As everyone knows, 14th July 1789 was a very significant day in the history of revolutions. The same may not be true of 14th July 2021, but only posterity can judge that. Today my paper “On the problem of choosing subgroups of Clifford algebras for applications in fundamental physics” was published by Advances in Applied Clifford Algebras. In order to get it published, I had to hide the revolutionary ideas very carefully behind a camouflage of respectability. But they are there, and the seeds of the revolution are sown.

Four more of my “revolutionary pamphlets” are on the arXiv, and many more exist in samizdat. Two are apparently being refereed by respectable journals, but who knows what that really means? Yesterday, a correspondent pointed me to arXiv:gr-qc/0602003, which is extremely interesting, as it contains a penetrating analysis of the concept of time, that distinguishes three different concepts: parametric time, atomic time and astronomical time.

Now, I don’t know if you remember, but in arXiv:2102.02817 I showed that in a discrete model of quantum mechanics there are three distinct concepts of spacetime. One is parametric spacetime, which has a symmetry group SL(4,R), that underlies the theory of general relativity. Another I called electromagnetic spacetime, which appears to contain what the above paper calls atomic time, that is anything that is determined by frequencies of electromagnetic radiation. This has SL(2,C) or SO(3,1) as its symmetry group. The third I called gravitational spacetime, which appears to contain what the above paper calls astronomical (or proper) time, with SL(3,R) as its symmetry group.

My paper that explains why electromagnetic spacetime has a different symmetry group from gravitational spacetime was (predictably) summarily executed. But shooting the messenger does not change the message. Vive la revolution!

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July 15, 2021 at 12:55 am |

Is the Lorentz group therefore *wrong* as it assumes there is only one spacetime, thus trying to approximate all three of these?

With Zeno’s paradox, continuous motion actually turns out to be the answer, which is why Einstein declared the universe continuous, as well as Lorentz covariant for the relativistic affects of the arrow in acceleration.

As Sophus Lie discovered, a group element represents a continuous transformation, and when you take an element and decompose it into an infinite amount of infinitely small transformations, each of them belongs to the Lie algebra of the group.

Zeno’s paradox is a thought experiment concerning the infinite series. The theory of limits resolves the product of the infinite series as 1, representing continuous motion and making it real after all. In this limited, classical theory sense, anyway.

Immediately, I notice the generators of Sl(2,C), Sl(3,R), and Sl(4,R), add up numerologically as 3+8+15. Like the fundamental representation of F4, the number of dimensions is 26.

July 15, 2021 at 9:09 am |

I disagree with your numerology. You are adding apples and oranges. SL(2,C) has 3 complex dimensions, SL(3,R) has 8 real dimensions. Adding up real dimensions you get 29.

“The” Lorentz group is indeed trying to act on all three spacetimes at once. I am going to have to write a whole new paper on this problem, explaining how a spin 2 graviton w.r.t. parametric spacetime has spin 1 w.r.t. astronomical spacetime, and spin 1/2 w.r.t. atomic spacetime, so that it becomes possible to identify gravitons with neutrinos.

July 16, 2021 at 1:11 am

I took only the generators from Sl(2,C) that can be likened to the infinite series in Zeno’s paradox. The other three do not fit the continuous limit. It has to do with Sl(2,C) being decomposed as Sl(2,R)+Sl(2,R).

You are absolutely correct that what I did there was not logical or correct. When I start a sentence with “I immediately notice that…”, that’s a red flag and I’m just wrong. ğŸ™‚

July 16, 2021 at 1:43 am

Richard Feynman once admitted that when an electron emits a photon, no one really has any idea what is truly going on. People would ask him, is the photon waiting inside the electron? is the energy level of the electron changed? how can one imagine a quantum interaction in an n-dimensional setting? Etc… and he would be honest and say no one had any idea about that real fundamental picture…

And then Feynman diagrams helped some. And spinors gave a powerful algebraic tool (or a geometric one via Clifford algebra), that describes sets of rotation and makes sense of every particle in terms of quantum spin.

As the graviton shows up as a spin-1 particle in one of these spacetimes, which would actually be a photon, that seems to finally resolve what Feynman was saying.

And asking whether the universe is continuous versus discrete would certainly not be a truly answerable question if the one Einstein-Lorentz So(3,1) was the only point of contention. In a universe of three spacetimes, the answer either comes from all three, or the one that the other two embed into and possibly split off from(?)

So until then I shouldn’t be talking about Zeno’s arrow.

Fermions have three generations and spin1/2, normally described with spinorial representations of So(3,1). It is a profound insight that that right there is the wrong spacetime.

As they have similarities and differences with nuetrinos, if an electron turns out as nuetrino but differentiated by its respective spacetime, then Feynman’s answer that no one ever had any idea is truer than ever.

July 16, 2021 at 6:42 am |

In the paper I referred to above, Ranada and Tiemblo argue for a coupling of gravity to the quantum vacuum, in order to separate atomic clocks from astronomical clocks. This already goes against the standard model of particle physics, which assumes that no such coupling exists. But I’m with Ranada and Tiemblo on this one. Now to measure space as well, one requires rulers and gyroscopes. If one assumes that the speed of light is constant, one can use clocks as rulers, but if we drop this assumption we have more difficulty. However, no reasonable assumptions allow one to use a clock as a gyroscope. Ordinary gyroscopes are, of course, astronomical. According to the standard model, an atomic gyroscope is impossible in principle. My interpretation of the experimental data is rather different, which of course means I am a crackpot (by definition). It seems to me that atomic gyroscopes are not only possible in principle, but have already been built. In at least four independent ways: chirality of beta decay, muon g-2, CP-violation of neutral kaon decays, and neutrino oscillations.

July 16, 2021 at 7:06 am |

Incidentally, all the standard theories, both of particle physics and gravity, assume that one only needs clocks and rulers, not gyroscopes. What nonsense. You can’t even walk without a gyroscope in your head. How can you possibly expect to do rocket science without a gyroscope? In particle physics, you cannot talk about mass unless you have a gyroscope – because you don’t know which way to point your weighing scales.