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Foundations of Physics

Looking for the Source of Change

Lawrence S. Schulman, M. G. E. da Luz

Published Jul 29, 2016• 5 citations
Publisher

Abstract

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 $$J_x$$ (x component of angular momentum) but $$J_z$$ 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.

DOI
10.1007/s10701-016-0031-x

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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.
While the Stern–Gerlach experiment is an old and familiar problem, no analysis of this experiment is presented in the pedagogical literature using modern quantum mechanical techniques. Expositions of the Stern–Gerlach experiment are usually based on ‘‘old quantum theory,’’ i.e., semiclassical Bohr–Sommerfeld quantum mechanics. The experiment is also a popular one in discussions of the postulate of quantum measurement, which asserts that the process of measuring an observable forces the state vector of the system into an eigenvector of that observable, and the value measured will be the eigenvalue of that eigenvector. The most enduring of the philosophical arguments associated with quantum mechanics ultimately revolves around the mechanism of quantum measurement. Since the postulate of quantum measurement is expressed in terms well outside the realm of the old quantum mechanics, the traditional analysis of the Stern–Gerlach experiment cannot reveal any information about the relationship between dynamics and measurement. Therefore, a modern analysis of the Stern–Gerlach experiment must be made if this experiment is to reveal any information about the relationship between dynamics and the mechanism of quantum measurement. This paper presents such an analysis, and develops some of the implications for the theory of quantum measurement.
The successful results of phase echo multilayer mirror interferometer for cold neutrons at C3-1-2 (MINE) in JRR3M of JAERI-Tokai enable us to perform `double Stern Gerlach` (dSG) experiment which was proposed by Machida and Namiki in 1987 to test the quantum mechanical measurement theories, especially Many World Interpretation of Everett`s, Environment Theory by Zurek and Many-Hilbert-Space Theory (MHST) by themselves. There are many measurement theories where they don`t distinguish the two steps, a spectral decomposition step and a detection step, through the measurement process while they explain how to derive the wave function reduction theoretically. In MHST they proposed these two steps and clarify the issue of the coherence during the measurement process. This experiment can clarify not only these three theories but also the fact whether these two steps function differently during the measurement process in terms of coherence phenomena. This experiment consists of two spectral decomposition (two magnetic mirrors to divide each beam into two spatially divided beams according to its spin states) put after the simple beam splitter. We investigate the existence of the coherence in the super posed beam after the spectral decomposition. Clear coherence patters are measured with rotating the second composite mirror. This clarifies that the spectral decomposition never plays any role to decrease the coherence between the eigenstates of the superposed state and that we have to investigate the detection step to find the mechanism of the wave packet reduction during the measurement process. (author)
Change is built into the structure of a quantum state. State collapse is a very particular and distinctive process, but it is not the only way that quantum states can change. For most of the time, various quantum systems that exist in nature wander about the universe without being involved in experiments, yet clearly, things can and do change. Eigenstates describe systems as having a definite fixed value of a given physical property. Such states are very important. If we know that an object is in an eigenstate, we can predict with absolute certainty what a measurement is going to produce. It’s very important to be able to tell if a state is a mixed state or an eigenstate with reference to a given measurement. There are many different operators in quantum theory, which have different jobs to do. Perhaps the most important ones are the operators that represent the process of measuring a physical property.
Abstract In 1921, Otto Stern conceived the idea for an experiment that would decide between a classical and a quantum description of atomic behavior, as epitomized by the Bohr–Sommerfeld–Debye model of the atom. This model entailed not only the quantization of the magnitude of the orbital electronic angular momentum but also of the projection of the angular momentum on an external magnetic field – the so‐called space quantization. Stern recognized that space quantization would have observable consequences: namely, that the magnetic dipole moment due to the orbital angular momentum would be space quantized as well, taking two opposite values for atoms whose only unpaired electron has just one quantum of orbital angular momentum. When acted upon by a suitable inhomogeneous magnetic field, a beam of such atoms would be split into two beams consisting of deflected atoms with opposite projections of the orbital angular momentum on the magnetic field. In contradistinction, if atoms behaved classically, the atomic beam would only broaden along the field gradient and have maximum intensity at zero deflection, i. e., where there would be a minimum or no intensity for a beam split due to space quantization. Stern anticipated that, although simple in principle, the experiment would be difficult to carry out – and invited Walther Gerlach to team up with him. Gerlach's realism and experimental skills together with his sometimes stubborn determination to make things work proved invaluable for the success of the Stern–Gerlach experiment (SGE). After a long struggle, Gerlach finally saw, on 8 February 1922, the splitting of a beam of silver atoms in a magnetic field. The absence of the concept of electron spin confused and confounded the interpretation of the SGE, as the silver atoms were, in fact, in a 2S state, with zero orbital and spin angular momentum. However, a key quantum feature whose existence the SGE was designed to test – namely space quantization of electronic angular momentum – was robust enough to transpire independent of whether the electronic angular momentum was orbital or due to spin. The SGE entails other key aspects of quantum mechanics such as quantum measurement, state preparation, coherence, and entanglement. Confronted with the outcome of the SGE, Stern noted: “I still have objections to the idea of beauty of quantum mechanics. But she is correct.”
It is suggested that a thorough treatment of electron spin has advantages as a method of presenting many of the concepts and techniques of intermediate quantum mechanics. The starting point is the Stern-Gerlach experiment, from which the anticommutation relations for the spin operators may immediately be deduced. The commutation relations, which demonstrate that the spin is an angular momentum, are derived from these and it is shown that the anomalous gyromagnetic ratio is a natural consequence of the properties of the spin operators. The Pauli theory, which is the simplest example of the use of matrices in quantum mechanics, is briefly summarised, and employed in an analysis of the double Stern-Gerlach experiment. This example of a change of representation is used to introduce Dirac's transformation theory which, together with a variant of the double Stern-Gerlach experiment, is made use of in a discussion of the EPR paradox, Bell's inequality and hidden-variable theories. It is emphasised that the quantum mechanical description of these phenomena is consistent and that, from the viewpoint of quantum theory, no action-at-a-distance is required to explain them.