On the Role of Einstein-Cartan Gravity in Fundamental Particle Physics:
This site is for comments and questions about our recent paper, entitled “On the Role of Einstein-Cartan Gravity in Fundamental Particle Physics”, which can be found here. A key result of the paper is the following fundamental radius, which is a function only of the Planck length and the fine structure constant:
Abstract of the paper:
Two of the major open questions in particle physics are: (1) Why do the elementary fermionic particles that are so far observed have such low mass-energy compared to the Planck energy scale? (2) What mechanical energy may be counterbalancing the divergent electrostatic and strong force energies of point-like charged fermions in the vicinity of the Planck scale? In this paper, using a hitherto unrecognised mechanism derived from the non-linear amelioration of the Dirac equation known as the Hehl–Datta equation within the Einstein–Cartan–Sciama–Kibble (ECSK) extension of general relativity, we present detailed numerical estimates suggesting that the mechanical energy arising from the gravitationally coupled self-interaction in the ECSK theory can address both of these questions in tandem.
We consider this observation to be a major breakthrough in fundamental particle physics, at least for the following reasons. Our treatment
(1) provides a natural path to solving the Hierarchy Problem,
(2) completes electrodynamics without any divergences,
(3) predicts the fermion radii to be near the Planck length,
(4) determines uniquely the normalization volume for charged fermions,
(5) combines gravity with particle physics in a natural way, and
(6) leads, possibly, to a successful theory of quantum gravity.
As we have discussed in the paper, in our treatment Planck scale physics produces electroweak scale physics in terms of the masses of elementary fermions. That addresses the hierarchy problem. Moreover, since we have a finite radius for electrons near the Planck length, and since we have found the counter-balancing mechanical energy, electrodynamics is complete in our treatment, with the so-called “bare” mass rendered fictitious. Also, renormalization is no longer a necessity (although it can be useful). The normalization volume in quantum field theory is also uniquely determined in our treatment because the radii of elementary fermions are predictable.
As we can see from the Hehl-Datta equation (which is a generalization of the Dirac equation), gravity is coupled to matter via gravitational constant G, through the spin-density-squared term. That is the most natural way for gravity to meet particle physics. Time is thus quantized at the fundamental level by fermions, at least for their proper time. One would expect that eventually electron clocks will replace atomic clocks for the fundamental definition of the second. And similarly, space is quantized at least for the volume of the elementary particle.
We note that in our proposal we have instituted a minimal length in using the Planck length as a cutoff (which we have removed in the new version). Some would claim that this is a direct violation of Lorentz invariance. However, we claim that it only applies to the spacetime that the elementary fermion is itself defining. Question: Is there a minimal length in Nature?
Next, let us address some sign discrepancies we found in the literature. The original Hehl-Datta equation (C’) from their 1971 paper reads as
![\left [ \gamma^{\alpha} \nabla^{\{\}}_{\alpha}- \frac{3}{8}i l^2(\psi^{+}\gamma_5 \gamma^{\alpha}\psi)\gamma_5 \gamma_{\alpha}\right]\psi = im\psi \,,](http://s0.wp.com/latex.php?latex=%5Cleft+%5B+%5Cgamma%5E%7B%5Calpha%7D+%5Cnabla%5E%7B%5C%7B%5C%7D%7D_%7B%5Calpha%7D-+%5Cfrac%7B3%7D%7B8%7Di+l%5E2%28%5Cpsi%5E%7B%2B%7D%5Cgamma_5+%5Cgamma%5E%7B%5Calpha%7D%5Cpsi%29%5Cgamma_5+%5Cgamma_%7B%5Calpha%7D%5Cright%5D%5Cpsi+%3D+im%5Cpsi+%5C%2C%2C&bg=ffffff&fg=000&s=1 "\left [ \gamma^{\alpha} \nabla^{\{\}}_{\alpha}- \frac{3}{8}i l^2(\psi^{+}\gamma_5 \gamma^{\alpha}\psi)\gamma_5 \gamma_{\alpha}\right]\psi = im\psi \,,")
where 
![\left [- i\gamma^{\alpha} \nabla^{\{\}}_{\alpha}- \frac{3}{8} l^2(\psi^{+}\gamma_5 \gamma^{\alpha}\psi)\gamma_5 \gamma_{\alpha}\right]\psi = m\psi \,.](http://s0.wp.com/latex.php?latex=%5Cleft+%5B-+i%5Cgamma%5E%7B%5Calpha%7D+%5Cnabla%5E%7B%5C%7B%5C%7D%7D_%7B%5Calpha%7D-+%5Cfrac%7B3%7D%7B8%7D+l%5E2%28%5Cpsi%5E%7B%2B%7D%5Cgamma_5+%5Cgamma%5E%7B%5Calpha%7D%5Cpsi%29%5Cgamma_5+%5Cgamma_%7B%5Calpha%7D%5Cright%5D%5Cpsi+%3D+m%5Cpsi+%5C%2C.&bg=ffffff&fg=000&s=1 "\left [- i\gamma^{\alpha} \nabla^{\{\}}_{\alpha}- \frac{3}{8} l^2(\psi^{+}\gamma_5 \gamma^{\alpha}\psi)\gamma_5 \gamma_{\alpha}\right]\psi = m\psi \,.")
We contend that the negative sign on the derivative term presents a problem with respect to the sign on the mass term. We suspect that the original equation should be
![\left [ i\gamma^{\alpha} \nabla^{\{\}}_{\alpha}- \frac{3}{8} l^2(\psi^{+}\gamma_5 \gamma^{\alpha}\psi)\gamma_5 \gamma_{\alpha}\right]\psi = m\psi \,,](http://s0.wp.com/latex.php?latex=%5Cleft+%5B+i%5Cgamma%5E%7B%5Calpha%7D+%5Cnabla%5E%7B%5C%7B%5C%7D%7D_%7B%5Calpha%7D-+%5Cfrac%7B3%7D%7B8%7D+l%5E2%28%5Cpsi%5E%7B%2B%7D%5Cgamma_5+%5Cgamma%5E%7B%5Calpha%7D%5Cpsi%29%5Cgamma_5+%5Cgamma_%7B%5Calpha%7D%5Cright%5D%5Cpsi+%3D+m%5Cpsi+%5C%2C%2C&bg=ffffff&fg=000&s=1 "\left [ i\gamma^{\alpha} \nabla^{\{\}}_{\alpha}- \frac{3}{8} l^2(\psi^{+}\gamma_5 \gamma^{\alpha}\psi)\gamma_5 \gamma_{\alpha}\right]\psi = m\psi \,,")
so that when multiplied through by 
![\left [ -\gamma^{\alpha} \nabla^{\{\}}_{\alpha}- \frac{3}{8}i l^2(\psi^{+}\gamma_5 \gamma^{\alpha}\psi)\gamma_5 \gamma_{\alpha}\right]\psi = im\psi \,.](http://s0.wp.com/latex.php?latex=%5Cleft+%5B+-%5Cgamma%5E%7B%5Calpha%7D+%5Cnabla%5E%7B%5C%7B%5C%7D%7D_%7B%5Calpha%7D-+%5Cfrac%7B3%7D%7B8%7Di+l%5E2%28%5Cpsi%5E%7B%2B%7D%5Cgamma_5+%5Cgamma%5E%7B%5Calpha%7D%5Cpsi%29%5Cgamma_5+%5Cgamma_%7B%5Calpha%7D%5Cright%5D%5Cpsi+%3D+im%5Cpsi+%5C%2C.&bg=ffffff&fg=000&s=1 "\left [ -\gamma^{\alpha} \nabla^{\{\}}_{\alpha}- \frac{3}{8}i l^2(\psi^{+}\gamma_5 \gamma^{\alpha}\psi)\gamma_5 \gamma_{\alpha}\right]\psi = im\psi \,.")
In our paper, we have used
which we believe is the correct form for the equation and it also agrees with eq.(2.1) of this paper.
Then, according to the above analysis, Poplawski has the wrong sign on the non-linear term in his eq.(2) of this paper. Perhaps if that sign error had not occurred, he might have discovered the relation that we were able to discover. We also note that the entry on the Wikipedia page here has the wrong sign for the non-linear term which we suspect was carried over from Poplawski’s work. Someone should fix that. We have published a comment paper on the arXiv that further addresses this situation for a recent paper by Poplawski.
[2103.04468] Comment on `Relativistic wave-particle duality for spinors’ (arxiv.org)
Furthermore, in a recent citation to our paper, the authors claim that “In fact, the second term in the mass equation for 
We hope to take this research further into the investigation of the complete Standard Model of Particle Physics as well as Quantum Gravity. We are looking for someone that would like to collaborate on this further research. If interested, please send an email to the addresses found on the first page of our paper. Thank you for your interest in our paper and we hope that you will enjoy reading it:
Citations: We would like to thank the following for citing our paper.
Note: You can use LaTeX in your comments. See here for instructions.
Very nice. I’m wondering if your results are compatible with string theory?
Thank you for your question. I suppose it could be. I believe they want the strings to have a “size” near the Planck length. However, I suspect that supersymmetry and extra dimension may not be necessary but our theory does not rule them out.
A few questions re your theory:
1: What was the reaction from any in particular particle physicists present at the APS 2016 annual meeting at Davis California, as per:
http://www.sciphysicsforums.com/spfbb1/viewtopic.php?f=6&t=282&sid=f94ba252d0af09fbc50b3b78a81a5446#p6937
2: I can find no indication of any submission to a relevant journal(s) for publication. Have you done so, and which one(s) if so? Any reaction(s) back from referee(s) or editor(s)?
3: Has there been any check as to perturbative stability i.e. any tendency of your Fermionic particle model to spontaneously collapse or explode etc.?
The talk I gave at the APS Far West Section was basically rained-out. Most of those in attendance was that of other presenters. No one presented any objections to the ideas given.
The paper has been much improved by feedback from reviewers. It has been submitted to a journal for review.
It is not really a particle model but is just results of the Hehl-Datta equation which is a result of the ECSK gravity theory. That allowed us to solve for the basic size of elementary fermions which appear to be near Planck length. Is it a brane-like sphere or is it like a string? Is it a 3 or 7-sphere? We don’t know at this point but my personal favorite would be a special 7-sphere constructed from Euclidean primitives.
Thank you for your interest.
Very interesting. Have you discussed/corresponded about this with Prof. Poplawski as well as others who work on torsion? What do they think
Thank you for your interest. We emailed Prof. Poplawski and Prof. Hehl when we first developed this idea but did not get a response from them. If any questions or critical comments, please post them. We welcome all feedback positive or negative. Thanks.
Oh, I just discovered that you co-authored a paper with Prof. Poplawski.
https://arxiv.org/abs/1510.08834
“Non-parametric reconstruction of an inflaton potential from Einstein-Cartan-Sciama-Kibble gravity with particle production”
Fantastic! Perhaps you could bring attention to Prof. Poplawski our paper as it proves he is right about the spatial extent of elementary fermions in ECSK gravity theory. I am studying the above paper to see if our results affect the results in it.
Much as the current furor concerning dark matter/dark energy arose from the rather simple observation that galactic rotation curves do not not match prediction I would like to submit for consideration another seperate observation…that being WHY does all matter (on galactic scales) appear to want to ‘clump’ into the spinning whorls which we see all about us as Galaxies?
Given the assumed correctness of inflation as a de facto principle underlying the anisotrophy seen everywhere today it beggars imaginattion that the spinning galactic structures we see today – far predominating over all other aggragations of matter on that scale – would arise naturally in any universe in which Torsion was either non-existent or negligible…ie, what fundamental process could otherwise lead to such a result?
I am keenly interested in your thoughts hereon…after due consideration.
Thank you for your comments and questions. The answer to your first question is a bit tricky. Of course the immediate answer is gravity. But even Einstein’s formula doesn’t really explain the exact physical mechanism. IMHO, matter creates a low pressure gradient with respect to the quantum vacuum. The low pressure gradients are naturally attracted to each other.
For your second question, I haven’t studied that aspect very much but perhaps you can find some answers in what Poplawski has presented.
https://arxiv.org/search/?query=poplawski&searchtype=all&source=header
Thanks for the swift reply Sir,
It has become abundantly clear that the Physics community is missing some truly fundamental principle in the search for a TOE. Naturally, the question is ‘what’. My personal intuition is that that missing component is sitting there staring at us full face-on.
As such, having recently come across Saa’s earlier paper asserting that the accepted volume element (The Riemann volume element ubiquitous in GR and by extension String and M Theory(s)) is – in fact – inappropriately applied in all forementioned is extremely intriguing.
I have seen papers purporting to invalidate his assertion based on Solar dynamics but frankly those oresentations are a bit too involuted for me to follow.
Instead, perhaps a truly thorough treatment (read as ‘rigorous’) of the reformulated GR including Torsion at it’s root would point the way. I have a sneaking suspicion that ‘Dark Energy’ is wholly artifactual in nature…as a consequence of GR’s misformulation in discounting Torsion arbitarily from the start…but time will tell, will it not?
My Thanks Sir…
Addenda to my most recent reply,
Wading through Polowski led to work by Luongo relative to the apparent existence of an observed asymmetry in observed galactic rotations measured whole sky beginning at redshifts at or beyond .04. Luongo’s sample size is quite large (above 100,000) and his conclusion is that in the clearly discernable cases a near 5 sigma confidence is warranted indicative of an actual hemispheric dipole with respect to.
“Astonishing” is the only word that comes to mind in consideration of that conclusion.
That said, it has been a mystery to me since I first apprehended Cartan’s formulation of GR why the greater community seems to have utterly no interest in ECSK theory in which spin exist at the fundament…utterly at variance with GR and explicitly in accord with the quantum frame.
My thanks for the direction you previously indicated; I am more and more of the mind that a rigorous re-formulation of the basis of LQG and GR, thence String and M theory (likely a life’s work for several dozen physicist unfortunately…) will eventually allow for the reconcilliation of the currently unreconcilable; Gravity vs SM.
Our paper “On the Role of Einstein-Cartan Gravity in Fundamental Particle Physics” is now published in the Universe journal special issue “Torsion-Gravity and Spinors in Fundamental Theoretical Physics”.
https://www.mdpi.com/2218-1997/6/8/112
You can comment on the paper at that site. Comments are being closed here.
Apparently commenting is not working on the MDPI site so comments are turned back on here.
If in fact Fred Diether is still monitoring this page, an odd datum dropped in my lap a bit ago which I strongly believe might be the proverbial “Smoking Gun” in favor of the fundamental superiority of ECSK as a fundamental startling point for both QM and String theory.
Specifically, it was recently announced that the vast filaments existing and linking super clusters of galaxies are themselves actually exhibiting rotation uniformly… without variance for those so examined. Hence, quite literally everything in the Universe as we perceive it *appears* to intrinsically possess intrinsic spin…from Galaxies, to Super Clusters of Galaxies, to extra-Galactic filaments of Galaxies linking Super-Clusters AND as is already firmly established, every fundamental particle thus far established in the Standard model.
Thus then the evidence of intrinsic spin is seen to be scale invariant!
This came as something of a shock to me upon reading through those results (the reference for which I’d be happy to provide on request) since the scale invariance very much seems as if it would all but directly imply that Space itself appears to be invested with a Torsional component which manifest as spin across every scale. Just as I mentioned previously relative to the otherwise oddly inexplicable propensity for all large gravitationally bound distributed mass aggregations to all but invariably form spinning whorls of mass, this recent revelation appears to extend both from the smallest scales of the Quantum to the largest scales…and thus to all matter of which we are aware.
I can fully grasp why Messr. Einstein would in formulating GR be inclined to arbitrarily set Torsion to Zero since nothing arising from observations of the age indicated any pressing need for it to be otherwise…and the full ECSK equations are vastly more formidable to solve than are those of simple GR. Feel free to illuminate my ignorance here if so warranted, but wasn’t every attempt over the last several decades predicated on the equations of GR as a fundament, sans any consideration of a non-zero Torsion?
If so, then it occurs to me that at a minimum, ‘Dark Energy’ if not ‘Dark Matter’ (for which no empirical evidence has been found utilizing some exquisitely sensitive detection experiments) *might* indicate that GR does not suffice as a proper fundamental for the oft pursued ‘Holy Grail of Physics…an actual TOE.
Finally, a paper published some while ago by Alberto Saa treated directly the use of the Riemann metric in the presence of non-zero Torsion concluding that a real discrepancy existed between the two approaches. Saa concluded that in the presence of real, non-zero Torsion the Riemann metric was – point in fact – invalid in evaluating volumes in Space-Time. (!!!)
I truly hope that this reaches you: I would be utterly fascinated to hear your take on this new information since clearly your grasp of the subject far exceeds my own.
Regards…Jeff
Hi Jeff,
Yes, please provide references for the scale invariance. The twisting of spacetime is a tricky business.
Best,
Fred
Hello Fred,
Color me delighted that this forum is still operational!
The reference to rotating interstitial intergalactic filaments can be found at:
https://www.universetoday.com/151553/the-largest-rotating-objects-in-the-universe-galactic-filaments-hundreds-of-millions-of-light-years-long/
Regards… Jeff
Hi Jeff,
Whoa! That link had too many ads. Perhaps this is better,
https://www.nature.com/articles/s41550-021-01380-6
But even though the cosmic filaments might have spin, it doesn’t necessarily mean there is a twisting of spacetime involved with it. It is probably like ordinary spin like how the earth spins on its axis.
Best,
Fred
Hello Fred,
That wasn’t the salient I was focusing on, FWIW.
Perhaps I might illuminate this another way, if you’ll bear with me.
Every fundamental particle is invested with the property of intrinsic spin…
excepting only the Higgs, which is a basic fact of Physics…as we currently
understand the Standard model. Solar Systems have planetary bodies tied to
them, all possessing angular momentum (spin) which isn’t at all surprising
since otherwise no other possible dynamic equilibrium allows for even quasi-
stable systems of any sort we could imagine. All well and good…
Witherspoon the exception of odd little galaxies such as the dwarf variety or colliding galaxies, recoverywhere we look are we seen vast whirls of stars all presumably gravitationally bound to the resident SMB’s which serve as the gravitational anchor therefor…again, all well and good. But at this scale one does begin to wonder if possibly – just possibly – there might be a fundamental principle at work which we’re either unaware of OR failing to account for.
However, the recent observation that inter-cluster filaments are rotating about their common axis seems to me to be right off into deep left field for any potential explanation we could suggest based on current physics.
Which brings us back to the heart of the matter. IF Torsion – at a very deep level – was operant as a defining element of Space-Time then wouldn’t it be probable if not likely that everything from the realm of the Quantum all the way to the very largest scales would rather naturally respond to that action to produce exactly what we do see all about us? Food for thought perhaps.
The history of the basic intractability of reconciling GR with Quantum Physics – both indisputably correct within their respective domains – suggest that we have failed in our assumptions regarding one or the other or even both.
As an example, consider the Equivalence Principle…a fundamentally of GR.
As originally set forth by Messr. Einstein, the person in deep space cannot distinguish between the influence of Gravity vs a linear acceleration. BUT that is very much scale dependent…if we then shrink the observer down to the atomic scale then likely it’s still valid most likely but what happens if we then shrink the observer down to the size of a Proton, then shrink that again down to somewhere around the Plank scale?
At the smallest of scales can the Equivalence Principle be viewed as valid? Consider that at THAT scale a Tsunami of virtual particles is popping in and out of existence AND similarly at that scale an observer would almost certainly be able to detect variations from the stated principle due to the presence of tidal effects potentially rendering the EP invalid as a fundamental assumption.
FWIW, the subject is purely avocational for me: My background is that of separate degrees in Mathematics and Physics with a Master’s in Nuclear Engineering…to clarify matters. SURELY, the intricacies of ECSK are FAR above my pay-grade as it were…which I here duly note. All I can state with surety is that we are definitively missing a central and fundamental feature of physical reality…and it might well be the case that – in fact – we’ve bypassed the proper formalism by accepting a more limited theory in order to lighten the calculations load, so it speak.
Schrodinger’s Wave equation vs Bohr’s Matrix approach might well be another such error; we’ve already become aware that various aspects of the world at the quantum level are NOT reversible…Bohr’s Matrix calculation is more formidable but embodies the essence of this as generally matrix multiplication is not commutative…a rather hot topic of late as I’m sure you’re aware.
Best Regards Sir…Jeff
PS: IF you’d rather confine this dialogue out-of-forum feel free to utilize the email addy provided Sir.
Hi Jeff,
This site is fine for this discussion. We also have a physics forum
https://sciphysicsfoundations.com/index.php
That you are welcome to become a member of to see if more people might be interested in joining the discussion. Also, the section Sci.Physics.Foundations allows guest posting so you don’t have to be a member but is subject to moderation before posts are seen. I’m not sure why WordPress had me moderate your last post here.
Anyways as far as I can tell presently, gravitational torsion is completely contained within elementary fermions. So, no scale invariance. But I could be wrong about that. I would need to see some actual formulas where gravitational torsion might be present at larger scales. Another big problem of course is that gravitational torsion has never been detected as far as I know.
Best,
Fred
Thank you for your invitation to join the forum Sir,
As it happens I did follow the link you provided, entered my relevant personal data and then discovered that regardless of what I attempted, the submit button on the page was unresponsive.
I admit to a particular fascination with ECSK theory from my first contact therewith a couple of decades ago, however, per your reply, it occurs to me that quite possibly I have misapprehended both the physical and mathematical meaning of Torsion as it is defined therein. Clearly, you have a mathematical physicist’s understanding of exactly what that means. As such, if you’d suffer the question, “What – to you – is the functional/physical definition of Torsion being non-zero?” I always (perhaps wrongly) presumed a degree of freedom roughly corresponding to Space-Time at the scale of the macro to manifest a ‘twist’…in the case of a non-zero value of T to correspond to an operant Torque in effect of some sort.
If this interpretation is wholly incorrect then likely I’m so far out of my depth as to have to gain a significantly improved understanding of what Cartan meant in expanding GR as he did. I am wholly earnest in the foregoing and not in the least wise being ‘snarky’ (in any sense!) whatsoever Sir.
Thank you for replying again…I do appeciate you suffering through dialogues with non-initiates! The Universe is a truly startling and unspeakably sublime construct to contemplate.
Best Regards…Jeff
Hi Jeff,
I tried the registration for the other forum and it worked fine for me. The answer to the question is “All Other Physics” without the quotes.
Well, I don’t think there is anything that rules out the twisting of spacetime (gravitational torsion) on a macro scale other than it has never been detected but perhaps Nature is tricking us somehow about that.
Best,
Fred
Hello Fred,
Yes, I did input ‘All Other Physics’ without quotes. Perhaps it was a vagary of my internet connection; AT&T has been updating our local 5G towers of late and at times it has resulted in some ‘squirreliness’ on our end. I will return and re-attempt to get logged in.
Also, thanks for the clarification above as well
Best Regards…Jeff
Hello Fred,
I finally had enough free time to actually sit and examine your paper which is the basis for this article in full…and I find it intriguing in the extreme. Many thanks for your effort in producing it; there is much contained therein that bears thinking through!
Additional – external – points that might be relevant in the greater tapestry of reality have come to my attention of late and I thought to forward those along to you hoping that after due consideration you – with your profound understanding of such – could if you chose to might weigh in on the validity of same.
The first of these is located at;
https\\core.ac.uk/download/pdf/25189886.pdf
Authored by J Madore and J Mourad
Titled “Non-Commutative Kaluza-Klein Theory”
and second fascinating paper authored by Alberto Saa titled,
“Einstein-Cartan Theory of gravity revisited”
The latter – which I described as ‘fascinating’ appears to assert that the Riemannian volume element used in virtually every formulation derived from GR is – in fact – inappropriate in the context of ECSK theory whomsoever Torsion is non-zero. The implications – if true – are significant naturally.
As a sidebar here…did you ever publish with Sabine Hosenfelder? It seems that I saw a paper coauthored by you both. Just curious Sir.
Regards…Jeff