Towards a test of the Born rule in high-energy collisions

TL;DR

The paper investigates testing the Born probability rule at the shortest collider-accessible timescales ($~10^{-25}$ s) by focusing on spin/polarisation probabilities in two-state systems within a Bell hidden-variable framework. It parameterises potential deviations with nonlinear expectation values and explores two experimental avenues: short-time photons from top-quark and $\pi^{0}$ decays, and average tau-helicity measurements from $Z$ decays, deriving concrete experimental targets such as $N_{\min}$, $\Delta n$, and $\Delta \Theta$ and contrasting them with existing data. It provides preliminary bounds on deviations from the quantum mean for tau leptons using CMS results and evaluates feasibility for photon polarisation tests, while highlighting how background modelling could influence sensitivity. The work situates collider tests as complementary to laboratory tests, offering constraints on quantum-nonequilibrium scenarios (e.g., pilot-wave theories) and informing the robustness of foundational quantum principles under extreme conditions.

Abstract

We consider how the Born rule, a fundamental principle of quantum mechanics, can be tested for particles created on the shortest timescales ($\sim10^{-25}\,\mathrm{s}$) currently accessible at high-energy colliders. We focus on targeted tests of the Born rule for spin or polarisation probabilities, which offer a particularly clean experimental signal, and which can be described by a simple hidden-variables model of two-state systems proposed by Bell. These probabilities test a remarkable feature of the quantum formalism, whereby expectation values for incompatible experiments are linearly related. Born-rule violations can be parameterised by nonlinear expectation values for quantum measurements of spin or polarisation, together with anomalies in ensemble averages, which may then be constrained by experiment. Notable experiments considered here include the recent detection of single photons from top-quark decay, and the indirect measurement of tau-lepton polarisation. Repurposing these experiments as tests of the Born rule, however, presents several challenges, which are discussed in this paper.

Figures (7)

• Figure 1: An ideal test of (\ref{['Malus']}) for single photons emerging from a high-energy collision.
• Figure 2: Bell's hidden-variables model of a two-state quantum system. In the example shown, $(\boldsymbol{\lambda}+\mathbf{P}_{\mathrm{QT}})\cdot \mathbf{m}<0$ and the outcome of the quantum measurement is $\sigma=-1$.
• Figure 3: Feynman diagrams showing (a) photon radiation from the top quark before decay and (b) photon radiation from a lepton in the decay products.
• Figure 4: Schematic view of the ATLAS detector, showing the inner detector, electromagnetic calorimeter, hadronic calorimeter, and muon spectrometer. The proposed polarimeter (for individual or mean polarisation) would be integrated between the inner detector and EM calorimeter.
• Figure 5: Schematic diagram of a forward $\pi^0$ decay at the RHIC. A high-energy proton collides with another polarised proton (not shown), producing a forward $\pi^0$ that decays into two photons.