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arXiv:1310.2602 · Entropy

Experimental Test of the “Special State” Theory of Quantum Measurement

Lawrence S. Schulman

Published Apr 2, 2012• 11 citations
arXivHTMLPDF

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.

DOI
10.3390/e14040665

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•Sep 18, 2026•0 citations
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.
By a radical modification of statistical mechanics the measurement process of quantum mechanics can be described in terms of pure, unitary time evolution, with no wave function collapse or many‐world ideas. The key notion is “special states,” rare microscopic states of a complex system. Recovering the standard probabilities requires of this theory the appearance of Cauchy‐distributed noise in some measurement processes. This article treats experimental situations where such noise might be detected and correlated with the need or absence of need for special states. Included in this possibility are “delayed choice” experiments, in which the correlation contravenes conventional ideas on causality. Background material on all topics is provided.
The “special state” understanding of the measurement process is presented, namely there is no “measurement process,” only unitary time evolution. However, in contrast to the many worlds interpretation, there is only one world. How this can be accomplished and how statistical mechanics is changed as a result are also discussed. The focus though is on experimental tests of this theory and the in-principle realization that this can give rise to feasible experimental tests. Those tests rely on the particular feature of having only one world, so that any change in the wave function must have a proximate cause, and it is the detection of that cause that constitutes the test. In a companion article there is further exploration concerning the details of the test. In addition, in the present article, the special state theory is extended theoretically through evidence of the uniqueness of the Cauchy distribution as well as explicit recognition of the role of entanglement.
In most theories of the quantum measurement process changes in an observer’s perception of a state can take place without forces, as for example if a state is prepared in an eigenstate of JxJ_xJx​ (x component of angular momentum) but JzJ_zJz​ is measured. In the “special state” theory (explained in the previous article) any change in wave function requires forces. This allows experimental tests to distinguish these ideas and in the present article two examples of such tests are considered. The first is a kind of double Stern–Gerlach experiment, the second a check for angular momentum changes in a polarizer.
Establishing (or falsifying) the special state theory of quantum measurement is a program with both theoretical and experimental directions. The special state theory has only pure unitary time evolution, like the many worlds interpretation, but only has one world. How this can be accomplished requires both “special states” and significant modification of the usual assumptions about the arrow of time. All this is reviewed below. Experimentally, proposals for tests already exist and the problems are first the practical one of doing the experiment and second the suggesting of other experiments. On the theoretical level, many problems remain and among them are the impact of particle statistics on the availability of special states, finding a way to estimate their abundance and the possibility of using a computer for this purpose. Regarding the arrow of time, there is an early proposal of J. A. Wheeler that may be implementable with implications for cosmology.
Quantum states are the key mathematical objects in quantum theory. It is therefore surprising that physicists have been unable to agree on what a quantum state represents. There are at least two opposing schools of thought, each almost as old as quantum theory itself. One is that a pure state is a physical property of system, much like position and momentum in classical mechanics. Another is that even a pure state has only a statistical significance, akin to a probability distribution in statistical mechanics. Here we show that, given only very mild assumptions, the statistical interpretation of the quantum state is inconsistent with the predictions of quantum theory. This result holds even in the presence of small amounts of experimental noise, and is therefore amenable to experimental test using present or near-future technology. If the predictions of quantum theory are confirmed, such a test would show that distinct quantum states must correspond to physically distinct states of reality.
Since its completion in 1922, the Stern-Gerlach experiment has long been regarded in mainstream quantum mechanics as a key experimental evidence for the 1/2 intrinsic spin of electrons, and a foundational observation for spatial quantization and quantum state collapse theory. Based on the basic standpoint of the light-origin theory, this paper adheres to the core criterion that magnetism is a secondary effect derived from the directional motion of electric charges, and re-examines the phenomenon that silver atomic beams split into two streams in a non-uniform magnetic field. This paper points out that the "intrinsic spin magnetic moment" defined by mainstream quantum theory cannot correspond to closed charge circulation inside the electron (the classical rotation model leads to the contradiction of superluminal speed), and violates the unified origin principle of "electricity generating magnetism" in electromagnetism. Essentially, it is a mathematical degree of freedom artificially introduced to fit experimental results. This paper proposes that the bifurcation effect of silver atomic beams can be fully explained by the orientation coupling between magnetic dipoles formed by ordered charge circulation of electrons inside atoms and an external non-uniform magnetic field. The magnetic dipoles of incident silver atoms are randomly distributed in orientation statistically, yet only two orientations, parallel and antiparallel to the external magnetic field, can remain stable in the gradient magnetic field, while intermediate orientations are unstable and excluded. Eventually the atomic beam separates into two discrete streams, with no need to introduce the hypothesis of intrinsic spin without physical carriers. This paper further designs a discriminative experimental scheme: in a single-electron trapping system with ultra-low temperature and strong magnetic shielding, after thermal jitter is sufficiently suppressed, if no stable self-sustained static magnetic dipole signal of the electron can be detected, it will constitute a direct test for the hypothesis of intrinsic spin magnetic moment.