Raphael Neelamkavil You are missing the possibility that the finite Universe is a Hyper-sphere (as is the case in my theoretical model). In such a Universe, the speed of light is inversely proportional to the energy density of the gravitational potential field - thus, at the edges of the Universe where the gravitational potential field peters out to nothing, the speed of light tends to the limit of infinite speed. As all matter/energy is Electromagnetic waves, in such a Universe any signal or object that travels outwards to the edge of the Universe will automatically be curved around back inward. This is like a huge cosmic refractive lens. Thus, no matter/energy is ever lost from the Universe and it will tend to follow cycles of Big-Bang, expansion then Big-Crunch (followed by another Big-Bang) and so on.... forever...

Declan Traill, all that you said is the case only when the universe is a hypersphere. We cannot first decide that it is so and then claim that the conclusions and implications are true.

But we do not find any astronomical body like galaxies, clusters of galaxies, etc. curving in completely. In notions alone can such a theory exist. Not in reality. Merely because the mathematics chosen says something, we do not say that it exists in the physical world.

Raphael Neelamkavil One would not expect to see such inward curvature in galaxies or clusters of galaxies as they exist in the gravitational potential field of the rest of the Universe.

Such a hyper-sphere Universe is a necessary consequence of a Classical interpretation of Relativity. If we have Euclidean space and a variable speed of light - as is required to explain effects such as gravitational time dilation and lensing - then extending these same principles to the entire Universe (even the extreme edges) then one finds that the Universe necessarily curves back in on itself.

There are too many ``... no xyz that ..." such as ``there is no force at the outskirts..." Also something`` must be ''. How do you know such statements are true? The universe exists, so many of these statements are false. For example, the STOE suggest the gravity can attrack at the edge of the universe to pull the stuff of the universe back , thus establishing a border.

Declan Traill, The universe may curve in, not always. If the curving in is the contraction (however intense or not intense it is), then there is no guarantee that the energy propagated off beyond the outskirts should JUST RETURN AS IF REFLECTING FROM A MIRROR!

Raphael Neelamkavil

The electromagnetic waves at the 'edge' of the universe with zero gravitation lose by their infinite c location and direction, so there is no need for a 'mirror' or reflection. They can be found anywhere in the universe in complete thermodynamic equilibrium as the omnidirectional microwave background radiation which behaves as the resonating electromagnetic frequency of the universe.

Willy Verhiest,

If what you say must be true, then the outermost astronomical bodies in the universe must be permitting energy propagation only in in directions other than the direction outwards from the universe! Fantastic.

If that is the case, then the galaxies and systems of galaxies with a central gravitational body will have to do the same!

Raphael Neelamkavil Kind of like a mirror, but with a LOT of curvature to the emitted and returned rays. Essentially, looking outward near the edge of the Universe appears to be looking inwards to the center.

"Essentially, looking outward near the edge of the Universe appears to be looking inwards to the center."

I find it difficult to accept this statement. If this is the case, you could make any statement of this kind about any point or region in the universe. This is very counter-intuitive. Now one may say that the mathematics says it all. Which mathematics says it all? What is the justification for applying any counter-intuitive math to physics?

I would repeat: IF GALAXIES AND OTHER ASTRONOMICAL BODIES PROPAGATE ELECTROMAGNETIC AND GRAVITATIONAL EFFECTS TO ALL DIRECTIONS, THEN THE LOCAL UNIVERSE TOO DOES IT. IF I SAY "RAYS" INSTEAD OF "EFFECTS", THERE WILL BE PEOPLE TO OBJECT AND SAY THAT GRAVITATION IS JUST AN CURVATURE BECAUSE THE MATH SAYS IT ALL....

Raphael Neelamkavil

There are no outermost celestial bodies, there is only a point where the gravitational field has a strengt which allows resonance of the CMB. Every celestial body is its own center of gravity, the field strengt decreases linearly with the distance because it increases linearly with the mass ( equally distributed over the universe ) but decreases quadratic with the distance (Newton ). The decreasing field strengt increases c giving red-shift and ultimately the CMB. The universe is endless if studied with electromagnetic waves.

Willy Verhiest,

You said: "The field strength decreases linearly with the distance". But I was speaking of the propagations that left the outskirts a long time ago. For this you even said "There are no outermost celestial bodies." In that case, there are no inner celestial bodies too!

To help obtain some more clarity on what we discuss here, I think the following discussion will be of use -- especially the question by Richard Marker and my reply:

https://www.researchgate.net/post/The_Irrefutable_Argument_for_Universal_Causality_Any_Opposing_Position

Raphael Neelamkavil

If you accept that c is infinite at G=0 there are no outskirts at the universe. At an infinite c all residual electromagnetic energy is found in the CMB radiation which is omnipresent and omnidirectional, so having infinite time and space.

And if G never gets equal to 0....? Mathematically this is an end-effect of a phase. But then at that mathematically artificial moment all matter-energy will go into nothing without any gravitational effect at all.......! That is, this sort of math games show only that MATH SHOULD HAVE LIMITS OF APPLICATIONS TO PHYSICS, ESPECIALLY AT MATHEMATICAL JUNCTIONS OF ASYMPTOTIC APPROACH. Another example for such asymptotic approach is the central singularity of our finite-content universe. It never gets realized. Read recent works (even interviews) with Penrose, Hawking, etc.

And now I hope we need not speak of what you termed "omnipresent and omnidirectional" CMB....

G gets only equal to zero if you accepts c gets infinite as I said. c never gets infinite , the electromagnetic energy gets red-shift with decreasing G and ultimately gets the resonance frequency of the CMB radiation which proves that the EM energy in our universe is in thermodynamic equilibrium, no lambda, no dark energy or matter or other fantasies.

Even when there is CMB, that too from the start to the so-called end, there are material bodies in the universe. They do experience and exert gravitation. Such a universe, at least sufficiently large locality, will have a common gravitational centre. Each such group will have some gravitational influence on a finite number of its neighbours -- not by EM but by gravitation. Thus, each group will lose some gravitational energy into the neighbours. This then becomes yet another gravitational grouping. This is called gravitational coalescence formation. This tendency will have to get widened, but at no time there can be a group with infinite number of such local groups within its gravitational influence.

This is what I have been discussing in this discussing. Not CMB. Of course, CMB too will have something to do with such a universe. But here the coalescence is be reason of gravitation.

Raphael Neelamkavil

There is no center of gravity in the universe. Newtons' shell theorema leads to the conclusion that the center of a spherical celestial body always has zero gravity, in quantum terms only its outer surface composed of electrons creates the gravitation field. The total gravitational energy of all spherical celestial bodies in the universe is zero . The universe is in a gravitational and electrodynamic equilibrium. There is of cause gravitational energy in dust clouds a. s. o. giving rise to star creation.

Do the earth, sun, our galaxy,etc. have a centre of gravity? If nothing has a centre of gravity from the GTR viewpoint, you will have to rewrite the whole of GTR.

Or, only these celestial bodies have a centre of gravity, and finally, only the universe does not have? Any proof?

I HAVE IMPROVED THE TEXT OF THIS DISCUSSION SESSION:

Gravitational Coalescence Paradox (GCP) [INTRODUCTION TO GRAVITATIONAL COALESCENCE COSMOLOGY]

Even if there is no common big bang within a fully finite-content universe, there will be partial expansions and contractions locally everywhere. Moreover, the universe will have outer limits due to its content finitude. At the outer limits, some gravitational and non-gravitational energies must be lost, because there is no force at the outskirts to block these from escaping.

One may argue that there is no such outer limit. But in that case gravitation should be an influence only at directions other than the outer linear direction from the celestial objects at the outskirts! This is unjustifiable.

Additionally, if the universe has a finite but fixed speed limit of energy propagation, then the energy that is lost at the outskirts from the very beginning of formation of this universe can never be brought back by propagations that issue later.

If there is a general expansion (however small-scale in reach), then there will be either general contraction or a mere expansion. Constant expansion will bring up the question of the fixable age of the universe and the origin of the universe from something other than physical! I leave this question at that.

Naturally, in the second sub-case, if there are also general contractions, there are consecutive overall expansions and contractions, however limited they are. This need not exactly be extreme oscillations. These cannot go on infinitely, since the finite-content universe loses energy (convertible in terms of mass) at the outskirts. IF ANYONE CLAIMS THAT THERE IS NO LOSS OF ENERGY AT THE OUTSKIRTS, IT IS THEIR RESPONSIBILITY TO PROVE THEIR CASE.

Thus, a fully cyclic and geometrically fully spherical oscillating finite-content universe existing as the sole finite universe can never be defended. Within a finite (of course, very long) time, it will exteriorize its matter-energy and be entirely rarefied over a finite number of oscillations. This raises the question of the causal horizon of the first big bang of a finitely cyclic universe and/or the very beginning of this universe.

If other such separate universes exist, the final residues of the first need not form part of one or many of them even if the distances between them are always finite, and all of them have some gravitation -- if they all have some velocity from each other. If they possess a meager velocity, their common gravitational power may bring them together. This is not of much consequence in a finite-content universe.

There are the following two possible lines of solution for the first big bang of a finite-content universe: (1) the matter of our universe has come from other universes or (2) it was created in some way from a Source that is not a form of matter-energy with finite activity and finite stability (which finite activity and stability is the case only of the cosmos).

If the matter-energy of a finite oscillating universe is from other universes, there remains only the case of existence of an infinite number of such universes. All of them eventually will exteriorize their matter-energy into becoming parts of other universes at finite distances, in finite durations. Such universes exist at finite distances. Gravitation from one such universe will affect similar neighbouring universes in a finite time. So, they should coalesce gravitationally with each other and with others over the course of time.

Gravitation has a finite propagation velocity, not infinite. It is either (1) unique to each universe or group of universes and differ at least between groups of universes, or (2) the same for the whole cosmos.

If gravitation can vary in velocity, each such local gravitational coalescence will have a highest limit, whatever, of gravitational velocity at each phase of expansion from a common central black hole. NOW THERE MAY BE PERSONS WHO CLAIM THAT THE LOCAL UNIVERSE HAS NO CENTRE, HAS ONLY CENTRES THAT ARE ALSO PERIPHERIES, etc. THEY ARE FREE TO HAVE THEIR MATHEMATICAL ABSOLUTES FOR THE COSMOS. I leave them for their imaginative reasoning.

Moreover, at any time with respect to any one finite-content universe, there are only a finite number of universes in mutual gravitational attraction, since an infinitely spatiotemporal universe can never form a fully gravitationally well-related infinite-content conglomeration. If it could, there would again appear in the cosmos the contradictions created by infinite mass, density etc. and infinite velocity, which is the same as the absolutely miraculous action-at-an-infinite-distance. We do not need such contradictions.

The mass-and-volume differences among coalescences do not matter. Due to the tendency of matter as groups of island universes to form ever wider gravitational conglomerations or coalescences, the formation of an eventual common center for each such wider coalescence is a must.

There cannot be a special instant or case where a coalescence of such universes existed or exists without gradually forming a common gravitational center. This conclusion is absolutely inevitable if all existing universes and parts thereof are gravitational.

No such coalescence, however wide, can bring back the gravitons it has radiated to the peripheries from the common gravitational center at a time before or during or after its big bang or big crunch, however mild they are – i.e., and even if there is no big bang and big crunch of a grand scale.

This process can only continue forwards forming ever wider coalescences; and never backwards in a de-coalescence or de-coherence of gravitational coalescences, because gravitational propagation is an outward, not inward, process.[1]

At no time relative to the coalescing universes of universes can an infinite coalescence be actualized via gravitational influence from a central black hole common to all the infinite number of universes, although infinite such gravitationally coalesced universes, groups of universes, etc. do exist in an infinite-content multiverse.

Hence, no gravitational coalescence of universes, however big, is a gravitational member of an infinitely large gravitational coalescence. This fact and the fact of loss of energy at the fringes of universes flow logically from the foregoing discussions. I shall now define in the following paragraph the paradox of matter-energy creation implied above.

The Gravitational Coalescence Paradox (GCP): At any time in an infinite multiverse, there will be an infinite number of gravitationally ever broadening coalescences, none of which can be traced back to other such coalescences for their origin.

Each maximal gravitational coalescence at any time relative to the local set of coalescences is irreducibly finite and hence has a finite past in the absence of any past contact with any other outer universes.

IN OTHER WORDS, each of the infinite number of coalescences is thus cosmogenetically isolated from other such coalescences, because, at any time, there exist an infinite number of coalescences which are cosmogenetically isolated and cannot be traced for any causal inheritance from an infinite number of them.

All the universes from which a certain universe has had causal inheritance is already included within its broadest possible gravitational coalescence.

This facilitates the question to be posed concerning the origin of each such gravitational coalescence in the finite past of each such, since at any given time, none of the designated infinite coalescences has had past gravitational or any other causal contacts with any other cosmic entity. I term the foregoing discussion as the core of Gravitational Coalescence Cosmology (GCC).

[1] If the cosmological scalar Λ-addition is a dark energy qualified solely by its alleged ability to repel, no amount of dark energy should possess the capacity to attach itself to any other dark energy quantum. Ipso facto it never exists in any real universe. If it includes also gravitational radiation, it is impossible to understand why there should be these ad hoc quanta of repulsion if, naturally, the limits of density that each conglomeration of matter-energy possesses by reason of its mass, volume etc. can produce repulsion between parts of the conglomeration after the conglomeration has attained critical density. As has already been evident, it is irrational to posit the existence of repulsons – as quanta / wavicles of repulsion to keep dark energy on par with gravitation. Hence, I discuss gravitational coalescences to theoretically circumvent any problem that dark energy can offer.

Raphael Neelamkavil

There is no loss of energy from the universe because the CMB radiation is a perfect black body radiation which is only possible in an universe in perfect thermodynamic equilibrium.

Celestial spherical bodies have a centre of gravity with a zero gravitational potential ( Langranian points ) as proved since more than 250 y in Newtons' shell theorema.

At which time is the zero gravitational potential of celestial spherical bodies? Are celestial bodies spherical bodies? Is the universe a sphere? For mathematical purposes Newton will have done many things. But this sort of mathematizing has been child's play. And do you say that Newton had proved that celestial bodies have such a centre of gravity? Had he proved using the math of his time, or experimentally, observationally?

CMB is the radiation that still remains within the universe from the "beginning". It need not be exactly from the beginning, but from the various inflations. I AM SPEAKING OF THE ENERGY THAT ESCAPED -- from the so-called beginning of the universe till today.

Now you or someone else may come up with a theory that there was no beginning. In that case, why CMB?

Raphael Neelamkavil

If the CMB energy escaped in the beginning how can it be observed now?

The universe has an observable electromagnetic limit wich is not the same as a real limit.

This is why I say that I am not speaking of the CMB which is available within the universe, but instead the gravitational and EM propagations that left the universe, outwards. If you argue that they would not leave the universe, then you will have to show me how the same sort of propagations are leaving the galaxies and groups of galaxies and reach us.

What is that protective-reflective shirt that the universe has such that all energy propagations should return instantly from there?

Raphael Neelamkavil The speed of light increases towards infinity as the gravitational potential decreases to zero at the edges of the Universe. This WILL curve everything and anything back inwards. Why this doesn’t occur in the galaxies we observe is that these galaxies exist in the substantial gravitational potential of all the other galaxies and matter that surround them.

The speed of light does not increase towards infinity, but our relativistic calculations let it so, because of the proportionalities involved. Hence, the gravitational potential decreases to zero.

I am not speaking of the gravitational potential, but of the gravitational and EM radiations that have already left the universe before a new expansion or contraction phase sets in.

I have already set forth my arguments about it earlier. Why to insist that the universe at any stage will not propagate gravitational or non-gravitational energy outwards?

Raphael Neelamkavil,

the CMB is created inside the galaxies as I have shown (book IV).

Willy Verhiest,

you say the same thing as I have said earlier. In the Big Bang light was first generated, some time after that galaxies. The galaxies are not superluminal.

Declan Traill,

the speed of ligth does not change, only the energy of the photons.

Raphael Neelamkavil That is not GR but the Classical version of it where space is Euclidean and the speed of light changes. The speed of light must change otherwise someone in a region of increased potential level such as on a planet‘s surface where gravitational time dilation exists would measure the speed of light to be greater than c. He does not!

The gravitational potential field IS the medium through which all Electromagnetic waves propagate - even gravity waves - so if this field peters out to nothing, then no waves can propagate. As the field thins out, it’s inertia to oscillations in it decreases which causes waves in it to propagate faster.

The gravity field which in fact is an electrostatic field forms the impedance field for EM waves, the lower the impedance the higher c. If impedance is near zero speed is near infinite and in fact the EM wave is everywhere and omnidirectional in the universe = CMB radiation. As it is everywhere there is no need for 'mirrors', it reflects on its own transverse waves as in the standing waves of a black body.

Each EM wave is not omnidirectional. See how you mislead or have been misled by defects in statements! Each wave propagation have only one general, overall, direction. The general direction can change if there are suitable obstructions on the way. If not, it will continue.

What you should have said is: The totality of all EM waves is, in general, omnidirectional. This is CMB. But this is not the whole of what was propagated off from the universe from the very beginning. It is the only directly available sample of that totality. See how you got misled by mistakenly totalized statements!

Now, what I am speaking of is not the CMB portion available within our universe, but of the propagations already lost forever beyond the outskirts of the finite-content universe of ours. This need not mean that there are no other universes beyond it. There may be.

Now again, I am sure, you will come up with arguments claiming -- not proving -- that the universe did not have (outtermost) outward propagations of gravitational and EM energy at the beginning of expansions.

Raphael Neelamkavil

I don't claim anything but observe.

For an observer on earth with gravity G c is always constant in vacuo but c is infinite at zero G at very long distances from the observer. You can call that the limit of the universe as observable from the earth which is not equal to the total universe. If the earth had double mass with a double G the observable universe would be double.

Time does not have a meaning for a photon as it travels at c. For a photon the observer is nearing it at -c so total time is zero = meaningless. It is impossible from the local observation of photons or other EM waves to determine a beginning or an extension or limit of the total universe. Stop searching celestial mirrors. There is only local time and space, only valid in our local point of observation, the earth.

Willy Verhiest,

In the observations you have made above, notice how overstretching the relativistic paradigm confounds the observer and theoretician. If the gravity of the earth is G, then c is constant in vacuo. But c increases relativistically to infinity at 0 G at very long distances from the observer. (Or, at the centre of the earth?) Now, you say, if the earth had double the mass, it has 2G. The the observable universe will be at double the distance in almost a spherical manner everywhere.

Should we then say that our observationally relativistic measurements must be the same as what an earth at one spot at the periphery of the universe (not merely of the observable limits of the universe) would notice?

If observationally the reach of observation from an earth of G is a certain A, then should c be zero at the observational limits you spoke of, or at some other? How do you insist that G will be zero there? Observationally from the Relativity standpoint of observation from the earth, or from yet another specific Relativity standpoint of observation?

Will the same c be observable or experienceable for an earth at the peripheries of a finite-content universe? Or, will it be something different? Of course, relativistically it should differ widely for the stipulated earth (observational starting point). But is it merely because I observe / calculate from my earth (of G) some special value for c at that point where the earth at the periphery is situated? Perhaps it will be a certain value close to infinity or really infinity?

But asymptotic approach math does not permit that! No zero or infinity is ever reached!

Hence, the c will be near infinity! Will this be real? Relativistically from our earth, of course real. But real also for an earth there, where the value is supposed to be a certain near-infinie value for our earth?

Now you may again use relativity theory and assert it to be so. Bu the earth at the periphery will not observe it so!

Now you may say that we have a universe with an infinite-periphery (strictly, non-finite or potentially infinite periphery) universe with a finite volume and content! Of course, you can choose such a math, just as Einstein chose the Riemannian geometry for the finite-content universe, without mentioning the possibility of a different Generalized General Theory of Relativity (GGTR) for an infinite-content cosmos!

Now you see how misleading it will be, if you assume for a spot at the periphery of the universe the same relativistic spatial and temporal measurements, the same measuremental differentiation at velocity (also density, mass, etc.) as measured from the earth?

In short, to deal with the whole of the cosmos -- if it is of infinite content -- we need a highly generalized GTR. Now, if you ask me what that GGTR is, I cannot give it to you, because I have not formulated it. (I am sure that you will not ask me to shut up in that case, because we both are finite-brained creatures!)

And if we have only a finite-content universe, the relativistic measuremental variation from one region to the other with respect to our earth should also mislead the earth at the periphery of such a universe. THIS IS THE CASE I HAVE BEEN SPEAKING OF.

And so on....

In the cases where the values are infinity, zero, etc. that I mentioned above, there may be further confusions. What I mean is: Please accept that there will be confusions in what I mentioned above, in all the specific values that I mentioned above. These are due to human errors. I am happy to accept corrections and suggestions.

Let me make a general suggestion: GTR is to be taken as already very erroneous if we tend to consider other universes as existent and apply the same measuremental criteria from any two universes relatively simultaneously. Of course, the meaning of time will be different for both the universes. Not of time, but of the measurements of time, because the reference frames will differ. Moreover, there is no simultaneity of any absolute kind in the universe between any two different points of spacetime.

Please note also that this statement above already presupposes a standpoint of view or measurement that considers the relativistic measurements from one spot in the universe as non-absolute from another spot.

Now you see how well one can make erroneous statements by assuming universality to Relativity: You said, "Time does not have a meaning for a photon as it travels at c." And you said: "There is only local time and space, only valid in our local point of observation, the earth." Both these are very bad statements in my opinion. Why? Not that time will have no meaning, but specific temporal measurements will differ for a photon if measured from various frameworks. Similarly, not that there are only local time and local space, but there are only local temporal and spatial measurements with respect to respective frameworks. Naturally!

And the final advise is difficult to grasp: "Stop searching (for) celestial mirrors." I did not search for celestial mirrors. I asked whether a celestial body at the periphery of an individual universe will have gravitational effect to all its sides, or only to the sides other than the direction to the outer periphery of that one universe. And I suggested that if that celestial body is not able to exercise gravitation to the outer aspect of the universe, then there must be a mirror or mirrors there to reflect all the gravitation and EM being propagated off. That was not meant to assert that there are mirrors there, you know!

Now, insisting that all that happens everywhere in our local universe or in a neighbouring universe should be according to the measuremental values assigned to space, time, c, G, etc. from the criterial viewpoint of observation from the earth or from the centre of the universe, or any other point.... This is a nonsense in my opinion. This is a very misleading system of physical criteria wrought in by misinterpretations and stretching of the Relativistic viewpoint.

Another observation: Absolutizing the Relativitiy Theory for all observational points of "space" is in my opinion physically fallacious.

A suggestion to ponder: Have you noticed how, in the Lorentz factor in STR, the velocity of an object is compared with the velocity c? This means that we stipulate c to be the criterial velocity in our case, because we observe anything at luminal velocity. But then, if v is increased to approach c, then we get paradoxes in any equation. Does this mean that experimentally fixed velocity of light should be absolute? Or, does it mean that the paradoxes result because we have compared (in the Lorentz factor) v with c? And should we at all pronounce that c is the only criterial velocity in the universe?

Raphael Neelamkavil

Indeed c is the only critical velocity in our obsevation surface=the earth' surface because EM waves are the only signals we can observe from the universe but that does not mean that c is equal to it on other surfaces. It is constant because all measurements have been done an equal G.

Many observations confirm that c is dependent of G with higher G = lower c.

If you accept Newtons' shell theorema you have to conclude that every SPHERICAL celestial body has zero G in its center and maximum G at its surface. From its surface G decreases quadratic with distance and increases with encountered mass. As mass is equally distributed the net result is a linear decrease of G with distance giving the beautiful 45° slope of the red-shift/ distance relation.

In this view every spherical celestial body creates its own EM observable universe with zero G in its center, maximum G on its surface and as an universal observable limit the resonating frequencies of the CMB radiation.

You said. "but that does not mean that c is equal to it on other surfaces". I did not claim so.

"Many observations confirm that c is dependent of G with higher G = lower c." You used this to tell me that at the peripheries of the universe no gravitation and EM will escape the universe!

"f you accept Newtons' shell theorema you have to conclude that every SPHERICAL celestial body has zero G in its center and maximum G at its surface." BUT CAN YOU SHOW ME ANY CELESTIAL BODY THAT IS SPHERICAL? Hence, I do not accept Newton's shell theorem.

"As mass is equally distributed". But mass is never equally distributed anywhere in the universe. Anisotropy is always the net result.

"In this view every spherical celestial body creates its own EM observable universe with zero G in its center." Due to the absence of Newtonian spherical bodies, the universe is not Newtonian. Moreover, The G at the centre of the universe is zero for that point. But the gravitational influence of the central body and other nearby bodies upon the peripheries is decreasingly near zero. Hence, much energy will be lost at the peripheries.

Sorry Raphael but we have many different views, f. i. for me the mass distribution in the universe is isotropic over very long distances.

Respectfully.

If the mass distribution is anisotropic over short distances, how can their sum over long distances be isotropic? For pragmatic purposes, one may consider the sum to be isotropic. But this is not exact. To be exact, it is all anisotropic....!!!!

Willy Verhiest,

Raphael Neelamkavil,

the discussion about the speed of light seems a bit strange to me. The nature of gravity is completly different from that of EM. So, how can gravity affect the speed of light? If you claim it you have to prove it.

Secondly, the creation of the universe is a stochastic process. The resulting distribution of matter will show statistical fluctuations. Within these variations we could expect an isotropic distribution.

Hans Gennow,

Gravitation and EM are in my opinion different, not parts of the same propagation. Clear. But if they cannot influence each other in their own fashion, it will be strange. Of course, I feel that most probably gravitons cannot reduce the speed of each EM wavicle. Instead, they can retard their direction. As a result, an automatic retardation in overall velocity of many EM waves together is a possibility.

About stochastic processes. A statistical fluctuation is nothing but a "mathematical" fluctuation. But it is not a thing that happens as such there in physical processes. In physical processes happen physical processes. Our mathematical perception of what happens in certain physical processes may be calculated in the stochastic manner. But what is calculated stochastically is not stochastic in the processes!

Now, the isotropic distribution that you speak about is an approximation. Can you show anywhere absolute isotropy in nature? If in minute spacetimes the state is anisotropic, then how does their sums be isotropic?

Raphael Neelamkavil,

you have not understood.

Gravity cannot affect an EM wave. The fields are different. It does not help to invoke the graviton. It changes nothing, it is just the mediator of the force. However, a photon may loose energy in a gravitational field but its speed will not change.

A stochastic process will lead to statistical fluctuations. What else? It just means that the outcome will vary. We are talking about a collection of processes, not a single process. It has nothing to do with mathematics.

The distribution I am talking about is the average distribution that will show statistical fluctuations. Very strange? There is no anisotropy, just fluctuations.

If the fields differ, gravity cannot affect EM waves? What sort of a reasoning is this? What is just the mediator of the force? I did not say that the speed of the EM wave will change! I meant, due to gravitons affecting the EM waves they can be deflected a lot, continuously, and hence their effective ability to reach a target will be retarded. This is not a redardation of the velocity of any EM wave, but continuous deflection causes of luminal-velocity waves causes the effective increase in the time to reach a target. Moreover, many EMs will not reach the target due to the deflection.

Is there a statistical fluctuation or a physical fluctuation that we name statistical due to their measuremental appearance in theory? A physical fluctuation is physical. The probabilities that we discover are not probabilities in the physical fluctuation, but instead, probabilities in our ability to predict or see certain patterns! Is it such a difficult thing to grasp that, when I look at a distant object using a small instrument I do not see its exact spot in relation to its neighbours, but instead, the exact spot shifts from time to time (due to the extent of inability of the instrument, usign which I calculate the probability of the exact spot being this, that, or something else?

You said, "We are talking about a collection of processes, not a single process. It has nothing to do with mathematics." If we are taking of a collection of processes, the collective statistical calculations about them yields a statistical picture, and this picture is a mathematical affair. This statistical picture is not an exact picture of the physical processes. It is just a mathematically / statistically derived picture. Now do you call the process a statistical / stochastic / mathematical process?

If the fluctuations are really within the processes, it is a proof that there is anisotropy there. The picture of the anisotropy is not the exact picture of the process. Nor is the averaged isotropy at a large-scale level a picture of an isotropy of the process. But if we can say that even in minute physical processes there is no uniformity of mass, volume, etc., then their sum cannot be called isotropic, too!

https://www.youtube.com/watch?v=XE7u2G68kbs

Raphael Neelamkavil,

You say: "retardation in overall velocity of many EM waves together is a possibility". Retardation means to me slowing down.

We know about the bending of light which is a different thing. I have in my first book shown that my relativistic formulation of Newton gives the right bending.

I have in my simulations used random numbers. Acting on a given process it leads to statistical fluctuaions of that process. The case of the CMB is just an example of this. It will show variations but to say there are anisotropies is just wrong. This is physics, not mathematics.

Secondly you are mixing up things.

Why do you read my explanation as "Retardation means to me slowing down" without reading the explanation? I did not say that the velocity is being brought down. Suppose you travel from a city to another which is 10 km by direct distance measurement, you can either choose this path or a wavy path. The wavy path represents in our case the path in which gravitation leads the EM waves through. If the 10 km is reached in 1 hour directly at a velocity A, you can still move at the velocity A through the wavy path and reach late the target city. Do you understand this?

Your said: "Acting on a given process it leads to statistical fluctuaions of that process." I claim that these are not statistical fluctuation in a sense different from physical fluctuations. The fluctuations before and after the action on them are physical. But your calculations of the difference caused by the action is statistical. For this reason, why should you call the new state as statistical fluctuations? Exactly what you predict probabilstically is not happening in the physical fluctuation. The probabilism is not in the material of the fluctuations, but in your probabilstic explanation.

If you have used random numbers in your simulations, will the physical processes you are simulating in the computer become random? What are random processes? You can only have a random-number-induced measurement or explanation of the real physical processes out there!

The mathematics of physical processes can take the processes as isotropic for mathematical purposes. But there is another unchangeable fact behind all these: just like in my room there is anisotropy, there is anisotropy in this whole city, in the earth, in our galaxy, etc. For simulation purposes you can average out the data about this city as isotropic. But the fact is not that. Because, nothing in the world is exactly of the same mass, volume, etc. of any other thing. Can you accept this fact? Or, will you call also this as random / statistical / probabilistic and average it out into isotropy?

Raphael Neelamkavil,

I have been working with simulations of physical processes since the 1970th. It includes e.g. simulations of various detector systems. People were quite happy with my work. What experience do you have?

As an example I can mention that when the cores build up a lot of debris will be created. The cores can accrete them but in doing so the debris will certainly undergo collisions. That will spread them out and to simulate that process you have to randomize them. No collisions will be the other alike.

That leads to a statistical distribution concerning their speeds and their directions of flight.

You say "nothing in the world is exactly of the same mass". From what I know, e.g. a given electron has the same mass as another electron.

Raphael Neelamkavil Hans Gennow

The gravity field normally is a static field but has intermittent shock waves. The velocity of these waves measured on the earths' surface by LIGO is equal to c measured on the earths' surface, this is no coincidence.

The gravity field being in fact an electrostatic field forms the mediator on witch the EM waves 'travel', for EM waves it is an impedance affecting c in analogy to c affected by the impedance of the crystal structure in a prisma.

Willy Verhiest, why is gravity a static field? What do you mean by this term? Without knowing what you mean by it -- what in the literature is meant, or what you specially mean by it -- a reply is impossible.

Similarly, what you mean by "gravity field being in fact an electrostatic field forms the mediator on witch the EM waves 'travel'".

Hans Gennow, on a lighter weight, a counter-question to your claim on long experience in simulation: I have been working in the philosophy of physics for more than 25 years. What experience can you claim?

In the work on debris you say there are statistical distributions of speeds and directions of flight. Not so. Instead: there are distributions of speed (out there, not in our minds or computers) and directions of flight. And we interpret them statistically because we are not able to see them all as such.

You say: "a given electron has the same mass as another electron." But what I meant is different: If two electrons or two suns have exactly the same mass as another electron or sun respectively, then only their respective measurements of masses are equal, not the mass that they in fact have in themselves within a given gravitational context.

Raphael Neelamkavil,

50 years is more than 25 years. I work with physics, not bananas.

You obviously do not understand statistics.

All electrons has the same mass irrespective of surroundings. Gravity does not change it.

Willy Verhiest,

do not mix up the electrical force with gravity. The nature of the two are completely different.

The speed of ligth is determined by vacuum polarisation. A vacuum bubble can for a very short time create a pair of electron-positrons. A photon passing by may be absorbed but ejected almost instanly. The result is a tiny delay. I discussed it in my first book.

Hans Gennow, you said: "I work with physics, not bananas. You obviously do not understand statistics." Wonderful!!!! This is the way you speak. All right.

I did not say that electrons have different masses on earth. But the relativistic mass (i.e., with respect to the gravitational backdrop) of the electron on earth cannot be the same on a star, because the gravitation on it is much different. This I say because I believe that even on earth the earth's gravitation has something to do with the weight and mass of anything on earth. If relativity is not physics for you, alas, there goes Einstein!

Raphael Neelamkavil,

the mass of the electron is always the same, independent of location. The relativistic mass is something else. That term is a bit missleading. It just tells us that the energy of the particle is increasing with speed, not its mass.

Gr has gone away, not SR. Half an Einstein?

If you claim that the mass depends on gravity, then you have to prove it. Empty words is of no use.

We spoke about equality of mass. If any two things are of the same mass by all possible measurements, should it mean that their mass must be the same taken in themselves? The concept of physical equality of any two things in themselves should be based on space and time. But identical space and time is imaginable only in mathematics and measurements. Physically, non-identity implies differences in all possible dimensions -- but in most cases the differences are so minute that the differences fail to strike.

Now, instead of digressing to other themes, let us concentrate on Gravitational Coalescence Paradox, on which we began our discussions.

Hans Gennow, are energy and mass in any way related?

Hans Gennow, did you say that only STR is acceptable and not GTR? If so, what theory of gravitation do you have to submit? Does gravitation influence EM waves?

Of course, every theory has defects. But if you overthrow GTR, how do you account for gravitation and measurements using c?

Now, what are the cosmological implications of these at the outskirts of the finite-content universe of ours, and if the cosmos is made of an infinite number of finite-content universes, what would be the dynamics by which the contact or non-contact between the universes is to be understood? This is the basic question in this discussion. Not merely EM waves.

If an electron A at a specific spacetime loses a certain number of quanta of energy (say, 100 quanta), naturally its total energy has come down. Or, will anyone claim that it has thus increased or that it is in a constant state? Now imagine that it is accelerated later by other forces.

Consider another electron B at another spacetime. It has not lost so many quanta of energy (say, only 50 quanta). Like A, now B is also being accelerated with the same amount of energy.

Of course, whether our measurement of the acceleration energy in the two cases is absolutely exact is yet another ambiguous matter, but we suppose that they are equal.

Will the latter be at a better position in the total energy content than the former? Or, will it be claimed that their energy, mass, etc. After receiving equal acceleration from outside, are equal, merely because they are both electrons already taken to possess a certain mass?

Moreover, we know that in the path that both the electrons take there will be other physical influences which we do not determine and cannot. These influences must be at least slightly different from each other.

In short, the mass, energy, etc. of the two electrons will never be equal at any physical state, not have they been absolutely equal at any time. And we know that nothing in the world is in a static state. So, there is no reason to suppose that electrons will have a static mass, energy, etc.

Of course, we can calculate and fix them as supposedly static mass, energy, etc. These will be useful for practical purposes, but not as absolutes.

That is, our generalized determination of an exact mass for an electron need not be the exact energy, mass, etc. of an electron in various physically processual circumstances. At normal circumstances within a specific chemical element, and when freed from it, the electron will have different values.

This shows that no electron (in itself) will be identical in all its properties with any other. Our description of these properties may be considered as identical. But this description in physics is meant merely for pragmatic purposes! One cannot now universalize it and say that the mass, energy, etc. of electrons are the same everywhere.

What about the said values (mass, energy, etc.) of other particles like photon, neutrino, etc.? I believe none can prove their case to be otherwise in the case of these particles / wavicles too.

That is, there is nothing in the world, including electrons, quarks, photons, neutrinos, etc., with an exact duplicate anywhere else. This is the foundation for the principle of physical identity.

Richard Lewis added a reply

6 hours ago

Raphael Neelamkavil This is a very good point about the variable energy of the electron. All electrons will have energy given by E=hf where f is the frequency of the looped wave.

Where it is a free electron the energy is continuously variable. Where it is an electron bound to an atom the energy is restricted to specific energy levels. This is the cause of the quantisation of light.

The energy of the photon is h(f2-f1) when the electron moves from energy level 2 to 1.

Also for all matter particles the energy and frequency increase by sqrt(1-v^2/c^2) when moving with velocity v relative to the space rest frame.

This paper about the hydrogen bond includes a description of the electron as a looped wave in the medium of space.

Preprint The Hydrogen Bond (June 2022)

Richard

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Raphael Neelamkavil added a reply

5 hours ago

Richard Lewis, thanks. I will read the article given.

Practically nobody noticed this discussion of mine. So I put it in some other discussions too. But none read it or none responded. They all know much better.

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Raphael Neelamkavil added a reply

3 minutes ago

If the case of measurements of values regarding an electron is such, what about the very Planck constant? Is it not a proportionality? If the masses, energies, etc. of each electron should be different from those of all others, will the constant proportionality be constant or relatively constant?

Clearly, the range of values of the proportionality will differ from universe to universe, because of the varying densities of each universe. And we sit here thinking that these are all physical laws applicable to all universes!

I believe that most physical laws are relative to the specific universe or groups of universes. But there must be pre-physical laws. WHICH ARE THEY? ANYONE HAS GUESSES?

Raphael Neelamkavil

Raphael, there are no universal physical laws. These 'laws' are human inventions to which nature should obey? Are men super - god that they can command nature? We only can do local measurements and try to find locally more or less valid correlations and that's all. Projecting these local findings to the universe is going from 'minorem ad majorem', not allowed in logic. If there are no definable universal physical laws there are certainly no pre-physical laws.

Willy Verhiest, I am fully agreed with you on this. This is the vein from which I work.

But when great physicists and even great philosophers of physics do not recognize this and make some renderings of the laws of physics, meant for this universe or part of the universe of group of universes, to govern all of the cosmos, it becomes a matter of surprise.

But this does not mean that I know more than they in anything. I just happen to suggest this argument. That is all.

Moreover, I do not also claim that all physical laws are meant for this local universe of ours. Maybe, some of them are universal. Perhaps one example is gravitation. The only argument that comes to mind in favour of the universality of gravitation is that without some sort of adhesive tendency nothing can stick together and form entities....

Thanks, friend..... We are all friends in search of some treasures, which we all define differently and each one thinks of one's own definition being better. I too belong to that lot. I try to relativize my concepts, claims, and theories....

Raphael Neelamkavil,

You are really messing things up. In my first booked I showed how particles can be created through a quantum mechanical process. The result will always be the same for a given particle, i.e. identical masses.

Do you now claim that quantum mechanics is wrong?

Your funny talk about other universes having some influence as well as spacetime. Where did you see another universe?

Hans Gennow, I do not insist on the existence of other universes. I treat of the various cases: if there is only one universe and if there are infinite other universes.

Universe means all there is - so how can there be more than one Universe?

Declan Traill,

As you may already know or can imagine, if one decides (as many in physics and philosophy have done) to name one gravitationally well-connected group within the cosmos, behaving well enough like a a local group in its own gravitational unity, AS ONE UNIVERSE, would that be totally unacceptable? If you will simply grant that, and if there are other such local gravitational groups, then they are other universes.

Merely because I name the local group as a universe, it need not be the only universe in the cosmos. Now, there are two possibilities: (1) There is only this one local universe or there are a few of them in the cosmos -- in this case what would be the behaviour of gravitational propagation within and out of this / these few universes? (2) There are an infinite number of them in the cosmos -- here how to treat of the gravitational propagations within and out of these infinite universes?

This is what I the Gravitational Coalescence Paradox discusses.

Thanks for the question.

Yes, but i think the word Universe should be reserved for ‘all that exists’.

Having more than one Universe is like saying ‘two times infinity’ - it is still infinity…

Raphael Neelamkavil,

you have not understood how a universe can be created. In the picture I have given galaxies are created at random. They move outwards and in doing so they may also clump together by the standard gravitational force. This is just a natural stochastic process.

One universe is enough.

Hans Gennow,

You are correct! I did not "understand" how "galaxies are created at random" from where or what. The "how" or the "that" they are created -- that alone does not suffice, at least to my mind.

Do you know if this creation is infinite and eternal, or only for a few times? Are these by causality or non-causality? You might say that since they are random, they are just non-caused, and are just occurring without causation. I do not claim that you hold so. There seem to be hundreds of physicists who hold so. I wait for clarity on these things.

Declan Traill, a finite-content universe is not an infinite-content universe. Hence, there does not seem to be a problem in what I said.

Raphael Neelamkavil,

if you do not want to understand I cannot help you. I have explaind how the fundamental particles can be created through a stochastic process. As a biproduct the cores of the galaxies will be created which in turn accrete debris to form the galaxies. Everything will move outwards and galaxies may very well clump together in a natural way (randomly).

The probability for such a process should be quite small. However as I said such a process might have occured many times leading to other universes. But how can we know?

Just think that you are the result of random processes. Discusting? The DNA was build through a chain of random processes. It was not created in one go by some supreme being.

Just read my books and learn.

Hans Gennow, I am happy with the first paragraph of your reply.

My difficulty is only about the attribution of randomness to existing physical processes. I can accept if randomness is randomness due to our mathematical inability to capture all the details of whatever happens in a process. But if there is no causation in the physical processes, one can even call randomness as non-causal randomness in the very physical universe. This is what I find it difficult to understand.

Raphael Neelamkavil,

we cannot calculate a random process by mathematics. We can only estimate the probabilty for a certain outcome.

Just think you through a pair of dices. Then repeat. The second trial is completly independent of the result of the first trial.

In the case of dice, the procedure of "throwing the dice and having the results calculated" can be random. But the very movements of the dice when I throw them is not random They are completely causal -- not determined by my calculations but by the very movements caused by my physical act of throwing.

Similarly, the happenings in the universe are not random. They are fully causal in the very way in which they happen. The stochastic calculations (the procedures) of those processes (not the procedures of calculation) can be made stochastically. What do you think?

WHAT ARE VIRTUALS IN SCIENTIFIC THEORIES?

CRITERIA TO DIFFERENTIATE THEM?

Raphael Neelamkavil, Ph. D., Dr. phil.

Existents in Extension and Change are physical, not virtual. Space and time are just the epistemic notions of the physical-ontological Extension and Change respectively.

A DENOTABLE has reference to something that either (1) has physical body (physically existent processes), or (2) is inherent in bodily processes but are not themselves a physical body (e.g., potential energy), or (3) is non-real, non-existent and just a mere notion (say, a non-physical possible world with wings, or one with all characteristics absolutely different from the existent physical world).

(1) belong to existents. They are existent Realities. They are matter-energy in content. (2) belong to non-existent but theoretically necessary Realities. (3) are nothing, vacuous!

DIFFERENCE between non-existent, real virtual, and existent denotables:

Non-existents have no real properties, and generate no ontological commitment. Real virtuals have the properties that theoretically belong to the denotables that are lacunae in theory, but need not have Categorial characteristics. Existent denotables have Categories (characteristics) and properties. These are Extension and Change.

Hence, virtuals are versions of reality different from actual existents. They are called unobservables. Some of them are non-existent. When they are proved to exist, they become observables and are removed from membership in virtuals.

Theories yield unobservables (elctrons, neutrinos, gravitons, Higgs boson, vacuum energy, spinors, strings, superstrings …). They may be proved to exist, involving detectable properties.

Note: properties are not physical-ontological (metaphysical) characteristics (Categories). Instead, they are concatenations of Ontological Universals.

Virtual unobservables fill the lacunae in theoretical explanations.

As is clear now, the tool to discover new unobservables is not physical properties, but the physical-ontological Categories of Extension and Change. Virtuals are non-existent as such, but are taken as solutions to lacunae in rational imagination.

Discussion in ResearchGate:

https://www.researchgate.net/post/What_Are_Virtuals_in_Scientific_Theories_Criteria_to_Differentiate_them

Raphael Neelamkavil "At any time in an infinite multiverse..."

Before we consider something infinite, we should check if something finite also could do the job. The job is explaining cosmology.

The finite thing, we should consider is a 3-sphere structure of the universe.

A 3-sphere does not have a surface or an outer rim. It has a constant scalar curvature 1/R² and a volume of 2π²R³. The symmetry is that high, that every point is the centre of gravity of the whole volume. Because of this symmetry we can exclude a gravitational collapse for a universe with this structure.

A universe of this structure cannot lose anything to the outside or can get something from the outside. It is hermetically sealed.

Wolfgang Konle, Raphael Neelamkavil

'every point is the center of gravity'

A 3- sphere universe fits also when the center of gravity of all celestial bodies has a zero gravitational potential. Newtons' shell theorema leads to this conclusion, at least for spherical bodies. In this case the total gravitational energy of the universe is zero and the universe is thermodynamic stable what is suggested by the black body spectrum of the CMB.

Wolfgang Konle, Willy Verhiest,

I did not claim that the universe is infinite. Instead, I treat of the case where the universe is finite and the case where it is infinite in content. In content, not in the spherical mathematics that is attributed to it. After claiming that the universe is "3-spherical", you can claim many more conclusions. But first we should know that it is "3-spherical". And is this as a possible case? If so, which are the other possibilities?

Raphael Neelamkavil "But first we should know that it is "3-spherical". And is this as a possible case? If so, which are the other possibilities?"

If the universe is eternal, there are no other possibilities.

If not, we can assume what we want.

Willy Verhiest "A 3- sphere universe fits also when the center of gravity of all celestial bodies has a zero gravitational potential."

Sorry, but a 3-sphere geometry has nothing to do with celestial bodies. It is a purely geometrical consideration. It also has nothing to do with a potential.

If in terms of large distances celestial bodies are equally distributed in the 3-sphere volume, any point in this volume also is a centre of gravity of the celestial objects.

In this respect, "the centre of gravity of all celestial bodies" does not exist within a 3-sphere geometry.

Wolfgang Konle, you said:

"If in terms of large distances celestial bodies are equally distributed in the 3-sphere volume, any point in this volume also is a centre of gravity of the celestial objects."

How can celestial bodies be equally distributed at the large scale, if at small distances they are not equally distributed? So, your first assumption is evidently difficult to accept.

Hence, the paradoxical assumption of any point becoming a centre of gravity does not arise!

Raphael Neelamkavil "How can celestial bodies be equally distributed at the large scale, if at small distances they are not equally distributed? So, your first assumption is evidently difficult to accept."

This can be easily explained. We calculate the mean density of matter within a certain radius. If the radius becomes larger and larger, the deviations of the mean density become smaller and smaller. As soon as they are small enough to be practically equal to a homogenous value, then at this large scale the celestial bodies are equally distributed.

Wolfgang Konle,

"Calculating the mean density of matter within a certain radius" and "the deviations of the mean density becoming smaller and smaller" are not any guarantee for matter-energy density to be equally distributed. I came to this conclusion soon after 1980, as a schoolboy, as I read for the first time about the big bang and other theories, and cosmological isotropy, anisotropy, etc. And when I read of the steady state theory, I felt confirmed.

Let me state the matter slightly differently: The homogeneity, isotropy etc. are given in the choice of mathematics, and not in reality.

I think we need a theory of extent and manner of application of math and statistics to physics, cosmology, and other sciences.

Raphael Neelamkavil "Calculating the mean density of matter within a certain radius" and "the deviations of the mean density becoming smaller and smaller" are not any guarantee for matter-energy density to be equally distributed."

It seems, that you do not understand the 3-sphere geometry. This geometry guarantees that a radius exists, which leads to an equally distributed mean mass desity within the complete 3-sphere.

This radius simply includes all mass. The inclusion is complete from any point within the 3-sphere volume.

Thanks. But the supposed homogeneity is what induces the physicist and mathematician to take the shape of the universe in terms of the 3-sphere model. Such a distribution is only an averaging-phenomenon, not the reality! Hence, the commonsense merits of the geometry does not correspond to the reality. And energy must escape the universe in the course of time, since it is not the geometry that determines the movement of energy outwards.

Raphael Neelamkavil,

nothing will escape the universe. As I have predicted the universe will start to retract some day. If something escapes, conservation of energy will be broken.

Raphael Neelamkavil "energy must escape the universe in the course of time"

This is just contradicting eternity. Only the 3-sphere structure seals the universe hermetically and therefor allows an eternal existence.

Hans Gennow "As I have predicted the universe will start to retract some day."

Having a 3-sphere structure, the universe will never retract.

An eternal existence of every part of the universe together in close vicinity to each other is not guarantee by the gravitation of the universe. The 3-sphere math might permit it. But before that, you should show that only this math is applicable to the cosmos.

Wherever matter-energy from within this cosmos is, there -- in constant motion -- they all can exist! If there are other similar universes, they may absorb some of the energy lost from our universe and vice versa. And then will not the energy from this universe exist in another universe for the future eternity?

You have been insisting that the universe should have the 3-sphere geometry. Please show first that there is no other way than this geometry!

Wolfgang Konle,

conservation of energy do not care about any spheres. Before the original explosion total energy was 0. After that total energy was still 0. The cause is gravity.

Raphael Neelamkavil,

If our universe would overlap with another one, we have to add them up to make the equation right.

Hans Gennow,

True. Before the original expansion began, the total potential energy may have been zero. Some might say it was infinite, so as to make the expansion possible in each universe!

But the actual energy of each finite-content universe cannot be zero or infinite. It must be finite, because the total matter is not infinite, and hence the equivalence with finite energy.

Is Mathematics an Exact Science? If Yes, and If Not, Why?

Why are numbers and shapes so exact? ‘One’, ‘two’, ‘point’, ‘line’, etc. are all exact. But irrational numbers are not so. If notions like ‘one’, ‘two’, ‘point’, ‘line’, etc. are defined to be so exact, then it not by virtue of the exactness of these substantive notions, but instead, due to their being adjectival: ‘being a unity’, ‘being two unities’, ‘being a non-extended shape’, etc. A quality cannot be exact, but may be defined to be exact. It is in terms of the exactness attributed to these notions by definition that the adjectives ‘one’, ‘two’, ‘point’, ‘line’, etc. are exact. This is why the impossibility of fixing these (and other) substantive notions as exact miss our attention. If in fact these are inexact, then there is justification for the inexactness of irrational numbers too. If numbers and shapes are in fact inexact, then not only irrational numbers but all mathematical structures should remain inexact except for their having been defined as exact. Thus, mathematical structures, in all their detail, are a species of qualities, namely, quantitative qualities.

https://www.researchgate.net/post/Is_Mathematics_an_Exact_Science_If_Yes_and_If_Not_Why

Raphael Neelamkavil "You have been insisting that the universe should have the 3-sphere geometry. Please show first that there is no other way than this geometry!"

Yes, the 3-sphere is a relevant geometry for the universe, which hermetically seals the universe from any outer influence. This guarantees energy conservation.

But showing the non-existence of another way is not an applicable option. The only possible option is to find another way. But I would be surprised if you would be successful in that task.

Hans Gennow "conservation of energy do not care about any spheres. Before the original explosion total energy was 0. After that total energy was still 0. The cause is gravity."

It is a fact, that a 3-sphere does not have a surface. Without a surface, energy cannot pass the surface. The Gauss' law then ensures the global conservation of energy.

Raphael Neelamkavil "‘One’, ‘two’, ‘point’, ‘line’, etc. are all exact. But irrational numbers are not so."

Irrational numbers are exact as well. The square root of 2 is an exact number. If squared it exactly gives 2. Only the decimal representatin is not exact. But the decimal representation of 1/3 also is not exact because the number of digits must be finite.

But there is a thread in RG about the occurrence of irrational numbers in nature. "Do irrational numbers exist in nature?" asked by Andre Gontijo Campus, May 24, 2018.

Wolfgang Konle, thanks. You said it well. I wanted only to give an example, and that was irrational numbers.

"If squared it exactly gives 2. Only the decimal representation is not exact." Exactly this is what I meant.

I have seen the question "Do irrational numbers exist in nature?" asked by Andre Gontijo Campus. I appreciate the reminder.

While working on something, and when I move to correct the texts, I feel a bit of boredom. Then appear a good intuition. I write it down in a few paragraphs and post it in RG. This is the style of working for me in these my discussion sessions. Hence, there will be lack of exactness in them. Not that I am perfect in other works. If I had been, I would not have worked on my new books again and again and not have accused myself of being inattentive!

Wolfgang Konle, I may not be successful in the search for an alternative math for the cosmos. But there do exist many. The 2-sphere stuff looks a bit too Newtonian.

Raphael Neelamkavil "The 2-sphere stuff looks a bit too Newtonian."

Is it a typo or intentional? We are talking about a 3-sphere!

A 3-sphere is a geometrical object, which is described mathematically. But nobody can produce a model of a 3-sphere. Surely a 3-sphere has nothing to do with "Newtonian" or "Einsteinian". A 2-sphere is the surface of a ball.

Wolfgang Konle, but if there are specific boundaries for the universe, from beyond which all the energy lost must automatically return, or beyond with energy will not move, is already a spherical boundary. This is what I meant.

Raphael Neelamkavil "but if there are specific boundaries for the universe..."

No, there are no boundaries at all, if the universe has the structure of a 3-sphere.

In that case, every part of the finite-content universe will lose some energy, which is never to be brought back into that universe but will continue to exist out-there!

And if there are other universes at finite distances? (There cannot exist other universes at infinite distances from any other.) In that case, they will have to exchange energy, including gravitational. Some of them will attract each other ever stronger due to gravitational circumstances similar to those between galaxies and other more massive structures.

If the number of other universes is the finite, then the state will eventually be the same as in the finite-content universe. They will all coalesce into one. And if there are an infinite number of such finite-content universes?

It is here that we have the following: At any time (relative at least to a finite number of such universes), there will be an infinite number of gravitational coalescences, which, at those durations have no gravitational contact with an infinite number of others or other conglomerations of universes.

This is what I called the Gravitational Coalescence Paradox. Is there a solution for this paradox?

Now, I believe you will not say that all these are imaginary cases. If you say so, there is nothing wrong in claiming that the 3-sphere math too is just an imagination!

Raphael Neelamkavil

There is no excess gravitational energy in the universe. In my preprint on RG 'Gravity and electrostatics' I come to the conclusion that the center of a spherical celestial body has zero gravity, the gravity field has maximal force at its surface and is fully compensated by its motion force as the CMB ( the ultimate red-shift ) spectrum indicates thermodynamic stability in the universe.

Raphael Neelamkavil "In that case, every part of the finite-content universe will lose some energy, which is never to be brought back into that universe but will continue to exist out-there!"

No, in that case, the case of a 3-sphere geometry, the finite-content universe will not lose any energy. Local lost of energy without a flow across a surface is excluded by the energy conservation law.

"And if there are other universes at finite distances?"

We should not care because they are isolated as well.

The conservation law does not state what you said. It means in general only that energy is not to be created or annihilated. Loss of energy from one universe is not annihilation.

I do not understand what else you mean by "Local lost of energy". Could you please clarify? Or, at least write a sentence in your mother tongue, which I believe is Deutsch.