambda (Λ) (later disowned by the same), would be internal to our cosmos and would turn out to be a characteristic of space.

This feature (as a repulsive force) would have developed, according to recent announcements, it would have developed billions of years ago, ('epoch of the birth of our planet Earth...')[43].

For an in-depth analysis of the subject, please refer to the extensive literature published.

Comment:  Recourse to the idea of a ‘dark energy‘ that would develop that thrust from within, responsible for the acceleration of our galaxies to escape, does not constitute a ‘necessary condition‘ to justify this acceleration.

Given that the Universe is infinite (see the chapter “Types of Universe“), there is at least one other condition that can be defined as ‘sufficient‘: that of the attraction by celestial bodies external to our Cosmos.

Cosmological acceleration

Cosmological acceleration is a phenomenon observed in the Universe that indicates that its expansion is accelerating over time.

This means that galaxies are moving away, towards the outside of our Cosmos, at an ever-increasing speed. This discovery, anticipated by one of the predictions of the “axiomatic model“, was particularly surprising and led to new understandings in modern cosmology.Newton’s second law allows us to shed some light on this issue.

A force F acting on a mass m determines an acceleration a of this mass.

This law is expressed by the following formula: F = m · a

Using “common mathematical language“[44], we would write: [F = m \cdot a ] If we apply this law in the context of our Cosmos, we can think of a force F that determines an acceleration a towards the outside of this Cosmos of our galaxies and our galaxy clusters. It is

[42] See note 13 on p. 4.

[43] This explanation is not convincing. Question: "If this energy is a characteristic of space, why should it have remembered that it is so (repulsively), only after more than four billion years have passed since its birth? (See p. 10: "Creation?"). Theoretical physicist and cosmologist Michael Levi is director of DESI (Dark Energy Spectroscopic Instrument), a research project based in Arizona that studies dark energy by analyzing thousands of distant galaxies. Levi has recently announced that the recent 3D map of the Universe, would seem to suggest that dark energy [what has been called the 'cosmological constant', (denoted by lambda Λ eleventh letter of the Greek alphabet)], actually evolves over time, so is not constant. What Levi announced agrees with what the 'axiomatic model' predicts.

[44] There exists a type of “common mathematical language” that has taken shape also thanks to the work of physicists such as Alexandr Alexandrovich Fridman and Georges Lemaître, in the context of Einstein’s general relativity, which allows us to write complex equations, on the same line, without having to use any fraction lines.

useful to remember that, by the axiomatic model, this is an “attractive” force and not a “repulsive” one. See, in this regard, the chapter “conoid effect“.

The acceleration of the expansion of our Cosmos was discovered in the late 1990s by two groups of astronomers studying type 1a supernovae. The teams, led respectively by Saul Perlmutter, Brian Schmidt and Adam Riess, discovered that the light emitted by supernovae was fainter than what could be imagined. This led to the conclusion that galaxies and galaxy clusters in our Cosmos were subject to an accelerated expansion. The discovery earned its authors the Nobel Prize in 2011. The results of these long and complex observations were published in 1998.

This acceleration, however, seems to have begun billion years ago, following an initial period in which the expansion of our Cosmos was decelerated due to the gravity of the masses present and the continuous increase in the volume of space occupied.

To explain this mysterious “cosmological acceleration“, our physicists, astrophysicists and astronomers have decreed that every galaxy, every cluster of galaxies and more generally every celestial body undergoes an acceleration towards the outside of our Cosmos, due to the action of a repulsive force. This incredible and inconceivable push has been defined: “dark energy” and would be, according to our scientists, one of the fundamental components of our Universe, together with “dark matter” and “baryonic matter” (that which we, our stars and not only are made of).

The cosmological acceleration is currently justified by the equation of state of the cosmological fluid, which is commonly associated with what is called “dark energy“. The most well-known formulation that attempts (but fails) to describe the evolution of the universe, including acceleration, is given by the Friedman equations, derived from Albert Einstein’s General Theory of Relativity.

The present “axiomatic model” offers a very different interpretation of our Cosmos and of our entire Universe, infinite in time, in the quantity of mass/energy and therefore in space.

For the “axiomatic model” this “cosmological acceleration“, on which much ink has been spilled and today appears in many physics texts, even high-level ones, is meaningless.

It contradicts what the “model” states and it also contradicts the recent discoveries that our galaxies and our clusters of galaxies do not have equal acceleration towards the outside of our Cosmos and, in this behavior, they obey Newton’s second law and not a fanciful “cosmological acceleration“.

Isaac Newton

With the advent of the theory of relativity developed by Albert Einstein in the early 20th century, Newton’s figure, while still fundamental in the history of physics, has been somewhat overshadowed. Isaac Newton (* 25/12/1642 †21/03/1727, according to the Julian calendar and *4/01/1643 [according to the Gregorian cal.] †31/03/1727), in the 17th century, revolutionized the field of physics with his laws of motion and the law of universal gravitation. His approach, based on geometric intuitions and a

principle of linearity[45], provided the tools necessary to describe the motion of objects both on Earth and in the heavens. Newtonian physics dominated science for centuries, creating a solid foundation for classical mechanics.

With the introduction of the theory of special relativity (1905) and general relativity (1915), Einstein proposed a radically different view of the nature of space, time and gravity.

Special relativity, in particular, challenged the notions of simultaneity and absolute space, showing that time and space are interconnected in a way that had not been considered until then.

General relativity further transformed the interpretation of gravity, describing it not as a force acting at a distance, but as the curvature of space-time caused by mass.

I think it is useful to remember that, for the “axiomatic model“, the gravitational force is not a “force that acts at a distance“, but is the result of an interaction between gravitational fields, which constitute a whole with the masses to which they are associated!

While Newton treated gravity as an attraction between masses, Einstein’s general relativity attempted to explain that what we call “gravitation” should be the result of the geometry of space-time.

Newton’s partial exit from the scene does not mean that his ideas have been completely overcome; on the contrary, in the context of classical physics and for objects at low speeds compared to light, Newton’s laws remain extremely useful and applicable.

However, relativity has opened new avenues for scientific research, leading to inevitable repercussions in the field of theoretical and cosmological physics. In this sense, the figure of Newton, while remaining central to the teaching and understanding of physics, has been partly “overshadowed” by relativity.

This “axiomatic model” questions and disputes the recent concept of “cosmological acceleration“. He claims that this is a misconception and unfounded.

What emerges, proposes an alternative interpretation of cosmic dynamics, demonstrating, in this way, the inadequacy of some postulates of Einstein’s relativity. This can only lead to a partial and substantial re-evaluation of the figure of Isaac Newton. His work, therefore, deserves to be recognized and appreciated in a context that goes beyond the limitations imposed by contemporary theories.

This idea offers an alternative interpretation of cosmic dynamics, demonstrating, in this way, the inadequacy of some postulates of Einstein’s relativity. This can only lead to a partial and substantial re-evaluation of the figure of Isaac Newton. His work, therefore, deserves to be recognized and appreciated in a context that goes beyond the limitations imposed by contemporary theories.

We must not forget that this great figure is also credited with other scientific merits, such as:

[45] This principle is fundamental in many areas of science and engineering, as it simplifies the analysis of complex systems.

– the one concerning the dispute with Christian Huygens on the nature of light. Regarding this subject, the two have different and opposing views.

One, Newton, supports its corpuscular nature, while the other, Huygens is convinced that it is a wave phenomenon. Different experiments produce different results;

– the contrast with Gottfried Wilhelm Leibnitz, regarding the invention of infinitesimal calculus, a branch of mathematics that deals with the analysis of changes and infinitesimal quantities.

Both mathematicians independently developed the foundations of calculus in the 17th century, but in different ways and with different notations.

According to this ‘axiomatic model’

To explain the reasons for this acceleration in the escape velocity of our galaxies, there is no need to resort to what is called 'dark energy' in the Lambda CDM cosmological model.

Such acceleration would simply be the result of the mutual interaction between the gravitational fields of our galaxies and those of those celestial bodies that are nearby, out there, outside our Cosmos.

In his recent book: 'Lost in Math (BASIC BOOKS), physicist-theorist Sabine Hossenfelder writes: 'The cosmological constant is not natural. But it has to do with gravity ...'. 

It is safe to assume that Sabine has intuited the true nature of this energy, called the 'cosmological constant', from our physics.

Not a few theoretical physicists, among them Sabine Hossenfelder, express doubts about what is called the 'cosmological constant' and consider it problematic and above all not natural.

They attribute to it problems of naturalness (smaller than theoretically predicted), problems of hierarchy (vacuum energy too low) and, in particular, problems of agreement with observations (not tuned to observed effects).

This model also predicts that our galaxies or clusters of galaxies do not have a homogeneous outward escape acceleration.

This acceleration depends essentially, though not exclusively, on the ever-decreasing distances of the masses, which can vary, and on the intensity of the gravitational fields involved.

It is not possible to exclude that some galaxies in our cosmos have disappeared from our sight, not only because they are now too far away from us, but because they may have already concluded their race towards the outside, swallowed up by that 'something'[46] that out there was calling them to him.

It should also be noted that: 'What we see today does not represent the current situation at all because, in reality, this received light is none other than the one emitted a long time ago.'

[46] This ‘something‘ could be a very massive black hole or something else.

Always according to this “model“, once the effect of the initial propulsion due to a possible explosion has ended, it has generated a very rapid expansion (Big Bang) and lasted a very short time (according to astrophysicists)[47], the speed of escape towards the outside, of the material composing our cosmos should slow down and continue to decrease its speed, due to the increase in the space occupied and the gravitational field generated by the entire mass of our Cosmos.

The duration of this slowdown is destined to end, however, when, having reached and then passed a certain threshold, the gravitational fields of what is out there exceed the attractive values ​​of our entire Cosmos.

From this moment on, the escape speed will only grow and continue to grow[48].

The destiny of each of our galaxies is therefore, according to this axiomatic model, to end up sucked/engulfed by the celestial body or bodies (black holes, …) which, out there, through their intense gravitational fields, exert that attraction, responsible for their escape acceleration.

Dark matter

In scientific publications, you can read a lot of news about this subject, such as: 'Although the existence of dark matter has apparently been confirmed by several independent observations, its true identity remains, for now, a mystery ...'.

Theoretical physicist Frank Wilczek (born in 1951 and winner of the Nobel Prize in Physics in 2004) argues in his book 'THE PARTICLE AT THE END OF THE UNIVERSE' that the subatomic particle, called an 'axion', could be a candidate to represent 'dark matter'.

Theoretical physicist Gordon Kane (born 1937), in his book "The Particle Garden", in his chapter "Standard theory has no candidate for dark matter", writes: "The standard theory, while describing our visible world, has no room for dark matter particles. For many physicists, this is a further indication that the standard theory will be extended."

Sabine Hossenfelder (born 1976) was a theoretical physicist at the Frankfurt Institute of Advanced Studies, where she heads the Analog Systems for Gravity Duals group. He deals with quantum gravity.

In one of his articles, he states: 'The matter we, the planets and galaxies are made of, all together makes up only 4.9 percent of the matter in the Universe. About 26 percent of the cosmos is invisible matter: we don't know what it's actually made of The remaining 69 percent or so of the Universe is 'dark energy', of which we know ... little or nothing. The fact that the most widespread matter in the Universe is 'dark' does not just mean that it is invisible to our eyes or almost completely unknown: it is dark because it does not emit any type of electromagnetic radiation, neither in the spectrum of visible light, nor in X-rays and not even in very high energies. 

[47] In the following time frame, the different transition phases would take place, leading to the development of various interactions (electromagnetic interaction, weak interaction, ...), electrons, positrons, neutrinos, ...

[48] This "moment", according to recent discoveries, should have taken place over four billion years ago, around the time of the birth of our planet Earth.

According to the predictions of this ‘axiomatic model‘, it would seem legitimate to imagine that, from this moment on (given that the possibility that the celestial body responsible for this attraction has, in the meantime, seen an increase in mass, as a result of possible amalgamations of masses, cannot be ruled out), the escape velocity of our galaxies could have to do with a derivative of the acceleration with respect to time, i.e. the third-order derivative of the position vector with respect to time. I know this argument would require further exploration, since higher-order derivatives are not common in current theories.

This hypothetical ‘dark matter‘[49] it would therefore be currently detectable only indirectly through gravitational effects, such as:

a) «higher level of 'cohesion[50]', compared to the amount of matter present in a galaxy or in a cluster of galaxies»;

b) «higher gravitational lens effect, compared to what would be expected from the emitted brightness, emitted infrared or x-rays detected in a galaxy or cluster of galaxies»;

c) «Tendency to gravitational aggregation of galaxies in galaxy clusters (see works and discoveries by Vera Rubin)»;

d) Speed of approach between the two galaxies, Milky Way and Andromeda, far greater than the effects of the gravitational fields generated by their masses alone;

e) The Standard Model of physics does not contemplate the existence of dark matter.

The presence of "dark matter" in a system would certainly represent a sufficient condition to justify gravitational phenomena greater than those expected, but it is necessary to ask: "would it also represent a necessary condition?"

Evidently NO! Since there is at least one other, different and sufficient: that of a higher 'cohesion', due to the 'conoid' effect (to be understood as non-straight conoid, see the chapter "Conoid effect").

The gravitational effects, listed in the previous points are justified, by this 'axiomatic model', without any need to invoke the concept of 'dark matter' and not even by resorting to the MOND theory (MOdified Newtonian Dynamics) that is: 'Modified Newtonian Dynamics'[51].

With regard to point b): 'higher gravitational lens effect, compared to what would be expected from the emitted brightness, emitted infrared or x-rays detected in a galaxy or cluster of galaxies':

- Suppose we have two photons: γ1 and γ2 that pass very close to two Masses: γ1 to m1 and γ2 to m2;

- Suppose that m1 and m2 contain the same amount of baryon matter;

- Suppose that m2 has a smaller volume than m1 (smaller spaces between its celestial bodies);

- It will emerge that m2 has a higher level of cohesion than m1;

- The value d2 (distance between photon γ2 and the center of gravity of m2) will be lower than the value d1 (distance between photon γ1 and the center of gravity of attraction of m1);

- It will result that: [F = (G. m1. m2) / d22] > [F = (G. m1. m2) / d12]. In Einstein's General Relativity, gravitation turns out to be an attribute of curved spacetime. Einstein uses complicated formulas, complex tensor differential equations;

- Therefore γ2will undergo a greater change in direction than γ1.

  The curvature of its path will necessarily be more pronounced.

[49] By ‘dark matter’ we mean a hypothetical component of matter that, unlike known matter, would not emit any electromagnetic radiation and would currently only be detectable indirectly through its gravitational effects.

[50] I made use of this term, used in Physics to indicate an electrostatic force of attraction, because it gives an immediate idea of the concept I intend to convey, that is, that of a force of aggregation, of a strong union of the constituent parts of a set of components.

[51] The MOND theory, to explain the problem of the rotation curves of spiral galaxies, proposes a modification of the second law of dynamics: F = m a where: F = force, m = mass, a = acceleration or of the universal law of gravitation : F = (G · m1 · m2)/d², modifying, as appropriate, the factor (1/d²).

Whoever decides to measure the direction variation of γ₂, without knowing that m₂ is subjected to the ‘conoid effect‘ (see a few lines below what is meant by ‘conoid effect’) and intends to establish the mass of m₂, on the basis of its brightness (so did Fritz Zwicky), on the basis of infrared or through x-rays, would arrive at the conclusion that the quantity of matter in m₂ is not sufficient to justify this change in direction and would be induced to imagine the presence of some ‘dark matter‘.

It is clear that F₂> F₁, since: m₂ is not less than m₁,  γ₂  is equivalent toγ₁ while d₂ < d₁. Therefore, the path of the photon γ₂  can only follow a more pronounced curvature than the one that follows the photon γ₁.

Concerning this ‘dark matter’: if it really existed and, as claimed by several sources, completely enveloped and permeated entire galaxy clusters (in the form of ‘axions’, ‘WIMP’ or something else), then: how would it be possible to explain the fact that celestial bodies rotating in their outermost orbits have a very similar angular velocity to those rotating in their innermost orbits?

The reason for this behavior is explained, in a different, certainly more sensible and convincing (though rather disturbing) way, by the ‘axiomatic model’.

Conoid effect

In this figure (to be imagined as a representation of a four-dimensional situation, including time variable), the apex of the ‘universal conoid [52]’ represents the center of gravity (barycenter) of one or more celestial bodies (super massive black hole / binary systems of black holes / …) [53] which, there outside, they generate that gravitational field, responsible for the escape acceleration of our galaxies / galaxy clusters / … In the present work, the graphic representation of a cone will always be used, in order to simplify the concept that is intended to be conveyed, also taking into account the fact that the curvature of our Cosmos is not very accentuated, given its size. In reality, the morphology of each ‘conoids’ (to which they are subjected), especially in the terminal part (near the vertex), [today]  is very diversified and complex, and depends on various factors: amount of mass of the celestial body or bodies exerting their attraction, either from outside or inside our Cosmos; the direction of movement of this mass or these masses and their barycenter; the speed of movement of this barycenter; the possibility of the growth of this mass or these masses, through possible combinations, over time; …

[52] ‘universal conoids’ are defined as those that have their vertex outside our Cosmos. ‘premises’ have it on the inside.

[53] The concept of ‘center of mass‘ understood as ‘center of gravity‘ was known, already in the third century BC, by the great Greek physicist, mathematician and engineer Archimedes of Syracuse.

With the passage of time (t) [each reference system has its own reference system], the volume of a galaxy or cluster of galaxies in our Cosmos (green in the graph) tends to decrease, as each of its ‘elements’ (stars, solar systems, …) follows a path within the conoids that are gradually narrowing.

The degree of 'cohesion' of each galaxy / cluster of galaxies /… instead tends, in an inversely proportional way, to grow. So, as time (t) passes, taken in a certain reference system, the variables volume and degree of cohesion are linked by a relationship of inverse proportionality. Thanks to this effect, all the celestial bodies present in a 'conoid' necessarily behave as if they were immersed in an ever increasing gravitational field.

Therefore, the value of this degree of cohesion would be one of the main reasons that required the need to introduce the concept of 'dark matter' in the 'in the Lambda CDM cosmological model' (See works by astrophysicists Fritz Zwicky, who first proposed its existence, and by Vera Cooper Rubin).

Binary systems

The "axiomatic model" predicts the existence of multiple and diverse types of binary systems, that is, pairs of celestial bodies that, for a certain period of time, find themselves rotating, one next to the other, around a common gravitational center. To date, many have been identified. These are: x-ray binary systems, spectroscopic binary systems, eclipsing binary systems, contact binary systems, and others. The "conoid" effect certainly plays an important and determining role in this type of phenomena and justifies the reasons for it.

When two or more galaxies, of our Cosmos, feel the effects of the same gravitational field, generated by one or more celestial bodies, they begin to share the same 'conoid' that will determine their path to the final destination (the vertex of the conoid).

If these galaxies make their way at similar distances from the vertex of the conoid and in equal gravitational paths, they will eventually merge together.

This merger will most likely not have the characteristic of a head-on collision, since their approach is along weakly converging[54] lines that will favor a gradual approach and result in the formation of these binary systems. When two celestial bodies travel along the same cone, at similar, but not exactly equal, distances from the apex of the cone, an effect is generated that will cause the two celestial bodies to rotate, one around the other, before merging into a single body.

—-  _*  —-

According to the ‘Axiomatic Model‘, the force or rather the forces that regulate the acceleration, towards the outside, of the galaxies and clusters of galaxies of our Cosmos are constantly growing.

These forces are, in each ‘conoid‘ (for Newton’s law, described in his ‘Principia‘)[55], directly proportional to the product of the masses m₁ (vertex of the conoid) and m₂ (center of gravity of the celestial body approaching this vertex) and inversely proportional to the square of the distance that separates them:

F = (G·m₁·m₂ )/ d ².

[54] Resulting from the composition of at least two vectors: one determined by the gravitational force developed by the celestial bodies and the other determined by the force of gravitational attraction with the vertex of the conoid.

[55] With General Relativity, Einstein corrected this formula, also adapting it to situations that have to do with speeds approaching that of light. For Einstein, gravity is not seen as a force in the traditional Newtonian sense, but rather as a manifestation of the curvature of space-time caused by the presence of mass/energy.

Thus, during their journey, our celestial bodies are subjected to an ever-increasing force of attraction since this is inversely proportional to the square of the distance, which is continually decreasing.

If, for some reason, we wanted to replace these forces of attraction with a repulsive one (‘dark energy’ for example?) which, from the inside of our Cosmos exerts a negative pressure towards the outside, then we would be forced to imagine that this repulsive force is divided into a plurality of forces, in different directions (since not all galaxies or clusters of galaxies are subjected to the same outward acceleration. See also note 48, regarding derivatives of order higher than the second).

Universal, archaic and ever-present law

Once the race outwards from our Cosmos is over and beyond the event horizon of those who call, these galaxies / clusters of galaxies of ours will constitute an interesting and appetizing compensation for those celestial bodies that, thanks to their intense gravitational fields, have ended up attracting, new mass / energy. It is therefore safe to assume that there may exist a primitive and fundamental law of the infinite Universe, namely that concerning the necessity and need for growth in the quantity of mass/energy[56] … in the complex mineral kingdom.

It should be attributed to this archaic and ever current law the main responsibility of the fact that our infinite Universe is not only not static but possesses that dynamism capable of generating cosmos without end and destroying them and then generating others, in a sequence without a beginning and endless.

This would be the law that requires everybody, endowed with mass/energy, to sacrifice a part of itself in order to further increase its own and others’ mass/energy, thanks to the energy of the associated gravitational fields and perhaps not only.

Depriving our Universe of this fundamental law would simply mean making it static and preventing it from being able to produce cosmos and with these, all that follows: plant life, animal life, including our own,…[57].

[56] This law is declined, afterwards, in the need for ‘survival’ and ‘evolution’ of every living species (animal or plant) through processes of adaptation by which living species mutate, from generation to generation, in order to adapt to their environment and to increase their hope/need for conservation.

[57] The ‘axiomatic model’ cannot but express some legitimate doubts about the corpuscular nature of gravity. The idea of the ‘graviton’ was first introduced by the theoretical physicist Peter Higgs in 1964 as part of his ‘Higgs field’ theory. To date, there is no confirmation of its existence.  The particle accelerator LHC, (Large Hadron Collider, located in the Department of Ain, France, and the Canton of Geneva, Switzerland), which has been in operation since 2008, has so far detected no trace of it. In his book ‘THE PARTICLE AT THE END OF THE UNIVERSE‘, theoretical physicist and cosmologist Sean Carrol writes on page 36: ‘All fields are subject to microscopic vibrations due to the intrinsic indeterminacies of quantum mechanics. A major vibration appears to us as a particle, in this case the Higgs boson”. And on page 37: «The world is made up of fields: entities spread throughout space that manifest themselves to us through their vibrations that appear to us as particles. The electric field and the gravitational field might sound familiar, but according to quantum field theory even particles like electrons and quarks are actually vibrations of certain types of fields. · The Higgs boson is a vibration in the Higgs field, just as a photon of light is a vibration in the electromagnetic field.”» on p. 113:”When we talk about particle physics, we do not usually emphasise that we are, in fact, talking about field physics….

Fields are not ‘made of something’ … they are the very substance of which the world is made …

Even what we call ‘matter’ – particles like electrons and protons – is actually just a collection of vibrating fields. The particle we call the ‘Higgs boson’ is important, but not in itself; what matters is the Higgs Field from which it springs and which plays a central role in the universe…”

This is a universal law (used as a second axiom in this work):

1. is the law that allows / imposes a body to increase its mass / energy and not only, to the point of preventing the release of photons of light, thus becoming a ‘black hole‘;
2. it is the law that allows/requires super massive black holes to further increase their mass/energy until they reach or exceed that level beyond which something particular happens: a possible Big Bang that will give rise to a new cosmos;
3. is one of the laws that govern the stages of development of each cosmos until the total outward dispersion of its galaxies, clusters of galaxies, …;
4. is the law that, in a perpetual cycle, alternates between births and the end of the cosmos and then other births and another end.

The destiny of each celestial body is to contribute to increasing the mass/energy of other celestial bodies out there and, at the same time, to increasing its own mass/energy as well. This process that has taken place, is taking place and will take place again and again, in the infinite Universe cannot but respect and corroborate that archaic law of ‘increasing the quantity of mass / energy, …’ and so in a perpetual, endless cycle, in the infinite Universe!

The so-called ‘Gravitational Waves’

When two or more ‘black holes/neutron stars/…’ collide and merge into one ‘black hole/…‘, they give rise to a new celestial body formed by the mass/energy of those that collided and a new, more intense gravitational field. As a result of this event, a small percentage of this new mass/energy (about 4.6% – see the event called GW150914, 14 September 2015) is destined to increase the intensity of the new gravitational field.

This increase in energy from the new, more intense gravitational field propagates, in the space surrounding the event site, as if it were ‘a wave‘/’a gravitational wave‘ but, there is nothing moving, i.e. nothing going “from … to …“, excluding this variation in the intensity of this gravitational field. For the ‘axiomatic model’, what actually happens is a very rapid transformation of the gravitational field value of the new, more massive black hole.

This transformation takes place, without interruption, starting from the center, i.e. the place where the collision/fusion took place, and propagates radially, outwards, in space and time.

Such an event cannot but create a disturbance in the surrounding space-time and this disturbance is generated by the increase of the new and more intense gravitational field of the recent celestial body that has come to form, following this collision/union.

The energy required for this transformation of the new gravitational field is, of course, subtracted from the mass/energy that has recently been generated.

Gravitational waves travel in a vacuum at the speed of light. Unlike other waves, such as sound waves, which travel at much slower speed.

According to the “axiomatic model“, the movement of each mass/energy, with respect to other masses/energies, corresponds to a movement of its gravitational field and therefore space must necessarily be permeated by gravitational waves.

These will be weaker the weaker the masses/energies that generate them. Each grouping of objects generates a grouping of their relative gravitational fields, with consequent emanation of gravitational waves. For the “axiomatic model“, the displacement of each mass/energy, with respect to other masses/energies, generates a displacement of its own gravitational field.

It remains problematic and not easy to explain to two fiancés that, when they meet and hug, they are responsible for the production of gravitational waves!

—-  *  —-

Types of ‘Universe‘

and

The law/principle of conservation of mass/energy in a non-closed infinite system, but with the characteristics of a ‘perfectly and completely isolated system’

————-  _*  ————-

The existence of a Universe [infinite in time, endowed with a finite or infinite amount of mass/energy] without a beginning and with an end in ‘ω’ is Impossible because it would violate the first axiom of this model (the principle of conservation of energy).

————-  _*  ————-

For the ‘axiomatic model’, the existence of a Universe [endowed with a finite or infinite amount of mass/energy] without a beginning and with an end in ‘ω’ is Impossible because it would violate the first axiom of this model (the principle of conservation of energy).

a) The existence of a Universe [endowed with a finite amount of mass/energy] without a beginning and with an end in ‘ω‘(could also be endless), turns out to be Impossible because, for any arbitrarily chosen point ‘ω‘ on the time half-line{-∞            }, the elapsed time between {-∞ and ω } is infinite, and therefore, by the second axiom (law of universal gravitation, with continuous emission of the energy of gravitational fields), a finite amount of mass/energy could only dissolve totally, in a finite time.

More generally, nowhere in this half-line of time can any Universe with a finite amount of mass/energy exist, since it is shown that there is always, in this (infinite) half-line, a place prior to this one, where any Universe with a finite amount of mass/energy would already be completely exhausted.

b) The existence of a Universe [endowed with an infinite quantity of mass/energy] with no beginning and with an end in ‘ω‘, is Impossible, because:

– even a continuous decrease in its mass/energy, apart from being impossible, would not change its characteristic as an entity endowed with infinite mass/energy and therefore the end of this type of ‘universe’ would never take place[58];

– neither is it reasonable to suppose that an infinite quantity of mass/energy (occupying a necessarily infinite space/time) decides to cease its existence, at a precise and determined instant (ω). In order to be able to do so, everywhere and simultaneously, it would have to violate one of the fundamental principles of the theory of special relativity, for which, ‘simultaneity’ is a concept linked to the observer, i.e. to his reference system, and cannot be applied indiscriminately to a diverse and, in this case, infinite plurality of inertial reference systems.

————-  _*  ————-

Given that there is a Universe (it is not possible to deny its existence) and given that this Universe cannot have a beginning (it would have to invoke some creation) and cannot have an end (it would contradict the principle of conservation of mass/energy, posited as the first axiom of this work), it follows that this Universe can only be infinite in time, without beginning and without end.

The question is whether this Universe, infinite in time (without beginning and without end), is endowed with a finite amount of mass/energy or is endowed with an infinite amount of mass/energy.

[58] Let us suppose that we are dealing with the infinite set of natural numbers (0; 1; 2; 3; 4; …) and imagine subtracting from this set its own subset proper , a finite or even infinite quantity (the set of even numbers, for example); what remains will be an infinite set, even if we subtract from it an infinite quantity. In fact, the set of natural numbers, deprived of the set of even numbers, is an infinite set.

In the dichotomous tree, which follows, the 16 different solutions were examined, considering that we are dealing with:

• Universe infinite in time (∞ in t., without limits)    or   with its complement a Universe finite in time (∞ in t.);
• Universe with an infinite amount of mass/energy and space (∞ in m./e. and in sp.) or with its complement (∞ in m./e. and in sp.);
• Universe with a beginning    or   its complementary, the one without a beginning;
• Universe with an end    or   its complement, the one without an end.

[59] A Universe that has no beginning, cannot have an end. Let us imagine that we are dealing with the set of natural numbers (0, 1, 2, 3, … ∞). Now imagine that we start not with ∞ (which is not a number; which is not a number. For more details, see ∞ in limits), but with any large number. We subtract 1 and then subtract, again and again, a unit from the number obtained and so on, without end. At this point, we could make use of an algorithm, the following: once we have reached (with this procedure) a certain number, of our choice and between ∞ and ω (omega, an arbitrary value chosen at will), a unit is added to that ‘any large‘ number and we repeat, all over again, the procedure, with this new beginning (this procedure has no term and is always permissible because we are dealing with infinity). This algorithm will ensure that ω will never be reached (this procedure has no end and is always legal because we are dealing with infinity). The same goes for the reverse process, i.e. ω +1+1+1+1+… we will never reach ∞ (which is not a number).

The procedure (-1, -1, …) is therefore infinite because, since it is possible to make the starting number larger and larger, ω will never be reached. Not only will ω never be reached, but neither will any natural number, even a large one chosen at will. To conclude, a Universe without a beginning cannot have an end. Let us imagine replacing natural numbers with seconds (e.g. 1= one second, 2= two seconds, … ); the time elapsed between a number of seconds tending to ∞ and any number ω of seconds, chosen at will, will necessarily tend to infinity and therefore this ω will never be reached. This argument highlights a contradiction in the sequence considered (beginning – end) and invalidates it. Our Universe, therefore, cannot be associated with the idea of semi-route (∞… end of semi-route). Someone, following in the footsteps of the great mathematician Georg Cantor (_*1845  †1918), might say: ‘I see it but I can hardly believe it’.

[60] See footnote 59.

[61] See, in the next paper, the experience I had with the pupils of a fifth grade class at the Verrès high school in 1994, where I was called upon to give single-subject lessons on essentially mathematical topics.

[62] See footnote 59.

[63] See footnote 59.

This relational structure shows unequivocally that, of the 16 solutions examined, there is one and only one possible solution, namely that our Universe can only be infinite in time[64], endowed with an infinite amount of mass/energy, occupying infinite space, and that this Universe cannot have had a beginning and cannot have an end.

Ten of these hypotheses (1, 3, 5, 7, 10, 11, 12, 14, 15, and 16) are to be rejected, since they contain a sequence of conditions that makes use of some contradiction, which makes the hypothesis unacceptable. Hypotheses 1, 5, 10, and 14 make use of an absurd concept of creation;

The contradictions:

the first sequence: if the Universe is infinite in t. (time), it cannot have a beginning and also an end. This would contradict the first hypothesis posited, namely that of being ‘infinite in time’;

the third sequence: if the Universe is infinite in t. (time), it cannot end and therefore contradicts itself. For its explanation, mathematics comes to our aid. See footnote 59 on the previous page;

the fifth sequence: as with the first sequence, if the Universe is infinite in t. (time), it cannot have a beginning and also an end. This would contradict the first hypothesis posed, i.e. ‘infinite in time’;

the seventh sequence: as with the third sequence, if the Universe is infinite in t. (time), it cannot end and therefore enters into contradiction. For its explanation, mathematics comes to our aid. See footnote 59;

the tenth sequence: the fact that it is without end makes it infinite in time but, in this way, contradicts the initial hypothesis that it is: ‘finite in time’;

the eleventh sequence: the fact that it is without beginning makes it infinite in time but, in this way, contradicts the initial hypothesis and that is the one that claims to be: ‘finite in time’; and

the twelfth sequence: the fact that it is without beginning and without end makes it infinite in time but, in this way, contradicts the initial hypothesis, namely that which claims to be: “finite in time“.

the fourteenth sequence: the fact that it is without end makes it infinite in time but, in this way, contradicts the initial hypothesis, namely that which claims to be: “finite in time“.

the fifteenth sequence: the fact that it is without beginning makes it infinite in time but, in this way, contradicts the initial hypothesis and that is the one that claims to be: “finite in time“.

the sixteenth sequence: the fact that it is without beginning and without end makes it infinite in time but, in this way, contradicts the initial hypothesis and that is the one that claims to be: “finite in time“.

Four of these hypotheses (2, 6, 9 and 13) invoke the unacceptable concept of creation which makes them inadmissible;

[64] Bosons are particles that obey the Bose-Einstein statistic and represent the particles that transmit the fundamental forces between matter particles. Examples of bosons are photons (light particles), W and Z bosons (responsible for the weak nuclear interaction, these bosons have mass: about 80.4 GeV/c^2 for the W boson and about 91.2 GeV/c^2 for the Z boson) and Higgs bosons (responsible for giving mass to particles). Fermions, on the other hand, obey the Fermi-Dirac statistic and represent the particles that make up matter. Fermions include quarks (which make up protons and neutrons), electrons, neutrinos and all other particles of matter found in the periodic table of elements. Bosons are responsible for the fundamental forces in the universe, while fermions make up the matter that surrounds us.

One of these hypotheses (Hypothesis 8) proposes a “Yo-Yo” cosmological model, i.e. a finite amount of mass/energy alternating between ‘Big Bang’ and ‘Big Crunch’, in a continuous and endless manner.

Such a hypothesis can only be impossible because:

All ‘big crunches’ would, of necessity, have to wait for the last and most distant of the emitted photons (or of some other subatomic particle, including the totality of the energy contained in gravitational fields, electric, magnetic, electromagnetic, Higgs fields, … which extend, theoretically, to infinity) before implementing the next ‘Big-Bang’[65]. With this type of Universe, it would be problematic and even impossible to explain the reasons why our galaxies are in a phase of accelerated expansion and even with differentiated accelerations.

The “Yo-Yo” cosmological model would not justify, in any way, the two recent discoveries:

– that of 1998 concerning the escape acceleration of galaxies in our Cosmos, which suggested the idea of a negative pressure from within our Cosmos being responsible for this acceleration. This idea came to be known as ‘Cosmological Constant/Dark Energy’;

– the more recent one, from 2020, which refers to the fact that not all galaxies have the same acceleration towards the outside of our Cosmos. This discovery made US astrophysicist Gerrit Shellenberger, who was responsible for announcing the discovery, say and write: “Based on our observations of clusters, we may have found differences in the speed at which the Universe is expanding, and this finding would go against one of the most basic assumptions we use in cosmology today (Lambda CDM model) .”

the Universe, therefore, can only be endowed with an infinite amount of mass/energy.

The solution proposed in point 4. of the dichotomous tree graph on the previous page is therefore the only one possible, namely that we are dealing with a Universe that is infinite in time, infinite in the amount of mass/energy and therefore infinite in space.

The only possible solution therefore remains that of a Universe (or of some other subatomic particle, including the energy contained in gravitational fields, electric, magnetic, electromagnetic fields, … which extend, theoretically, to infinity) without a beginning and without an end, an ‘infinite system which, although not closed, possesses the characteristics of an perfectly isolated system ‘, in which, and only in its entirety, the law of conservation of mass/energy applies without exception.

On p. 121 of his book ‘Physics and Philosophy’ Werner Karl Heisenberg (_*1901  †1976)  writes: “The two laws of conservation of mass and conservation of energy lose their separate validity and are combined into a single law that can be called the law of conservation of energy or of mass.”

For this ‘axiomatic model’, no proper (finite and non-empty) subset of the infinite Universe can be said to be ‘perfectly and completely isolated’. Absolutely, this characteristic only belongs to the totality of this infinite Universe of ours!

Infinity

The problems that arise with the introduction of the notion of infinity in Physics are complex and certainly related to the specific context in which this concept is used. It seems to be safe to say that physicists do not disdain infinity, they are simply aware that conceptual challenges inevitably arise

[65] If this were not the case, then each Big-Bang would be different and inferior to the previous one in terms of the amount of mass/energy. That is, there would be a continuous loss of the quantity of mass/energy that, in an infinite time, would cause the total exhaustion of a hypothetical and absurd ‘Yo-Yo Universe’.

when trying to introduce infinity into physical theories and models, which in certain situations are not easy to handle.

Certainly this concept is sometimes undesirable in physics because it is certainly complex and complicated.

The concept of infinity, studied in depth by the German mathematician Georg Cantor (*1845 †1918), is often undesirable because:

1. physical phenomena involving infinity often cannot be studied and proven experimentally. This poses many problems and makes it difficult to verify or refute those models that make use of it, and can only suggest a necessary and inevitable caution in its use;
2. infinity can often raise questions as to the completeness and consistency of the physical theories that make use of it;
3. infinity is certainly not easy to analyze and, above all, to understand. Not a few physical phenomena require the manipulation of rather complex mathematical concepts in order to be comprehensively and adequately understood;
4. infinity often leads to complex mathematical results that are not easy to manipulate. There are not a few aspects that have to do with this concept that challenge our ability to understand it.

That said, it must be acknowledged that in Physics, and in particular in Astrophysics, this concept cannot be dispensed with. The ‘axiomatic model’ in fact demonstrates the existence of a Universe infinite in time, infinite in the amount of mass/energy and therefore infinite in space. This means that if one wishes to deepen one’s understanding of this Universe of ours, one must, of necessity, make use of this concept.

The ‘infinite space’

Since ‘the quantity of mass/energy in our Universe can only be infinite‘, it follows that this quantity cannot be contained in a single dimensionless point (that which has no part, according to Euclid’s definition), since it would negate the assumption: ‘infinite quantity of mass/energy’.

Therefore, this infinite amount of mass/energy must necessarily occupy a surrounding of any of its points and this surrounding can only be infinite, i.e. without any limit.

Going into detail, it must be said that:

– ‘bosons’, which have no mass, can be ‘stacked’ and do not occupy space;

– ‘fermions’ have mass and cannot be ‘stacked’. These occupy space, as the mass/energy is infinite. The ‘fermions’ are in infinite quantity and therefore the space containing them can only tend to infinity.

‘bosons’ and ‘fermions’ are two classes of elementary particles that constitute matter. ‘bosons’  follow Bose-Einstein statistics, which allow an unlimited number of particles to occupy the same quantum state, while fermions follow Fermi-Dirac statistics, which prevent two particles from occupying the same quantum state at the same time. Examples of ‘bosons’ include photons and the W and Z ‘bosons’, while examples of ‘fermions’ include electrons, quarks and neutrinos.

‘bosons’ and ‘fermions’ are two fundamental classes of elementary particles that constitute matter in the universe.

‘bosons’ are particles with integer spin. This means that they can occupy the same quantum state at the same time, which leads to collective behavior such as the formation of electromagnetic waves, responsible for forces such as the electromagnetic force and the weak nuclear force. Examples of bosons include photons, W and Z ‘bosons’ and ‘mesons’.

‘Fermions, on the other hand, are particles with a half-integer spin. This implies that they cannot occupy the same quantum state at the same time, a principle known as the ‘Pauli exclusion principle’. ‘Fermions’ make up most of the visible matter in the universe and include particles such as electrons, protons, neutrons, quarks and leptons.

In short, ‘bosons’ transmit the fundamental forces between particles, while ‘fermions’ constitute matter and interact through these forces. Both classes of particles are fundamental to understanding the structure of

For this ‘model’, such an ‘infinite, unbounded surround’ could therefore be taken as the definition of ‘infinite space’. A finite proper subset of the infinite quantity of mass/energy can only occupy a finite surrounding of any of its points. One can speak, in this case, of ‘finite space’. It must be said that ‘space’ itself is not a concrete/existing entity. What is concrete and really exists are the particles of matter / gravitational fields / the Higgs field / electromagnetic waves / gravitational waves / cosmic rays /… that permeate this ‘space’ and, since we are dealing with an infinite quantity of mass/energy, this quantity will, of necessity, occupy an infinite surrounding of any one of these particles.

The relative position of everything contained in this ‘infinite Universe of ours’ is governed by the various known forces:

1. the ‘gravitational‘ acting essentially, but not exclusively, on a large scale. [Gravitational force is the attraction that two bodies exert on each other due to their gravitational fields, generated by their respective masses.. It is responsible for the attraction that the Earth exerts on bodies and for phenomena such as the movement of planets around the Sun];  the ‘electromagnetic’ one;
2. the ‘electromagnetic‘ force; [The electromagnetic force is one of the four fundamental forces of nature acting between electric charges and electric currents. It is responsible for the interaction between charged particles and causes bodies with opposite charges to attract, while those with charges of the same sign repel. The electromagnetic force is also responsible for electromagnetic phenomena such as light, radio waves and magnetization].
3. the ‘strong nuclear‘; [The strong nuclear force is a force that holds protons and neutrons together within the atomic nucleus. It is responsible for the cohesion of the nucleons and prevents their repulsion due to the positive electric charge of the protons.];
4. The “weak nuclear” [The weak nuclear force acts at the subatomic scale. It is responsible for certain types of radioactive nuclear decay, such as beta transformation. Beta transformation is a process by which genetic information is transferred from one organism to another. This allows the genetic make-up of an organism to be modified, introducing new characteristics or functionality].
5. any others, as yet unknown. It must be kept in mind that the four forces listed are what our science has been able to discover, to date, in a tiny, tiny corner that represents only an infinitesimal part of this infinite Universe of ours.

It should be remembered that if it were possible to carry out experiments at even smaller distances than at present and it were possible to achieve distances of around 10-30 cm, then the last three forces would even become one and the same force (Theoretical physicist Gordon Kane addresses this topic in chapter 9 of his book: “The Garden of Particles“).

The metric expansion of space

By ‘metric expansion of space’, we mean the average increase in the measured distance between two celestial bodies in our Cosmos as time varies[66].                                                                                                                                                                             According to the ‘Lambda CDM cosmological model’, this expansion, valid on large scales, would necessarily require an incessant ‘production‘ of space, indispensable to contain this ever-expanding Cosmos of ours[67].

It would also be caused by the inertia resulting from the Big Bang and, for current Physics and Astrophysics, it would be a repulsive force whose nature is still unknown, called ‘dark energy’, which would represent a ‘cosmological constant’ responsible for the acceleration of expansion.

A rather fanciful explanation conjures up a curious comparison with a ‘panettone’ that rises and has the effect of pushing all the raisins inside away from each other.

According to this ‘axiomatic model‘, the dynamics of our Cosmos develop according to a different principle and, above all, do not require any ‘creation‘ (pseudoscience) of space, as this is infinite always and forever (see previous page).

Experimental observations tell us that the Milky Way and the Andromeda galaxy are approaching, at a speed of about 110 km/s.                                                                                                                                                                                           For this ‘axiomatic model’, such an approaching (at this speed) can only depend, necessarily, on a plurality of concomitant factors:     

1. mutual gravitational attraction [condition alone not sufficient];
2. belonging to common ‘conoids’ [necessary but not sufficient condition];
3. convergence of their paths, within the conoids to which they belong [necessary condition but not sufficient condition];
4. equidistance from the vertices of the ‘conoids’ [necessary condition][68];
5. continuously increasing cohesion level during the approach to the summit of the ‘conoid’;
6. effects due to belonging to several ‘conoids’, due to the presence of ‘large attractors’, including Shapley.                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           

For the ‘axiomatic model’, our planet, together with the Milky Way, which contains it, and an indefinite number of other galaxies/clusters of galaxies, … is subject to a global translation movement in the direction of the vertex of that ‘universal conoids’ to which it belongs and not only.

[66] This ‘expansion’ is also called the Fridman – Lemaître – Robertson – Walker metric, or more simply (FLRW), from the initials of those who contributed to its development. This metric represents a fundamental model for describing the universe on large scales, assuming that it is “homogeneous” and “isotropic“. These assumptions are now crucial for many of the conclusions derived from the theory of general relativity, in particular for the description of the expansion of the universe and its evolution. See the chapter dedicated to the theory of general relativity.

[67] In the abundant literature on this topic, it is not uncommon to find statements that evoke the concept of a continuous ‘creation’ of this space.

[68] It would perhaps be more correct to conjure up the concept of ‘equi-gravitational paths’.

It must be said that for the theory of special relativity, the relativistic mass of an object does not vary significantly as its speed varies, as long as this speed does not approach that of light.

According to this theory, the mass of a moving object increases as its velocity increases with respect to an observer at rest, according to the relativistic mass equation:

m(rel) = m(0) /   where ‘m(rel)‘ is the relativistic mass, ‘m(0)‘ is the rest mass of the object, ‘v‘ is the speed of the object and ‘c‘ is the speed of light in “vacuum“.

According to common mathematical language: [ m_{rel} = \frac{m_0}{\sqrt{1 – \frac{v^2}{c^2}}} ].                                                                                                              It should be added that it has not been specified (because it is not known) how fast our galaxy and Andromeda are approaching the vertex of our common ‘universal conoid’. It is possible that present-day astrophysics can trace this speed. In this equation, however, it is clear that if (v˄2) tends to (c˄2) then: tends to zero and therefore ‘m(rel)‘ tends to infinity.

According to this 'axiomatic model', the receding velocity of a celestial body (belonging to a 'universal conoid' different from ours) is directly proportional to its distance, i.e.: the greater the distance, the greater its receding velocity and thus the greater the red shift of its light.

This phenomenon is called 'redshift'. This 'redshift' is due to the fact that the axes[69] of each 'universal conoid' diverge, between them, and also to the fact that billion years have now passed since the accelerated outward flight of our Cosmos began, and thus each celestial body is deeply inward in its own 'universal conoid'[70].

Similarly, we can explain the same behavior (the greater the distance, the greater the receding velocity) of those galaxies that, although belonging to the same 'universal conoid' and not only, travel it at substantially different distances. The force of attraction between these galaxies and the vertex of our (common) 'universal conoid' is expressed by the following equation: F=(G . m1 . m2 )/d2 (for speeds not tending to that of light) and therefore the speed of receding, between two of these galaxies, will be directly proportional to their distance.

The galaxies of our Cosmos are immersed in a plurality of gravitational fields that permeate our Cosmos and, more generally, our infinite Universe, and are therefore subject to diverse forces.

If, for the sake of convenience, we limit our considerations to two galaxies: the Milky Way (ours) and Andromeda, we conclude that they obey various imperatives:

1. radial inertia due to the effect of our Big Bang;
2. gravitational field of our entire Cosmos;
3. gravitational fields exerted by the two galaxies;

[69] These ‘axes’ are not to be imagined, necessarily, as straight lines.

[70] The latter is confirmed observationally by the work of Fritz Zwicky (anomalies in the orbital velocities of galaxies around their galactic centers) and Vera Rubin (anomalies in the orbital velocities of stars around the center of gravity of the Andromeda galaxy ‘M31’).

[71] Equidistant and/or subject to the same gravitational force attracting them towards the same point.

d.gravitational field that is exerted around the vertex of the “universal cone” and the ‘universal conoid’ and the ‘local conoids[72]‘ common to the two galaxies;

e. it is good to remember that, for the “Milky Way” and for “Andromeda“, the “Great Attractor“[73]constitutes a center of attraction, since these two galaxies move towards this center, that is, towards its gravitational barycenter and then, all together, they are attracted by the gravitational center of the universal conoid to which they belong;

f….

The path followed by the two galaxies is represented by the curves generated by the plurality of all the forces that are exerted by and on them, through their respective gravitational fields, and could even be associated with “transcendent” curves, that is, non-algebraic curves.

The ‘Lambda CDM cosmological model’ tries to explain this speed by invoking the presence of ‘dark matter’.

In Focus - April 29, 2015: '... Now, however, thanks to the extraordinary capabilities of the Hubble Space Telescope and ESO's 8.20-meter VLT (Very Large Telescope), a team of astronomers have observed the simultaneous collision of four galaxies in the central region of the rich cluster of galaxies Abell 3827, which is about 1.4 billion light years away from us, collecting the first evidence of interaction of dark matter with other dark matter in a way other than gravitational attraction. '

Some difficulties would arise if one were to resort to the 'Lambda CDM cosmological model' to explain such events. It is certainly simpler to explain these phenomena by resorting to the 'axiomatic model' that classifies them as possible and predictable events. In fact, there is nothing to prevent us from supposing that, since the gravitational field generated by celestial bodies, which are out there (beyond our Cosmos), has taken over, two or more galaxies in our Cosmos may find themselves sharing the same universal 'conoid' , because they are attracted by the same celestial body/ bodies, (Black Hole/...) that exert that gravitational attraction on them (our galaxies).

In all likelihood, this will not be a 'head-on collision'.

In all likelihood, this will not be a 'head-on collision', given the dynamics present in 'conoids'.

Predictions made by the 'axiomatic model', regarding some gravitational effects which, for the 'Lambda CDM cosmological model ', require the presence of 'dark matter', they agree with the verified experimental data and are able to provide an explanation for them.

[Recent observations made with the 'Very Large Telescope' in Chile suggest that about 10 billion years ago the galaxies, then very young, were devoid of dark matter: the speed of rotation of the stars farther from the center dropped dramatically, instead of remaining constant. Dark matter would have been added later, and this 'late' behavior surprised everyone: at the moment there is no clear explanation ...] [erik-peter-verlinde[74]]

[72] These local’s are represented by the various ‘superclusters’ of our Cosmos (the Great Attractor, the Shapley supercluster, …). They are proper subsets of the ‘conoids’ that contain them.

[73] The Great Attractor consists of a complex branching structure of gigantic galaxies and represents the gravitational center of the supercluster Laniakea, which, in Hawaiian, means ‘immense paradise’. Among the billions of galaxies that make it up are the Milky Way and Andromeda.

[74] Professor Verlinde, theoretical physicist at the University of Amsterdam has recently developed an interesting theory that predicts the effects of gravity based exclusively on the mass associated with baryon matter, the visible one.

According to the most accredited version today, regarding ‘dark matter‘, this would be:

-          Necessary for the formation of galaxies, which occurred about 13 billion years ago;

-          Necessary to explain Einstein's arcs / rings;

-          Necessary to explain the dynamics of galaxies in clusters (James Jeans equations);

-          Necessary to explain the dynamics of stars in spiral galaxies;

-          Necessary to explain the rate of approach between our galaxy and the Andromeda galaxy;

-          …

Relatively recent discoveries, would state that dark matter did not exist about 10 billion years ago and that: 'it would have been added later'. See some previous lines (Verlinde).

The fact that these discoveries testify that ‘dark matter‘ did not exist 10 billion years ago confirms the predictions of the ‘axiomatic Model‘. In fact, at that time our galaxies had not yet started their path inside the ‘universals conoids‘ and their masses had not yet suffered that effect of continuous growth of their level of cohesion.

For current cosmology, it would therefore appear that:

1.       Dark matter would have existed about 13 billion years ago, due to the fact that astrophysicists believe it is necessary for the formation of galaxies;

2.       It didn't exist about 10 billion years ago. See: 'Recent observations made with the  Very Large Telescope (in Chile) suggest that about 10 billion years ago the galaxies, then very young, were devoid of dark matter ... ';

3.       It would exist today and would allow to explain a certain number of phenomena, such as: dynamics of galaxies in clusters, dynamics of stars in galaxies, ... .

One wonders: ‘How is it possible to justify the fact that this dark matter should have existed about 13 billion years ago, then disappeared around 10 billion years ago and finally make its reappearance today?‘.

Astrophysics Silvia Galli of the Paris Institute of Astrophysics (IAP), was able to affirm that this ‘dark matter‘, as well as ‘dark energy‘ were introduced ‘by hand‘, to justify phenomena that science current does not know how to explain. Finally, for this ‘axiomatic model‘, there is a causal relationship between:

- the gravitational interaction('our galaxies' → ← ' masses present outside our Cosmos ')

and

- the growth of the cohesion value of each galaxy / galaxy clusters /… in our Cosmos.

In an interview: ‘The constant of discord‘, astrophysicist Silvia Galli, of the Paris Institute of Astrophysics (IAP), stated: ‘… We know what the effects of these two ingredients (dark energy and dark matter) are , but we don’t know their physical nature. So what we are looking for are failures of this model (Λ CDM), something that gives us hints to better understand what these basic components are. ‘

[75] Excluding that baryonic component that can be considered 'obscure' since it does not emit light or emits very little and which is made up of massive objects, such as: satellites, planets, neutron stars, brown dwarfs, white dwarfs (stars with large mass but which emit very little brightness), black holes, ...

[76] At least as regards the forces responsible for the ‘escape acceleration‘ and ‘cohesion‘ of our galaxies.

Effects predicted, by deduction, from the axiomatic model of the universe[77]

1. this model assumes the existence of an infinite Universe, endowed with an infinite 'mass / energy'. This conclusion is a direct consequence of the first and second axioms on which the model is based (see the chapter "Types of Universe");

2. in the "infinite Universe", by the second axiom, mass/energy attracts mass/energy, thanks to their respective gravitational fields; It is one of the main reasons why celestial bodies, galaxies, black holes are formed[78], ... ;

1.      in a space-time[79] of the 'infinite Universe', mainly due to the law of universal gravitation, black holes, through their gravitational fields, attract surrounding matter and, consequently, increase their mass, their energy (hence their gravitational field) and therefore their capacity to attract other matter. Again as a result of gravitational fields, black holes end up attracting each other and forming black holes with increasing mass, energy, temperature and pressure. They perform a 'sweeping' work, around them, of a certain finite (non-empty) proper subset of this infinite Universe;

2.      this process will end once a 'critical threshold'[80] is reached or exceeded, the one necessary to trigger an deflagration: a possible 'Big Bang'. In this case, a new cycle, a new 'cosmos,' begins;

3.        in the moments following the first very rapid expansion, which followed our Big Bang, the temperature must have been very high and the kinetic energy of what was thrown, in all directions, at very high speed must have been very high;

• after the effect of this initial propulsion (which lasted a very short time, according to the experts), the speed of escape towards the outside, of the material that makes up our newborn Cosmos must have started to slow down, because the value of energy initial, distributed in an ever increasing volume, can only decrease, in equal volume of occupied space, and this speed will continue, subsequently, to decrease also due to the gravitational force, exerted by the entire mass of this Cosmos of ours;

According to this axiomatic model, the duration of this slowdown is destined, however, to end when, having reached and then exceeded a certain threshold / dimension, the gravitational force of what is out there (beyond the borders of our Cosmos), exceeds the values of attraction exercised by our Cosmos.

From this moment on, the escape velocity of each galaxy / cluster of galaxies can only undergo an inevitable acceleration[81].

The destiny of each of our galaxies is therefore to contribute to increasing their own mass/energy and, at the same time, that of those celestial bodies (black holes/...) and more, which generate the gravitational field responsible for their escape acceleration.

It is possible that on the occasion of one of these 'Big Plouf', somewhere, the threshold of the critical value of energy / temperature / pressure / is reached or exceeded ... in this case another will be generated 'Big Bang' will take place, resulting in the birth of a new cosmos; 

[77] When the sophisticated and promising James Webb Space Telescope is finally operational, new horizons will certainly be opened and we will certainly have answers to many of our questions.

[78] See chapter 'black holes'.

[79] Proper subset and nonzero, of the 'infinite Universe'.

[80] This process of matter accretion can only have a limit, since a proper subset of the infinite Universe cannot contain the entire infinite Universe. 

Invoking set theory, a proper (finite or infinite) subset of a certain set cannot contain the entire infinite set of which it is a proper subset. 

For the 'explosion/deflagration' effect, see the process that occurs in a white dwarf.

When: mass / temperature / pressure /… exceed a permitted limit, an explosion occurs.

[81] This prediction was verified observationally in 1998.

1.      the laws (not all) of each new ‘cosmos‘ will probably depend on the value of the energy .developed at the time of the ‘Big Bang‘, that is, following the last and fatal encounter / collision between black hole and other surrounding matter (black holes , galaxies, clusters of galaxies,…). This energy, the result of this last and fatal union, will not necessarily be the same for all cosmoses, on the contrary …

2.      the thermal spectrum of the Cosmic Microwave Background Radiation (CMBR – from Cosmic Microwave Background Radiation) could, reasonably enough, depend on the amount of energy that generated each of the infinite Big Bangs;

3.      the 'Fermi paradox' takes shape and becomes evident, since the intelligent extraterrestrial life becomes a certainty and the number of evolved civilizations of the entire Universe, in every instant, can only tend towards infinity;

• differentiated escape velocity of our galaxies, galaxy clusters, …

According to this 'model', not all our galaxies or clusters of galaxies have the same escape velocity, outwards[82]. The force of attraction, which develops between these and the vertex of a 'universal conoid' to which they belong results from the following equation: 

F=(G . m1 . m2 )/d2 (for speeds approaching that of light, it is necessary to resort to Einstein’s field equations) and thus the approach speed increases as the distance decreases.

A separate discussion must be made for those galaxies that are located in the same 'universal conoid' and 'local conoids (Milky Way and Andromeda, for example). These, by the second axiom underlying this work, should have the same escape velocity if they are at equivalent distances from the vertices of the common 'conoids' [F = (G. m1. m2) / d2], or suffer the same attraction.

5.      Hubble's law

Taking into account that this 'axiomatic model' provides, in principle, differentiated escape velocities of the galaxies / galaxy cluster of our Cosmos (belonging to different universal conoids), it can only result in I disagree with the idea that, in the equation relating to Hubble's law (v = H0 · d)[83] there may be a single value, denoted by 'H0' and called: 'Hubble constant / parameter' applicable, in a general way to every galaxy/galaxy cluster. Since, then, Since this escape velocity has been accelerating for more than 4 billion years, this value (approximately) years, this value (called 'constant / parameter') applicable for each galaxy / cluster of galaxies should also necessarily undergo a growth, at the grow by 't' (time variable);

[82] 2020: A new study by researchers from the Center for Astrophysics – Harvard & Smithsonian, was commented in a video, posted on Youtube [https://www.youtube.com/watch?v=TZ3TqMvbM60] entitled ‘ The challenge to the Hubble constant ‘. In this video, it was announced that: ‘… A team of Harvard scientists further feeds doubts about the Hubble constant, claiming that our universe is expanding, but its acceleration is not constant at all and that is why the notorious value hypothesized by Edwin Hubble, in 1929, is so difficult to find. According to the new study, the universe (‘our Cosmos’, for this model) may not expand equally in all directions.’

‘Based on our observations on clusters we may have found differences in the rate at which the Universe is expanding and this would run counter to one of the most basic assumptions we use in cosmology today (Lambda CDM model).’ Said Gerrit Schellenberger, (PostDoc Fellow at Harvard-Smithsonian Center for Astrophysics, co-author of the research).

[83] Where: v = speed of recession of a galaxy, H0 = (H zero) Hubble constant, d = distance that separates us from that galaxy.

1.      the gravitational dynamics present in the ‘conoids‘ would seem to favor the birth of binary systems (pairs of stars, black holes, galaxies, …) that would end up rotating around a common gravitational center, before merging into a single agglomeration, with final destination the ‘Big Plouf‘, or other.

For this 'axiomatic model', the probability and mode of 'collision' of galaxies sharing the same conoids would depend on a number of variables. They could travel at distinctly different distances from their vertices, given also that their respective paths might not be symmetrical with respect to the 'axes' of the conoids. 

With different distances from the vertices of the conoids, they would, inevitably, have different velocities [F = (G. m1. m2) / d2] and therefore different approach times to the 'Big Plouf';

2.      the The level of cohesion of galaxies and galaxy clusters undergoes continuous growth as they approach the apex of the conoids.

3.      the growth in the level of cohesion of our galaxies, within each conoid: universal and local, is in turn responsible for a continuous increase in the angular velocity of stars around the galactic center. The further away a celestial body is from the barycenter around which it orbits, the greater the momentum of approach to that barycenter (L= r x p, where L is the angular momentum, r is the position vector and p is the linear momentum vector of the object);

4.      tendency to gravitational aggregation of galaxies in galaxy clusters (see works and discoveries by Vera Rubin); According to the 'axiomatic model', the constant and continuous increase in the cohesion of the material present in each of the conoids as they approach their respective vertices is mainly responsible for these aggregation processes;

5.      according to the 'axiomatic model', the increase in the escape velocity of galaxies / clusters of galaxies towards the outside of the Cosmos and the increase in their level of cohesion are evidently linked to each other by a relationship of proportionality direct. It would therefore be absolutely normal to note that, for the 'Lambda CDM cosmological model ', as the parameter ' Λ ' increases, there is a corresponding increase in the 'CDM' parameter;

6.      this 'model' presupposes the existence of infinite proper subsets, each containing infinite 'cosmoses' born from an equivalent energy impulse. Since it is not possible to set an arbitrary limit to this energy value which, by its nature, can only tend towards infinity[84], it follows that it is legitimate to suppose the existence of infinite 'cosmoses' born from an energy impulse much higher than the minimum threshold necessary for their development and therefore for their existence. In each of these 'cosmoses' there could be the case in which another cosmos or still others develops within them and a 'matryoshka' effect is not excluded at all; The 'Fermi paradox[85]' it evokes the question concerning the possible and perhaps inevitable existence of intelligent life forms, in addition to those present on planet Earth[86];

[84] In probability theory, in processes that have to do with repetitions tending to infinity, what is not impossible tends to certainty. See paradoxical proof of the mathematician Félix Edouard Justin Émile Borel (according to the Borel-Cantelli lemma).

[85] From the Greek παρά (parà → against) and δόξα (doxa → opinion). A mathematical paradox is a logical and coherent proposition, but one that goes against intuition, which is 'anti intuitive'.

[86] Fermi exposes the following thought: 'Given the enormous number of stars in the observable universe, it is natural to think that life could have developed in a large number of planets and that many evolved extraterrestrial civilizations appeared during the life of the universe.' From this statement, a question arises:

'If the Universe and our galaxy are teeming with developed civilizations, where are all of them?'

According to this 'axiomatic model', not only is it possible that, out there, other forms of intelligence exist, but for the infinity of cosmoses existing in the 'infinite Universe', this 'possibility' becomes a 'certainty'.

In this regard, the ‘axiomatic model‘ goes further, because it includes the possibility / certainty that each sequence of events can repeat itself, in an identical way, infinite times and that it has already happened an infinite number of times.

1.      for the ‘axiomatic model’, the composition of our Cosmos is different from that indicated by the ‘Lambda CDM cosmological model ‘ which provides:

– 70% (approximately) of ‘dark energy’;
– 25% (approximately) of ‘dark matter’;
– 5% (approximately) of ‘baryon matter’.

The 'axiomatic model' in fact provides:

– 95% (approximately) of ‘gravitational field energy’
– 5% (approximately) of ‘heavy elements, neutrinos, stars, …’

The two values indicated above are to be considered hypothetical and the first of the two in continuous growth. Their ratio (in percentage), can only change, continuously, and in favor of the 'energy gravitational fields'.

In fact (limiting ourselves to Newton's law), this energy is destined to grow according to a ratio inversely proportional to the square of the distance that separates our galaxies from the apex of the 'conoid' they belong to, to which they are attracted and towards which they are directed, at an ever increasing speed;

2.      this 'model' accords with the principle of cause and effect. 

If an event, taken as small as we like, let's call it: 'epsilon' (ε), were able to violate this principle, then it would mean that (ε) or a part of it, would lack that complete link with their past more next one. Therefore (ε) or a part of it would be without an origin, but this would mean that (ε) or a subset of it should necessarily have the characteristic of a creation. This hypothesis contradicts the first axiom, placed at the basis of this work. This conclusion can only deny the possibility of the existence of 'free will'; [For a more in-depth look at this issue, see Sabine Hossenfelder's work: 'Ten conceptual errors in free will' - © Hans Wretling/Matton Collection/Corbis].

Werner Heisenberg, Nobel Prize winner for physics, in his book 'Physics and Philosophy' (il Saggiatore), states on page 93: 'The theory of relativity has changed our knowledge of space and time, it has indeed revealed entirely new aspects of space and time, of which there is no trace in the Kantian a priori forms of pure intuition. The law of causality no longer applies in the theory of quanta, and the law of conservation of matter is no longer true for elementary particles.'

and, on pages 95-96: 'But why has the scientific method really been transformed after Immanuel Kant (*1724 †1804) in this very important problem?  Two answers are possible to this question. The first is that we have convinced ourselves through experience that the laws of the quantum theory are correct[87] and that, if they are, we know that a previous event to be considered as the cause of the emission at a given time cannot be found. The other answer says: we know the preceding event, but not entirely precisely. We know the forces in the atomic nucleus that are responsible for the emission of the 'α' particle, but this knowledge contains the uncertainty produced by the interaction between the nucleus and the rest of the world. If we wanted to know why the 'α' particle was emitted at that particular moment, we would have to know the microscopic structure of the entire world including ourselves, which is impossible.'

‘If the Universe and our galaxy are teeming with developed civilizations, where are all of them?’
According to this ‘axiomatic model’, not only is it possible that, out there, other forms of intelligence exist, but for the infinity of cosmoses existing in the ‘infinite Universe’, this ‘possibility’ becomes a ‘certainty’.
In this regard, the ‘axiomatic model’ goes further, because it includes the possibility / certainty that each sequence of events can repeat itself, in an identical way, infinite times and that it has already happened an infinite number of times.

[87] A few years later, Richard Feynman, Nobel Prize winner for physics, would say: « ”If you think you understand quantum theory, it means you don’t understand it!” and again: ”I think I can say that nobody understands quantum mechanics.‘»

The fact that: ‘a previous event, to be considered as the cause of the emission at a given time, cannot be found‘ and that it is not possible ‘to know the microscopic structure of the whole world including ourselves‘, does not at all negate the principle of ‘cause and effect’.

We simply note that it is not possible to understand everything.

In this regard, I am reminded that, at the age of eighteen, following a lecture given by the newly-appointed bishop of Aosta, Monsignor Ovidio Lari, and dedicated to men of age (for women there was a lecture dedicated to them), I listened with great interest to his speech, as I was looking for confirmation or, possibly, refutation of the ideas I had formed on the existential question and my beliefs that were being elaborated.

At one point in his long and impassioned chat, Monsignor Ovidio says: 'you have to believe, because ...'

I was absolutely interested to know the reasons for this 'why', and Monsignor reveals it with a broad smile and with his well-known and proverbial calmness and composure: 'one must believe, because it is beautiful'. I confess that this explanation, for me, was a real surprise and a tremendous blow. I never expected it to be so simple a matter that had been occupying my thoughts with some frequency for quite some time.

'because it's nice'!!!   I remember coming home very disappointed. With that statement, our bishop had completely disappointed my expectations.

I needed someone to explain to me how it was possible that that God, so much declaimed in the Sunday sermons of our parish priest, really existed and with the qualities attributed to him, namely that of the one who is infinitely good, who knows everything and everything.

I used to ask myself: 'how is it possible that there could exist a being who knows everything?' 

Answer: 'it is not possible at all, since there cannot exist any entity that knows everything, since to fulfil this condition, this someone should, necessarily, also be able to know himself (since he cannot but be an integral part of this totality) and that is to say, he should be able to know himself completely and even at the precise moment in which he exercises this knowledge. But every time he adds to his knowledge a knowledge of his knowledge, he finds himself having to add a further knowledge of the knowledge of his knowledge and so on ad infinitum.  One would be dealing with a mathematical procedure, recursive in nature, which cannot have an end and therefore, such a conjecture remains as a conjecture and nothing more.'

Many years later, since that distant 1968, although I have not changed my mind, I have come to appreciate and respect that 'because it is beautiful', of our bishop and all those who have their own 'creed', a deep faith and live it with passion and consistency. Freedom of thought was an important and fundamental conquest, of which we can only be proud and which we must defend at all costs.

Many years later, since that distant 1968, although I have not changed my mind, I have come to appreciate and respect that 'because it is beautiful', of our bishop Ovid and of all those who have their own 'creed', a deep faith and live it with conviction and consistency, with full respect for all. Freedom of thought and of all beliefs has been an important and fundamental conquest by our society. We cannot but be proud of this freedom, and we must protect and defend it at all costs. 

I do not feel that I have sacrificed anything of that way of thinking that had the smell of my 18 years, quite the contrary.

1.      this ‘model‘ is in accordance with the ‘Copernican principle‘, according to which the Earth does not represent a privileged observation point since, for this ‘model‘ every celestial body and, more generally, every proper subset (satellite, planet, star , solar system, galaxy, cosmos, …) of the infinite Universe is nothing more than an infinitesimal of the latter and it makes no sense to speak of privileged centrality, because in reality every ‘place‘ can, and with good reason, boast of being so and no one is more so than any other (See: Nicola Cusano – 57 manuscripts of science, geography and cosmology);

2.      for this 'model' therefore even the smallest and simplest ant could, and without fear of being contradicted, consider itself at the center of the infinite Universe!

3.      for this model, it is not necessary and makes no sense to use the concept of 'dark energy' to explain the reason for the acceleration of the escape of galaxies / clusters of galaxies in our cosmos. (See chapter 'dark energy');

4.  for this model, it is not necessary and makes no sense to use the concept of 'dark matter', to explain the degree of 'cohesion' of each galaxy / cluster of galaxies in our Cosmos. (See chapter 'dark matter ') nor to justify the effects of gravitational lenses (see next point), as this degree of 'cohesion' is bound to grow, within each 'conoid';

5.      gravitational lenses

The 'gravitational lensing' effect consists in the deflection of light around a body with mass and in the production of those phenomena called 'Einstein's rings' or 'arcs of light'[88]. The greater the mass, the greater the deflection of light passing through its immediate vicinity.

Since the 'conoid effect', according to the 'axiomatic model', leads to an increase in the cohesion of galaxies/galaxy clusters, due to the decrease in the space occupied by them, the latter (conoid effect) is the real culprit behind the increased deflection of light rays that has been observed: F = (G·m1·m2 )/ d2. (see the chapter 'dark matter'). It is therefore not necessary to invoke the existence of any 'dark matter' to justify this discrepancy between the amount of baryonic matter present and the degree of deflection produced;

6.      each 'Black Hole' is destined to become a cosmos or in any case to contribute to its birth! In reality, every single particle of mass / energy, sooner or later, will end up contributing to the birth of a new cosmos, somewhere, in this infinite Universe of ours[89];

7.      according to the 'Axiomatic Model', the vertices of the 'conoids' do not maintain the same position in the space-time of our infinite Universe. This change in position depends on various factors. 

8.      One of these is undoubtedly due to a possible merging of the vertex mass with some other mass (black holes, ...) located nearby;

9.      a variation in the position of the vertex of a 'conoid', due to an amalgamation with surrounding masses, correspond to a variation in the direction and / or acceleration of escape of the masses present in that 'conoid';

[88] They are luminous effects which, thanks to the deflection / curvature of the photons of light, due to the mass of a galaxy or a cluster of galaxies, allow the light of a luminous body hidden behind this galaxy / cluster of galaxies to reach us. These effects appear in the form of a ring, called Einstein’s (the one who predicted its existence) or a simple arc if the hidden object is not centered with respect to the observer axis and the center of the galaxy, which performs the function of ‘lens‘.

[89] See chapter ‘Black holes‘.

1.      there is ‘something‘ out there waiting for us …

We spend our existence on this planet Earth of ours and when we are not moving, with respect to the environment that surrounds us, we perceive the sensation of being 'still'. In reality, it is only because we are not sensitive to the numerous shifts to which we are constantly subjected [90].

· in one day we make a full circle around our earth axis[91];

· in one year we even complete an entire revolution around the sun (about 150 million km away from us);

· our solar system is not 'stationary' within the Milky Way that hosts it;

· the Milky Way, that is our galaxy, is undergoing an accelerated movement in the direction of that 'something' that awaits us out there.

We do not know how much longer this will continue to wait for us. What we do know is that more than four billion years have passed (or so) years (almost a third of the current age of our cosmos) have now passed since our escape velocity stopped slowing down and began to accelerate as those ‘somethings’ out there, they began to make the effect of their gravitational fields felt.

An important part of the radius of that empty ‘vacuum[92]’ has been covered, which was created as a result of the ‘brushing‘ which then led to our Big Bang.

The ‘axiomatic model‘ assigns a value of 95% (approximately) to the ‘gravitational field energy’ of this our Cosmos. This means that the caller out there has raised their voices sharply. We can only adapt. According to this ‘axiomatic model‘, sooner or later the fatal encounter / clash between our galaxy and this ‘something’ will take place and then: ‘Good night to everyone and for a while!‘[93]

It is therefore legitimate to ask: ‘how much longer ? …’

'How beautiful is youth

which escapes however.

Who wants to be happy, either,

of tomorrow there is no certainty. ' [94]

2.        effects and consequences of an existential and philosophical nature.

The scenarios that emerge as effects, on a philosophical level, consequent to the predictions of this 'axiomatic model' are certainly of considerable complexity and also quite shocking.

These deserve a separate chapter and effort; therefore it is preferable that they are not even mentioned in this work.

[90] The 'Lorentz invariance' is a characteristic of nature for which the physical laws that govern it do not depend on the speed and translation orientation of the reference system.

[91] The distance traveled is very different for those who live on the equator than for those near the poles.

[92] This term ‘empty‘ is certainly not appropriate. It simply indicates that much of its content has flowed to where our Big Bang took place.

[93] This 'for a while' was not inserted at random or even as a joke. Its meaning could and perhaps should be deepened in a subsequent work, to be developed in relation to the subject: 'Effects and consequences of an existential and philosophical nature due to this axiomatic model of the Universe'.

[94] From the ‘Canzona di Bacco‘ by Lorenzo de ‘Medici, called Lorenzo the Magnificent. The ballad probably dates back to 1490, two years before the author’s death. The rhyming refrain ‘who wants to be happy, be it, there is no certainty of tomorrow‘ is repeated several times in this ballad.

The theory of general relativity

John Archibald Wheeler[95] summarized Einstein’s general relativity, as follows:

‘space-time tells matter how to move; matter tells space-time how to bend‘[96]. That is:

a. space-time tells matter how to move (it means that it indicates the path that matter must follow);

b. matter tells space-time how to bend (it means that it is the matter that determines what this path is and how it should be).

Wheeler highlights an asymmetry in this relationship. According to him, it turns out that matter acts as the ‘cause’ of the curvature of space-time, while space-time turns out to be the ‘context’ that drives the movement of matter. On careful analysis, it turns out that this ‘space-time’ does not, in fact, have a say in the path of mass, since:

it would be matter itself that would dictate to space-time (if it is an entity that actually exists in practice) how it should curve and therefore: the latter could not do anything other than adapt to what is decreed by matter, through its gravitational fields, which therefore determines: wat its path is and how it should be[97].

I have a feeling that the good Albert Einstein is now in some circle of that Olympus of science and there he spends a good part of his free time listening to and watching the bickering that his ‘theory of general relativity’ has caused and is causing down here in this so-called scientific society of ours.

By using a hypothetical deductive argument of the type: ‘as if …’  he has managed to give a high-voltage ‘shock’ to the entire scientific world and beyond.

With this “as if …“, invoked by Einstein, and solved, in his own way, with complicated field equations, to which he resorted and in particular, but not only, to the complicated tensors of Gregorio Ricci Cubastro (*1853 †1925, to whom Einstein dedicates a very special thanks) reminds us of the solution found by theoretical physicists to resolve the question of the “metric expansion of space”, which is contested by the “axiomatic model”.

In fact, the latter is based precisely on the theory of general relativity of the good Albert.

[95] Born in 1911 and died in 2008, he was with Enrico Fermi and Niels Bohr one of the pioneers of nuclear fission.

[96] Wheeler did nothing but explain, in words, the meaning of Albert Einstein’s famous field equations:

• (Rμν) the curvature tensor of the mathematician Gregorio Ricci Cubastro;
• (gμν) the metric tensor; it is a contraction of the Riemann tensor;
• (R) the scalar of Ricci.

In the first member appear:

These represent the curvature aspect of what Einstein calls ‘space-time‘.

The second member of this equation contains instead:

• (Tμν) the energy tensor and the impulse tensor.

[97] See the definition of ‘infinite space’ on page 31.

One of the many famous quotes, by good Albert, goes like this: “I think and think for months and years. Ninety-nine times, the conclusion is false. The hundredth time I am right.“

I am aware that Albert is right when he states that time and space are linked by a close, indeed very close relationship. He illustrated this to the scientific community and beyond through his famous and valuable ‘theory of special relativity’ of 1905.

In his general theory of relativity, Einstein correctly postulated that mass (and, in general, energy) affects the way objects move, but also the way “time” passes. In the presence of higher masses, “time” passes more slowly than in places without such masses. This is a phenomenon known as “gravitational time dilation“.

Considerations:

If a theory contains, within it, one and even just one incorrect prediction, it is absolutely not possible to maintain the complete acceptability and incontestability of this theory.

Now, since it is evident that Einstein’s “general theory of relativity” contains not one but several incorrect predictions, within it, we cannot but conclude that this theory must, necessarily, be revised and corrected!

It is clear and evident that Einstein’s field equations lead, through Friedman’s equations which are based on Einstein’s own equations, to the statement that the universe is “homogeneous“, is “isotropic” and that Einstein’s field equations also predict the existence of “singularities“, that is, places, located in a certain finite space-time and endowed with a finite quantity of mass/energy, in which some quantities assume infinite values, in this universe of ours.

Since neither our “observable universe“, nor our “Cosmos” and even less the “infinite Universe” are “homogeneous” and “isotropic” and there absolutely cannot exist proper subsets that contain “singularities“, since this condition would contradict the starting assumption, then we cannot help but conclude that in Einstein’s field equations, on which an important part of the theory of general relativity is based, there is something wrong!

That there is something wrong, Einstein himself admitted (see the blog, dated 08/30/2024, of theoretical physicist Sabine Hossenfelder).

The idea I got is that this “theory of general relativity” is really a big “soup” (in the good sense of the expression, since I like it a lot). Personally, I consider it a “soup“, because it is composed of several ingredients and of different types.

This theory uses:

a. the equivalence principle. Stated by Einstein around 1907, it establishes that the effects of gravity in a gravitational field are indistinguishable from those of a uniform acceleration. This principle is articulated in two forms: the weak equivalence principle states that gravitational mass is equivalent to inertial mass. The strong equivalence principle considers gravity as a manifestation of the curvature of space-time. These concepts are generally considered fundamental to general relativity.

b. of incorrect field equations. Einstein himself admits it see the recent (30/08/2024) blog by Sabine Hossenfelder: « As soon as Einstein had finished his theory of general relativity, the German physicist and astronomer Karl Schwarzschild (*1873 †1916) discovered a solution to Einstein’s equations that described what we now call black holes. But this solution has singularities, places where some quantities take on infinite values. Einstein thought that this could not be right. Singularities should not occur in reality. And if his theory allowed them, then there was something wrong with it.»

c. of insights and ideas that blossomed and grew directly under the hat of good Albert.

These insights essentially refer to the idea linked to the concept of curvature of space-time. In general relativity, Einstein states that gravity is not simply a force, as conceived in Newtonian mechanics, but rather a manifestation of the curvature of space-time caused by the presence of mass. The greater the mass of a body, the greater the curvature it generates, thus influencing the path of objects moving in its vicinity.

Each of these three points: a. – b. – c. It consists of a series of arguments and all together they form an important part of the Einstein “theory of general relativity“.

Now, since the “the principle of equivalence” and not only turns out to be absolutely correct and turns out to be made up of a large number of phenomena (see the issue regarding the use of GPS and not only) which are explained exhaustively by this principle, then it is, partially but only partially, understandable the fact that a whole vast array of physicists, even high level ones, are tied by a solid feeling of affection “theory of general relativity“.

This does not remove and does not eliminate the inconsistencies that emerge, essentially but not exclusively, from point c. (incorrect field equations).

These inconsistencies require a necessary revision of the “theory of general relativity“.

What will come out of it will no longer be the “general theory of relativity” that we know today, it will be called something different, it will have to be amended from all those erroneous predictions that have undermined its solidity and validity!

And what about Einstein’s “intuitions” ??? Who and what can tell us whether they are correct or not???  Only the conclusions to which his theory arrives can tell us.

One of his quotes goes like this: «I just imagine it is so! Then I try to prove it.»

It was Einstein himself who stated: “10, 100, 1,000 proofs in favor are not enough to confirm the validity of a theory. One contrary proof is enough to demolish it !”

On the question relating to the disputed “space-time fabric“, this “space-time fabric” is an idea of ​​the good Albert, his “intuition“, inserted in his theory of general relativity and described through complicated field equations of great mathematicians such as Gregorio Ricci Cubastro and others.

If a theory contains errors and makes, even just one, and only one, false prediction, it cannot help but be entirely revised and corrected!

This “axiomatic model” cannot help but express its own judgment, regarding what is called the “curvature of space-time“.

First of all, it must be said that he agrees with Wheeler’s interpretation and maintains that the main role is played by mass/energy which (through the infinite associated gravitational fields available to it, in this Universe of ours, infinite in time, infinite in the amount of mass/energy and therefore infinite in space) represents the motor that moves the entire world, the ‘Deus ex machina[98]‘.

Each of the infinite entities made up of mass/energy, not excluding the smallest of grains of sand, enters the scene and plays its own specific role on the stage of this infinite Universe of ours.

It is, essentially, through these gravitational fields that each ‘object/entity’ interacts with a large number of other surrounding ‘objects/entities’.

A photon of light, thanks to its ‘energy of motion’ [99] interacts with the gravitational fields of the masses it encounters, and when these are particularly intense, it cannot but deviate its path.

The eclipse of 8 May 1919 confirmed this and further confirmation came ten years later with the eclipse of 29 January 1929.

For this ‘axiomatic model’, Albert touches on reality when he states that masses produce the effect of bending the fabric of space-time.

I have often wondered, without understanding him, what Albert really meant by the ‘fabric of space-time’.

Each mass is associated with its own infinite gravitational field and it is the interactions of these fields that guide and determine the movements of these masses

Photons that change their direction of motion, in the vicinity of a very intense gravitational field, do not follow the path traced by a “space-time fabric” but obey, simply and rigorously, the laws that regulate the interactions between the gravitational fields involved.

The field equations used by Einstein are certainly not easy and immediate to digest.

These equations, the result of the contribution of great mathematicians, his contemporaries and not only, were not understood even by good Albert.

[98] The origin of the phrase dates back to Greek theatre, where, in some plays, an actor impersonating a deity was brought on stage with a machine (a kind of mechanical device) to solve seemingly unsolvable situations.

[99] Photons do not have “rest” mass, but during their journey they possess a “momentum” and therefore, although we cannot speak of mass for photons, in a certain sense we can use the concept of “equivalent mass” through relativity. In fact, special relativity tells us that energy and mass are equivalent through Einstein’s famous equation (E = mc²). Therefore, a photon has an energy that can be associated with a sort of “relativistic mass“.

Photons, during their motion are equipped with their own gravitational field. The shape of this field can only be particular, given that the photon, by its nature, travels at the speed of light and the propagation of variations in gravitational fields occurs at this speed that cannot be exceeded (see the findings of two of the three Ligo observatories, in the United States, on 09/14/2015).

In fact, after realizing that, according to these equations, the universe should have collapsed on itself, he introduced what he called ‘cosmological constant lambda (Λ)’.

In vain, the mathematician Aleksandr Aleksandrovich Fridman and the mathematician and physicist, as well as parish priest, Georges Lemaître tried to convince Einstein that one of the solutions of his field equations predicted the expansion of the universe.

Albert did not listen to them and changed his mind only when Edwin Hubble, in 1929, discovered, through observation, that the universe was indeed expanding.

Einstein removed this cosmological constant from his field equations and had the courage and good sense to declare openly and publicly that the inclusion of this cosmological constant lambda (Λ) was his greatest mistake.

Every mass/energy, however small it may be, possesses its own gravitational field that has no end, in the infinite Universe and when two or more gigantic masses, e.g. two or more black holes merge into a single black hole, by the ‘axiomatic model/theorem of the infinite Universe’, they put into action a behavior that seems to be suggested by a right/need for survival and deprive themselves of a part of their mass which will be destined to generate a new and more intense gravitational field.

This gravitational field will interact with an infinity of other fields and these cannot but be responsible for the birth of new celestial bodies that will end up, one day or another, generating another of the infinite Big-Bangs.

In each of these a complex process will be triggered that will generate a new cosmos that, here and there, will be able to generate new plant and animal life that will be able to be endowed with intelligence and even very great intelligence!

I have had occasion to state that Albert misses the point when he states that masses produce the effect of folding the ‘fabric of space-time’.

In numerous blogs, some physicists, even high-level ones, use the image of a ‘fabric’ being folded by a mass. In a graph below, I have tried to visualize an imaginary phenomenon that would make use of this ‘fabric’.

When two bodies (the smaller one on the left, blue, and the larger one on the right, yellow – see figure below), travelling on this imaginary fabric of space-time, approach that (brick-colored) mass by mutual attraction, the two will initially point in the direction of the brick’s barycenter (as was also claimed, some time ago, by a certain Archimedes of Syracuse {*287 †212 BC}, mathematician, physicist and inventor).

According to the theory of general relativity, these two bodies will follow the path indicated by the fabric.

Now, hold on tight! While the yellow body, the larger one on the right, will crash more or less around the equator of the brick, the smaller one on the left will crash between the equator and the south pole of the same brick. You can swear that the ‘Syracusan’ mathematician, physicist and inventor, and surely not only he, will be astonished, indeed scandalized, and will have every right to be; and yet this is indeed the case, the theory of general relativity states so!

According to several articles published by the magazine “Le Scienze“, photons of light coming from our Sun will be forced to follow this phantom fabric of “space-time” and will end up passing our planet Earth, bypassing it and leaving it, therefore, completely in the dark.

The theory of general relativity is based on the idea that gravity is not simply a force, but an effect of the curvature of space-time caused by the presence of mass and energy. The “space-time fabric” is therefore a fundamental concept for understanding how gravity interacts with the geometry of the universe. It is well known that, in the face of arguments that make the concept of space-time fabric superfluous, a radical revision of the theory of general relativity is necessary.

Graphs:

                               A group of Italian researchers has published a theoretical study linking general relativity and …

This type of graph is widely used by various scientific journals and television reports.

Let’s imagine that a swarm composed of millions of particles, of different masses, grazes a celestial body, the Earth for example.

Each particle will follow its own path; the curvature, more or less accentuated, of each of these paths, will evidently depend on the quantity of motion (p=mass·velocity) of each particle, as well as on the minimum distance, at the moment in which it grazes our planet.

A similar discussion, but much, much more complex, could be made by reasoning on all the rays of light emitted by all the stars in our entire firmament.

Who would dare to draw or even just imagine the complexity of this “imaginary” space-time fabric that imposes on each particle/photon of light the path to follow?

One wonders: would the various and complex field equations be enough to describe such a space-time fabric? If we use the concept “interactions between gravitational fields“, rather than “curvature of space-time“, then, since a photon of light has a “momentum” and therefore has energy (it produces electrical energy when it collides with a photovoltaic panel), so a photon of light is able to attract a mass!

Now, since a photon of light is able to attract a mass, then a mass is able to attract a photon of light.  So: if a mass is able to attract a photon of light, it is not necessary to invoke any phantom “curvature of space-time” to explain the phenomenon of “gravitational lensing“!

Hypothetical-deductive reasoning “as if…” is a mental construction that is based on the formulation of a hypothesis and reasons about it as if it were true, even if there is no irrefutable confirmation of its truthfulness. This approach is particularly useful in experimental or theoretical contexts, where the consequences of hypotheses are explored to better understand a phenomenon or to develop new theories. This “as if …“, invoked by Einstein, and solved, according to him, with those complicated field equations to which he resorted and the complicated tensors of Gregorio Ricci Cubastro (*1853 †1925, to whom Einstein dedicates a very special thanks) recalls the solution found by theoretical physicists to resolve the question of the “metric expansion of space“.

The concept of “metric expansion of space“, fully contested by the “axiomatic model“, is mainly inspired by non-Euclidean geometry and, in particular, by Albert Einstein’s general relativity.

General relativity describes gravity as a curvature of space-time caused by the presence of mass and energy.

The (FLRW) metric to explain the reasons for the expansion of the universe, over time, invokes nothing less than a continuous “creation” of space, essential to contain a continuously growing volume, as predicted by the “axiomatic model” and confirmed by the 1998 discovery.

In short, physicists have drawn inspiration from ideas from differential geometry and general relativity to address the concept of metric expansion of space.

It turns out that both Einstein’s theory of general relativity and this “metric expansion of space” must absolutely be revised and corrected.

The use of mathematics, to describe our observable Universe and not only, must evidently be done “with tweezers” and not “in any way” and at all costs.

In my opinion, it should be made clear what is meant when it is stated: “… Einstein’s theory of general relativity predicts it” and that is, whether it is a thought, an idea, a personal intuition of Albert or a consequence due to the field equations used by him, in his theory or even both together!

Let’s try to clarify a little.

Since in propositional or enunciatively logic, the effective implication of two propositions P and Q is that proposition that expresses the concept: “if P, then Q; that is, (P→ Q) to be read P implies Q”.

1) P(True) → Q (T) – the implication is true;

2) P(T) → Q (False) – the implication is false;

3) P(F) → Q (T) – the implication is true;

4) P(F) → Q (F) – the implication is true;

In summary, this logical implication is false only and exclusively in the case where: P is true and Q is false. In the other three cases, the implication is true!

Now, since we often hear statements like: “… Einstein’s theory of general relativity predicts it“, for example: “the homogeneity and isotropy of our universe are predicted by the theory of general relativity” which, translated into the language of propositional logic, is: “the theory of general relativity” implies “the homogeneity and isotropy of our universe“, where P stands for: “the theory of general relativity” and Q stands for: “the homogeneity and isotropy of our universe“.

Since the “axiomatic model” denies “the homogeneity and isotropy of our universe” (it would also be enough to deny only isotropy) and since experimental observations, from 2020 and later, have also confirmed this hypothesis, then: substituting: “the theory of relativity” for P and “the homogeneity and isotropy of our universe” for Q, it would result that: when Q is false, P is also, necessarily, false.

Considering, therefore, that Q is false, then:

a. The Hubble constant, which should provide a way to quantify the expansion of the universe, must necessarily be revised and corrected;

b. Solution 2) tells us that the theory of relativity is true, but the resulting implication is false;

c. Solution 3) tells us that the theory of relativity is false. For both solution 2) and solution 3) some observations should be made. What we call “general theory of relativity” uses various field equations. The equations of the mathematician Fridman, describe and illustrate some type of curvature, but do not imply it at all (with the meaning that, in propositional logic, the word “imply“). What they do imply, instead, is the isotropy[100] and homogeneity[101] of our universe. It would seem reasonable to assume that if there are any errors in the equations involving homogeneity and isotropism, then these errors must be found in Einstein’s equations. This assumption is confirmed by Einstein himself. In her recent blog, theoretical physicist Sabine Hossenfelder states: « You see, just as Einstein had finished his general theory of relativity, the German physicist and astronomer Karl Schwarzschild (*1873 †1916) discovered a solution to Einstein’s equations that described what we now call black holes. But this solution has singularities, places where some quantities take on infinite values.

[100] Isotropy [iso (ισο→equal) and tropia (τροπία→direction)] of the universe is a concept in cosmology that indicates that the characteristics of the universe are the same in every direction. This means that, on average, there are no directional preferences in the universe and that the physical laws are uniform in all directions.

[101] Homogeneity means that if you look at large volumes of the universe, the distribution of matter is the same everywhere. There are no “special” regions of the universe that contain more or less matter than others.

Einstein thought that this couldn’t be right[102]. Singularities shouldn’t occur in reality. And if his theory allowed them, then there was something wrong.»

It turns out that, through two completely different paths[103], one comes to the conclusion that something important is not working at all, that there is something wrong with this theory of general relativity! 

I am tempted to think that, having completed his work on “special relativity”, Einstein explored the aspect that links “time” with “velocity” in this theory, discovering that a similar relationship also exists between “time” and “mass“.

The second law of dynamics, formulated by Isaac Newton, can be summarized in the equation:

[ F = m \cdot a ] or: F = m · a

where:

• ( F ) is the resulting force acting on the body,

• ( m ) is the mass of the body,

• ( a ) is the acceleration of the body.

From this relationship, it can be deduced that the force is directly proportional to both the mass and the acceleration: the greater the force applied, the greater the acceleration, provided that the mass remains constant. Likewise, if you increase the mass, with the force constant, the acceleration will decrease, which confirms the idea that acceleration is inversely proportional to mass when considering a constant force.

For the statement of the second law of dynamics: “The force acting on a body is directly proportional to the mass of the body and to the acceleration, and has the same direction.” Acceleration turns out to be proportional to the force and inversely proportional to the mass.

Newton’s second law of motion states that: ( F = m \cdot a ) [Force equals mass times acceleration]

or if you prefer (F = m · a), it means that: if (with a constant) m increases then F increases and also if (with m constant) a increases then F increases.

Therefore both acceleration and mass have a characteristic that they have in common and it is, presumably, this characteristic that Einstein exploited to build the supporting pillar of general relativity.

Reflecting on this formula offers insights into the relationship between “mass“, “acceleration” and “force“. Newton’s formula shows how “force” is influenced by both the “mass” of the object and the “acceleration” to which it is subjected.

[102] Einstein knew very well that a finite proper subset cannot possibly contain an infinite amount of mass/energy!

[103] The first is the one just described, which concerns the impossible “singularities“; the second concerns the conclusions reached by the present “axiomatic model“, that is, that neither our observable universe, nor our Cosmos and therefore not even the infinite Universe are “homogeneous” and/or “isotropic“.

In his “general theory of relativity” Einstein revolutionized our understanding of gravity and inertia by introducing concepts such as the “equivalence principle“, which states that the effects of “gravity” are indistinguishable from those of “acceleration“.

To summarize briefly: the “axiomatic model”, a theorem with the status of a demonstration, contests, with demonstrations, both the “metric expansion of space“, and the “isotropism“, and the “homogeneity” of our universe and also contests the “singularities“. This means that if this “axiomatic model” is right (I don’t see how it is possible to contest it) then, the conclusion that can be drawn is that this theory of general relativity must be entirely revised and corrected because, as it is, it is absolutely inconsistent and devoid of scientific validity!

—-  *  —-

Theoretical physicist Sabine Hossenfelder (born in 1976), in her interesting and meticulously documented book: “Lost in Math: How Beauty Lead Physics Astray” [Seduced by Mathematics – How Beauty Led Physicists Astray] lashes out against that excessively unbalanced behavior in favor of mathematical beauty, pursued at all costs.

Carlo Rovelli, physicist, essayist and popularizer took charge of the preface, in Italian, of the book and had the opportunity to state: «The problem is that a part of theoretical research has allowed itself to be too carried away by its own imagination towards increasingly hypothetical and less plausible scenarios, sometimes losing its critical sense and struggling to keep its feet on the ground.» In this book, Hossenfelder nevertheless points out that: «Mathematics keeps us honest – it prevents us from lying to ourselves and to others. You can be wrong with mathematics, but you can’t lie,» he says.

“I want to know how the universe began, whether time consists of single moments, and whether everything can really be explained with mathematics.»

He concludes by writing, «The next revolutionary event in physics will happen in this century. It will be beautiful.»

—-  *  —-

The fact that, for the universal axioms inserted at its foundation, this ‘axiomatic model’ has gone beyond the ‘Big Bang‘ and beyond the ‘Big Plouf‘ and that it has included them as predictable events, does not mean that it claims to explain everything[104].

It simply confines itself to enunciating a series of predictions, which fall within those conclusions consequent to the universal axioms posed as ‘hypotheses‘.

[104] Kurt Gödel’s incompleteness theorems remind us of this.

The first twenty-eight points of the chapter ‘Effects predicted, by deductive way, from the axiomatic model of the universe’, sketched in some way, should not be thought of as an exhaustive list of the consequences derived from the ‘model’.

I am convinced that there are others and certainly many others[105].

Each 'model' should present itself as an articulated structure, capable of giving a coherent and sensible location to the data collected by observation, and should allow us to understand, frame and even predict the phenomena that characterize the reality in which we live.

The appreciability and reliability of each model should therefore essentially depend on the degree of correspondence between the prediction and the known reality of the facts.(the experimental observations).

First question

Would the 'lambda CDM cosmological model' ultimately lose its validity?

I see no possible alternative, since both the cosmological constant Lambda and dark matter (CDM) are rejected by the 'axiomatic model', which explains in an alternative way the phenomena that suggested the need for a non-existent dark matter and an equally non-existent dark energy, as described by this model, i.e. a negative pressure that would exert a push outwards from within our Cosmos.

The Standard Model and its counterpart the Concordance Model, based on the principle known as 'gauge symmetry' or 'scale symmetry[106]'. Are able to explain with relatively few equations a good part of the approximately 5% (for the Lambda CDM cosmological model) of our entire Cosmos, consisting of baryonic matter (that of which we, planets, galaxies, ...).

About this 5% : 'It is by examining the map of the cosmic background that we have understood that we are minority shareholders in a universe dominated by unknown and therefore obscure components. The stars, galaxies and everything that is made of the matter of which we are made barely reaches 5% of the total matter that is mapped by geometry. 25% is due to matter that weighs but we do not know what it is, while the remaining 70% is obscure in name and in fact.' [Patrizia Caraveo, director of INAF Iasf in Milan]

For the ‘axiomatic model’ it is not necessary to invoke the presence of some dark matter to explain those phenomena studied by astrophysicists Fritz Zwicky (40s, regarding the orbital speeds of galaxies) and Vera Cooper Rubin (70s, regarding the orbital speeds of stars around the central core of the Andromeda

[105] From an objective analysis, it emerges that the predictions made by this 'model' (see: black holes, Big Bang, expansion of the universe, acceleration of the escape velocity of our galaxies, different escape velocities for our galaxies [see: 'Hubble's law'] are promptly confirmed by observations made (the forecast relating to the constant growth of cohesion of our galaxies or clusters of galaxies and much more remains to be verified).

To argue that these predictions may be the result of pure and simple coincidence seems to make little sense.

The reasons for this correspondence, between forecasts and observed phenomena, must certainly be sought in the solidity of those two axioms that have been placed at the foundation of this work, that is: 'the principle of conservation of energy ' and the 'law of universal gravitation'. The choice of these axioms was not accidental and required specific and careful reflection which allowed, finally, to identify a minimum but necessary and sufficient starting point.

[106] By this principle, each particle has its own direction in its internal space, somewhat (but only vaguely and just to get an idea) like the needle of a compass. This, however, points in a very specific direction and not just any direction. This ‘principle’ is defined by physicist-theorist Sabine Hossenfelder as: ‘ … what we have invented to express the observed behavior of particles in a quantitative way, a mathematical tool that helps us make predictions.’

galaxy, in particular), as these are explained in a simple way through the ‘conoid effect’[107] [generated by those gravitational fields mentioned above]

The energy / mass of our entire cosmos would therefore be made up of:

- 5% (approximately) of detectable matter (heavy elements, neutrinos, stars, hydrogen, helium, ...)

and

- 95% (approximately) of energy represented by those gravitational fields, generated, in particular, by celestial bodies outside our Cosmos and responsible for its accelerated expansion[108].

In the following graph, for the ‘axiomatic model’, the energy value of these gravitational fields should be a variable quantity, because it is subject to inevitable and continuous growth[109]. This energy value would be the equivalent of that ‘dark energy’ responsible (according to the Lambda CDM model) for the accelerated, outward motion that has been going on for billions of years and to which all the galaxies/clusters of galaxies/… of our Cosmos would be subjected.

According to the “axiomatic model“:

The two values indicated above are to be considered hypothetical and the first of the two in continuous growth. According to the ‘axiomatic model‘, their ratio (in percentage) can only change continuously, over time, and in favor of the ‘energy gravitational fields‘.

In fact, this is destined to grow, as the celestial bodies of our Cosmos approach the vertices of the ‘universals conoids‘ to whom they belong.

Second question

Having acknowledged that according to this axiomatic model: 'there is no certainty about tomorrow', one wonders: is it possible to hope to obtain, from the 'model', some answer or some prediction regarding the life span of this cosmos of ours and, in particular, of this galaxy of ours?

In the chapter: 'Effects predicted, by deduction, from the axiomatic model of this infinite Universe', point 10, sketches the question of the 'Differential escape velocity of our galaxies, clusters of galaxies,...' and reads:

«According to this 'model', our galaxies or clusters of galaxies do not necessarily have an equal escape velocity, outwards.

The value of this speed essentially depends on their mass, on the mass of the celestial body or celestial bodies (black holes / ...) and from the relative gravitational fields, which out there, exert their attraction on them and from the distance from the vertices of the 'conoids' they belong to.» 

[107] See chapter “conoid effect“.

This ‘conoid effect‘, due to the peculiarity of the gravitational dynamics that develop inside it, would deserve specific attention by the ‘experts‘, in particular as regards the ‘pairs / binary systems‘ aspect of stars, of black holes, of galaxies, …

[108] The gravitational energy, developed by the mass of our entire cosmos, would seem to somehow fall within this 95%.

[109] See the chapters ‘dark energy‘ and ‘dark matter‘. As regards this ‘growth‘ value, cf. note 48 and the question of the derivatives of: third order, fourth order, ….

This prediction of the model would therefore seem, in principle, to exclude the fact that all our galaxies end their life cycle, their race towards that ‘something‘ at the same time.

However, there are a few things worth paying attention to.

For this 'axiomatic model', the outward escape acceleration of our galaxies, which began more than four billion years ago (according to the discoveries made by astrophysicists in the late 1990s), would have begun in the moment in which those gravitational fields generated outside our Cosmos began to make their call felt.

This means that, at present, our Milky Way should be deep within its 'universal conoid'.

It remains to understand what the level of this depth is.

Taking into account that, according to this 'axiomatic model', the energetic value of those gravitational fields, generated by celestial bodies external to our Cosmos and responsible for the accelerated expansion of the latter, represents approximately 95% of the entire mass/energy of our Cosmos, it is legitimate to imagine a very high value of this depth, for each of its galaxy and for each of its clusters of galaxies. 

A confirmation of this prediction would also seem to come from other considerations, in particular:

-          by the fact that the angular speed of revolution of the galaxies that rotate in the outermost part of the cluster to which they belong is now close[110] at (angular) speed of those that rotate more to the internal, i.e. in the vicinity of the cluster's center of gravity (see measurements made by Fritz Zwicky and not only for galaxies in clusters of galaxies);

-          from the fact that the angular speed of revolution of the stars that rotate in the outermost part of the Andromeda galaxy has almost reached the angular speed of those that rotate further inside, that is, near its center of gravity (see measurements made by Vera Rubin and not only, for the stars of the Andromeda galaxy).

The predictions made by the 'axiomatic model' regarding orbital velocities agree (without resorting to the virial theorem[111]) with the discoveries made by Fritz Zwicky regarding galaxies and Vera Cooper Rubin regarding the stars of Andromeda.

The structure of the 'conoid' allows to explain this phenomenon in a simple and visual way. 

In their approach to the apex of the 'conoids' they belong to, the celestial bodies that are at a greater distance from the center of gravity of their galaxy undergo (over time) a greater shift / approach towards this center of gravity, compared to those that they are closer.

The value of this displacement is directly proportional to the value of the distance of each body from this center.

[110] It must obviously be taken into account that what we see today refers to a situation that took place a long time ago.

[111] The virial theorem (in classical mechanics) is a proposition that relates (in a stable system of n particles) the time average of the kinetic energy with the time average and the potential energy. This theorem finds applications in numerous branches of physics.

Therefore: in equal times, the greater the distance, the greater the approach the center of gravity of the galaxy or cluster of galaxies to which each celestial body belongs.

In this figure a ‘conoid‘ has been visualized with proportions useful to understand the concept you want to convey. In reality, ‘conoids‘ are very different. The size of their initial circumferences are but a nth part of their heights.

The line that, in the graph below, represents / displays the expansion speed of our cosmos, from the start of the stroke (Big Bang) to the end of the stroke (Big Plouf)[112], is configured as an asymptotic curve, whose tangent, in the vicinity of the ( Big Bang) and the (Big Plouf), tends towards the vertical (see graph below). In fact, in the vicinity of these two ‘places‘, in the fractions of a second following the Big Bang and preceding the overcoming of the event horizon (in the case of black holes), the speed is very high.

To be taken with the ‘pliers’

The change in slope (in the magnifying glass) of the line which, in the graph, represents the escape velocity of our galaxy, indicates the moment in which the latter began to move in an accelerated way towards the outside of our Cosmos. This change in slope has been placed here, in an arbitrary and hypothetical way, halfway between the Big Bang (      ) and Big Plouf (       ).

The place where [t (0)] comes to be, that is, today, is not known. In this graph it has been positioned near the Big Plouf, since I have taken into account the data collected by Fritz Zwicky (clusters of galaxies) and Vera Rubin (Andromeda stars), relating to their orbital speeds.

In this graph, the two sections of the curved line, the initial and the final one, are purely indicative and only serve to give the idea of a great speed of expansion, near the 'Big Bang' and the 'Big Plouf'. They are to be imagined, too, seen with a magnifying glass[113].

[112] ‘plouf’ → overcoming of the ‘event horizon’ in some ‘black hole’, by a celestial body that has been attracted by it.

The term ‘plouf’ and not ‘crunch’ was used, because the latter evokes a cosmological model that states: ‘the Universe will stop expanding and will begin to contract until it collapses on itself (Big Crunch), in a symmetrical way to the initial Big Bang. ‘

[113] Since the range of values ​​appears to be very large, it would perhaps have been more appropriate to use a logarithmic scale graph.

58

The result of this free and perhaps useless mental exercise (graph above) should be taken as purely and vaguely indicative since many variables come into play and some of these are not known precisely, such as:

a) precise date of the start of the escape acceleration of our galaxy;

b) intensity of the gravitational field of that body or bodies exerting their pull on it.

However, it seems that something manages to suggest this graph, an expression, in some way, of this 'axiomatic model', namely that the life of our planet Earth could end before and perhaps much earlier than (approximately) 5 billion years, presumed date, in which our sun is expected to end its current life cycle and evolve, first into a red giant and then into a white dwarf.

The possibility cannot be ruled out that there are not even signs that could announce the imminence of this 'Big Plouf'. 

The speed of our galaxy's approach to the celestial body that awaits it out there should be remarkably high, making the event very 'fast' and probably 'painless'.

                                                                                 The most beautiful thing we can experience is the mystery. [Albert Einstein]

The weather

That of 'time' is not an absolute idea that applies equally to the entire 'infinite Universe' but (with Einsteinian relativity) assumes an alternative role, that is that of a parameter that is different, depending on the system of chosen reference and that: reference systems, with different gravitational potentials, have 'times' that flow differently[114]. 

Newton (*1643  †1727) built a veritable monument to time and space.

The idea that he had of them is of two eternal and incorruptible containers, within which the events of nature take place.

For Leibnitz (* 1646 † 1716), time does not exist and neither does space. They absolutely do not exist and do not exist a priori, since their existence is necessarily connected to the presence of bodies from which the intellectual and physical elaboration of the concepts of time and space arises.

Hermann Minkowski (* 1864 † 1909) ‘… henceforth space itself and time itself are condemned to dissolve into nothing more than shadows, and only a kind of conjunction of the two will preserve an independent reality.‘ ‘Minkowski spaces’ might suggest solutions regarding ‘dark energy’ and ‘dark matter’.

The ‘Minkowski spaces’ could lead to the conclusion reached by this ‘model’, namely that ‘dark energy’ and ‘dark matter’ do not exist at all.

Richard Feynman, Nobel Prize in Physics (1965): ‘Perhaps we might as well resign ourselves to the fact that time is one of the things we probably don’t know how to define. In any case, what really matters is not how we define it, but how we measure it. ‘

For Albert Einstein, time has to do with the concept of ‘relative’ and not ‘absolute’ as it was traditionally conceived and described. Albert demonstrated that space and time are interconnected and depend on the speed and acceleration of one object relative to another.

[114] St. Augustine (Aurelius Augustinus Hipponensis): ‘What, then, is time? If nobody asks me, I know; if I had to explain it to anyone who asks me, I don’t know.‘ – (John Archibald Wheeler) ‘Time is the best expedient nature has come up with to prevent things from happening all at once.‘

This concept is the basis of his thinking, which revolutionized our understanding of the ‘observable universe’ and the nature of time. According to the theory of relativity, time flows differently for moving observers than for observers at rest (special relativity) and is influenced by gravity (general relativity). Furthermore, Einstein demonstrated that time is not a uniform and constant quantity, but can be distorted by factors such as the speed and mass of objects. Time can be likened to the concept of measurement: a measure we use to quantify and organize the unfolding of events in our history. For the ‘axiomatic model’, it is an abstract concept that allows us to distinguish between past, present[115] and future, and to organize our activities according to time sequences. The past represents a unique experience that cannot be changed in any way, since it is part of a sequence of causes and effects, on which it is not possible to intervene. For every cause, there is an effect. The present is an effect, it is the result of the plurality of causes that generated it and cannot be changed.The future will be the result of the plurality of causes that combine to generate it.

We have the feeling that we are free to do what we want. However, we must ask ourselves: are we really free to want what we want ? ? ?

Sets and subsets

Every proper and finite subset of an infinite whole is an infinitesimal with respect to the latter.

So, what is today called the “observable universe” can only be an infinitesimal of this infinite Universe. Compared to the infinite Universe, what is today called the “observable universe” can only be an infinitesimal of this infinite Universe.

Since it is not possible to explore what exists beyond a certain limit, In the infinitely large of the infinite Universe, it cannot be excluded that the same can happen for what exists, beyond another limit, in the opposite direction. and that is towards the infinitely small (for us) in this infinite Universe.

Thus, for the ‘axiomatic model’, our ability to explore and observe the physical environment around us is in fact limited, since it cannot go beyond two well-defined limits, one defined as ‘large/very large’ and the other as ‘small/very small’, of what current astrophysics calls the ‘observable universe’.

What is contained between these two identities/boundaries is nothing but an infinitesimal of our infinite Universe.

Hoping to be able to explain this infinite Universe of ours, from within this limited range, using only experimental observations and the physical laws that derive from them, is perhaps a vain and sterile illusion.

This would explain, at least in part, the difficult situation that current Physics and Astrophysics are experiencing.

In this ‘axiomatic model‘ an alternative path has been followed, which makes extensive use of mathematics and is based on two axioms that have evident and indisputable characteristics of universality.

[115] It should be remembered that, according to Albert Einstein’s Restricted Relativity (enunciated in 1905), it does not make sense to speak of simultaneous events, in an absolute manner, for two observers, placed in different places.

A novelty introduced by the special theory of relativity concerns the fact that two simultaneous events in an inertial reference system are not necessarily so for other inertial systems and this does not apply only to time, since at ‘relativistic speeds‘, i.e. comparable to those of light, not only a variation of the times is detected, but also a variation of the lengths and mass of the objects.

Thus the measures of ‘time‘, ‘distance‘ and ‘mass‘ take on a subjective character, losing that of absoluteness they possessed until the beginning of the twentieth century.

For the ‘axiomatic model / theorem‘, it makes sense to ask: «The maximum attainable speed, which for us turns out to be ‘ c ‘ (celeritas in Latin), has the same value in each of the infinite cosmos of this infinite Universe of ours?‘.

Since it is impossible to maintain that ε0 (dielectric constant of vacuum), μ0 (magnetic permeability of vacuum), C (speed of light in a ‘vacuum’), … are Universal constants, i.e. that they have the same value in each of the infinite cosmos that populate our infinite Universe, and perhaps not only in the cosmos[116], we certainly cannot afford to give an affirmative answer to our question.

Maxwell’s equations show that the speed of light (C ) is inversely proportional to the square root of the product of the dielectric constant (_ε0)in a ‘vacuum‘ and the magnetic permeability (μ₀) in a ‘vacuum‘.

With the equations of the ‘loop quantum gravity model‘[117] (LQG – Loop Quantum Gravity), through which Carlo Rovelli (born in 1956), Lee Smolin (born in 1955), Abhay Ashtekar (born in 1949) and other physicists, intend to identify the basis for a unification of Einstein’s general relativity with quantum mechanics[118], the ‘time‘ with its variable ‘t ‘ disappears. What really exists are only ‘space atoms‘.

The whole universe is none other than the way in which these ‘space atoms‘ are placed.

^—  *   ^—

A gravitational interaction process between the Boote (Boote constellation) and Leo (northern hemisphere) galaxy clusters appears to be taking place today because shifts and distortions in the galaxies within these clusters have been recorded. What our astrophysicists are monitoring today should, in fact, have taken place around 170 million years ago. The distance separating us from the place where this event would have taken place is such that light

[116] In reality, this ‘vacuum’ is at least completely permeated by gravitational waves, and the intensity of the gravitational field in which we are immersed depends, to a significant degree, on the mass generated by those vertices of the ‘conoids’ towards which we are directed. It would therefore seem legitimate to assume that the energy of this gravitational field of ours plays a non-zero role on the values of the parameters relating to ‘our dielectric constant’ and ‘our magnetic permeability’. If this is the case, then the value of ‘C‘ (speed of light) may not necessarily be a constant for all the galaxies in our entire Cosmos, and it certainly does not make sense to speak of a constant throughout our infinite Universe.

[117] See the chapter Quantum Gravity on the next page.

[118] In the chapter: ‘Three things to remember about quantum mechanics’, of the book ‘The God Particle’, written by the theoretical physicist Leon Lederman (*1922 †2018 – his contributions to the discovery of the muon neutrino in 1962 and the quark bottom in 1977 are worth mentioning) we read: “Despite the great practical and intellectual success of quantum theory, we cannot be sure what it really means.“

signals only reach us after these 170 million years. At that time, our Cosmos had an estimated age of 13.6 billion years. To explain this event, current science invokes the principle of universal gravitation.

The ‘axiomatic model’ disagrees with this explanation because it argues that gravitational attraction alone cannot justify this phenomenon. In fact, according to this principle, one would have to be able to explain why the two clusters of galaxies did not collide a long time ago when, in their divergent path towards the outside of our Cosmos, they were at much closer distances. And thus this same gravitational attraction was of much greater intensity.

Quantum gravity

Quantum gravity is that branch of theoretical physics that seeks to bring together, in a unified theoretical framework, both quantum mechanics, which studies manifestations concerning the microscopic (atomic and subatomic) world, and gravity, which governs gravitational phenomena on a large scale, namely: those of solar systems, galactic and intergalactic systems.

This ‘axiomatic model’ allows some considerations to be made in this regard.

First of all, it should be pointed out that our quantum mechanics has to do with the atomic and subatomic world of one (ours) of the infinite cosmos belonging to that proper subset (of the infinite Universe) generated by a well-determined and equivalent ‘energy quantity’ at the moment of the Big Bang.

According to ‘quantum field theory’, matter particles interact through the exchange of one or more particles.

It makes sense to assume that, at these levels, the ‘amount of energy’ responsible for the origin of each cosmos, through a specific Big Bang, plays a decisive and certainly diversified role in the processes that have taken place, are taking place and will take place at the atomic and subatomic levels in each of these cosmos.

This diversification is further confirmed by the fact that no upper limit can be set to this value of energy and it therefore becomes impossible and nonsensical to claim that, for example, ε0 (dielectric constant of the vacuum), μ0 (magnetic permeability of the vacuum), C (speed of light in the ‘vacuum’), … have precisely the same constant value in the totality of our immense infinite Universe.

e.g. ε0 (dielectric constant of the vacuum), μ0 (magnetic permeability of the vacuum), C (speed of light in the ‘vacuum’), … have, precisely, the same constant value in the totality of our infinite Universe.

I realize that this consideration/conclusion can only bring down the monument that has been painstakingly built around what has been called the ‘universal constant’ par excellence and indicated with ‘C‘ [speed of light].

This would allow the assumption that cosmos generated by substantially different ‘energy quantities’ are endowed with substantially different ‘classical physical laws’ and ‘mechanics’.

If this were indeed the case, and it is hard to see how it could not be, then the accommodation of quantum mechanics and large-scale gravity in a single, general theoretical framework would make no sense, because each of the subsets proper to cosmos endowed with equivalent energy would be endowed with its own ‘quantum mechanics’, different from that of the other infinite subsets proper to cosmos.

It should not be forgotten, however, that for this ‘axiomatic model’, both macroscopic reality (galactic, intergalactic, cosmic and inter-cosmic) and microscopic reality (of quantum mechanics) obey the same and only principle, i.e. that principle which governs all the states/manifestations of this ‘infinite Universe of ours’ that find their reasons and the origins of their ‘being’ in something immediately preceding them (in their space and time). Cf. the principle of ‘causality’ i.e. of ‘cause-effect’, mentioned at the beginning of this ‘model’.

Supersymmetry

Developed as part of string theories (in the 1970s), it exploits the principle that the vibration of these strings generates subatomic particles, namely

– ‘fermions’ [particle that follows Fermi–Dirac statistics (e.g. the electron, the neutron, the proton). Generally, it has a half-odd-integer spin: spin 1/2, spin 3/2, etc. are reminiscent of the Italian physicist Enrico Fermi]  and

– ‘bosons’ [any particle with integer or null spin that satisfies the Bose-Einstein statistics (such as photons, π, k mesons, etc.), reminiscent of the Indian physicist Satyendranath Bose]

This supersymmetry, identified by the acronym: SUSY, from the English ‘SUper SYmmetry’, is a theory that identifies a symmetry according to which, to each of the ‘fermions’ and each of the ‘bosons’ correspond respectively a ‘boson’ and a ‘fermion’ of equal mass[119].

The American physicist Daniel Wayne Hooper of Fermilab, in his ‘Nature’s Blueprint’, had this to say: ‘despite the efforts put into the search for these (supersymmetry) particles by a large number of experimental physicists (several hundred), no supersymmetric partner has so far been observed or detected’.

The mathematician Alain Connes, CNRS medalist (1977), Ampère Prize (1980), Fields Medal (1982), … Professor at the Collège de France, the Institut des Hautes Études Scientifiques and Vanderbilt University (Nashville), on the subject of ‘supersymmetry’, wrote: ‘un beau rêve, mais il est trop tôt pour croire que ce soit la vérité…‘ (‘a beautiful dream, but it is too early to believe that it is the truth…‘).

In her recent book: ‘Lost in Math:How Beauty Leads Physics Astray’ in the chapter ‘What we are made of’, physicist-theorist Sabine Hossenfelder said:

‘The modern faith in beauty’s guidance is, therefore, built on it use in the development of the standard model and general relativity; it is commonly rationalized as an experience value: they noticed it works, and it seems only prudent to continue using it. ‘

Frank Wilczek, winner of the Nobel Prize in Physics in 2004 (together with David Gross and Hugh David Polizer) for his work on strong nuclear interaction, writes in his book, entitled: «A Beautiful Question, Discovering Nature’s Deep Design‘: ‘Our innate sense of beauty is not connected in any obvious way to the basic mechanisms of nature.»

‘ However, «Having appreciated the beauty inherent in the world, we want more of it. I believe there is no more reliable guide in this quest than beauty itself.»

[119] In the chapter “Now that we’ve found Higgs, what do we do?“, of the book “Knocking on the Gates of Heaven“, Theoretical Physicist Lisa Randall (born 1962) writes: “The problem is that certain indications from current experimentation are beginning to make ordinary, poorly elaborated supersymmetric models appear increasingly unnatural…”

String theorist Joseph Polchinski gave an interview to physicist-theorist Sabine Hossenfelder, in which he stated: «Supersymmetry could only be broken at higher energies, compared to the current capacities of the LHC (Large Hadron Collider, at CERN in Geneva, used for experimental research in the field of particle physics) and this would explain why ‘super symmetrical partners’ have not yet been detected‘.»

It is useful, however, to remember that, in this sub-atomic world of ours, we are dealing with ‘quantum mechanical’ laws that are proper and specific to one of the subsets (see previous chapter) that populate our Universe and that, for this reason, we may also have to resign ourselves to the fact that that  energy value of our Big Bang, of which we are the legitimate children, may have decided to ignore here, and certainly not only here, those ‘criteria of beauty’ particularly prized by many physicists, depriving us of the right to dispose of that precious and vainly sought after ‘added value’ called ‘supersymmetry’.

Supersymmetry remains a fascinating and potentially useful proposition, but experimental challenges and philosophical reflections on scientific truth and beauty highlight the difficulties of matching theory and experimentation.

Isotropy

Isotropy is the characteristic of a system or simply of a material that possesses the same particularities, the same physical properties in all directions.

An isotropic material can only have the same properties in any direction you look at it. Anisotropy is its opposite. An anisotropic system or material has different properties in different directions.

This concept is widely used:

– in engineering, when structures or materials need to have equal properties in each direction, in order to ensure the solidity and strength of a building, a bridge or something else;

– in geology, this isotropy has to do with properties of a certain structure or material, the penetrability or permeability of which is to be studied;

– particularly in physics and astrophysics, where the same properties can be observed in any direction one turns one’s gaze and attention. An isotropic structure or material will, necessarily, have the same physical properties in all directions; an anisotropic structure or material will not.

Konstantinos Migkas of the University of Bonn in Germany, had this to say: ‘One of the pillars of cosmology, the study of the history and fate of the entire Universe, is that the cosmos is ‘isotropic’, i.e. that it has the same characteristics everywhere, on a large scale.‘ He added: ‘Our work, however, shows that there may be cracks in that pillar.‘

These cracks were confirmed by astrophysicist Gerrit Schellenberger of the Center for Astrophysics/ Harvard & Smithsonian (CfA) in Cambridge.

Gerrit, in fact, wrote: ‘Based on our observations of galaxy clusters we may have discovered discrepancies in the expansion rate of the cosmos, depending on which object we observe‘ and added: ‘This finding may contradict one of the most basic underlying assumptions used in cosmology today.’ [see cosmological lambda (Λ) CDM model].

The ‘axiomatic model’ argues that the ‘observable universe’, i.e. that proper finite subset of our Cosmos, and more generally that our entire Cosmos is by no means ‘isotropic’ as has long been claimed and as is still tended to be claimed today.

This ‘model’, in fact, states that the expansion of our entire Cosmos cannot, by any means, be uniform in all directions, since the escape velocities and relative accelerations, outwards, of our galaxies and galaxy clusters depend on the distance and mass of those celestial bodies that, out there (outside our Cosmos), exert their gravitational attraction on these our galaxies and galaxy clusters.

Concluding remarks

As stated in point 30: ‘The scenarios that emerge as effects, on a philosophical level, consequent to the predictions of this ‘axiomatic Model’ are certainly of considerable complexity and also rather shocking.‘ of the chapter: “Effects predicted, by deduction, by the Axiomatic Model of the Universe“…

these allow us to develop a philosophical framework that is consistent with the conclusions reached by this “model“.

I am aware of the fact that the predictions and conclusions of this ‘axiomatic model‘ move horizons significantly further, given that a new and relevant element comes into play:

the infinite.

The novelties, introduced by this new element, are undoubtedly not easy to ‘digest‘, because they require and even impose a revision of many theories and beliefs, by now deeply consolidated.

I know that these innovations cannot but upset the panorama of knowledge, beliefs, convictions and dogmas, to which we have long been accustomed and certainly a little fond of.

However, it must be said that:

– if we start from the ‘assumption / axiom‘ that our entire ‘Cosmos‘ (the one that began with the Big Bang) and which is called ‘Universe’ by current cosmology, represents the totality of what exists,

– then it is very difficult and perhaps impossible to grasp the idea and the solutions proposed by this ‘axiomatic model / theorem‘.

Kurt Gödel’s second incompleteness theorem, stated in 1931 and which can be proved by formalizing a part of the Austrian mathematician’s first theorem[120], states that:

‘Let P be a mathematical theory sufficiently expressive to contain arithmetic (the standard model Λ CDM makes use not only of arithmetic but also of algebra, geometry, infinitesimal analysis,…): if P is coherent, then not it is possible to prove the coherence of P within P. ‘

This leads us to suppose that it is impossible to fully explain our Cosmos and its origin starting from the ‘assumption / axiom / postulate‘ that our entire ‘Cosmos‘ represents the totality of what exists.

[120] In any mathematical theory T sufficiently expressive to contain arithmetic, there exists a formula φ such that, if T is coherent, then neither φ nor its negation (¬ φ) is demonstrable in T.

For completeness, it should be remembered that the limitations highlighted by this Gödel theorem concern the axiomatic method of logical proof, and not a simple property of the propositions to be proved. It is true that it is always possible to transform a true proposition that is unproven within a given system of axioms into an axiom of some extended system, but in this case there will be further unproven propositions in this extended system itself.

It is as if someone, claiming to represent the totality of what exists, found himself in the need to explain why and how his own birth took place.

I had welcomed with pleasure the news that, in 1998, it announced the acceleration of escape of the galaxies of our cosmos[121]. It made me foresee that conclusion reached by the Lambda CDM model of cosmology and instead then …

The conclusion reached in point  28): ‘There is something out there waiting for us‘ does not bother me at all. Some perplexities, on the other hand, are generated by the conclusions which cannot be avoided in the development of point  29), which has as its object: ‘Effects and consequences of an existential and philosophical nature.’

This axiomatic model / theorem makes a series of predictions:

1. black holes (also foreseen by the general theory of relativity of 1915 and confirmed by recent observations) [consequence deriving from the validity of the 1st and 2nd axioms];
2. Big Bang (the first idea of the Big Bang emerged following the discovery of the expansion of our Cosmos);
3. expansion of our Cosmos (Hubble-Lemaître 1929) [consequence deriving from the validity of the 2nd axiom];
4. acceleration of the expansion rate of our Cosmos (discovery announced in 1998) [consequence deriving from the validity of the 2nd axiom – see ‘Conoid effect’];
5. differentiated escape velocities of our galaxies (recent discovery of the group of which the astrophysicist Gerrit Schellenberger belongs) [consequence deriving from the validity of the 2nd axiom – see ‘Conoid effect’];
6. continuous increase of cohesion within our galaxies / galaxy clusters (experimental verification of this prediction of the “model” is still missing) [consequence deriving from the validity of the 2nd axiom – see ‘Conoid’ effect];
7. the increase in the level of cohesion of our galaxies, within each conoid, is in turn responsible for a continuous increase in the orbital speed of stars around the galactic center or of galaxies around the center of the cluster that contains them, as the variable ‘t ‘ [time] flows (experimental verification of this prediction of the “model” is still missing) [consequence deriving from the validity of the 2nd axiom – see ‘Conoid’ effect]. To my knowledge, Vera Rubin did not detect any ‘continuous increase in orbital speed …‘;
8. for this ‘model’ therefore even the smallest and simplest ant could, and without fear of being contradicted, consider itself at the center of the infinite Universe! [consequence deriving from the validity of the 1st and 2nd axioms];

for point 8 above and the question concerning ‘free will’, this model cannot but attribute the same dignity and importance to each being and more generally to each state of this infinite Universe of

[121] In the next work, see the experience I had with the pupils of a fifth class of the Verrès high school in 1994, where I held single-issue lectures on essentially mathematical topics.

ours, since each of these represents a unique, transitional moment between the reality immediately preceding this moment and the one immediately following it;

on their way to the vertex of the ‘conoid’  they belong to, the orbital velocity of the stars around the nucleus of the galaxy containing them cannot but undergo a continuous increase (see Vera Rubin’s observations) – [a consequence deriving from the validity of the 2nd axiom – see ‘Conoid’ effect. According to this axiomatic model, the existence of dark matter is not required to explain this phenomenon];

in the approach path to the apex of the ‘conoid’  to which they belong, the speed of revolution of the galaxies around the nucleus of the cluster to which they are part, can only undergo a continuous growth. (see Fritz Zwicky’s observations) – [consequence deriving from the validity of the 2nd axiom – see ‘Conoid‘ effect. According to this axiomatic model, the existence of dark matter is not required to explain this phenomenon.]. The anomalous orbital velocity of the outermost galaxies and stars around their cores led Fritz Zwicky and Vera Rubin to assume the existence of ‘dark matter’;

according to the predictions of this model, it would seem reasonable to assume that: many physical laws (certainly not all), the value of Planck’s constant (h), that of the ‘cosmic background radiation‘ (CMBR) energy, probably the Heisenberg principle and certainly much more depend on that specific energy value that gave rise to each cosmos, following a Big Bang;

tendency to gravitational aggregation of galaxies in galaxy clusters (see works and discoveries of astrophysics Vera Cooper Rubin);

reflection on so-called ‘gravitational waves’;

reflections on the fact that our Cosmos cannot be considered “isotropic“, cannot be considered “homogeneous“, cannot contain “singularities” in finite proper subsets, it makes no sense to speak of “metric expansion of space“, …

Considerations

The current ‘scientific literature’ is unable to provide convincing and comprehensive explanations for many aspects of cosmology:

– the model, currently in vogue, assumes that 95 per cent (approx.) of the entire contents of our Cosmos are dark in nature.  Some 69% (approx.) would be ‘dark energy’ and some 26% ‘dark matter’.

The physical-theoretical Sabine Hossenfelder had this to say:

‘ … The fact that the most widespread matter in the Universe is ‘dark’ does not just mean that it is invisible to our eyes or almost completely unknown: it is dark because it does not emit any type of electromagnetic radiation, neither in the spectrum of visible light, nor in X-rays and not even in very high energies.’

For that model, only the remaining 4.9 per cent (approximately) would be of known nature;

– in this ‘scientific literature’, it is not uncommon to come across violations of the ‘principle of conservation of energy’ when it is stated that our ‘Cosmos’ will one day cease to exist;

– again in this ‘literature’ it is not uncommon to come across the concept of ‘creation’ (pseudo-science) when trying to explain the ‘metric expansion of space’.

Since its birth, our Cosmos has been continuously expanding and, for more than four billion years now, it has been undergoing a phase of accelerated expansion.

For those who are convinced that, with the Big Bang, ‘everything’ originated, not only ‘mass/energy’ but also ‘time’ and ‘space’, it inevitably becomes necessary to invoke some form of ‘creation’ of ‘space’ to justify the possibility of this continuous expansion.

The laws of physics (2)

The laws of physics were enunciated on the basis of experimental observations.

Scientists conducted experiments and collected the data necessary to understand the workings of the physical world. From this collection, regular and repeatable relationships have emerged that have been described through what are called ‘the laws of physics’.

Importantly, the physical laws that emerged can be validated or refuted through further experiments and further observations.

One of the first to enunciate laws of physics that are still valid today is considered to be Isaac Newton (*1642 †1726), who wrote them down in his ‘Philosophiæ Naturalis Principia Mathematica’, published in 1687.

Newton formulated the three laws of motion, the law of universal gravitation and the concept of conservation of “angular momentum“. These laws are fundamental and indispensable for understanding physical phenomena and are still, to this day, widely used in modern physics. It should, however, be remembered that Newton was not the only one who contributed to the development of physical laws, but he was certainly one of the first to provide a coherent and mathematical formulation of these laws. At the beginning of the 20th century, with the ‘uncertainty principle’ (also called the ‘uncertainty principle’) enunciated in 1927 by Werner Karl Heisenberg, that part of physics that today goes by the name ‘quantum mechanics’ took shape. The term was coined by Werner Karl Heisenberg (*1901 †1976), Max Planck (*1858 †1947) and other physicists of that time.

It must be remembered and emphasized that the laws, used by us today, describe that part of our Cosmos that is located in a certain vicinity, relative to us, called the ‘observable universe’. This surround is nothing but a finite subset of our Cosmos which is, in turn, a proper subset of the infinite Universe, hence, a tiny, tiny part of an infinitesimal of the latter.

Such laws, enunciated and valid in this tiny subset proper of the Universe, cannot claim to describe our entire infinite Universe.

We must therefore resign ourselves to admitting that our laws, including those of quantum mechanics, can only be absolutely limited, since they do no more than describe a tiny and insignificant part of our entire infinite Universe.

Kepler’s three laws are valid in our solar system and describe the motion of planets and satellites, but they are no longer valid and applicable on a galactic level. See, in this regard, the discoveries announced by Fritz Zwicky (*1898 †1947) and Vera Cooper Rubin (*1928 †2016).

Photographs of spiral galaxies show, visually, the fact that those stars orbiting in the outermost belt of one of these galaxies perform a revolution, around the galactic center, in substantially similar time frame as those stars orbiting in the innermost belt of the same galaxy. It is as if the entire galaxy constituted a compact and almost rigid whole revolving around its galactic center.

Similarly, in the direction of the immensely small, our laws of classical physics lose their validity and are replaced by those of quantum mechanics.

Conclusions

The reason why this ‘axiomatic model’ (although it makes no use of experimental observations) succeeds in making predictions, which are punctually confirmed by observations made, probably lies in the fact that it is, and to all intents and purposes, a theorem with the status of a demonstration since it draws its conclusions from two universal axioms, from two solid laws of physics and develops in a correct and coherent way.

According to the law of universal gravitation, namely: F = (G-m1-m2 )/ d² (and Einstein’s field equations for speeds close to that of light) it would seem safe to assume that the gravitational fields generated by each mass can extend without end, in the infinite Universe.

In the book “The Particle at the End of the Universe” by theoretical physicist Sean Carroll (born 1966), chapter “Superconductivity“, we read: “… particle-mediated forces, which have no mass, extend over infinite distances… Gravity and electromagnetism are the obvious examples “

No matter how large one imagines the variable ‘d‘ (distance) to be, it turns out that ‘F‘ can never be equal to zero.

With ‘d ‘ → ∞ (read: ‘d ‘ tending to infinity), ‘F ‘ → 0 (‘F ‘ tends to zero), but ‘F ‘ (force) will never be equal to 0, i.e. F ≠ 0. This means that it would not be permissible to set or imagine a limit to this ‘d ‘ (distance between two masses m1 and m2 that suffer, between them, a non-zero gravitational attraction: F ≠ 0 ).

 This conclusion can only be difficult to digest, since imagining that a small ant could have an endless gravitational field raises some legitimate and justified doubts.

In fact, on careful reflection, we can only conclude that: both what we call ‘big’ and what we consider ‘small’  both represent nothing more or less than two infinitesimals of the infinite Universe and their difference is, in turn, an infinitesimal.

Newton’s theory of ‘universal gravitation’ has been an undisputed and well-deserved success.

It has succeeded in predicting and describing many celestial motions and other gravitational phenomena.

It must be said, however, that it contains some limitations that were overcome and resolved by Albert Einstein’s theory of General Relativity and other physical theories that came later.

In this work, extensive use has been made of the ‘constructive demonstration’ which consists in using the initial conditions of the hypotheses (the axioms) to arrive at the thesis, through a series of logical implications (not excluding the ‘semantic‘ ones).

Since some conclusions of this “axiomatic model” were not to my liking, I tried to find a way to challenge it. The efforts made, in an attempt to deny its “consistency” and therefore its complete validity, failed.                                                 

To succeed in the enterprise, it would have been necessary to be able to deny the legitimacy of at least one of the two axioms used in this work or to detect errors in the deductions, inferences, logical implications, demonstrations, …

The impossibility of denying the legitimacy of this ‘model’, on a logical mathematical level (since it is presented as a theorem, with the status of a demonstration) justifies the reason why many predictions announced have been regularly and punctually validated by experimental observations.

It would seem safe to assume, therefore, that predictions that have not yet been validated (in green in the text), can only be confirmed, following more accurate and in-depth scientific observations, in the near future.

The fact that: an ‘axiomatic model/theorem’, drawn up exclusively on the basis of logical-mathematical principles (and without making use of experimental observations) has succeeded in predicting what is illustrated in the chapter ‘Effects predicted, by deduction, by the Axiomatic Model of the Universe’ and went even further (see the green print in this model), suggests that:                      

Erwin Schrödinger’s[122] hypothesis is not at all unreasonable when (in the wake of the philosophical thought traced by Plato) he states that everything is form, everything is wave, everything is mathematics.

In “The God Particle – if the universe is the question, what is the answer?” by theoretical physicist: Leon Lederman (*1922  †2018) and writer and journalist Dick Teresi (*1948 †2023), we read: “Mathematics is such a complex component of the fabric of science, especially physics … on a practical level, mathematics makes it easier to explain how ideas have developed, how tools work, how it all fits together …“.

‘I am convinced that we can discover, by means of purely mathematical constructions, the concepts and laws that connect them to each other, thus arriving at a basic understanding of natural phenomena. … In a certain sense, then, I believe that pure thought is capable of understanding reality, as dreamt of in the ancient world.’ [Albert Einstein: Einstein’s Essays in Science].

The physicist-theorist Sabine Hossenfelder, in her recent book, ‘Lost in math (How Beauty Leads Physics Astray)‘: ‘ What failed physicist wasn’t their math; it was their choice of math. They believed that Mother Nature was elegant, simple, and kind about providing clues. They thought they could hear her whisper when they were talking to themselves. Now Nature spoke, and she said nothing, loud and clear. ‘                                                                                                                           

According to ‘mathematical realism’, ‘mathematical entities’ exist autonomously and independently of human will.

[122] One of the greatest physicists of the 20th century, for his fundamental contributions to quantum mechanics and, in particular, for the equation that bears his name, thanks to which he won the Nobel Prize in Physics in 1933.

Hence, mankind would not have invented ‘mathematics’ but would only have discovered, slowly and by successive degrees, fragments of a very vast and complex whole, which surely still holds many surprises in store.                                                                         

However far we manage to peer into the infinitely large and the infinitely small, we are and will always be unable to completely understand everything around us and all its laws!

Since, in the realization of the ‘axiomatic model’, there is a component that has played an absolutely prominent role and which has not been mentioned, I would like to make a few remarks on the issue of intuition.

Despite what one reads in many quarters, it seems to me that there is a substantial difference between ‘quantum mechanics’ and ‘intuition’.

Quantum mechanics’  finds its application in the atomic and sub-atomic world, i.e. near that boundary which, in the direction of the extremely small, separates the world of the known, studied and described by classical physics from that world which is not yet sufficiently known (essentially because of Heisenberg’s ‘uncertainty principle’).

This ‘quantum mechanics’ has its own laws and theorems, which are often not very intuitive and, therefore, not easy to understand[123].

In this connection, it should be remembered that Richard Feynman had this to say: ‘If you think you have understood quantum theory, it means that you have not understood it!’ and again: ‘I think I can say that nobody understands quantum mechanics’.

It cannot be ruled out then that ‘intuition’ could even lie beyond this boundary, in a territory of which, today, we know practically nothing.

We do not know its extent, we do not know its theorems, we do not know if it has any and we do not know the laws that govern it.

Hence, there could be a substantial difference between ‘quantum mechanics’ and ‘intuition’.

The mathematician Kurt Gödel (*1906 †1978) saw mathematical intuition as a form of real, and not purely abstract or conceptual, knowledge.

With his enunciation of the incompleteness theorems, according to which the truth underlying a formal system cannot be proven from within the logical system itself, he intended to refer to the logical path already used by Plato (*428/427 b.c. †348/347 b.c.).

For Plato, intuition is a capacity of the human mind that allows access to universal and immutable truths that lie beyond the sensible world. Georg Cantor was a 19th century German mathematician who extensively studied the concept of infinity in mathematics. He demonstrated that there are infinite levels of infinity, and that infinity is

[123] Theoretical physicist Leon Lederman, in his chapter “Three things to remember about quantum mechanics“, of the book “The God Particle: If the universe is the question, what is the answer?”, writes: “Quantum mechanics can be said to have three remarkable qualities: (1) it is counterintuitive; (2) it works; (3) it has problematic aspects that made it inadmissible to the likes of Einstein and Schhrödinger …”

not just a single, simple abstract idea but a mathematical reality with well-defined properties and particularities.

This ‘axiomatic model’ makes extensive use of this concept and it would even seem legitimate to ask the question: “Does it make sense to imagine that infinite Universes (infinite in time, endowed with an infinite amount of mass/energy and therefore infinite in space) could exist???”.

Each of these Universes or each set of them could be distinguished from the others by the intensity of the gravitational fields associated with the masses present in each Universe or set of Universes and by the physical laws that govern them.

Some of the main original features introduced by this ‘model’ are summarized and listed below: It introduces undoubtedly innovative concepts such as:

1. idea of a Universe infinite in time, infinite in space and infinite in the amount of mass/energy;
2. b. dark energy (as proposed by the ‘ΛCDM ‘ cosmological model) does not exist and it is explained why;
3. c. dark matter does not exist and it is explained why;
4. d. there is no point in invoking the principle of “metric expansion of space“;
5. e. free will does not exist;
6. f. our Cosmos is anisotropic, since it does not have the same properties and/or characteristics at all, in its different directions;
7. g. the principle of cause-and-effect applies and always does, even at the level of ‘quantum mechanics’. To reject this principle would mean having to, necessarily, invoke some form of ‘creation’;
8. h. present-day physics is drastically reduced in size, since it is limited and constrained by impassable frontiers and is limited to the description of a tiny, tiny corner of an infinitesimal of the infinite Universe.

Why does something exist instead of nothing and why are things the way they are?

In chapter seventeen: “Towards Infinity and Beyond” of the book “The Enigma of Infinity“, written by theoretical physicist Frank Close (born 1945), we read: “Why does something exist instead of nothing and why are things the way they are? Here are the questions for the 21st century“. The “axiomatic model” and in particular the “philosophical framework“, which emerges from some of its corollaries, seem able to answer these two questions.

Firstly, it must be said that: if there is someone who asks why existence exists, it can be said that existence is intrinsically meaningful and that there is something fundamental in reality that goes beyond mere ‘nothingness’.

This first question: “Why does something exist instead of nothing?” is, however, one of the fundamental questions of philosophy and cosmology. There are, of course, different perspectives on this question:

– The Philosophical: Some philosophers, such as Martin Heidegger, have explored this issue in depth, suggesting that existence itself is a mystery that defies our ability to understand;

– The Existentialist: Some existentialist philosophers argue that existence precedes essence and that each of us must find meaning in our lives, even in the face of the absurdity of existence;

– Theological: Various religious traditions offer answers based on the idea of a creator or first cause. These answers try to explain the existence of the universe as the effect of a divine will.

– The scientific one: for the ‘axiomatic model’, the absolute vacuum, ‘absolute nothingness’ does not exist, cannot exist, because every corner of this Universe of ours, infinite in time, infinite in the amount of mass/energy and therefore infinite in space, is permeated entirely by the various fields that occupy it.

Since it is shown that this Universe of ours can only be infinite in time, in the amount of mass/energy and therefore in space, and that this Universe is entirely and totally occupied by the various fields that permeate it, it seems more than justified to assume that ‘absolute nothingness’ can have no right of citizenship here! As far as the various ‘fields’ that populate this infinite Universe of ours are concerned, they are worth mentioning:

a. the Gravitational: Newton’s law of universal gravitation states that every mass exerts a gravitational force on every other mass, and this force decreases with the square of distance, which means that, although the force becomes very weak at great distances, it never completely cancels itself out;

b. the Electromagnetic: This field is generated by electric charges and describes electric and magnetic forces;

c. the Strong Nuclear: Plays a crucial role in atomic and subatomic physics;

d. the Weak Nuclear: plays a crucial role in atomic and subatomic physics;

e. the Higgs field, which, according to the standard model of particle physics, is a scalar field (a scalar field is a quantity that varies from point to point in space, but has no direction: it is only a numerical value.) that permeates all of space;

– Others: …

Regarding the second question: “Why are things the way they are?”

The ‘axiomatic model’ holds that there are an infinite number of realities, each of which has already taken place infinite times in our past, takes place infinite times in our present and will take place infinite times in our future. It is through these realities that this infinite Universe of ours manifests itself.

If this ‘axiomatic model …

If this ‘axiomatic model’ had been proposed at the beginning of the 20th century or during the Middle Ages or even during the period of ancient Greece (could very well have been written then, since it makes no use of experimental observations or even scientific discoveries or knowledge acquired over time, Newton’s laws included), such a ‘model’, which uses only logical-mathematical structures that are easy to understand, is said to have anticipated all the main observations and some of the scientific data collected since the 20th century through experiments and direct observations of reality, which have led to the current conclusions, namely to affirm the existence of:

– black holes;

– Big Bang;

– expansion of our Cosmos (1929 discovery);

– discoveries due to the observations of Fritz Zwicky, in the first half of the 20th century, regarding the orbital velocities of galaxies, around the gravitational center of the cluster containing them;

– discoveries due to the observations of Vera Cooper Rubin, in the second half of the 20th century, regarding the orbital velocities of stars, around the gravitational center of the galaxy containing them, particularly Andromeda;

– states that “dark energy“, as a cosmological constant lambda, has no meaning and does not exist at all and explains in a simple way those phenomena that have suggested its existence (Fritz Zwicky does not see it right);

– states that “dark matter” does not exist at all and explains in a simple way those phenomena that have suggested its existence;

– states that “the metric expansion of space” has no meaning;

– acceleration of the expansion of our Cosmos (1998 discovery);

– the recent discovery in 2020, concerning the non-homogeneity of the escape accelerations of our galaxies and galaxy clusters, confirms what the ‘model’ predicted and scuttles the concept of the ‘isotropy’ of our Cosmos, as anticipated by the ‘model’ itself;

– and much more that, for the moment, is not yet part of the baggage of our scientific observations and thus of the knowledge of our scientific community.

Such a ‘model’ would have avoided questionable twentieth-century and even later assumptions concerning: ‘dark matter’, ‘dark energy’, the ‘isotropy’ of our Cosmos, the ‘metric expansion of space’, …

Although it does not make use of any experimental observations, this ‘model’ has proven to be capable of making a number of predictions that have been confirmed over time.

In addition to these predictions, he made others that, according to the ‘model’, can only be confirmed in the near future.

In addition to these predictions, it has made others that, according to this ‘model’, can only be confirmed in the near future.

The recognized skills and knowledge of our theoretical physicists and astrophysicists will surely succeed, through this tool that is the “axiomatic model“, in seeing much more deeply what the undersigned has, surely, only grazed or has not yet seen at all and has not yet thought about.

In an age where so much information and images are accessible to everyone, the real value lies in the ability to understand and interpret this information in new and courageous ways!

In the end:

According to the principles of dynamics (Newton’s laws), every object, every mass/energy, including a photon of light, has its own well-defined gravitational field that has no limits, it is infinite.

The idea of ​​a “gravitational potential field” that pervades and fills space was understood and enunciated already by the mathematician, physicist, astronomer and also politician Pierre-Simon Laplace, Marquis of Laplace ( *1749 †1827. It was he who first put together the definition of probability in the classical conception, in his book “Essai philosophique sur les probabilités“).

Each object and its associated gravitational field are a single whole.

Exercising a gravitational force on a “field” means exerting it on the mass/energy associated with this “field“.

This force decreases with distance inversely proportional to the square of this distance.

This means that, although there may be a gravitational influence at any point in space, the strength of this influence becomes negligible (for us and perhaps only for us) at sufficient distances, but never, ever nothing!

This allows us to affirm and even implies a sort of “connection” between all, absolutely all the masses/energies in the universe, even those very far from each other!

In this total “connection” we cannot help but evoke the concept of “quantum entanglement[124]”.

This vision could suggest a global “bond” that connects every mass, even the smallest and most insignificant, to every other mass in the entire infinite Universe, even if it is not a direct bond in terms of instantaneous interaction.

Comment:

When I reread the preceding paragraphs, I had a pleasant and welcome feeling.

The fact of feeling, ideally connected with the entire infinite Universe made me forget the idea I had before, that is, of being nothing but a small, small and absolutely insignificant speck, in this infinite world!

To tell the truth, I am not really convinced, and fully aware of knowing for sure what it means, for me, to be “ideally connected with the entire infinite Universe“, but I am pleased all the same and I even feel a little relieved!

Finally, it is worth reminding ourselves that we live in a finite prison camp: our “observable universe.” This “observable universe” is limited in what we call large/very large by distances of the order of 46 billion light years or so. It is limited in what we call “small” by the Planck length ≈ 1.6 x 10^-35 meters.

Brunet    Piero (a.c.)

The task is not to see what no one has seen yet, but to think what no one has thought yet, about what everyone sees.’

Arthur Schopenhauer  (*1788 †1860)

‘

I dedicate what I have written to my two granddaughters: Hélène and Julie Brunet, because it all began with the intention of making sure that they could read, one day, what was going on in their paternal grandfather’s head. I would like to thank: the mathematician and friend prof. Domingo Paola, the mathematician and scientific popularizer prof. Piergiorgio Odifreddi, friend and university lecturer in Physics Fabio Truc and my son Jean-Pierre Brunet, for their precious considerations, which allowed me to reformulate, with greater clarity, some passages a little delicate.

[124] See the chapter “The Universe and our Cosmos“.

Summary

Premise: 1

Subjects treated: 2

First axiom: ‘ the principle of conservation of energy or mass ‘ 2

Second axiom: ‘the law of universal gravitation‘ 3

Observations regarding other cosmological models 4

The starting point 5

Introduction  5

Preview: 6

The Universe and our Cosmos 8

The laws of physics (1) 10

Creation  ?  10

Our cosmos 11

Expansion of our cosmos 12

Some important stages, from antiquity to the beginning of the 20th century: 12

Black holes  14

Possible scenario  14

Dark energy  15

According to this ‘axiomatic model’ 19

Dark matter 20

Conoid effect 22

Binary systems 23

Universal, archaic and ever-present law   24

The so-called ‘Gravitational Waves’ 25

Types of ‘Universe‘ 27

Infinity  31

The ‘infinite space’ 32

The metric expansion of space  34

Effects predicted, by deduction, from the axiomatic model of the universe  38

The theory of general relativity  45

First question  55

Second question  56

To be taken with the ‘pliers’ 58

The weather 59

Sets and subsets 60

Quantum gravity  62

Supersymmetry  63

Isotropy  64

Concluding remarks 65

Considerations 67

The laws of physics (2) 68

Conclusions 69

Why does something exist instead of nothing and why are things the way they are?  72

If this ‘axiomatic model …    73

In the end: 74