Quantum averages from Gaussian random fields at the Planck length scale

Andrei Khrennikov

doi:10.1117/12.801900

29 April 2008 Quantum averages from Gaussian random fields at the Planck length scale

Andrei Khrennikov

Proceedings Volume 7023, Quantum Informatics 2007; 702309 (2008) https://doi.org/10.1117/12.801900
Event: Quantum Informatics 2007, 2007, Moscow, Russian Federation

Abstract

We show that the mathematical formalism of quantum mechanics can be interpreted as a method for approximation of classical (measure-theoretic) averages of functions f : L₂(R³) → R. These are classical physical variables in our model with hidden variables - Prequantum Classical Statistical Field Theory (PCSFT). In this paper we provide a simple stochastic picture of such a quantum approximation procedure. In the probabilistic terms this is nothing else than the approximative method for computation of averages for functions of random variables. Since in PCSFT the space of hidden variables is L₂(R³), the role of a classical random variable is played by a random field. In PCSFT we consider Gaussian random fields representing random fluctuations at the prequantum length scale. Quantum mechanical expression for the average (given by the von Neumann trace formula) is obtained through moving from the prequantum length scale to the quantum one (the scale at that we are able to perform measurements).

Citation Download Citation

Andrei Khrennikov "Quantum averages from Gaussian random fields at the Planck length scale", Proc. SPIE 7023, Quantum Informatics 2007, 702309 (29 April 2008); https://doi.org/10.1117/12.801900

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