Eur. Phys. J. Plus (2016) 131: 141
https://doi.org/10.1140/epjp/i2016-16141-4

Regular Article

Derivation of quantum probability from measurement

Serbian Academy of Sciences and Arts, Knez Mihajlova 35, 11000, Belgrade, Serbia

^* e-mail: fedorh@sanu.ac.rs

Received: 18 January 2016
Revised: 24 February 2016
Accepted: 11 March 2016
Published online: 10 May 2016

Abstract

To begin with, it is pointed out that the form of the quantum probability formula originates in the very initial state of the object system as seen when the state is expanded with the eigenprojectors of the measured observable. Making use of the probability reproducibility condition, which is a key concept in unitary measurement theory, one obtains the relevant coherent distribution of the complete-measurement results in the final unitary-measurement state in agreement with the mentioned probability formula. Treating the transition from the final unitary, or premeasurement, state, where all possible results are present, to one complete-measurement result sketchily in the usual way, the well-known probability formula is derived. In conclusion it is pointed out that the entire argument is only formal unless one makes it physical assuming that the quantum probability law is valid in the extreme case of probability-one (certain) events (projectors).