# A recent "pre-quantum, pre-spacetime theory" an 8D octonic theory more fundamental than QM or QFT/the standard model (and explaining it) predicting 6 particles, e.g. dark photon

@ExpandingMan You may not have heard Prof Singh, and his new theory:
https://www.tifr.res.in/~tpsingh/

According to it the fine-structure constant is (and the other (mass) constants tend to also include √(3/8)):

julia> @interval 1/(9/1024 * exp((1/3 - √(3/8)) * 2/3))
[137.04, 137.041]


The European Physical Journal Plus

We have recently proposed a pre-quantum, pre-spacetime theory as a matrix-valued Lagrangian dynamics on an octonionic spacetime. This theory offers the prospect of unifying internal symmetries of the standard model with pre-gravitation. We explain why such a quantum gravitational dynamics is in principle essential even at energies much smaller than Planck scale. […] We use the octonionic representation of fermions to compute the eigenvalues of the characteristic equation of this algebra and compare the resulting eigenvalues with known mass ratios for quarks and leptons. We show that the ratios of the eigenvalues correctly reproduce the [square root of the] known mass ratios. In conjunction with the trace dynamics Lagrangian, these eigenvalues also yield a theoretical derivation of the low-energy fine structure constant.

# Relativistic weak quantum gravity and its significance for the standard model of particle physics

There ought to exist a reformulation of quantum theory, even at energy scales much lower than
Planck scale, which does not depend on classical time
[…]
We construct an action principle in which the only free parameters are Planck length, Planck time and Planck’s constant. Every other physical constant, dimensional as well as dimensionless, is intended to be derived in terms of these three parameters. Note that in comparison with the usual studies of quantum gravity, we have traded Planck mass for Planck’s constant ̄h. This enables us to treat both UV and IR quantum gravity in the same analysis. Constants such as Newton’s gravitational constant G, speed of light c, and Planck mass mP are all now regarded as derivative quantities.

To construct the aforesaid desired reformulation of quantum theory, we must propose a new
physical space [which replaces 4D Minkowski space-time] on which fermionic spinors are to be
defined. We must then propose a dynamics on this new physical space, and work out the conse-
quences of the new space and the new dynamics, and compare them with known but unexplained
data. Finally we must show how classical spacetime geometry, and quantum (field) theory as we
know it, are recovered from this new formulation.

# Quantum Theory without Classical Time: a Route to Quantum Gravity and Unification

We identify the Left-Right symmetry breaking with electroweak symmetry breaking, which also results in
separation of emergent four-dimensional Minkowski spacetime from the internal symmetries which
describe the standard model. This ‘compactification without compactification’ is achieved through
the Ghirardi-Rimini-Weber mechanism of dynamical wave function collapse, which arises naturally
in our theory, because the underlying fundamental Hamiltonian is necessarily non-self-adjoint.
Only classical systems live in four dimensions; quantum systems always live in eight octonionic
(equivalently ten Minkowski) dimensions. We explain how our theory overcomes the puzzle of
quantum non-locality, while maintaining consistency with special relativity. We speculate on the
possible connection of our work with twistor spaces and spinorial space-time, and with Modified
Newtonian Dynamics (MOND).

Note, GRW spontaneous collapse theory, resolves Schödinger’s cat (i.e. is an alternative to Everettian multi-verse QM interpretation):

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This is a great information, although I do not comprehend all, yet.

It could be great to create a Julia package / notebook so people can learn about Professor Singh’ theory and works.

Like AstroNBodySim.jl where I can see the collision simulation of 2 galaxies. Basically, picture worht a thousand words, and to get wider audience without the need to have a Physics background.

FYI: If you want to do something with his theory, then up to octonions supported here (but not sedenions):

I recall sedenions also mentioned in some of his papers, here from the first link, at least sedenionic:

### Quantum worlds vs. Classical worlds

Our universe, as it is today, is dominated by classical bodies, which produce, and live in, a classical spacetime. This is the substrate shown in Fig. 7. […]
The octonionic theory achieves a formulation of the upper quantum level, relating quantum systems to a quantum spacetime, i.e. the octonionic spacetime.

In the octonionic theory, the transition from the classical substrate to the upper quantum level is very elegant and is reflected in the simplicity of the action principle of the theory.
[…]
the action principle of the theory is [an atom of spacetime-matter (STM)]

[Formula (66)]

where the degrees of freedom are on sedenionic space. This action is nothing but a refined form of the action of a relativistic particle in curved classical spacetime
[…]
and obey the Fano plane multiplication rules.
[…]
Equation (68) defines an octonion, whose eight direction vectors define the underlying physical space in which the ‘atom of spacetime-matter’ [the Q matrices = elementary particles] lives. The form of the matrix is shown in Eqn. (69). The elementary particles are defined by different directions of octonions.

Our fundamental action is a relativistic matrix-particle in higher dimensions. The universe is made of enormously many such STM atoms which interact through ‘collisions’ and entanglement. From their interactions emerges the low-energy universe we see. There perhaps cannot be a simpler description of unification than this action principle.
[…]
Once again, we see the great importance of Connes time τ. The universe is a higher-dimensional spacetime manifold filled with matter, all evolving in an absolute Connes time.

There he referenced from other people:

# [1904.03186] Three fermion generations with two unbroken gauge symmetries from the complex sedenions

can be described using the algebra of complexified sedenions C⊗S

I had never seen sedenions mentioned in any (physics) paper, at the time I wrote this post (after seeing them used for the first time in neural networks):

As I recall there have been several E_8 and E_8 \times E_8 theories since this one in the late 2000’s. They were interesting but none of them could reproduce the standard model, despite claims. Note that even GUT’s suffer from potentially having an extremely complicated Higgs sector and there is no consensus let alone any evidence of what that will have to look like, as I recall E_8 \times E_8 theories suffered from even more severe versions of this problem… I vaguely remember them having a lot of problems in the electroweak sector… maybe that one of them couldn’t have a Z or something like that, but maybe it was something less crazy. I don’t think I understood what the status of gravity was in any of these theories other than that they purported to have gravitons. It’s then not clear to me whether they’d be relying on a non-trivial UV fixed point to be rendered finite or something more exotic, though for the linked paper my guess would be that they imagine some way around it by virtue of their claim that it can be used to derive QFT.

Anyway, I’d be highly skeptical. It would certainly take a lot more than is shown here to demonstrate they can reproduce the standard model.

For what it’s worth, I think there are a lot of theories that are well worth spending some time thinking about which are not necessarily true. String theory may not be true either, that doesn’t mean it’s not a useful exercise. The Lisi theory probably falls in this category of not-true-but-worth-thinking-about but of course the media had to spoil everyone’s fun with nonsense hyperbolic claims.

On spontaneous collapse: I had thought some versions of this were ruled out, but perhaps not GRW (wikipedia doesn’t seem to think so). I know they tended to have big problems with basis independence, or lack thereof (i.e. inability to explain what are called “einselected” bases in the quantum decoherence sense). They’ve tried to explain their way out of it, but I personally would be pretty surprised of spontaneous collapse turned out to be true. On the other hand, they have the great virtue of being testable (whereas many other QM “interpretations” may not be) so again, they are worth thinking about, especially if you can come up with experiments.

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Right Garret Lisi was shot down at the time, and I didn’t understand his claims or the issues with at the time.

I can’t say for for Tejinder Singh’s theory, so I wanted your opinion, or someone in HEP. He seems to have lots of breakthroughs.

Do you think a theory can define constants, e.g. the fine-structure constant? I thought the 26 constants of the universe were an unsolved problem, including that one, and if he reduces to 3 and the others derived, that’s a major thing? I haven’t yet seen formulas for all the (mass) constants, only for the 6 quarks, plus positron, muon and tau lepton. I only calculated and verified some of the [square of] mass ratios for myself. It seems to hold up, but I’m not sure how the formulas are derived, except from the theory.

What would you look for as good features of the theory, or as possible fatal flaws? Anything you can quickly see? It’s testable, since it makes predictions (not just postdictions), the new particles, but I don’t know their exact properties.

He reproduces the three generations (as I recall Lisi was unable) and the standard model (“the symmetries of the standard model and its dimensionless constants are determined by the algebraic properties of the 8D octonionic spacetime. There is no freedom.”).

It seems so obvious to me that people should have been looking at octonions to help, so it’s unclear to me why not earlier, i.e. successfully.

I was reading Sean Caroll’s (2019). Something Deeply Hidden: Quantum Worlds and the Emergence of Spacetime

It’s really good regarding explaining Everettian (why most fundamental QM interpretation), but doesn’t rule out GRW (mentioned briefly as an alternative), which is not just a different interpretation, but testable as a different theory.

And “Our results here seem to suggest that the neutrino is a Majorana particle, and not a Dirac particle.” Elsewhere he calculates assuming Dirac, and then gets totally wrong values.

I graduated in late 2015 and haven’t been part of the physics community since. All I can offer is some perspective. Regarding which, I would say that it’s a very long road to show that anything is consistent with the SM and the more novel the theory the longer that road is going to be. Frankly this is exactly the kind of thing that I plan to studiously avoid spending any real time on as I unfortunately have to work for a living and can no longer spend all my time thinking about physics. It will be far more personally fulfilling for me to try to follow what the experts are doing in less speculative fields and keep reading textbooks for fun so I don’t forget my education. I think there is a media selection effect here where things with grandiose claims get undue attention and it takes more personal responsibility to not fall victim to that when outside the community. I can assure you that if e.g. a novel quantum gravity theory is shown to have the SM in its IR limit you will hear plenty about it from the mainstream physics community, but it takes a lot of time and effort to see that. Keep in mind that loop quantum gravity has been around for many years and its widely considered a QG candidate but last I checked they still cannot even show that they have a Minkowski vacuum (and perhaps not even unitarity but don’t quote me on that).

Yes, I strongly recommend any of Caroll’s stuff on interpretations, though I haven’t read any of his popular science stuff. He’s played a big role in making me what I would now tentatively describe as “fully satisfied” with the Everettian interpretation. For years I believed that Everettian, consistent histories, relational QM and maybe even some whackier things like Bayesian QM were equivalent and I somewhat favored the relational interpretation. While this may still be true in retrospect I now find some of my former thinking on the subject rather silly. The Everettian interpretation is by far the simplest and is consistent with everything we know. The insistence on “throwing out” branches is a flaw of human intuition (in retrospect I believe a big part of the cognitive deficiency here is lack of intuition for “weighting” the branches). Caroll and his colleagues have made some very simple arguments which I find highly effective, for example I recommend reading the argument here against branch counting. Having an intuitive appreciation for the lack of self-consistency of branch counting gives you a deeper understanding of QM.

For what it’s worth, there are some “interpretations” which are definitely inequivalent to Everettian and the others I’ve mentioned, spontaneous collapse and pilot-wave theories being the most prominent examples. This inequivalence is a virtue of these theories because it means that they can be ruled out. I’m quite sure some spontaneous collapse theories have already been ruled out but I can’t comment on how close they are to GRW (don’t see references in my lists for this).

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This theory doesn’t have a graviton. That much I remember, and if I recall gravity isn’t quantized.

FYI: I thought based on GRW, since I saw it mentioned, but I see based on trace dynamics a different collapse theory (or both it and GRW?):

The gravitational effect of an electron is equivalent to curving of this 8D octonionic spacetime and is described by the dynamical equations of a generalised trace dynamics [5].
[…]
This theory generalises Adler’s theory of trace dynamics [6,7,8], which is a pre-quantum theory on a four-dimensional Minkowski spacetime [9, 10].

Spontaneous localisation is a falsifiable, phenomenological, mechanism for explaining the
absence of macroscopic position superpositions, currently being tested for in the laboratory.
The theory of trace dynamics provides a possible theoretical origin for spontaneous local-
isation.
[…]
The theory of trace dynamics developed by Adler and collaborators [5, 10–12].
provides a framework for understanding spontaneous collapse. Trace dynamics is a matrix
dynamics of Grassmann valued matrices, possessing a global unitary invariance. In this
dynamics, classical point particles (as well as classical fields) are raised to the status of op-
erators/matrices. The theory operates at the Planck scale; gravity is not included however.

Stephen L. Adler, Quantum theory as an emergent phenomenon (Cambridge University Press,
2004).