K

Kwan Chiang

Hi Steve,

I didn't get involve with quarks and gluons too much, because in my mind, I was always thinking about the 3 sub-geometries which are sufficient to account for the complete particle spectrum without quarks.

Best regards,

Kwan 1/19/22

Hi John and Steve,

When the majority talk about Maxwell equations, it is based on (assumed) well-defined geometrical scales. What concerned Einstein was how the spacetime scales themselves are defined. (What concerns me is the equivalency among these scales.) No theory is meaningful unless scales are defined by correct physics. EM is simplified because spacetime was redefined correctly by special relativity.

But, today and in history, few people think about geometry definitions. Even Lorentz, who found his transformation, did not think about spacetime definitions. Standard Model and strings are based on geometry with no definitions. Just like EM, particle theories and UFT will be simplified and finished when all relevant scales are correctly defined.

When I say 362 degrees, I don't mean it's an anomaly. I mean when plane angle scales are not physically defined, assumption of equal full circles on different planes are but a dream. We dreamed that every circle is 360 degrees, but in fact physically, some of them are 360, some 362, some 356, even though we define all of them to be 360 "mathematically". Different people have different mathematical definitions, but nature doesn't know which to follow. Nature will only follow the one defined by relevant physics. Therefore, unless concrete physical definitions exist, no symmetry would surface as wished.

If you send an email to qchiang2@yahoo.com , I can send you a paper.

Best Regards,

Kwan Chiang

1/15/22

Hi Steve,

Just let you know here that I just sent a message through LinkedIn. I am not sure if it will reach you because I am not familiar with LinkedIn.

Best,

Kwan 1/13/22

Dear Steve,

Yes, I believe there are a lot to explore. I posted a post in FQXi category "Ultimate Reality", topic "The Present State of Physics, Mathematics, and Science" 4 days ago, but haven't seen any response yet. Hope it's still active and more people will join to discuss.

Best

Kwan

Dear Steve,

Since TFUO is the foundation of answering the ultimate reality, I just posted the sub-geometry concepts with perspective of ultimate reality under FQXi category "Ultimate Reality", topic "The Present State of Physics, Mathematics, and Science". Hope more different people will find it interesting.

Best Regards,

Kwan 1/7/2022

here is the paper attached.

The ultimate UFT should be obtained from un-designed theories, which are not Standard Model or General Relativity

Regarding Ultimate Reality, it is most likely hidden in Einstein's ultimate question, "The most incomprehensible thing about the world is that it is comprehensible".

1, 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. While he didn't give an answer, it's an insightful direction and I don't think it's unanswerable.

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 (no designer), but simply cannot be otherwise, e.g. EM.)

3, Therefore, the problem is not that Einstein's question cannot be answered, but that, for non-EM forces, there DOES NOT YET EXIST non-designed theories. (Unfortunately, neither standard model nor GR is non-designed.) If non-designed theories for these forces are found, Einstein's question would be answered.

4, In order to reach non-designed theories, it's important that certain concepts must NOT be assumed, because assumptions are subjective and lead 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. pre-assumed 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, "pre-assumed plane angle scales". Take 4d spacetime (and EM) as an example. Special Relativity used light speed to define the 4 linear scales. Not mentioned explicitly 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 "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 angle scales are thus defined, 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 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 (conjectured to be CP-violation fields) and fields running in 5d-angles among 4d-surfaces (conjectured to be strong fields). Rotations in 5d-angles are believed to be causing baryon and various lepton numbers. The relations "between CP-violation fields and 3d-angle scales" and "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)". More discussions are also in FQXi forum topic Anatomy of spacetime and possible origins of internal symmetry and all particle quantum numbers under category "High Energy Physics".

9, If the 6 (or 10) angle scales are not defined to be equivalent to each other 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. More accurately, 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). EM 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 EM. 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 (i.e. automatic space flatness, or axes perpendicularity, or symmetry presence). We see assumption often deprives us of otherwise present possibility to uncover real nature of physics.

11, It is important to emphasize that, whether 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 defined equivalent to each other by physical fields running among them, then the space would be warped and perpendicularity of the 11 axes is lost and the 11d symmetry would not exist. 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, Let's consider the second assumption, "preselected inertial frames". It's well known inertial (uniform) frames are "preselected" before spacetime scales are defined to verify uniformity in SR. Removal of this assumption leads unambiguously to the "objective" 5d spacetime [3].

13, What is done here (and in sub-geometries/TFUO) is to restore the original Nature hidden behind assumptions. Without this restoration, it's highly doubtful quantum gravity and ultimate UFT can be successful.

14, To be published is the ultimate 5d non-designed gravitation (NDG), which is "linear" and quantize-able. It meets all 3 tests of 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 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 joins TFUO to form the ultimate theory, which answers Einstein's question.

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

With TFUO, we may be in a position to answer Einstein's question and the Ultimate Reality. The triplet: spacetime (with sub-geometries), forces and particles, come together. There is no hard cored particles, they feel like hard cored only because they have half spin, otherwise they would overlap on each other just like photons. (There is no real material objects, all stem from spacetime conceptually.) There is no other creator in the universe. As long as we are in a 4d- or 5d-spacetime, the same particles and forces would surface automatically. The world is like standardized vehicles (particles) powered by standardized engines (forces) running on standardized highways (spacetime and sub-geometries).

Therefore, when I came across FQXi and found it was eager to uncover the ultimate theory, I contacted them, saying the ultimate theory already exists, all needed is just "dissemination" and verification. Thanks to Professor Schindler for setting up a forum topic under High Energy Physics on Sep 9, 2021. Since this is also the key step toward the Ultimate Reality, I take this chance to post this from the perspective of Ultimate Reality.

Since the paper attached seems not working, anyone can send an email to: qchiang2@yahoo.com , I will send a free 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 Steve,

Your willpower is admired. You will achieve your goal.

You are certainly right. A revolution is long due. If FQXi member thinkers know no symmetries come automatically with 11d or 26d, they would certainly join the revolution, especially no micro dimensions are observed at all. As you said, we are not majority and too isolated. To question is how to let them know?

Best

Kwan

Dear Professor Dufourny and Mr. Cox,

Thank you for sharing your opinions.

As you mentioned: we cannot still affirm what are the truths, it's very true, because different "assumptions" lead to different models and universes. Nature doesn't know which to follow. However, my philosophy is that truth will surface when certain assumptions are replaced by concrete definitions, which leads to non-designed theories.

It was contended earlier that linear space with micro dimensions cannot be flat with automatic symmetry presence unless sub-geometries exist and once sub-geometries exist, micro dimensions are no longer needed. In fact, no micro dimensions are observed anyway. Therefore, whether it's spheres or strings, it may be more sensible to apply them at the sub-geometries level. The basic math of the sub-geometries, which is not visible at the linear dimensions level as they are on different platforms, is copied from my paper below:

Appendix A - Grand Plan for Future Development - Outline of Classical 3-d, 4-d and 5-d Angle Rotation Field Theories

Classical 2-d angle rotation fields, i.e. EM theory (for 4-d spacetime)

Lorentz gauge condition,

∂Aµ / ∂xµ = 0 (A1)

There are 6 electromagnetic fields rotating between each pair of the 4 linear axes,

FВµП... = ∂AВµ / ∂xП... - ∂AП... / ∂xВµ (Вµ, П... = 0,1,2,3) (A2)

Classical 3-d angle rotation fields (for 5-d spacetime) (conjectured to be weak fields)

For the 3-d angle fields rotating between planes, there are 10 2-d planes in the 5-d spacetime. Let them be named: px1x2, px2x3, px3x1, px0x1, px0x2, px0x3, pxmx1, pxmx2, pxmx3 and px0xm. Imagine a 10-d superspace with each axis being one of these "plane" angle scales running from 00 , 10 , 20 , 30 , .... 3600 , 3610 , 3620 to infinity. The origin of each axis, 0, could be any chosen 2-d surface on the 3-d spacetime. (It can be transformed if a different 2-d surface is chosen as the origin, 0. As to which side of the 2-d surface is pointing to positive of the axis, it is not rigidly defined here, but must be defined rigidly when detailed math is attempted.) To imitate EM, the corresponding 3-d angle Lorentz gauge condition is:

∂Dx1x2 / ∂px1x2 + ∂Dx2x3 / ∂px2x3 + ∂Dx3x1 / ∂px3x1 + ∂Dx0x1 / ∂px0x1

+ ∂Dx0x2 / ∂px0x2 + ∂Dx0x3 / ∂px0x3 + ∂Dxmx1 / ∂pxmx1 + ∂Dxmx2 / ∂pxmx2

+ ∂Dxmx3 / ∂pxmx3 + ∂Dx0xm / ∂px0xm = 0 (A3)

There are 45 3-d angle rotation fields running among the 10 planes:

GxВµxП..., xО»xПЃ = ∂DxВµxП... / ∂pxО»xПЃ - ∂DxО»xПЃ / ∂pxВµxП... (A4)

(where xВµxП... and xО»xПЃ run among the 10 planes and xВµxП..., в‰  xО»xПЃ)

Quantum fields will be obtained upon quantization of the classical fields.

Classical 4-d angle rotation fields (for 5-d spacetime) (conjectured to be CP-violation fields) (omitted)

Classical 5-d angle rotation fields (for 5-d spacetime) (conjectured to be strong fields)

For the 5-d angle theory, there are 5 4-d surfaces in the 5-d spacetime. Let them be named: qx2x3x0xm , qx1x3x0xm , qx1x2x0xm , qx1x2x3xm and qx1x2x3x0. There are 10 5-d angle rotation fields running between the 5 4-d surfaces:

HxВµxП...xПЃxП†, xО»xОѕxПѓxП‡ = ∂ExВµxП...xПЃxП† / ∂c xО»xОѕxПѓxП‡ - ∂E xО»xОѕxПѓxП‡ / ∂cxВµxП...xПЃxП† (A7)

(where xВµxП...xПЃxП† and xО»xОѕxПѓxП‡ run among the 5 4-d surfaces and xВµxП...xПЃxП† в‰  xО»xОѕxПѓxП‡ )

As observed from any 4-d Lorentz frame, the spatial axes, x1, x2, x3, are distinct from xm and time axes, x0, thus the 10 5-d angle rotation fields are grouped into 4 distinct categories: Rotations between 4-d surface pairs qx1x3x0xm-qx2x3x0xm, qx1x2x0xm-qx2x3x0xm and qx1x2x0xm-qx1x3x0xm are equivalent to each other under spatial rotations and are conjectured to cause baryon number. Rotation between 4-d surface pair qx1x2x3x0-qx1x2x3xm is conjectured to cause electron number. Rotations between 4-d surface pairs qx1x2x3x0-qx2x3x0xm, qx1x2x3x0-qx1x3x0xm and qx1x2x3x0-qx1x2x0xm are equivalent and are conjectured to cause muon number. Rotations between 4-d surface pairs qx1x2x3xm-qx2x3x0xm, qx1x2x3xm-qx1x3x0xm and qx1x2x3xm-qx1x2x0xm are equivalent and are conjectured to cause tauonic lepton number. (The reason for these designation is on the assumption that the more xm and x0 are involved, the more massive the particle is, but need to be verified.)

There are 3 5-d angle rotation fields corresponding to the 3 baryon rotations, qx1x3x0xm-qx2x3x0xm, qx1x2x0xm-qx2x3x0xm and qx1x2x0xm-qx1x3x0xm.

Hx1x3x0xm,x2x3x0xm = ∂Kx1x3x0xm / ∂qx2x3x0xm - ∂Kx2x3x0xm / ∂qx1x3x0xm (A8a)

Hx1x2x0xm,x2x3x0xm = ∂Kx1x2x0xm / ∂qx2x3x0xm - ∂Kx2x3x0xm / ∂qx1x2x0xm (A8b)

Hx1x2x0xm,x1x3x0xm = ∂Kx1x2x0xm / ∂qx1x3x0xm - ∂Kx1x3x0xm / ∂qx1x2x0xm (A8c)

Quantum fields will be obtained upon quantization of the classical fields.

There is a lot of math to be done in the sub-geometries. It would be a good idea to discuss with Witten and Susskind. Do you have contact with them?

I also agree with John. The universe may very well be curved, bending toward the xm dimension. But it is completely ignored because only 4 dimensions are recognized today, just like no one would imagine the 2d earth is curved toward the third dimension unless proved by accurate measurement of longer distances.

If accurate measurement of long distances proves the universe is in fact round, then accurate charting may clarify whether the accelerated expansion is actually an illusion.

Happy New Year and Best regards,

Kwan Chiang

1/4/2022

Dear Professor Dufourny and Dr. Cox,

Shall we take a break during this Christmas and New Year season and resume on Jan 4 in 2022. I'll reply to your posts then. (However, I will check this topic during this time anyway.)

Merry Christmas and Happy New Year!

Best,

Kwan Chiang

12/22/2021

Dear Dr. Cox,

The 6 magnetic and electric fields are simply the 3 circular magnetic and 3 electric fields described by Maxwell equations in empty space, with center at the origin (0,0,0,0),

curl E + (1/c) (∂H/∂t) = 0 (1a)

curl H - (1/c) (∂E/∂t) = 0 (1b)

Special relativity defined the 4 space and time scales by demanding light (which is derived from Maxwell Eqs.) to be measured at light speed. What Einstein didn't mention is that the above two equations also played "implicit" roles in defining the 6 equivalencies (on the 6 planes: x-y, y-z, z-x, x-t, y-t, z-t planes) between the 4 linear axes. Without it, light wouldn't be measured at the same speed.

We always draw lines with scales equivalent to each other on paper. This may be possible in mathematics, but not possible in physics. In physics, scales and scale equivalencies must always be defined by physics activity. (This is also why people always thought 11d would automatically be perpendicular to each other and symmetry automatically exist, which is actually not possible unless supported by proper physics definitions.)

Sorry, somehow the link on FQXi website doesn't work. If you can send an email to: qchiang2@yahoo.com , I can send a pdf copy to you directly.

Best regards,

Kwan Chiang 12/21/2021

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

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

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

Dear Professor Dufourny,

Yes, your questions are inspiring. I think it can be answered in 5d spacetime.

I think the problems lies in the fact that real natural spacetime is 5d. The 5th dimension, xm, is sealed up by 4d spacetime. Using mass to represent what is sealed up behind is just an expedient. As you can see there are 5 terms in the energy-momentum-mass relation, E2 - p2 - m2 = 0. When defined most naturally (i.e. assumption of inertial frames removed, as mentioned earlier), there are actually 5 dimensions. Mass is the momentum of xm dimension. Only by using 5d spacetime, the secret hidden behind can be opened up. The cause of mass, quantum numbers and electric charges in a particle will be revealed from the particle's sub-geometric structure.

Best regards,

Kwan Chiang

12/16/2021

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

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,

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

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 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