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CRC Press eBooks

Consecutive Quantum Measurements

Asher Peres

Published Oct 19, 2017• 1 citation
Publisher

Abstract

In some elementary textbooks of quantum mechanics, the quantum wave function ψ is treated as if it were a physical object, undergoing a “collapse” whenever a measurement is performed ( Bohm 1951 ). This collapse, which is a nonlinear transformation, is obviously incompatible with Schrödinger’s equation and leads to numerous paradoxes ( Schrödinger 1935 ).

DOI
10.1201/9780203741467-8

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In some elementary textbooks of quantum mechanics, the quantum wave function ψ is treated as if it were a physical object, undergoing a “collapse” whenever a measurement is performed ( Bohm 1951 ). This collapse, which is a nonlinear transformation, is obviously incompatible with Schrödinger’s equation and leads to numerous paradoxes ( Schrödinger 1935 ).
This study deals with the topic of “Analytical and numerical study of some problems in nonlinear mechanics.” The study aimed to analyze a problem in nonlinear mechanics, which is “wave function collapse.” Which is represented by the laboratory experiment "Schrödinger's cat", the interpretations of Heisenberg and Copenhagen, and an application of the method of Lagrange's equations to explain the phenomenon of wave function collapse and the EPR paradox, and Einstein's interpretation in pure algebraic theory and his interpretation of wave collapse, in addition to the Schrödinger equation. The study concluded with a set of results, the most important of which are: that the problem Wave function collapse represents one of the measurement problems in quantum mechanics. It has been proven that it can be solved based on quantum mechanics and does not require any additional assumptions or new theories. The processes of particle creation and annihilation described based on quantum field theory play a major role in measurement processes. Decoherence theory also refers to the creation and annihilation of particles and these processes are a nonlinear consequence of quantum mechanics, in which case the wave function collapse term becomes a consequence of other statements of quantum mechanics rather than a separate assumption of quantum mechanics.
Quantum mechanics is an immensely successful theory, occupying a unique position in the history of science. It has solved mysteries ranging from macroscopic superconductivity to the microscopic theory of elementary particles and has provided deep insights into the nature of vacuum on the one hand and the description of the nucleon on the other. Whole new fields such as quantum optics and quantum electronics owe their very existence to this body of knowledge. However, despite the stunning successes of quantum mechanics, there is no general agreement on the conceptual foundations and interpretation of the subject. The theory provides unambiguous information about the outcome of a measurement of a physical object. However, many feel that it does not provide a satisfactory answer to the nature of the “reality” we should attribute to the physical objects between the acts of measurement. The conceptual difficulty comes about because the wave function |ψ〉 is usually given by a coherent superposition of various distinguishable experimental outcomes. If we denote the collection of states that represent the possible outcomes of an experiment by |ψ j 〉, then |ψ〉 = ∑ j c j |ψ j 〉 where c j = 〈ψ j |ψ〉. The probability of the outcome |ψ j 〉 is P j =|c j | 2 . In the process of measurement, the so called collapse of the wave function takes place and a single, definite state |ψ i 〉 of the physical object is chosen. The difficulty comes about in the interpretation of the mechanism by which this definite state is chosen from amongst all the possible outcomes.