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

We consider how the Born rule, a fundamental principle of quantum mechanics, can be tested for particles created on the shortest timescales ( <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:mo>∼</a:mo> <a:msup> <a:mrow> <a:mn>10</a:mn> </a:mrow> <a:mrow> <a:mo>−</a:mo> <a:mn>25</a:mn> </a:mrow> </a:msup> <a:mtext> </a:mtext> <a:mtext> </a:mtext> <a:mi mathvariant="normal">s</a:mi> </a:mrow> </a:math> ) currently accessible at high-energy colliders. We focus on targeted tests of the Born rule for spin or polarization 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 parametrized by nonlinear expectation values for quantum measurements of spin or polarization, together with anomalies in ensemble averages, which may then be constrained by experiments. Notable experiments considered here include the recent detection of single photons from top-quark decay, and the indirect measurement of tau-lepton polarization. Repurposing these experiments as tests of the Born rule, however, presents several challenges, which are discussed in this paper.