Torsion as a Candidate Geometric Generator of Quantum Phase and Statistics: A Formalization and Falsifiability Analysis

In the paper's words

Quantum mechanics rests on postulates—the complex phase of the wavefunction, the quadratic scaling of state-space dimension, and the boson/fermion restriction on exchange symmetry—that are empirically successful but deductively unexplained. A conjecture in current circulation holds that spacetime torsion in Einstein–Cartan gravity generates all three: the axial torsion vector supplies the wavefunction's phase gradient, and the topology of torsional exchange paths permits only ± 1 exchange phases. This paper formalizes the claimed deductive chain link by link.

The abstract, verbatim, and its opening sentence is the claim. Every line below is quoted from the text.

Numbers it reports

1. The Tianyan platform paper [4] reports a 105-qubit superconducting processor with single-qubit gate, two-qubit gate, and readout fidelities of $99.90\%$, $99.56\%$, and $98.7\%$ respectively, cloud-accessible, and demonstrates random circuit sampling with 74 qubits and 24 cycles.

   from 2. Background and Related Work

2. We show that the exchange-phase restriction $e^{i\varphi}=\pm 1$ follows from the double-swap identity alone, that the normalized state space of an $N$-level system carries $K=N^{2}-1$ real parameters ($3$, $8$, and $15$ for $N=2,3,4$), and that the integral of the Lorentz factor over physical velocities evaluates to $\pi/2\approx 1.5707963$.

   from Abstract

3. As a labeled projection built on the gate fidelities of the Tianyan platform [4], a simple gate-count model yields a total error probability of $99.66\%$ for a 74-qubit, 24-cycle random-circuit sampling experiment; this figure characterizes the hardware error budget and is not a torsion-specific prediction.

   from Abstract

4. A derivation that the integral of the Lorentz factor $\gamma(\beta)=(1-\beta^{2})^{-1/2}$ over $\beta\in[0,1]$ equals $\pi/2\approx 1.5707963$, reproducing the conjecture's claimed angular normalization (Section 4.3).

   from 1. Introduction

5. We use its fidelity figures in Sections 4.5 and 5 as the quantitative input to a labeled error-accumulation projection, and we cite it in Section 7 as the class of currently available testbed on which statistics-sensitive interference experiments could be specified, without claiming any torsion-specific capability for it.

   from 2. Background and Related Work

6. The Lorentz factor for velocity fraction $\beta=v/c$ is $$\gamma(\beta)=\frac{1}{\sqrt{1-\beta^{2}}}.$$ We evaluate its integral over the full physical subluminal range $\beta\in[0,1]$: $$\int_{0}^{1}\frac{d\beta}{\sqrt{1-\beta^{2}}}=\Bigl[\arcsin\beta\Bigr]_{0}^{1}=\arcsin(1)-\arcsin(0)=\frac{\pi}{2}-0=\frac{\pi}{2}.$$ Numerically, $$\frac{\pi}{2}\approx 1.5707963.$$ This is the claimed angular normalization: the Lorentz factor, integrated over its physical domain, yields exactly a quarter turn.

   from 4.3 Link L3: the Lorentz-factor integral and the $\pi/2$ normalization

How it is done

1. As a labeled projection built on the gate fidelities of the Tianyan platform [4], a simple gate-count model yields a total error probability of $99.66\%$ for a 74-qubit, 24-cycle random-circuit sampling experiment; this figure characterizes the hardware error budget and is not a torsion-specific prediction.

   from Abstract

2. It does three things that a proof attempt requires first.

   from 1. Introduction

3. Their derivation of asymptotic Bayes-risk lower bounds via the quantum Cramér–Rao bound, including the collective-measurement advantage over separate measurements, presupposes this geometry rather than explaining it.

   from 2. Background and Related Work

4. Our method is analytic decomposition of the conjecture into links, each of which is either derived, formalized, or declared open.

   from 3. Methods

What would falsify it

1. As a labeled projection built on the gate fidelities of the Tianyan platform [4], a simple gate-count model yields a total error probability of $99.66\%$ for a 74-qubit, 24-cycle random-circuit sampling experiment; this figure characterizes the hardware error budget and is not a torsion-specific prediction.

   from Abstract

2. It writes the torsion-coupled Madelung equations explicitly, so that the phase-generation link has a definite mathematical form that can be checked or refuted.

   from 1. Introduction

3. A falsifiability analysis: the specific calculation whose outcome would confirm or break the torsion-phase link, and the observations that would falsify each derived link (Sections 5, 6, and 7).

   from 1. Introduction

Where the claim stops

1. Two of its three mathematical links—exchange-phase restriction and state-space dimension count—reduce to standard mathematics that does not require torsion: the double-swap identity gives $e^{i\varphi}=\pm 1$ from the permutation group alone, and $K=N^{2}-1$ follows from Hermiticity and normalization alone.

   from 6. Discussion

2. We discuss what this split means, how it could be wrong, and what remains open.

   from 6. Discussion

3. What the derivable links do and do not establish.

   from 6. Discussion

Where to read

1. Abstract231 words · 1 min
2. 1. Introduction506 words · 2 min
3. 2. Background and Related Work839 words · 4 min
4. 3. Methods449 words · 2 min
5. 4. Analysis1,215 words · 5 min
6. 5. Results279 words · 1 min
7. 6. Discussion849 words · 4 min
8. 7. Practical Implications and Engineering Pathways575 words · 3 min
9. 8. Conclusion228 words · 1 min
10. Provenance and AI Involvement225 words · 1 min