- #1
wfro64
- 1
- 1
- TL;DR
- Numerical simulation of Bell tests with quantized clocks (WAY theorem) shows a phase transition from Tsirelson bound to local realism driven by reference frame decoherence. Code/Paper on Zenodo.
Hi everyone,
I’ve been working on a numerical simulation to understand the limits of quantum measurement when the reference frames (clocks) are treated explicitly as quantum systems, consistent with the Wigner-Araki-Yanase (WAY) theorem.
My specific interest was to see how Bell correlations behave if we treat "time" not as a background parameter, but strictly as an ordering index, where operational access is mediated only by quantized clocks (e.g., harmonic oscillators).
The Simulation Model
I wrote a Python framework where measurement events act as a "global disentanglement" of the shared clock state. Instead of assuming a sharp measurement time t the measurement projects the clocks onto a new state (effectively resetting their local "creation time" relative to the ontic ordering).
The Results
The numerics are quite stable and show an interesting phase transition:
Does anyone know of existing literature that quantifies Bell violations specifically as a function of "reference frame coherence"? Most decoherence models talk about environmental coupling, but here the decoherence comes from the fuzziness of the clock reference itself.
I’ve uploaded the code (Python) and the mathematical write-up to Zenodo if anyone wants to check the method or the "clock reset" mechanism used in the simulation:
https://zenodo.org/records/18312249
I would appreciate any references to similar numerical studies!
I’ve been working on a numerical simulation to understand the limits of quantum measurement when the reference frames (clocks) are treated explicitly as quantum systems, consistent with the Wigner-Araki-Yanase (WAY) theorem.
My specific interest was to see how Bell correlations behave if we treat "time" not as a background parameter, but strictly as an ordering index, where operational access is mediated only by quantized clocks (e.g., harmonic oscillators).
The Simulation Model
I wrote a Python framework where measurement events act as a "global disentanglement" of the shared clock state. Instead of assuming a sharp measurement time t the measurement projects the clocks onto a new state (effectively resetting their local "creation time" relative to the ontic ordering).
The Results
The numerics are quite stable and show an interesting phase transition:
- Ideal Clocks: The model reproduces the Tsirelson bound (S ≈2.82) perfectly.
- Noisy Clocks: When introducing phase noise to the clock-coupling (simulating finite energy/coherence per the WAY theorem), the violation suppresses smoothly.
- Transition: There is a distinct crossover point where the system recovers classical local realism (S ≤ 2) once the local clock phase noise exceeds σ ≈ 0.94 rad (per clock).
Does anyone know of existing literature that quantifies Bell violations specifically as a function of "reference frame coherence"? Most decoherence models talk about environmental coupling, but here the decoherence comes from the fuzziness of the clock reference itself.
I’ve uploaded the code (Python) and the mathematical write-up to Zenodo if anyone wants to check the method or the "clock reset" mechanism used in the simulation:
https://zenodo.org/records/18312249
I would appreciate any references to similar numerical studies!