Khrennikov, A. Yu. (2006) *Random fluctuations at the Planck length scale: A source of quatum randomness.* Հայաստանի ԳԱԱ Տեղեկագիր. Մաթեմատիկա, 41 (5). pp. 69-80. ISSN 00002-3043

## Abstract

The mathematical formalism of quantum mechanics can be interpreted as a method for approximation of classical (measure-theoretic) averages of functions. These are the classical physical variables in Prequantum Classical Statistical Field Theory (PCSFT), as we call our model with hidden vaiales. The present paper provides a simple sochastic picture of a quantum approximation procedure equivalent to an approximative method for computation of averages of random variable. Since in PCSFT the space of hidden variables is L2 (R³), the role of classical random variable is played by a random field. In PCSFT we consider Gaussian andom fields representing random fluctuations at the prequantum length scale. Quantum mechanical expression for the average (given by the von Neumann trace formula) is obtained by moving from the prequantum to the quantim length scale (the scale that enables to perform measurements). The order of deviations of quatum (approximative) averages from the classical ones is given by the length scaling parameter, which is extremely small for quantum systems, for an electron.

### Actions (login required)