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Mathematical Physics Seminar

Born's rule for arbitrary Cauchy surfaces

Matthias Lienert, Rutgers University

Location:  HILL 705
Date & time: Thursday, 26 October 2017 at 2:00PM - 3:00PM

Abstract: Suppose that particle detectors are placed along a Cauchy surfaces Sigma in Minkowski space-time. Given an appropriate wave function psi_Sigma on Sigma, one can easily guess the respective "curved Born rule": the probability distribution of the detected configuration on Sigma has density |psi_Sigma|^2 (with |.|^2 suitably understood). However, simply postulating the curved Born rule seems neither appropriate nor necessary, as in principle the usual measurement postulates at equal times in any single Lorentz frame should already determine the results of all conceivable experiments.This situation has been the motivation of a recently finished joint work with Roderich Tumulka (arXiv:1706.07074), about which I will report in this talk. We define an idealized detection process by approximating a curved Cauchy surface by small horizontal (equal-time) pieces and prove that the probability distribution coincides with |psi_Sigma|^2. For this result, we make use of two crucial hypotheses on the time evolution: 1. no interaction faster than the speed of light, and 2. no particle creation from the vacuum.

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