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arXiv:1210.8110 · On thinking

The Problem of Time and the Problem of Quantum Measurement

Tejinder P. Singh

Published Jan 1, 2015• 13 citations
arXivHTMLPDF
DOI
10.1007/978-3-319-10446-1_8

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HNPS Advances in Nuclear Physics•Dec 5, 2019•1 citation
The model of weak measurements is applied to various problems, related to the time problem in quantum mechanics.The review and generalization of the theoretical analysis of the time problem in quantum mechanics based on the concept of weak measurements are presented.A question of the time interval the system spends in the specified state, when the final state of the system is given, is raised.Using the concept of weak measurements the expression for such time is obtained.The results are applied to the tunnelling problem.A procedure for the calculation of the asymptotic tunnelling and reflection times is proposed.Examples for δ-form and rectangular barrier illustrate the obtained results.Using the concept of weak measurements the arrival time probability distribution is defined by analogy with the classical mechanics.The proposed procedure is suitable to the free particles and to particles subjected to an external potential, as well.It is shown that such an approach imposes an inherent limitation to the accuracy of the arrival time definition.
The conventional tacit assumption that nuclear and sub-nuclear reactions take place in the Newtonian universal time is replaced in the present paper by a time topological space based on the interaction proper time neighbourhood. It is developed and used to solve a problem related to the nuclear reaction theory, the quantum measurement problem. The time topology is disconnected and satisfies the separation axioms of the topological space 3 , . In this topology the V+R Penrose dynamics is implemented by means of a time evolution operator,"?/ .constructed using a quantized version of CSel'fand's theory - the generalized random quantum field theory (QRQFT). As an application the quantum measurement problem solution is presented.