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A Testable Quantum Graph Theory of Spacetime

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This work aims, first and foremost, to construct a falsifiable model of quantum gravity, seamlessly linked to low-energy experiments.

— On the one hand, it derives the classical Newton–Maxwell–Einstein (GR) equations from a single "noisy" Hamiltonian on a discrete quantum graph, so it is essentially a candidate for a theory of quantum gravity.

— On the other hand, it also incorporates the symmetries of the Standard Model (U(1)×SU(2)×SU(3)), the spontaneous breaking of these symmetries, and even predictions about the "shor anomaly" and microwave resonances in cryogenic qubits.

Thus, this is not just "yet another" model of gravity, but a genuine attempt at a unified description of:

• quantum dynamics (via the σ-Hamiltonian),

• SM symmetries (via graph automorphisms),

• gravity (via discrete curvature and its continuous limit).

In this sense, the author claims a "theory of everything" on a discrete graph. But the key distinguishing feature is that it is constructed to yield specific laboratory predictions already at energies ≲10⁻⁴ eV and can therefore be quickly refuted or confirmed in cryogenic qubits and microwave experiments.

The theory itself is described in detail here: A Testable Quantum Graph Theory of Spacetime: Predictions for Cryogenic Qubits and Colliders

I had a quick look at this. Even though you guyz know my lack of knowledge etc in this field, it seems in some ways it might agree with my view. Does this Quantum Graph theory show how the Planck scale, relativity and quantum mechanics (the universe) are emergent from the nature of spacetime as described in the theory (or hypothesis as untested yet)? Has someone beaten me to it?

  • Author

My theory is currently undergoing experimental testing. Or rather, it's undergoing falsification, according to Popper.

Some questions:

What has quantum gravity to do with quantum computing?

What is a Shor anomaly?

How can graph theory be relevant for local continuous groups, as are those in the SM?

How can the non-linear sigma model be relevant in quantum gravity? And what is "noisy" about it in your implementation?

Can you present a summary of these completely bizarre-sounding connections w/o people having to click on your link?

32 minutes ago, SergejMaterov said:

My theory is currently undergoing experimental testing. Or rather, it's undergoing falsification, according to Popper.

Please do report on the results as soon as they're ready, falsified or not.

And last but not least,

are you aware of how much LLM-generated-garbage this sounds?

  • Author

Everything is described and written down in the mathematical language I am accustomed to at the link.

1 hour ago, BuddhasDragon23 said:

I had a quick look at this. Even though you guyz know my lack of knowledge etc in this field, it seems in some ways it might agree with my view.

If it was real physics of any value, we would be discussing it as a reference to a paper in a peer reviewed journal.

48 minutes ago, joigus said:

Can you present a summary of these completely bizarre-sounding connections w/o people having to click on your link?

This is not actually a request of mine, but one of the rules of these forums. You don't seem to be familiar with them:

28 minutes ago, SergejMaterov said:

Everything is described and written down in the mathematical language I am accustomed to at the link.

You have LateX "wrappers" to display any formulas you might need. We can help you with that.

  • Author

Abstract

This work is inspired by the book  Lloyd’s “Computational capacity of the universe” [5] and reports an explicitly falsifiable (already today) discrete–quantum‐graph model of spacetime and noise in quantum processors. Rather than invoking Planck‐scale assumptions or ad hoc temperature thresholds, we derive a single measurable scale:

[latex]k_BTc=Jz[/latex]

where J is the qubit‐qubit coupling (noise) energy and z the average vertex degree. Below T_c long‐range correlations

[latex]\Psi(r) = \left\langle \sigma_i^z \,\sigma_{i+r}^z \right\rangle[/latex]

persist; above T_c they vanish. We introduce the microscopic noise Hamiltonian

[latex]\widehat{H_{\mathrm{noise}}}= \sum_{\langle i,j \rangle} J_{ij}\, \sigma_i^z \sigma_j^z+ \sum_{i} h_i\, \sigma_i^x [/latex] allowing direct spectroscopy of [latex]\\ J_{ij} [/latex] and [latex] h_{i} [/latex] From this single relation we obtain multiple near‐term experimental tests—e.g. heat‐capacity and error‐rate crossovers at T≈T_c, correlation‐length collapse in small‐graph Monte Carlo, and spectral‐DOS corrections—all calibrated by measured J and z. Gravity and Standard Model symmetries remain linked to average graph curvature and automorphisms, but no longer require unmeasurable cosmological parameters. Appendix A presents the concrete protocol for extracting [latex] T_c [/latex] on existing QPU topologies.

The theory was developed deliberately to be falsifiable, and therefore I do not intend to defend it. At the same time, with regard to the work itself, constructive and well-founded comments or suggestions are welcome, but only after a thorough acquaintance with the theory.
This work proposes a concrete route from discrete graph degrees of freedom to effective continuum gauge dynamics and testable experimental signatures. To help the reader follow the chain of logic, we summarize the main conceptual steps here before the detailed derivations:

(i) start with local edge variables U_e on a finite graph and define a plaquette action

[latex]S_{lat} = \kappa \sum_{p} \left( 1 - \Re \ \operatorname{Tr}(V_p) \right), \quad V_p = \prod_{e \in p} U_e [/latex]
(ii) in the small-fluctuation, short-edge limit [latex]U_e\approx\exp{\left(iaA_\mu^aT^a\right)\ } [/latex] standard expansion of [latex]V_p [/latex] yields a leading [latex]F_{\mu\nu}^2 [/latex] term and an identification of the continuum coupling g with microscopic parameters [latex] \kappa,J,z [/latex],;

(iii) block-averaging and RG flow control whether the low-energy theory is governed by a Yang–Mills action and determine the sign and rate of running via the effective low-mode count [latex] N_f [/latex]; and

(iv) physical observables — critical crossover [latex] T_c [/latex], spectral signatures in Δtan δ , QPU error-rate crossovers, and topology sensitivity — follow from the same mapping and provide falsifiable tests.





Edited by SergejMaterov

2 hours ago, SergejMaterov said:

Everything is described and written down in the mathematical language I am accustomed to at the link.

Moderator Note

Material for discussion must be posted here. Not via links or uploads.

Hello again. Just from a dummies ignorant perspective, this theory seems to be based on lowering temperatures to reveal quantum effect. There seems to me to be a difference between quantum effects. Extreme cold reveals quantum effects in whole atoms, waves function and spin. Extreme heat reveals effects in what makes up atoms such as quarks, gluons and electrons. Would there be a prediction using raised temp in plasmas (unless this is what is testable in LHC collisions)?

Just if it helps this is available on SSRN website where i found it without using the link.

Edited by BuddhasDragon23

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