Today I have submitted a new paper to the arXiv, but because I expect them to reject it, I am posting it here, at https://robwilson1.files.wordpress.com/2024/04/c3ine8v2.pdf. It is rather technical, and mathematical, but that is unfortunately unavoidable, since what the paper really does is provide mathematical reasons, based on fundamental physical principles, for some things I wrote three years ago, in https://robwilson1.files.wordpress.com/2021/03/lorentz5s.pdf. That paper was also rejected by the arxiv, and by the journal I sent it to, without being seriously considered in either case. I have just re-read that paper, expecting that I would find it excruciating and full of nonsense. But that is not what I found. What I found is that it says more or less exactly what the new paper says about gravity, and talks a lot of sense about physics in general, but includes very little of what the new paper says about particle physics.
The old paper was really a discussion of why the Lorentz group is inconsistent with the known properties of spin of electrons and photons, and why the group needs to be replaced by a different group. The replacement I proposed three years ago is the same replacement that I propose in the new paper. But the justification provided in the new paper is stronger, because it is shown to be consistent both with the standard model of particle physics, and with general relativity.
The paper is written in the language of E8, because I really want to persuade the E8 crowd that this is a better way to look at E8 than the myriad of other ways that they have tried. But I am still not totally convinced that E8 is necessary for this exercise. As far as I can see, what is needed is SU(3,3), a group of type A5, which already contains the Riemann Curvature Tensor. On the other hand, to get three generations of electrons I seem to need to extend to E6. And when I do extend to E6, I get the Einstein Field Equations as well. That seems to be important. Because I don’t get the Einstein Field Equations if I only have one generation of electrons.
And if I do include all three generations, then I get an extension of the Einstein Field Equations from 10 equations to 20, in twice as many variables. So extending to three generations not only reproduces General Relativity, but also provides a physical mechanism by which the gravitational field can propagate, and corrects GR for neutrino oscillations. Well, you know, I’ve said all this before, and I know I will say it again, but I’m getting tired of casting pearls before swine (not you, obviously, you know which swine I mean).
Hidden assumptions 
April 22, 2024 at 2:44 pm |
Pearls of Wisdom”
Casting pearls at swine
Leaves diamonds in the rough
So casting pearls is fine
If diamonds are enough
April 22, 2024 at 2:49 pm |
If diamonds ain’t enough
Then casting pearls won’t do
At swine or other stuff
It’s bound to make you blue
April 22, 2024 at 2:55 pm
If blues are what you seek
Then casting pearls is fine
Although you’re up the creek
On oysters you may dine
April 22, 2024 at 3:02 pm
If oysters make you ill
Then casting pearls won’t do
Instead just take a pill
To turn your skies to blue
April 22, 2024 at 3:04 pm
Why do you think the sky is blue? What I want to know is, why is the sky black? Because I don’t believe the standard explanation, that it’s the colour of the Big Bang.
April 22, 2024 at 3:04 pm
I think that pretty much covers all the bases
April 22, 2024 at 3:11 pm
The sky was black during the day a couple weeks ago in my neck of the woods on account of a solar eclipse.
April 22, 2024 at 3:13 pm
Yes, so you at least have experimental verification that the sky behind the sun actually is black, despite the widespread opinion that it is blue. But can you explain why it is black, and not white?
April 22, 2024 at 2:52 pm |
Surely diamonds are forever, however rough they are?
April 22, 2024 at 2:53 pm |
And what about Lucy in the sky? Surely she has something to do with making the galaxies rotate?
April 22, 2024 at 3:21 pm
…with diamonds, of course – I assume that means the stars, but I could be wrong.
April 22, 2024 at 3:22 pm
Maybe I’m wrong, maybe “Lucy in the sky with diamonds” is a description of a solar eclipse.
April 22, 2024 at 2:55 pm |
I’d rather be a rough diamond than a polished turd.
April 22, 2024 at 3:36 pm |
Picture yourself in a boat on a river –
Lorentzian trees and Minkowskian skies.
Somebody calls you, you answer quite slowly,
A girl with kaleidoscope eyes.
Cellophane flowers of leptons and quarks,
Towering over your head,
Look for the theory of everything there –
And she’s gone.
Lucy in the sky with diamonds
April 22, 2024 at 3:48 pm |
“SUSY in the sky with diamonds”
Follow her down to the string theory fountain
Where rocking horse people eat marshmallow pies
Everyone laughs as you drift past the theories
That grow so incredibly high.
Conference journals appear on the shore
Waiting to take you away
Climb in the back with your head in the clouds
And you’re gone.
SUSY in the sky with diamonds
SUSY in the sky with diamonds
SUSY in the sky with diamonds
Urgh
April 22, 2024 at 4:01 pm |
Picture yourself on a train in a station
With toy-model porters with looking glass ties
Suddenly someone is there at the turnstile –
The boy with all-seeing glass eyes.
Rudy in the sky with diamonds
Ah!
April 22, 2024 at 4:20 pm |
RUDY = Relativistic Unification of Dirac and Yang-Mills
April 22, 2024 at 4:40 pm |
LUCY = Lorentzian Unification Contradicts Y’all
April 22, 2024 at 6:25 pm |
Interesting, but very abstract. Don’t see why arXiv would find it a threat. Regarding “J. Distler and S. Garibaldi (2010), There is no E8 theory of everything, Communications in Math. Phys. 298 (2), 419–436”, I don’t believe such “no-go theorems” that implicitly assume the number of generations in SM to be God’s final word. E.g., for leptons, the masses of their three generations appear to be analogous to a simple nuclear shell structure arising by a simple mechanism in the polarised vacuum (table 1 of https://vixra.org/pdf/1408.0151v1.pdf). Distler used similar bogus arguments to me in a discussion on his blog (note he used to be associated closely with arXiv blocking/removal/no-platforming of “alternatives to currently accepted superstring theories etc”, so if you criticise his fakey based allegations and you paper gets removed, you might guess why; doubtless there is a conspiracy, using arXiv censors to defend pet theory).
“The way that spacetime is treated in relativity, using the Lorentz group in the form SO(3, 1), is mathematically (never mind physically) inconsistent with the way that spacetime is treated in quantum mechanics, using the Lorentz group in the form SL2(C).” – Dr Wilson
Woit also make this point regarding the path integral. I don’t want to say it again, but this is fundamental. Dirac made progress (predicting antimatter) but formulating his (albeit half-baked) spinor to put space and time in Schroedinger’s equation on an equal footing: Schroedinger’s equation has the rate of change of the wavefunction proportional to the Laplacian operator on the wavefunction, i.e. the second order derivative with of that with distance. So Dirac sorted it, “sort of”.
Then Feynman came along and got rid of the single wavefunction: a charge is continually exchanging virtual photons with other charges along all possible paths. What we see as “radiation” is an asymmetry in this, caused by a motion of an electron (thus the basis for the compressive force during acceleration that produces the Lorentz transformation, together with Newton’s 1st law of motion). But Feynman’s path integral re-introduces differences in the mathematical treatment of space and time: ∫exp(iS) dx^4, where S = ∫Ldt.
One way to explain this asymmetry of course to to postulate the existence of a second path integral giving a symmetrical space-time mirror of the above equation, i.e. the “crazy” 1944 Feynman-Wheeler theory that they formulated in WWII: the path integral has a reversed interpretation applicable to the entire universe. In the Feynman-Wheeler theory, a single particle goes back and forth between times of start and end, some 10^80 cycles, with “forward” going particles called matter and the backward time-travelling versions appearing as “antimatter”. (This crazy theory still has uses in Feynman diagrams, where the time-direction arrow of a particle’s propagator is used to signify if it is matter or antimatter.) But there could be an alternative version of this way of thinking that works. I see you mention SO(3,3), which Lunsford thinks is the basis spacetime (see https://independent.academia.edu/DannyRossLunsford).
April 22, 2024 at 7:13 pm |
Yes, it is abstract. That’s my defence mechanism when people criticise my physics. But also, getting rid of the contradictions in the mathematics is important (it is what Sabine Hossenfelder says all the time, but she does nothing about it herself), and finding a way to get rid of the mathematical contradictions without destroying the physics as well is tricky.
The Distler-Garibaldi no-go theorem is a load of rubbish – I have written two or three papers explaining why, and one of them is even on the arXiv. They make a load of arbitrary (and, in my opinion, absurd) assumptions, that have nothing to do with physics, but only with their opinions about what a theory of physics “ought” to look like. The many clever people who are still working on E8 models understand this perfectly well, and wouldn’t waste their time if the Distler-Garibaldi conclusions were actually correct.
Much the same applies to other no-go theorems in physics – what is actually proved is always much much weaker than what physicists who haven’t understood the details think is proved. So I basically take no notice of them. Indeed, this is the main reason why I renamed my blog “Hidden assumptions” – because the assumptions that always have to go into a mathematical theorem are routinely ignored by physicists, who assume that the result is categorically true, when in fact it is only ever contingent.
Mathematics is not about truth. It is about correctness. They are not the same thing.
April 22, 2024 at 7:43 pm
There’s no “correctness” to the use of mathematics by physicists. I first came across complex phase space and the Fourier Transform in electronics for A.C. circuit phase interference and frequency vs waveform analysis, respectively; exactly the same equations are used in QM and QFT. I do hope you try to also look at mechanisms to understand the equations, which saves confusion.
If someone asks “x^2 = 4, what is x?” and you know for a fact that they are talking about a square carpet for a room, you don’t need to reply formally “x = +/-2”. You can simply say, “2”. So understanding the dynamics affects the possible solutions to an equation; in both 1st and 2nd quantization, you have to square the wavefunction to get a probability (which is proportional to the reaction rate or the scattering cross-sectional area, etc). The underlying and usually unobserved “wavefunction amplitude” (which is being squared to get probability) could be either positive or negative. Squaring ensures a positive probability.
But this isn’t really unobservable. You can do practical experiments using 1 m (say) wavelength radio waves, reflecting them or sending them through one another between two antennas, to simulate path integral effects. There was a very real path integral of this sort with skywave reflection of HF radio over long distances, where some frequencies could be partially reflected back by the D, E, and F layers of the ionosphere, at various different altitudes up to 100 km, causing “multpath interference”. It’s not an abstract QFT problem. All this stuff has physical mechanisms, analogies in hard experimental facts. It helps get a brain around them to look at the dynamics, sometimes.
April 23, 2024 at 12:03 am |
“ a charge is continually exchanging virtual photons with other charges along all possible paths”
Feynman once said he didn’t understand how so much stuff could be going on in the tiniest of spaces
but then he totally ignored his own concerns to propose an infinitude of interactions with particles that don’t exist.
April 23, 2024 at 9:25 am
Hi Lars: he didn’t say he didn’t understand, he said he understood that it debunked the concept that the universe can be described with mathematics! For the exact quote, transcribed by me from his November 1964 Cornell Lectures (which was recorded by the BBC for TV transmission in the UK), see for instance p22, column 1, in my 12+ years old unification theory book at https://vixra.org/pdf/1111.0111v1.pdf
“Why should it take an infinite amount of logic [calculating the infinite number of terms in a perturbative expansion to a path integral] to figure out what one tiny piece of spacetime is going to do? So I have often made the hypothesis that ultimately physics will not require a mathematical statement, that in the end the machinery will be revealed, and the laws will turn out to be simple…”
April 23, 2024 at 9:36 am
I think you may be referring to Feynman’s 1965 statement that “nobody understands quantum mechanics”, which refers to his view in 1965, not his view in 1985 when after long bongo-drumming sessions with people like David Bohm, he saw the light and published this explanation (which simplifies the path integral’s complex amplitude exp(iS) by showing that for practical understanding you use Euler’s equivalence: exp(iS) = i sin S + cos S, and simply ignore the complex phase information term i sin S, doing a summation of real path amplitudes, cos S): https://faculty.washington.edu/seattle/physics441/feynman-QED/qed2.pdf
“I couldn’t see how anyone could be educated by this self-propagating system in which people pass exams, and teach others to pass exams, but nobody knows anything.” Richard P. Feynman, Surely you’re joking Mr Feynman, 1988.
April 23, 2024 at 10:42 am
I would say that it depends what sort of mathematics he is talking about – since Feynman says “an infinite amount of logic” he is obviously talking about continuous mathematics, and series expansions (or worse). He is not including finite amounts of logic, or any kind of finite mathematics, in his blanket term “mathematics”.
Like all the deep thinkers, Einstein, ‘t Hooft etc, he is not excluding the possibility that what is actually “going on in a tiny bit of spacetime” is described by finite mathematics. It is unfortunate that he does not call this mathematics, but restricts his definition of “mathematics” to calculus only. This careless use of language has led to serious misunderstanding.
April 23, 2024 at 8:42 pm
seems to be a distinction without a difference.
Feynman had no problem accepting the prizes and other accolades for the very mathematics that he wanted everyone to think he didn’t believe in.
April 27, 2024 at 10:09 pm
∫exp(i∫Ldt)d^4 x ≠ ∑ exp(i∫Ldt)
I don’t believe the left hand side (which is the one in the textbooks) is either (1) true physically (calculus can’t deal with the discontinuity of real particulate interactions properly) or (2) analytically solvable in any useful sense, for any practical (complicated) real world situation.
The right hand side, on the other hand, is precisely the experimentally justified summation of discrete Feynman diagrams that occurs in reality. If you don’t like my papers or Feynman’s books, you might find a physically helpful discussion of the physical basis for the mathematical approximations of QFT in issue 11 of Los Alamos Science (Summer/Fall 1984; nothing much has changed in 40 years): https://la-science.lanl.gov/lascience11.shtml especially https://permalink.lanl.gov/object/tr?what=info:lanl-repo/lareport/LA-UR-85-5001 which has really good illustrations of the physical basis for the various equations.
April 27, 2024 at 10:25 pm
The issue for Feynman was whether the universe is mathematical, in the sense of being based on mathematics. It’s clear Feynman defines “mathematics” here in the sense of Sir James Jeans’ 1930 bestseller “The Mysterious Universe”. Jeans, a mathematician, was Eddington’s protage at Cambridge, and came up with the false theory around 1903 (repeated in that book) that the planets are bits of the sun thrown off in tidal waves on the sun’s surface (a bit crazy because spectroscopy had long shown the sun to be essentially hydrogen and helium, which doesn’t really account for solid planets).
In other words, if you can’t even in principle calculate the magnetic moment of the electron, then the universe isn’t fundamentally mathematical, according to Feynman 1964/5. This is not about measurement uncertainty; the vacuum polarization effect means the electron’s magnetic moment is 1 + α/(2 π ) + [infinite number of terms, each containing α raised to a successively higher power].
April 27, 2024 at 4:31 pm |
Feynman liked to claim a close agreement between experiment and the predictions of QED that were based on a sum of terms in powers of alpha in an infinite perturbation series.
But Freeman Dyson eventually found that that series was divergent as he relates here
and Feynman himself called the way of dealing with the divergence (renormalization) a “dippy” method.
I honestly don’t understand how one could simultaneously believe the mathematics are “dippy” while effectively bragging about the agreement between the results of experiment and the calculations obtained with the very mathematics that one considered dippy.
Regardless of whether renormalization is valid or not, it seems completely inconsistent to tout the results of a theory/ method that one believes to amount to bogus mathematics.
April 27, 2024 at 6:38 pm |
As a mathematician, I agree. I could not accept the bogus mathematics that I was taught 45 or so years ago under the pretence that it was physics, with the pathetic excuse that “rigour” was superfluous in physics. That is why I became a pure mathematician. Using mathematics that you know to be wrong is fraud, and should be punished as such.
April 27, 2024 at 9:33 pm
mathematical rigor is super-silly-us
April 27, 2024 at 9:15 pm |
I have also never understood why the series is in powers of alpha/pi.
why is the fine structure constant divided by pi?
surely, there must be some PHYSICAL significance for dividing alpha by pi
April 27, 2024 at 10:52 pm
Hi Lars: you’re referring to QFT perturbative calculations like the Lamb shift of the ground state of hydrogen and the fact that the vacuum polarization effect means the electron’s magnetic moment is 1 + α/(2 π ) + [infinite number of terms, each containing α raised to a successively higher power], Bohr magnetons.
This goes back to Bethe, Feynman and Dyson at Pocono in 1948, and the Shelter Island (I believe in 1947, from memory) conference which included Oppenheimer and others. The thing is, Dirac’s non-perturbative QFT included antimatter and the electron’s spin, but Dirac’s result for the electron’s spin is 1 Bohr magneton. The actual result (found by flipping electrons using high frequency fields, available thanks to WWII radar technology) was found to be higher, roughly 1.00116 Bohr magnetons.
The Lamb shift is a similar small error between theory and very accurate experimental data. Bethe first found a way to fiddle a perturbative calculation of this. The “fine structure constant” is usually represented by α = 1/137.036… or by the square root of that, because Feynman’s rules for calculating terms in the perturbative expansion use that to represent the relative strength of the electron’s charge, in a dimensionless way (i.e. a number without units). The 2 π factor is a geometry effect for a spinning particle. Back in Reagan’s Starwars programme, you would need to increase the power of your laser blast by a factor of 2 π if the dastardly reds made their missiles spin rapidly to reduce the received flux per per cm^2.
April 28, 2024 at 12:05 pm
Its easy to see where the factor 2pi comes from in the case of the Star Wars laser because the energy is distributed in a ring around the spinning missile, which reduces the power density necessitating a boost in the laser power.
but from my understanding, it’s not even accurate to speak of electrons as spinning in the classical sense.
so it’s not clear that the spinning argument works as a physical reason to explain dividing alpha by 2pi
also, the series is actually an expansion in powers of alpha/pi, not alpha /2pi
April 28, 2024 at 2:04 pm
Although it is always said that electrons do *not* spin in a classical sense, nobody can explain in what sense they *do* spin. My close study of the mathematics behind these assertions leads me to believe that in fact electrons spin like coins, and not like balls.
The standard mathematics of electron spin simply does not work. It is incorrect *as mathematics*, let alone the (non-existent) physical interpretation. The undoubted physical fact that electrons do not spin like balls has led physicists to an incorrect ansatz in the mathematics.
This incorrect ansatz is the reason why QM is inconsistent with gravity or any type of acceleration. To regain the necessary consistency of the theory, it is both necessary and sufficient to suppose that electrons spin like coins.
April 29, 2024 at 1:08 am
if electrons spin like coins, they are very strange coins because you have to spin them around twice to get them back to the state they started in
of course, the same argument applies if they are balls.
I have never understood electron “spin.”
not the first time I learned about it and not now.
I doubt I ever will.
and I still don’t understand the reason for dividing alpha by pi (and not 3, for example) since any change could be absorbed into the coefficient multiplying each term in the expansion.
April 29, 2024 at 1:29 am
that dividing alpha by 2pi gives the correct first corrective term for the magnetic moment doesn’t mean that pi is the divisor because even that first term has a coefficient out front and C*alpha/3 can be made equal to 1/2(alpha/pi) to any desired accuracy simply by choosing the value of C.
Without some physical justification for dividing alpha by pi, I don’t see why dividing by pi should be favored over dividing by 3, for example.
Simply saying that pi is involved because of electron spin doesn’t seem to me to be a particularly convincing argument.
April 29, 2024 at 7:03 am
You misunderstand me: the whole “go around twice” thing is an error in the mathematics. Turning a coin through 180 degrees flips heads and tails. For some reason, physicists call this a 360 turn, so that they need 720 degrees to get back to where they started. This is an error. Moreover it is THE catastrophic error that makes QM and gravity incompatible.