Towards violation of Born's rule: description of a simple experiment

Journal Article · Mon Mar 28 00:00:00 EDT 2011 · AIP Conference Proceedings

DOI:https://doi.org/10.1063/1.3578726· OSTI ID:21511512

Khrennikov, Andrei ^[1]

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1. International Center for Mathematical Modelling in Physics and Cognitive Sciences, Linnaeus University, Vaexjoe, S-35195 (Sweden)

Recently a new model with hidden variables of the wave type was elaborated, so called prequantum classical statistical field theory (PCSFT). Roughly speaking PCSFT is a classical signal theory applied to a special class of signals - 'quantum systems'. PCSFT reproduces successfully all probabilistic predictions of QM, including correlations for entangled systems. This model peacefully coexists with all known no-go theorems, including Bell's theorem. In our approach QM is an approximate model. All probabilistic predictions of QM are only (quite good) approximations of 'real physical averages'. The latter are averages with respect to fluctuations of prequantum fields. In particular, Born's rule is only an approximate rule. More precise experiments should demonstrate its violation. We present a simple experiment which has to produce statistical data violating Born's rule. Since the PCSFT-presentation of this experiment may be difficult for experimenters, we reformulate consequences of PCSFT in terms of the conventional wave function. In general, deviation from Born's rule is rather small. We found an experiment amplifying this deviation. We start with a toy example. Then we present a more realistic example based on Gaussian states with very small dispersion.

• OSTI ID: 21511512
• Journal Information: AIP Conference Proceedings, Vol. 1327, Issue 1; Conference: International conference on advances in quantum theory, Vaexjoe (Sweden), 14-17 Jun 2010; Other Information: DOI: 10.1063/1.3578726; (c) 2011 American Institute of Physics; ISSN 0094-243X
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
APPROXIMATIONS
BELL THEOREM
CORRELATIONS
DISPERSIONS
FIELD THEORIES
FLUCTUATIONS
FORECASTING
FUNCTIONAL ANALYSIS
HIDDEN VARIABLES
PROBABILISTIC ESTIMATION
PROBABILITY
QUANTUM ENTANGLEMENT
QUANTUM MECHANICS
SIMULATION
WAVE FUNCTIONS
CALCULATION METHODS
FUNCTIONS
MATHEMATICS
MECHANICS
VARIATIONS