Quantum Time and Quantum Evolution

Author:

Góźdź Andrzej1ORCID,Góźdź Marek2ORCID,Pȩdrak Aleksandra3ORCID

Affiliation:

1. Institute of Physics, Maria Curie-Skłodowska University, pl. Marii Curie-Skłodowskiej 1, 20-031 Lublin, Poland

2. Institute of Computer Science, Maria Curie-Skłodowska University, ul. Akademicka 9, 20-033 Lublin, Poland

3. Department of Fundamental Research, National Centre for Nuclear Research, Pasteura 7, 02-093 Warsaw, Poland

Abstract

The problem of quantum time and evolution of quantum systems, where time is not a parameter, is considered. In our model, following some earlier works, time is represented by a quantum operator. In this paper, similarly to the position operators in the Schrödinger representation of quantum mechanics, this operator is a multiplication-type operator. It can be also represented by an appropriate positive operator-valued measure (POVM) which together with the 3D position operators/measures provide a quantum observable giving a position in the quantum spacetime. The quantum evolution itself is a stochastic process based on Lüder’s projection postulate. In fact, it is a generalization of the unitary evolution. This allows to treat time and generally the spacetime position as a quantum observable, in a consistent and observer-independent way.

Publisher

MDPI AG

Subject

General Physics and Astronomy

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