## Some Reflections on my new Dirac Paper

Foundations of physics and/or philosophy of physics, and in particular, posts on unresolved or controversial issues

### Some Reflections on my new Dirac Paper

Dear friends,

Let me summarize briefly below, my journey over the past 2.5 years thorough which I arrived at the near-final paper http://vixra.org/pdf/1710.0159v4.pdf.

Very briefly, in December 2015, as memorialized in this forum, I took on the problem of trying to find a spacetime metric from which the electrodynamic Lorentz Force motion could be derived as entirely geodesic motion, using least action variation, in the exact same way that gravitational motion is obtained. As shown in section 2, I was able to do so mathematically, using the metric (3.3). But there were three problems: First, while the derivation worked mathematically, the metric I used appeared to be dependent upon the properties of individual charges travelling through the electromagnetic field, which is physically impermissible in field theory. The only way to overcome this was via an “inequivalence principle” laid out in section 5, which led inexorably to the finding that electromagnetic interactions between like charges dilate time, just as do gravitational interactions and special relativistic motion. Second, the Lorentz motion contained an additional A^2 term, see (2.12), which needed to be removed in some appropriate fashion. Third, interrelated, the metric had the rather unusual property of being quadratic in d\tau, see (3.4) and (3.5). This needed to be understood in a physically sensible way, and the having very same A^2 term in (3.5) made such an understanding challenging.

Now, I have long known, as do many others, that Dirac’s equation is an “operator square root” of the spacetime metric equation. So, about a year ago it occurred to me that if the A^2 term could be removed, then the quadratic line element (3.5) was in fact merely pointing toward a richer form of Dirac’s equation, which I have named the “hyper-canonical” Dirac equation. I had had a number of false starts over 18 months trying to remove the A^2 term. But last summer I finally realized that the correct way to do so was to employ Heisenberg’s equation of motion and Ehrenfest’s Theorem, see section 8, and to then use the two covariant gage conditions (9.4), (9.5) which are essentially the Lorenz gauge applied to both the “expected value of the spacetime divergence” and the “spacetime divergence of the expected value,” of the gauge fields. Not only did this remove the A^2 term noted above in a generally covariant manner, but the way in which it removed two degrees of freedom from the gauge field led precisely to the known properties of massless photons with two helicity states, see (15.1) through (15.3).

With this development, the challenging quadratic metric (3.5) became (11.3) which could be put into a form (11.5) that is very reminiscent of the “square root” from which Dirac’s equation emanates. Starting in section 13, using an electromagnetic tetrad analogous to the tetrads used for Dirac’s equation in curved spacetime, and after also adding a “spin connection” following the usual protocol to maintain proper spacetime covariance, I was able to obtain a “hyper-canonical” Dirac equation (18.8) which in momentum space is (18.10), see also (19.18). This is where I was in the Fall of 2017.

From there, I began the painstaking process of extracting the Hamiltonian from this new Dirac equation. This was a challenge mainly because this new Hamiltonian, as you can see in its final form complete form (21.1), contains a very large number of terms which I needed to check and recheck multiple times until I was satisfied that all had been correctly calculated. With the Hamiltonian finally obtained, the past few months I was able in section 23 to show how under the specific conditions where all external fields other than a constant magnetic field are “turned off,” this new Dirac equation inherently contains a magnetic moment anomaly.

This IMHO is hugely important, because if you understand the usual Dirac’s equation, you will understand that it only predicts a g-factor g=2 for the charged leptons, and no magnetic moment anomaly. But in the natural world of course, there is an anomaly which to first order loops is equal to the Schwinger factor \alpha/2\pi, where \alpha ~ 1/137.036 is the running low-probe electromagnetic coupling. The only known way to explain this anomaly is to introduce renormalization theory whereby some infinities are subtracted from other infinities. Beyond this ugliness that Dirac and Feynman and others complained about, renormalization theory is a separate appendage to – not an intrinsic part of – Dirac theory. This suggests that something is missing from the standard Dirac equation. So, at (23.5) through (23.9), I finally show how the anomaly is now made intrinsic to Dirac theory via the “hyper-canonical” Dirac equation and its Hamiltonian, and how infinite-number renormalization is thereby rendered entirely unnecessary.

Of course, it is always desirable for any new theory to offer some testable predictions. Over the past several weeks, I added sections 24 through 26 which lay out six distinct types of experiment through which this may all be tested. And with all of that, I look forward to your public or private feedback. If private, my email address is yablon@alum.mit.edu.

Best regards to all,

Jay
Yablon
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### Re: Some Reflections on my new Dirac Paper

Thanks for the summary, Jay. It is very helpful. You might want to consider adding something like it at the end of the paper before the Appendices as sort of a conclusion.

Now if one incorporates what you have discovered with the Dirac-Hehl-Datta equation, then I believe we will have a truly complete Dirac type of equation for fermions. If one solves your eq.(18.8), you obtain a "size" of a charged fermion of the order of the reduced Compton wavelength. And we know from experiment that is not correct.

http://einstein-cartan.org

As far as publishing goes, it is extremely difficult for independent researchers to get published in top journals. They are just not beholdened to us like they are to researchers from academic institutions because those institution buy their journals. I would recommend making this paper into a book and self-publish it. Then advertise it somehow via a website for it. You can have a comments section and hopefully some peer review via that.
FrediFizzx
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### Re: Some Reflections on my new Dirac Paper

FrediFizzx wrote:Thanks for the summary, Jay. It is very helpful. You might want to consider adding something like it at the end of the paper before the Appendices as sort of a conclusion.

Thanks Fred, that is exactly my plan, but this will be a preface of some sort. This was the first draft of that preface.
FrediFizzx wrote:Now if one incorporates what you have discovered with the Dirac-Hehl-Datta equation, then I believe we will have a truly complete Dirac type of equation for fermions. If one solves your eq.(18.8), you obtain a "size" of a charged fermion of the order of the reduced Compton wavelength. And we know from experiment that is not correct. http://einstein-cartan.org

Actually my section 26 addresses this question directly, see (26.7) and (26.8). But before I talk about that, I must point out that we have to be very careful when we talk about the "size" of an electron.

It is commonly believed that an electron is a "point" particle. But of course, the question has to be asked, how "pointy"? Nuclei have a "size" of about 10^-15 meters (1 Fermi), and there is good evidence that an electron is no larger than about 10^-22 meters, see https://en.wikipedia.org/wiki/Electron# ... properties. I am personally of the view, and have been for over 30 years ever since I first studied Wheeler's geometrodynamics (https://www.amazon.com/Topics-Modern-Ph ... B00IKIFZHC), that the charged leptons are Planck-scale vacuum fluctuations which become "impregnated" as it were with electrical field lines and then "polarize" the surrounding vacuum. What we observe some 20 order of magnitude away as charged leptons, are the behaviors of this polarized cluster of phenomena with a Planck scale core. Efforts such as your to understand the "hierarchy" from Planck scale down to observable energies are commendable. My best stab at those questions to date is in my 2013 published paper http://www.scirp.org/journal/PaperDownl ... erID=30822, DOI: 10.4236/jmp.2013.44A011.

But the above question about "size" is a a different question from that about the spatial expanse of the probability density of a lepton, which is what I study in section 26 and make the basis for one set (out of six sets, so far) of proposed experiments which I am confident will produce confirmation. Now, I do not like the phrase "wavefunction collapse" because it is a murky phrase that really tells us nothing. I prefer to think that when we do an experiment to detect a lepton and record as precisely as possible where we detected it, in a slit experiment or even unencumbered with no slits, we are making a probability record. Just like when we roll dice or flip a coin or draw a card. Over multiple experiments, the spatial landings of the leptons on our detectors accumulate into a probability density, and statistics allows us to define an "average draw" separation between any pair of detected landing locations which average draw is directly related to the standard deviation of the probability density in a known way that depends simply on the nature of the probability distribution.

Now, I can link a number of online articles, but this one will do: https://en.wikipedia.org/wiki/Compton_w ... easurement. The uncertainty principle establishes a lower bound on the position uncertainty of any particle, and that lower bound is half of the reduced Compton wavelength. I have used my hyper-canonical Dirac equation to dig deeply into this, and to predict in (26.7) and (26.8) that what I define as the "statistical diameter" for each lepton in fact has a lower bound that is half of the ordinary Compton wavelength, greater than the reduced wavelength by factor of $2\pi$. The actual statistical diameter depends on the distribution, but that too should be experimentally deducible and I would be inclined to expect a Gaussian probability cloud. But the place where this really meets the road in a way that cannot be fudged -- if we make the very fair assumption that the electron and the mu and tau leptons all have the same types of distribution -- is that in relation to their Compton wavelengths, the standard deviation of the muon is slightly smaller than that of the electron, and the tau even slight smaller than the muon. These ratios are in (26.8), and as stated, should be accurate to parts per 10^4 because these do neglect hadronic and electroweak loop contributions. And, these are all direct functions of the observed magnetic moment anomalies.

So that is what my paper has to say about the "expanse" of the probability density, which is a separate issue from the "size" of leptons being a "point" or a stable Planck scale fluctuation.
FrediFizzx wrote:As far as publishing goes, it is extremely difficult for independent researchers to get published in top journals. They are just not beholdened to us like they are to researchers from academic institutions because those institution buy their journals. I would recommend making this paper into a book and self-publish it. Then advertise it somehow via a website for it. You can have a comments section and hopefully some peer review via that.

I will not disagree that there is quite a bit of rot in the scientific publishing system these days. And physics as a whole has been stuck in a ditch for three decades. But self-publishing has a "vanity" rap, and I do not want to get trapped by that. Despite my cynicism, I have to believe that there are people in the scientific publishing business, at the top, who maintain their integrity and will help a solid research paper see the light of day. Especially this paper, which is relativity theory for electrodynamics just as SR 1905 was relativity for motion and GR 1916 was relativity for gravitation. This will see the light of day eventually. But at age 64, I cannot wait for four more decades. And I will not be content with simply knowing that this will happen someday. I intend to make things happen soon, this year or next, for the years of good research I have done the past ten+ years including solving the mass gap and explaining the true nature of protons and neutrons and confinement and binding energies, etc., and explaining what really goes on near absolute 0K. And I intend for this paper to be the one that will break the logjam and allow all the rest of my previous work to come to light as well. All it takes is one good person at the top with integrity who is willing to do more than scratch a surface, and I intend to find that person using this paper.

Jay
Yablon
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### Re: Some Reflections on my new Dirac Paper

Yablon wrote:
FrediFizzx wrote:As far as publishing goes, it is extremely difficult for independent researchers to get published in top journals. They are just not beholdened to us like they are to researchers from academic institutions because those institution buy their journals. I would recommend making this paper into a book and self-publish it. Then advertise it somehow via a website for it. You can have a comments section and hopefully some peer review via that.

I will not disagree that there is quite a bit of rot in the scientific publishing system these days. And physics as a whole has been stuck in a ditch for three decades. But self-publishing has a "vanity" rap, and I do not want to get trapped by that. Despite my cynicism, I have to believe that there are people in the scientific publishing business, at the top, who maintain their integrity and will help a solid research paper see the light of day. [...]
Jay

Submit your paper to Royal Scociety Open Science (http://rsos.royalsocietypublishing.org). They will likely accept it, and quickly. You will have to pay $1260 in "Article processing charges" though. Heinera Posts: 419 Joined: Thu Feb 06, 2014 12:50 am ### Re: Some Reflections on my new Dirac Paper Heinera wrote:Submit your paper to Royal Scociety Open Science (http://rsos.royalsocietypublishing.org). They will likely accept it, and quickly. You will have to pay$1260 in "Article processing charges" though.

Yes, Jay. I too recommend the journal Open Science of the Royal Society of London (of which Newton was once the President). It does have a media embargo, however, like Nature.

By the way, I did not have to pay publication charges for my paper. I got the special treatment from them, perhaps because of the significance of my paper for the future of physics.

***
Joy Christian
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### Re: Some Reflections on my new Dirac Paper

jay i thought you might find this of indirect interest:

https://www.researchgate.net/publicatio ... c_Equation

it is an additional exploration of the dirac equation which has extra terms.
lkcl

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### Re: Some Reflections on my new Dirac Paper

Jay,

I'm trying to catch up with the forum. You wrote: "I took on the problem of trying to find a spacetime metric from which the electrodynamic Lorentz Force motion could be derived as entirely geodesic motion, using least action variation, in the exact same way that gravitational motion is obtained."

That's my aim, too. Why equivocate on the electron's lack of point particle properties, though? A metric cannot be derived from less than two separable points, which because of e-e+ polarity, begs oscillation. That we only observe (without interference) one side of the interaction is exactly equivalent to the gravitational one-way interaction. Taking Einstein locality into account, coalescence of matter is assured.

All best,
Tom
thray

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