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Physics of Atomic Nuclei

Projection Evolution of Quantum States—the Delayed Choice Puzzle

Marek Góźdź, ANDRZEJ GÓŹDŹ, Alexander A. Gusev, Sergue Il'ich Vinitsky

Published Nov 1, 2018• 1 citation
Publisher

Abstract

We discuss the problem of the time variable in the nearly standard formulation of the quantum mechanics. In order to be able to describe the outcome of some of the experiments, we have used a novel formulation of the time evolution of quantum states called the projection evolution. As an example a delayed-choice experiment is described. We show that this description recreates the experimental results without relaying on the spatial parts of the wave functions.

DOI
10.1134/s1063778818060157

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We discuss the problem of the time variable in the nearly standard formulation of the quantum mechanics. In order to be able to describe the outcome of some of the experiments, we have used a novel formulation of the time evolution of quantum states called the projection evolution. As an example a delayed-choice experiment is described. We show that this description recreates the experimental results without relaying on the spatial parts of the wave functions.
In the Schrödinger evolution of a quantum state, time enters as a real parameter representing the coordinate. In a more consistent approach, time should be defined as a quantum observable, with the evolution taking place in a four-dimensional spacetime. This is possible in the projection evolution model in which the wave function is defined in both space and time. This allows to construct the time operator and discuss the temporal structure of the quantum processes. In this paper, we discuss a photon travelling through a Mach-Zehnder interferometer, focusing the description on the temporal profile of the wave function. We show that in this approach the delayed-choice experiments can be explained by the temporal overlap of the photon and the devices in the interferometer.
In the Schrödinger evolution of a quantum state time enters as a real parameter representing the coordinate. In a more consistent approach time should be defined as a quantum observable, with the evolution taking place in a four-dimensional spacetime. This is possible in the projection evolution model in which the wave function is defined in both space and time. This allows to construct the time operator and discuss the temporal structure of quantum processes. In this paper we discuss a photon travelling through a Mach-Zehnder interferometer, focusing the description on the temporal profile of the wave function. We show that in this approach the delayed-choice experiments can be explained by the temporal overlap of the photon and the devices in the interferometer.
We discuss the problem of time in quantum mechanics. In the traditional formulation time enters the model as a parameter, not an observable, which follows from the famous Pauli theorem. It is now known, that Pauli's assumptions were too strong and that by removing some of them time can be represented as a quantum observable. In this case, instead of the unitary time evolution, other operators which map the space of initial states into the space of final states at each step of the evolution can be used. This allows to treat time as a quantum observable in a consistent way. We present the projection evolution model and show how the traditional Schroedinger evolution can be obtained from it. We propose the form of the time operator which satisfies the energy-time uncertainty relation. As an example, we discuss the temporal version of the double-slit experiment.
We discuss the problem of time in quantum mechanics. In the traditional formulation time enters the model as a parameter, not an observable, which follows from the famous Pauli theorem. It is now known, that Pauli's assumptions were too strong and that by removing some of them time can be represented as a quantum observable. In this case, instead of the unitary time evolution, other operators which map the space of initial states into the space of final states at each step of the evolution can be used. This allows to treat time as a quantum observable in a consistent way. We present the projection evolution model and show how the traditional Schroedinger evolution can be obtained from it. We propose the form of the time operator which satisfies the energy-time uncertainty relation. As an example, we discuss the temporal version of the double-slit experiment.
The Quantum Mechanics is interpreted, in this article, in a simple and direct way. By combining the unitary evolution with the quantum condition that observations require the state vector to be an eigenstate of the observable, a discontinuity in evolution (the state vector reduction) seems to be mandatory. Thus, for each such discontinuity, new initial conditions for the time evolution state vector are needed, and they are obtained by measurements. Delayed-choice experiments suggest that these new initial conditions are specified after the discontinuity takes place. Consequently, because it needs initial conditions that can be specified with a delay, the time evolving state vector is semi-realistic (in the sense that it is not completely specified until the measurement is performed), and not entirely realistic. The collapse of the wave function, especially when it is combined with the entanglement, seems to be a non-local phenomenon. In fact, the non-locality is present only as a consistency requirement for the initial conditions needed to select a solution of the evolution equation. The Direct Interpretation is intended to provide to our intuition a physical background, for helping us thinking about quantum phenomena. It identifies the main counterintuitive parts of the Quantum Mechanics in the discontinuity and the delayed initial conditions. Because it makes minimal assumptions, it is compatible with the main interpretations of Quantum Mechanics. Two principal unclear points of Quantum Mechanics are identified in the discontinuities, and the measurement problem. Both problems will be approached in subsequent articles.