The Franson Experiment as an Example of Spontaneous Breaking of Time-Translation Symmetry

David H Oaknin

doi:10.3390/sym14020380

Abstract

We describe an explicit statistical model of local hidden variables that reproduces the predictions of quantum mechanics for the ideal Franson experiment and sheds light on the physical mechanisms that might be involved in the actual experiment. The crux of our model is the spontaneous breaking of time-translation gauge symmetry by the hidden configurations of the pairs of photons locked in time and energy involved in the experiment, which acquire a non-zero geometric phase through certain cyclic transformations.

Highlights

IntroductionIt is widely accepted wisdom that quantum phenomena cannot be fully described within the framework of any physical theory that shares the same notions of reality and relativistic causality that we acknowledge as a given in our classical descriptions of the macroscopic world [1]
The crux of our model is the spontaneous breaking of time-translation gauge symmetry by the hidden configurations of the pairs of photons locked in time and energy involved in the experiment, which acquire due to a holonomy a non-zero geometric phase through certain cyclic coordinate transformations
This model closely resembles the model of local hidden variables introduced in [8,9,10]. The crux of both models is the spontaneous breaking of a gauge symmetry by the hidden configuration of the described pairs of photons, which acquires a non-zero geometric phase through certain cyclic transformations

Summary

Introduction

It is widely accepted wisdom that quantum phenomena cannot be fully described within the framework of any physical theory that shares the same notions of reality and relativistic causality that we acknowledge as a given in our classical descriptions of the macroscopic world [1] This wisdom is precisely formulated through the Bell theorem on the attainable correlations between the outcomes of polarization measurements performed on pairs of photons prepared in a singlet polarization state [2,3]. In a series of recent papers, we have shown, that the proof of the Bell theorem relies crucially on a subtle implicit assumption that is not required by fundamental physical principles and, the Bell inequality does not necessarily hold for models of local hidden variables that do not comply with the said unjustified assumption [8,9,10].

The Franson Experiment

The Actual Experimental Set-Up

The Statistical Model

Findings

Discussion