Anatomy of spacetime and possible origins of internal symmetry and all particle quantum numbers

Dear Professor Mattfolk,

Sorry, not sure why the attachment cannot be opened. I am attaching an earlier pdf version and a WORD version. See if any works.

I will write more about the sub-geometries soon.

Kwan Chiang

12/12/21

Dear Professor Mattfolk,

Sorry, it appears neither version works, probably because something wrong in the interface between my computer and FQXi site.

If you can send me an email at: qchiang2@yahoo.com , I can send you a copy from there. Thanks.

Best regards,

Kwan Chiang

12/12/21

Dear Professor Mattfolk,

Yes, the sub-geometries are critical. Just like linear scales, if there are not 6 magnetic and electric fields running among the 4 linear axes to define the equivalencies among the 4 linear scales, light would not be measured at equal speeds in different directions, symmetry would not happen and photon would not be generated.

In the same way, there must be fields running among the 6 planes to define equivalencies among the 6 plane angle scales. Otherwise, a full circle on xy-plane may be 360 degrees while that on yz-plane is 362 degrees and the space is warped and the 4 linear axes are not perpendicular to each other. There is SO(6)~SU(4) symmetry from this sub-geometry. It's SO(10)~SU(5) for 5d spacetime.

These fields (conjectured to be weak fields) may be called solid (3d-) angle rotation fields, which run among plane (2d-) angle scales. One level deeper is 4d-angle rotation fields (CP-violation fields), which run among solid (3d-) angle scales. Yet another level deeper is 5d-angle rotation fields (strong fields), which run among 4d-angle scales. Without these 3 levels of sub-geometries, the linear spacetime on top would be warped and no perpendicularity among axes.

For 11 dimensions, there are 55 planes and 55 plane angle scales, which require real fields running among them to define their equivalencies. Without real fields running, the 11d space is warped and 11 axes cannot be perpendicular. But, it seems string physicists simply assume the 11 dimensions are "automatically" perpendicular, which is NOT possible.

Actually, there is no need of micro dimensions at all, as the 3 levels of sub-geometries already generate complete SO(10)~SU(5) particle spectrum without quarks.

Best regards,

Kwan Chiang

12/12/21

Dear Professor Dufourny,

Thank you sharing your ideas, although I don't quite understand. It seems interesting as it is related to the large numbers of Dirac, which I thought about sometime as well. I believe there should be a relation between these numbers. If there are other universes, these numbers could be different, but the relation should hold.

By the way, I am not quite sure about the meanings of these abbreviations: EFE, DE, DM. Thanks for explanation.

Best regards,

Kwan Chiang

12/13/21

Hi Dr Chiang,

I have searched answers since the age of 18 , I am 46 years old,I have so read the religious books but of course it was not sufficient and I find these religions not the truths. I have after read the philosophes , I like kant and spinoza but they are too limited about the origin of this universe, so I have ranked the sciences, maths, animalsm vegetals, minerals, chemistry , biology, evolution...and it is like this that I found my theory of spherisation, an evolution optimisation of the universal sphere or future sphere with quantum and cosmological 3D spheres. I consider an infinite eternal consciousness before this physicality, I don t know why this thing has decided to create this universe but I have remarked enormous philosophical problems in considering only the photons, the strings and the general relativity and the einstein fields equations.

That is why I consider a central cosmological sphere in 3D , a kind of super matter energy able to send all informations in the series of 3D spheres. If I have considered these series having the dirac large number, it is simply because I have calculated this number of cosmological spheres and it approachs this dirac large number, and so I have consider liek an universal choice the same number for these series. I have considered 3 main finite series , the serie of this Dark energy for the main codes of the vacuum and the 2 others are like fuels , the photons and the cold dark matter . I have considered simply that the photons had more energy than mass and the DM the opposite and when they are encoded in this vacuum possessing the main codes, so they create the baryonic matter. I have considered when they merge that the number does not change, nor the volumes, so it becomes relevant for the motions oscillations, densities, senses of rotations, angles......like I told you the deformations are made with the codes of this vacuum and they preserve the volumes with the synplectomorphisms.

I have remarked in considering a kind of infinite eternal cosnciousness that we have problems with the fields and oscillations of photons only, it seems not possible considering a kind of god , of course it is just my opinion, I don t affirm to possess the truth, but if a thing having been able to create a so complex universe with oscillations and fields , so this thing was able to create a more perfect universe more quickly and it is not the case, this thing that we cannot define has not made this and fruthermore it does not stop for exmple a murderer or other sad things with oscillations, so it is not possible for me that we have the fields , strings and oscillations to explain these topologies, geometries and this emergent consciousness.

For the multiverse I have thought about this, indeed the maths of Tegmark or others seems to imply this, but we don t know and already this universe we don t know well, so there are for me speculations not proved , and even with multiverse, we return at a kind of uniqueness if all is connected with this unique infinity. In fact all this is beyond our understanding still.

You know Dr Chiang, I believe that our main error is really to consider the philosophy alone of this GR, and photons. The universe seems more complex than this and if the universe has 3 spacetimes due to the dark matter and the dark energy superimposed in a superfluidity due to specific volumes for the 3 main series, that permits to return at this old school for the motions of particles instead of fields like primary essence, your idea so interest me in the sense that the primoary geometry can be the shere and so your subgeometries could converge.

Best Regards

You know Dr Chiang, I don t affirm of course about this infinite eternal consciousness, I respect the persons having chosen an other line of reasoning like a mathematical accident from a kind of infinite heat. But The hard problem of consciousness like other problems seem to need this parameter.

Why we exist, why we are , from what ? what is this universe really and why ? it seems that we are simply in a kind of project in evolution and that we are tools due to this consciousness like the particles and the comsological spheres too are tools . The energy is transformed and the informations and this evolution permit a specific universal mechanism. We don t know a lot still , we just analyse soem emergent properties with the electromagnetis, the general relativity, the thermodynamcis,....we have many things to add , the problem unfortunally is limitations in knowledges and in philosophy but the generality of the QM and the cosmology and philosophy give us roads .we try after all to add concrete pieces to this puzle in hoping to converge with the truths rationally speaking.

Dear Professor Mattfolk,

I am deducing the logic leading to the sub-geometries step by step here.

1, I think the ultimate theory is hidden behind Einstein's question, "The most incomprehensible thing about the world is that it is comprehensible", since this is a question about the ultimate nature of physics. My interpretation is that the great master wouldn't believe the world is intellectual designed, but he couldn't explain why it looks as orderly designed and who designed it. Even though Einstein didn't give an answer, it still offered a direction and I don't think this is an unanswerable question.

2, In fact, Weinberg answered it half way in a prescription for the theory of everything, "... [it] has to be simple ... equations that are based on a simple physical principle ... it has to give us the feeling that it could scarcely be different from what it is..." [1] (that is, it is based on one unified principle and is non-designed, but simply cannot be otherwise, e.g. electromagnetism.)

3, Therefore, the problem is not that Einstein's question cannot be answered, but that, for strong, weak and gravitation forces, there exists no theory as un-designed as EM. (Unfortunately, neither standard model nor general relativity looks as un-designed.)

4, In order to reach un-designed theories, it's important to note that certain critical concepts must NOT be assumed, because assumption is subjective and leads to intellectual (human-, not God-) designed theories.

5, Actually, two unnoticed assumptions exist in today's physics, namely, 1. Pre-assumed plane angle scales (i.e. automatic space flatness, axes perpendicularity and existence of symmetry) without physical definition, which leads to "designed" Standard Model. When we wonder why Standard Model looks like designed. The reason is simple: because it is in fact designed, not by God, but by ourselves. 2. Preselected inertial frames in special relativity leading to "designed" GR.

6, Let's consider the first assumption. What does it mean by "pre-assumed plane angle scales"? Take 4d spacetime (and EM) as an example. Special Relativity used light speed to define the 4 linear scales. What was not mentioned is the 6 circular magnetic and electric fields running among the 4 axes which define the "equivalencies" among the 4 axes. Without this definition, light would not be measured at equal speeds in different directions, rotational symmetry would not exist and photons cannot be generated.

7, Then, what are the fields running among the 6 "planes" to define the equivalencies among the 6 "plane angle scales". Just like linear scales, these equivalencies cannot be assumed, but "must" be defined by real physical fields running among the 6 planes. These fields are conjectured to be the "classical" weak fields. We may say these fields are running in solid (3d-) angles among planes (2d-surfaces). When equivalencies among plane angle scales are defined by 3d-angle rotation fields, an SO(6)~SU(4) (or SO(10)~SU(5) for 5d spacetime) symmetry surfaces, which is just the observed particle spectrum (without quarks). The relation between weak fields and plane angle scales are exactly the same as that between EM and linear scales, making weak fields as un-designed as EM.

8, Likewise, there are two more levels of sub-geometries: fields running in 4d-angles among 3d-surfaces, which is conjectured to be CP-violation fields, and fields running in 5d-angles among 4d-surfaces, which is conjectured to be strong fields. Rotations in 5d-angles are believed to be causing baryon and various lepton numbers. The "relation between CP-violation fields and 3d-angle scales" and "the relation between strong fields and 4d-angle scales" are also the same as that between EM and linear scales, making CP-violation and strong fields as un-designed as EM. Details are in reference [2], "Theory of Fields of Unified Origin (TFUO)".

9, If the 6 (or 10) angle scales are not defined to be equivalent by weak fields, a full circle on xy-plane may be 360 degrees, while that on yz-plane may be 362 degrees, then the 4d-spacetime would be warped and perpendicularity of axes cannot exist and symmetry would not surface. To be more precise, without TFUO, or 3 levels of sub-geometries, linear spacetime on top would be warped and perpendicularity of axes cannot exist and symmetry would not surface.

10, In TFUO, strong, weak, CP-violation and EM fields are all originated from the same principle as Weinberg prescribed (each defining a critical scale). Electromagnetism would be as complicated as other forces if not for the change of geometry by Special Relativity. What sub-geometries do to other forces is exactly the same thing as what Special Relativity does to electromagnetism. At the same time, complete particle zoo is generated from all layers of geometries. This is a big achievement through removal of assumption of automatic equivalencies of plane angle scales (or space flatness, or axes perpendicularity, or symmetry presence). We see assumption often deprives us of otherwise possibility to uncover real nature of physics.

11, It is important to emphasize that, whether it's 4d, 5d, 11d, or 26d, there cannot be automatic flatness of space, automatic perpendicularity of axes and automatic symmetry, unless sub-geometries exist to support them. (It may be possible in mathematics but not in physics, because two persons could define differently, but physics will only follow what is defined by Nature). Take 11d as an example, if the (11x10/2=) 55 plane angle scales are not made equivalent to each other by fields running among them, then the space would be warped and perpendicularity of 55 axes is lost and the 11d symmetry would not surface. Simply put, the wished-for 11d symmetry wouldn't exist if sub-geometries don't exist. But if sub-geometries exist, 11d micro dimensions are no longer needed, because the sub-geometries already offer all the symmetries needed for particle spectrum. In fact, the 11 micro dimensions are never observed. (Also, the sub-geometry of 55 planes should generate SO(55) spectrum, which is not observed either.)

12, For reason of completeness, the gravitation part of TFUO is included here. Let's consider the second assumption, "preselected inertial frames". It is well known that inertial frames (uniform frames) are "preselected" before spacetime scales are defined by light waves to verify uniformity. Removal of this assumption leads to 5d spacetime [3].

To be published is the ultimate non-designed 5d gravitation, which is "linear" and quantize-able based on the 5d-spacetime. It meets all 3 famous tests just like GR. Note that, the 3 tests: bending of light, perihelion motion of Mercury and gravitational red shift, did not test GR completely, as they are all based on Schwarzschild solution with Einstein/stress-energy tensor set to 0. This means the exact "non-0 expression" of Einstein/stress-energy tensor has not been tested, since a different expression (e.g. this 5d linear gravitation) could work just as well, as long as it can be set to 0 in these situations. The 5d gravitation eventually joins TFUO to form the ultimate theory, which answers Einstein's ultimate question.

There are reasons to believe this theory is "not" just another fancy idea, but is THE long-sought-for ultimate theory, as: 1. It meets Weinberg prescription for the theory of everything, as all forces originate from the same principle (i.e. each defining a critical geometrical scale). 2. It is able to answer Einstein's ultimate question, as intellectual designer is eliminated, since this is a non-designed theory for all forces and particles, just as EM and photons. 3. While more verifications are needed, the symmetry, SO(4) or SO(5), is already met with particle spectrum without quarks. 4. Linear gravity can be quantized. 5. The most important and most strong evidence is that no micro dimensions are observed for any symmetry for standard model or string theory or whatsoever. On the other hand, the sub-geometry is the most (or the only) plausible explanation for particle symmetries.

If you have other questions, we may discuss further. If you find it makes sense, your dissemination would be appreciated.

Since the paper attached through FQXi seems not working, you or anyone can just send an email to: qchiang2@yahoo.com , I will send a copy from there.

References

[1] Steven Weinberg, "Will a theory of everything reign?", TIME April 10, 2000, p. 86.

[2] Kwan C. Chiang, "Anatomy of spacetime and possible origins of internal symmetry and all particle quantum numbers", Physics Essays, Vol. 33, N.3 p342-347, 2020.

[3] K. C. Chiang: "A Unified Gravitation and Quantum Mechanical Space-Time Structure through a Unified Origin of Inertial and Gravitational Masses and a discussion of the Foundation of Special Relativity", Il Nuovo Cimento Vol. 68B, N.2 p322, 1982.

Dear Professor Dufourny,

I admire your deep thinking very much. Your theory has a comprehensive coverage of many aspects of today's complicated physics.

As I mentioned earlier, today's physics is based on certain assumptions. Since different assumptions lead to different theories and universes, it's hard to tell which the truth is. However, I think Nature has its own answer, which has these assumptions removed, as assumptions deprive us of the otherwise possibility of uncovering the real Nature.

I think about the same philosophical puzzles as well. I try to answer them with the simpler sub-geometries, which has the assumption of automatic axes perpendicularity removed.

As you know, electromagnetism was simplified because of geometry change by special relativity. Without special relativity, electromagnetism would be as complicated as other forces. What sub-geometries (TFOU) does to strong, weak and CP-violation forces is exactly the same thing special relativity did to electromagnetism. In my opinion, physics being complicated is not because of its own nature, but because of "wrong" geometry is being used.

I posted a reply to Professor Mattfolk, which deduce the complete logic. As you would see there, it is only a wishful thinking to have 11d symmetry in a flat 11d space with its axes perpendicular, unless sub-geometries exist to support these wishes. But if sub-geometries exist, there is no need of 11d symmetry anymore because the sub-geometries already offer all the symmetries needed to account for the whole particle zoo.

Same with gravitation. When assumption of inertial frames is removed, it inevitably leads to a 5d spacetime (extra dimension, xm, is a macro dimension, not micro dimension). Based on the 5d spacetime is 5d gravitation, which automatically answers many puzzles. There would be no dark matter, most likely no dark energy either. It should answer particle-antiparticle disparity as well. (It's not hard to imagine if there are 4 spatial dimensions, parity should be conserved in 4d, not just in 3d, which answers parity violation and particle-antiparticle disparity automatically.)

Best regards,

Kwan Chiang

12/15/21

Dr. Kwan Chiang,

Apart from any argument supporting a physical reality of SpaceTime as the progenitive condition (my own personally preferred paradigm), I noticed that you and others commenting have not broached the subject of the conventionally accepted assumption that gravitation, and electromagnetism extend to infinity.

This has always perplexed me, in that for any primary force effect to diminish continuously to infinity would require either that some medium exists independent of the force effects and responds to an infinite distance to an infinitesimal degree, OR that the energy of a unitary field particulate mass would be infinite itself to provide for the required energy for that force effect to translate across distance to infinity. So, as one of the baffling gaps in Classicism that migrates into QM, the question beggs resolution, and quantum gravity may require it.

While SR is mathematically complete, it is far from physically complete. Paradox burgeons forth from the invariant formulated 2D geometry of SR. Yet, as a reduction to first principles, the equivalence principle in the bounded interval of light velocity provides a realistic rationale for theorizing a finite energy capacity in any unitary field particle. GIVEN: that density of energy is a function of velocity, a rest mass accelerated to light velocity would not be mass long before it reached light velocity, it would become a volume of inertially bound energy of extremely low density. By the same token, a rest mass unitary field would extend beyond the volume of material density and that continuous gradient of density would be commensurate with a continuously increasing inherent relativistic velocity. Time would be going ever faster to equalize at light velocity at the minimum density limit of the field. If Time were existent at c, no physical motion of the field would be necessary or even possible. Relativistically, a Quantum Gravitational field would be one in which the speed of Time in an inertially bound mass would increase from nil at proportional maximum density to equivalent light velocity at the zero boundary of some empirically derived theoretical density minimum necessary to translate inertia. Hi again, Steve! best jrc

Dear Dr Chiang , thanks for these words.

I share the same points of vue about these assumptions and models.That said indeed this nature has a specific unique universal mechanism. I must say that your ideas intrigue me about these subgeonetries. I ask me if it could converge with these 3D spheres like foundamental objects. It is thre that your works is relevant when we consider that without special relativity, the electromagnetism would be as complicated as other forces.So I think it is very interesting that these sub-geometries (TFOU) does to strong, weak and CP-violation forces. That is why these quantum spheres like subgeometries could converge in considering their properties, motions, oscillations, deformations, with the poincare conjecture and the deformations with the symplectomorphisms all under main informations somewhere in codes, I consider the vacuum ,but if you have an other idea for kind of hidden variables , that seems possible to converge.

This 11D so being not necessary, so this 3D and the time for the motions and changes and Spheres can be suffient for the subgeometries, maybe the most difficult is to find the cause of the main informations. I know that you don t consider this DE and DM, but maybe this space vacuum of this DE possess these codes and informations giving the properties of these subgeonetries and correlated spherical topological geometrical algebras.The difference with the geom alg of lie or clifford so is philosophical about the origin of the universe, in considering particles in a superfluidity and 3 spacetimes instead of this GR alone and the fields. The pure 3D at all scales could answer at my humble opinion and these subgeonetries in 3D so also.

I am intrigued too about the 5D and the convergences with Kaluza Klein and the origin of this balance particles antiparticles. And this quantum gravitation too, I told me that the error of many is to consider still only this GR and the fields , and so the gravitons like quanta of gravitational waves,we could simply respect this newtonian mechanic in changing the distances and in considering quantum BHs and a fith force like if the SM was encircled by this gravitation, and so the gravitons are different and we just change the distances , we take the distances between a graviton and a quantum main BH. I have reached the QG like this in fact, I will publish in 2022 correctly with the spherical geometrical topological algebras. That implies that the SM is simply emergent from a deeper cause. Your ideas so are relevant because they are different and innovative and could converge with the geometrical algebras at my opinion and hidden variables not measurable , not observable and non interacting with our actual SM.

Dear Professor Cox,

Yes, your questions are inspiring.

Just as my post replying Professor Dufourny, I think your concern about mass is because the 5th dimension, xm, is hidden. Hence, it can be answered in 5d spacetime physics.

Best regards,

Kwan Chiang

12/17/2021

KC,

5D does seem to be the natural state of things. Where 4D subsumes that natural order is in the apparent arrow of linear Time which commonly is treated as a single dimension. That may be our human experience, but we also treat Time in a number of contexts that belie a deeper existential reality of Time. And of course, when we speak of dimensions, we are really stating that it is we whom are designating something by which we make some measure.

I go back to the rascal in Einstein's character, he really did like to provoke people and gain notoriety, and that has to be taken into account in regards the famous insight he related as envisioning himself riding a beam of light and realized that "Time stopped" at light velocity. Yet in GR we find just the opposite in effect, the rate of passage of Time slows the nearer the worldline is to the center of gravity. I think it is more true to state that Time appears to stop at light velocity from the vantage point of the rider on that beam of light only because light velocity is the limit to the rate of passage of Time. If Time could go faster than light velocity, we would continuously be left in the dark. So The Fifth Dimension in Kaluza-Klein can actually be attributed a real physical characteristic; that rate of passage of Time which is non-linear because it can be anything, anywhere between nil and light velocity, but can also be treated simply as a scalar value of Speed. Rather like a vernier caliper, we have the linear vector value of velocity for anything, calibrated to the non-linear scalar value of the Speed of Time at the point of measurement. best jrc

Dear Professor Dufourny,

Although I don't quite understand your sphere theory, it'll be great if you apply it in 5d spacetime which is free from assumption of inertial frames and in the sub-geometries (TFUO) which is free from assumption of automatic axes perpendicularity and automatic symmetry presence. I'll let you know when I have some new idea.

Best regards,

Kwan Chiang 12/17/2021

Hello dear Dr Chiang,

My theory is simple generally, it is the theory of spherisation, it is an optimisation evolution of the universal sphere or future sphere with quantum and csomological 3D spheres. I have considered them like the foundamental objects. An important point too is that I don t consider only these photons and GR like primoridal essence, I have considered the DM and the DE too like the two other spacetimes, som we have like 3 ethers . I have considered a superfluidity due to specific spherical volumes for these series. The main codes and informations are in the series of this space vacuum of the DE and this vacuum encodes the photons and the cold dark matter to create the baryonic ordibnary matters.

The 5D I have thought about this with the works of kaluza Klein and the planck scale , but I have remarked that we can consider a pure 3D at all scales and that this planck scale maybe is just a mathematical extrapolation not really existing.

These spheres are different than the other geometries, they can even create all the other geometries and even topolgies if we have a superfluidity with the 3 spacetimes.These spheres with the poincare conjecture are relevant and they are the perfect equilibrium of forces too and they permit furthermore the optimised motions. They are for the coice of the nature and universe, if we observe this universe cosmologically speaking we have just this, spheres, and if the quantum spheres are a reality, it is relevant and can create all shapes , like even the biology with the complexification of evolution.

Maybe we must just consider their motions and oscillations in this superfluidity, in all case they seem really the primordial choice of this universe, thay are not emergent for me the quantum spheres from fields , they are the primordial essence at my humble opinion.

My theory is different than the strings or points of course philosophically and physically but at my opinion they are more logic than the points of strings in 1D at this planck scale with just this GR and fields in 1D too of photons.

I am a little problem for the strings theorists and geometrodynamists , the philosophy is totally different.

The 5D spacetime and the planck scale can maybe consider just the 2 others spacetimes and for the planck scale we can just consider series of 3D spheres in this superfluidity , all is in contact in this logic due to specific series of Spheres with the biggest volume for the central sphere.

What is now important is to understand these main imformations of this vacuum of the Dark energy , a fith force appears even.

Best Regards

You know Dr Chiang, several friends Phd on facebook or linkedin told me but how is it possible that we have not thought about this before. I think that simply they were too much focus in this GR and the strings or the geometrical algebras and so they have forgotten to think beyond the box and maybe too they have forgotten to study the other sciences like the biology, the chemistry, the evolution....when you observe quietly this nature and the creations and the universe, the spheres, spheroids,ellipsoids....are everywhere , it is like if we had two main systems of spheres, the quantum spheres and the cosmological spheres and between we have the creations with the complexifications and the symplectomorphisms of these spheres preserving the volumes.

I have remarked too that the philosophy of osccilations, strings , fields , and these photons and GR alone have enormous philosophical problems. The universe seems to have chosen these particles in a superfluidity for the main informations and systems to build the matters baryonic evolving. It is more simple in this logic than with the fields of this GR and the geometrical algebras. That said the generality of these spheres is more simple but when you consider the 3 ethers and the series of spheres for the 3 main systems the complexity is incredible due to the numbers, variables and changes. It is the meaning of the tool that I have invencted the spherical geometrical topological algebras and the geom alg of lie and clifford and this GR can converge and be ranked too.

Dear Professors Dufourny and Cox,

Just note that the 5th dimension, xm, I talked about is not Kaluza-Klein kind micro dimension, but is a macro dimension. The logic goes like this:

1, The 4d spacetime scales for uniform frames are defined to measure all "lights" at the same speed. But, uniform frames are "pre-assumed" before spacetime scales are defined to justify its uniformity. At the same time, "light" cannot be sorted out from faster-than-light quantum mechanical plane waves until spacetime scales are available to measure their speeds.

2, The remedy is to define uniformity as "being measured by the spacetime scales being defined" and include light and non-light plane waves altogether. Just ask what is the spacetime which accommodates "all plane waves" most naturally? Without being pre-occupied with 4d-spacetime, the answer is a 5d-spacetime, as it accommodates all plane waves most symmetrically AT the "same light speed". It is because plane waves have just one more variable, speed. When the new dimension, xm, is added to account for that variable, all waves are leveled at the same speed, c, in the 5d-spacetime. 4d-Lorentz frame is but a subspace of the most objective 5d-spacetime.

3, This means all plane waves are "massless" and AT light speed in the objective 5d-spacetime. But they are "massive" and faster-than-light when "observed" from a subjective 4d-subspace. That is, mass and gravitation are but "observational effect". It is not necessary to rule out plane waves as they are NOT faster than light under the "most objective" 5d-spacetime.

4, The transformation between 4d and 5d spacetimes is

dx = dx, dy = dy, dz = dz

dt = dt • [(px)2 + (py)2 + (pz)2 ]½ / [(px)2 + (py)2 + (pz)2 + m2 c2]½ ≤ dt

where italics are 5d scales.

5, It is important to emphasize that the objective spacetime without pre-assumptions is 5d, not 4d. That is, 5d-spacetime is primary, which is NOT DERIVED FROM 4D-SPACETIME. On the contrary, 4d is a subspace of the 5d-spacetime. Therefore, between 5d- and 4d-spacetimes, there is not one single transformation for all waves, but a separate transformation for "each plane wave" (similar to SR, where a separate Lorentz transformation exists for each inertial frame).

6，The Philosophy Behind. In order to obtain an objective spacetime, we should let Nature define it by itself without imposing anything subjective. However, by pre-assumption of uniform frames and light waves, SR imposed preference and defined 4d-spacetime subjectively. Put differently, based on the energy-momentum-mass relation, E2 - (px) 2 - (py) 2 - (pz) 2 - m2 = 0 , space (inverse of momentum), time (inverse of energy) and mass can be defined. But there are 5, not just 4, quantities to be defined. All 5 should be defined "simultaneously", none should take precedence over the other. But 4d-spacetime (i.e. E, px , py , pz ) is defined prior to mass by EM, and hence is subjective. Incidentally, mass is made intrinsic, and the "real nature of mass and gravitation cannot be revealed". The subjectivity transforms into GR. What I do here (and in sub-geometries, or TFUO) is to restore the original form of Nature hidden behind assumptions. Without doing this, I doubt very much that quantum gravity and ultimate UFT can be successful. The question Professor Cox mentioned about mass may be unlocked by 5d spacetime as well.

7, The ultimate non-designed gravitation should be based on the 5d spacetime and can be linear and quantized. This 5d linear gravitation should meet the 3 famous tests of GR. As mentioned in my 12/15/21 post replying Professor Mattfolk, the 3 tests: bending of light, perihelion motion of Mercury and gravitational red shift, did not test GR completely, as they are all based on Schwarzschild solution with Einstein/stress-energy tensor set to 0. This means the exact "non-0 expression" of Einstein/stress-energy tensor has not been tested, since a different expression (e.g. this 5d linear gravitation) could work just as well, as long as it can be set to 0 in these situations. The 5d gravitation eventually joins TFUO to form the ultimate theory, which answers Einstein's ultimate question.

8, 5-d Cosmology and Possible Observations. Thus, excluding time dimension, our universe is a sheet of curved 3-surface in the flat 4d-space. To the 3d-sheet is confined everything, including vacuum. Thus, as Professor Dufourny mentioned, vacuum may not be really empty. Furthermore, our universe is most likely the 3-surface of a 4-sphere just like earth being the 2-surface of a 3-sphere. If this is true, there may be several possibilities:

a. Assuming we are at the south pole of the 4-sphere universe and quasars are at the north pole, then the same quasar may be observed from opposite directions (just like two persons traveling from north pole on earth in opposite directions at equal speeds would eventually meet at south pole.)

b. Numerous double quasars may serve as partial evidence, where the whole spherical universe serves as gravitational lens.

c. The scarcity of galaxies before quasar region might reveal the fact that the 3-volume near the pole region is small, as conjectured by this model.

d. Particle-antiparticle disparity can be explained naturally. The 4-sphere universe may be spinning just like earth. Since the local 3-space at any locality is heading in one direction, it is handed and hence causing parity violation and particle-antiparticle disparity,

e. Accelerated expansion (dark energy). The galaxy locations on curved 3-surface charted on a "flat" 3-surface may be distorted just like 2d-map of the 3d-earth is distorted.

9, The 5th dimension, xm, serves as a universally consistent scale which is missing in GR. In fact, I doubt how we can claim there is dark matter without even a universal scale. (Most people believe the assumptions of GR are correct based on the fact that it is tested. But as I mentioned above the tests are not complete.) Related to this is the flat universe puzzle. The fact that the universe is measured as flat already tells that our measurement is problematic. I believe, once xm (of the "non-designed" 5d-spacetime) is used as the universally consistent scale to measure everything, the universe would not be flat and there would be no dark matter, as the universe is a curved sheet according to the 5d spacetime. (It curves in a different way than GR expected.)

Best regards,

Kwan Chiang

12/16/21

Hi Dr Chiang,

Like I told you , I like a lot your innovative approach and this 5D improving the underastanding of this general relativity. It is mainly these transformations 4D to 5D the relevances and the fact that this 5D is primary instead to take this GR 4D like primary. I have a little bit the same kind of reasoning considering the two other spacetimes superimposed to this GR implying that this 4D GR is emergent and just a part of puzzle considering these photons that we observe. The difference in my model is just that I consider not only photons but I consider this DM and DE like foundamentals too . The WIMPS intrigue me , I belive that the interactions are different and that does not really contredict the bell theorem about the local hidden variables.It is just that we need to supeimpose deeper parameters and interactions for our standard model.

In all cases, we cannot still affrim what are the trths, the strings and extradimensions and 2 E8 for the GR and the planck scale , or my spheres or your innovative model or the geometrodynamics with points, it is still beyond our understanding, but I believe strongly that there is a conjecture correlating all this , maybe with the spheres , I don t know but I think strongly that they arethe foundamental objects in a superfluidity due to specific quantum spherical series.

Your work merits for me to be recognised in the sense that like I said it is innovative with a different interpretation of this GR and this 5D, that can converge with the kaluza klein model and even the strings in considering these 2 E8 exceptional groups of Lie. Maybe even that can converge too with my model in considering these spheres and so we don t consider the strings between the particles like the matter antimatter and a string betweem, there is like a conjecture between fields and particles and the primary essence.

I am intrigued too with your idea for this dark energy, I consider an antigravitational push for this DE and that this DE possesses the main informations and codes and it is the space vacuum and this DE encodes so the photons and this cold dark matter to create the topologies, geometries, matters baryonic and correlated fields, so the fields are emergent and not from this GR. But even if I am persuaded, your ideas intrigue me a lot, congrats and thanks for sharing them, friendly

Ps it could be very relevant to have the opinions of Witten and Susskind about all this , they works the strings and the GR and photons only but your ideas and my humble theory could be developed and superimposed , they are good in maths, so there are conjectures and rankings, sortings to predict a kind of relative TOE with the statistics and probablities.

Dr. Kwan Chiang,

The pdf does not seem to get through, so would you please explain and perhaps draw an illustration in words of #2 in the abstract provided in Schindler's introduction of your work. What provides a basis for "six circular magnetic and electric field lines" which you state as "running on the six planes"? What 'circular' fields? Are you proposing that we assign a separate plane to each octant of a sphere defined on the 3 axis orthogonal observed in electro-motive induction, and that those axes are the planar edges? And despite the hyperbolic function identified by Minkowski in the Lorentz Invariance Transformation, are you taking measurement in all four dimensions of Spacetime to be strictly linear? thanks - nonprofessor jrc