Abstract

An experimental test of the “special state” theory of quantum measurement is proposed. It should be feasible with present-day laboratory equipment and involves a slightly elaborated Stern–Gerlach setup. The “special state” theory is conservative with respect to quantum mechanics, but radical with respect to statistical mechanics, in particular regarding the arrow of time. In this article background material is given on both quantum measurement and statistical mechanics aspects. For example, it is shown that future boundary conditions would not contradict experience, indicating that the fundamental equal-a-priori-probability assumption at the foundations of statistical mechanics is far too strong (since future conditioning reduces the class of allowed states). The test is based on a feature of this theory that was found necessary in order to recover standard (Born) probabilities in quantum measurements. Specifically, certain systems should have “noise” whose amplitude follows the long-tailed Cauchy distribution. This distribution is marked by the occasional occurrence of extremely large signals as well as a non-self-averaging property. The proposed test is a variant of the Stern–Gerlach experiment in which protocols are devised, some of which will require the presence of this noise, some of which will not. The likely observational schemes would involve the distinction between detection and non-detection of that “noise”. The signal to be detected (or not) would be either single photons or electric fields (and related excitations) in the neighborhood of the ends of the magnets.

Highlights

  • In conference presentations in which I reported preliminary ideas on this subject [5,6] I focused on that experiment; but I later realized that the essential physical feature that would allow the experimental test did not depend on the “delayed” part of the story

  • That appendix tells you how to find the initial conditions, the ψ(0)’s, that lead to the all-decayed or all-not-decayed states at time-t0 . (That there are such states is equivalent to my demand for special states, as we shall see.) The blue curve in the figure is the time-dependence of an all-not-decayed-at-t0 state

  • This is a bold postulate, since the usual Born probabilities depend little on the apparatus and are computed from the wave function of the system being measured

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Summary

Introduction

There are many open theoretical issues, I felt that there could only be progress if these ideas were tested experimentally. In conference presentations in which I reported preliminary ideas on this subject [5,6] I focused on that experiment; but I later realized that the essential physical feature that would allow the experimental test did not depend on the “delayed” part of the story.

Quantum Mechanics
Use of the Special State
The Assumption Concerning Special States in Nature
Recovering Probabilities
The Arrow of Time
The Cat Map
Special States and Determinism
Requiring Special States
Properties of the Kick
Strength of the Field Inducing the Kick
Magnetic Fields along the Particle Path
Detection Scenarios
Scenario when the Fields Are Generated by the SG Magnets
Scenario when the Fields Are Generated by External Photons
Discussion
Findings
Search Technique for Special States
Full Text
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