# Time operator and quantum projection evolution

## Abstract

In this paper, we consider time as a dynamical variable. In particular, we present the explicit realization of the time operator within four-dimensional nonrelativistic spacetime. The approach assumes including events as a part of the evolution. The evolution is not driven by the physical time, but it is based on the causally related physical events. The usual Schroedinger unitary evolution can be easily derived as a special case of the three-dimensional projection onto the space of simultaneous events. Also the time-energy uncertainty relation makes clear and mathematically rigorous interpretation.

- Authors:

- University of Marie Curie-Sklodowska, Institute of Physics (Poland), E-mail: mdebicki@kft.umcs.lublin.pl

- Publication Date:

- OSTI Identifier:
- 21075918

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physics of Atomic Nuclei; Journal Volume: 70; Journal Issue: 3; Other Information: DOI: 10.1134/S106377880703012X; Copyright (c) 2007 Nauka/Interperiodica; Article Copyright (c) 2007 Pleiades Publishing, Ltd; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; EVOLUTION; FOUR-DIMENSIONAL CALCULATIONS; MATHEMATICAL SPACE; SCHROEDINGER EQUATION; SPACE-TIME; THREE-DIMENSIONAL CALCULATIONS

### Citation Formats

```
Gozdz, A., E-mail: Andrzej.Gozdz@umcs.lublin.pl, and Debicki, M.
```*Time operator and quantum projection evolution*. United States: N. p., 2007.
Web. doi:10.1134/S106377880703012X.

```
Gozdz, A., E-mail: Andrzej.Gozdz@umcs.lublin.pl, & Debicki, M.
```*Time operator and quantum projection evolution*. United States. doi:10.1134/S106377880703012X.

```
Gozdz, A., E-mail: Andrzej.Gozdz@umcs.lublin.pl, and Debicki, M. Thu .
"Time operator and quantum projection evolution". United States.
doi:10.1134/S106377880703012X.
```

```
@article{osti_21075918,
```

title = {Time operator and quantum projection evolution},

author = {Gozdz, A., E-mail: Andrzej.Gozdz@umcs.lublin.pl and Debicki, M.},

abstractNote = {In this paper, we consider time as a dynamical variable. In particular, we present the explicit realization of the time operator within four-dimensional nonrelativistic spacetime. The approach assumes including events as a part of the evolution. The evolution is not driven by the physical time, but it is based on the causally related physical events. The usual Schroedinger unitary evolution can be easily derived as a special case of the three-dimensional projection onto the space of simultaneous events. Also the time-energy uncertainty relation makes clear and mathematically rigorous interpretation.},

doi = {10.1134/S106377880703012X},

journal = {Physics of Atomic Nuclei},

number = 3,

volume = 70,

place = {United States},

year = {Thu Mar 15 00:00:00 EDT 2007},

month = {Thu Mar 15 00:00:00 EDT 2007}

}

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