# Multiple-event probability in general-relativistic quantum mechanics

## Abstract

We discuss the definition of quantum probability in the context of 'timeless' general-relativistic quantum mechanics. In particular, we study the probability of sequences of events, or multievent probability. In conventional quantum mechanics this can be obtained by means of the 'wave function collapse' algorithm. We first point out certain difficulties of some natural definitions of multievent probability, including the conditional probability widely considered in the literature. We then observe that multievent probability can be reduced to single-event probability, by taking into account the quantum nature of the measuring apparatus. In fact, by exploiting the von-Neumann freedom of moving the quantum/classical boundary, one can always trade a sequence of noncommuting quantum measurements at different times, with an ensemble of simultaneous commuting measurements on the joint system+apparatus system. This observation permits a formulation of quantum theory based only on single-event probability, where the results of the wave function collapse algorithm can nevertheless be recovered. The discussion also bears on the nature of the quantum collapse.

- Authors:

- Fakultaet fuer Physik, Ludwig-Maximilians-Universitaet, D-80799 Munich (Germany)
- (France)
- Centre de Physique Theorique de Luminy, Universite de la Mediterranee, F-13288 Marseille (France)

- Publication Date:

- OSTI Identifier:
- 21020402

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 8; Other Information: DOI: 10.1103/PhysRevD.75.084033; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ALGORITHMS; COSMOLOGY; GENERAL RELATIVITY THEORY; PROBABILITY; QUANTUM FIELD THEORY; QUANTUM MECHANICS; RELATIVISTIC RANGE; WAVE FUNCTIONS

### Citation Formats

```
Hellmann, Frank, Centre de Physique Theorique de Luminy, Universite de la Mediterranee, F-13288 Marseille, Mondragon, Mauricio, Perez, Alejandro, and Rovelli, Carlo.
```*Multiple-event probability in general-relativistic quantum mechanics*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVD.75.084033.

```
Hellmann, Frank, Centre de Physique Theorique de Luminy, Universite de la Mediterranee, F-13288 Marseille, Mondragon, Mauricio, Perez, Alejandro, & Rovelli, Carlo.
```*Multiple-event probability in general-relativistic quantum mechanics*. United States. doi:10.1103/PHYSREVD.75.084033.

```
Hellmann, Frank, Centre de Physique Theorique de Luminy, Universite de la Mediterranee, F-13288 Marseille, Mondragon, Mauricio, Perez, Alejandro, and Rovelli, Carlo. Sun .
"Multiple-event probability in general-relativistic quantum mechanics". United States.
doi:10.1103/PHYSREVD.75.084033.
```

```
@article{osti_21020402,
```

title = {Multiple-event probability in general-relativistic quantum mechanics},

author = {Hellmann, Frank and Centre de Physique Theorique de Luminy, Universite de la Mediterranee, F-13288 Marseille and Mondragon, Mauricio and Perez, Alejandro and Rovelli, Carlo},

abstractNote = {We discuss the definition of quantum probability in the context of 'timeless' general-relativistic quantum mechanics. In particular, we study the probability of sequences of events, or multievent probability. In conventional quantum mechanics this can be obtained by means of the 'wave function collapse' algorithm. We first point out certain difficulties of some natural definitions of multievent probability, including the conditional probability widely considered in the literature. We then observe that multievent probability can be reduced to single-event probability, by taking into account the quantum nature of the measuring apparatus. In fact, by exploiting the von-Neumann freedom of moving the quantum/classical boundary, one can always trade a sequence of noncommuting quantum measurements at different times, with an ensemble of simultaneous commuting measurements on the joint system+apparatus system. This observation permits a formulation of quantum theory based only on single-event probability, where the results of the wave function collapse algorithm can nevertheless be recovered. The discussion also bears on the nature of the quantum collapse.},

doi = {10.1103/PHYSREVD.75.084033},

journal = {Physical Review. D, Particles Fields},

number = 8,

volume = 75,

place = {United States},

year = {Sun Apr 15 00:00:00 EDT 2007},

month = {Sun Apr 15 00:00:00 EDT 2007}

}