Prequantum Classical Statistical Field Theory: Schrödinger Dynamics of Entangled Systems as a Classical Stochastic Process

The idea that quantum randomness can be reduced to randomness of classical fields (fluctuating at time and space scales which are essentially finer than scales approachable in modern quantum experiments) is rather old. Various models have been proposed, e.g., stochastic electrodynamics or the semiclassical model. Recently a new model, so called prequantum classical statistical field theory (PCSFT), was developed. By this model a “quantum system” is just a label for (so to say “prequantum”) classical random field. Quantum averages can be represented as classical field averages. Correlations between observables on subsystems of a composite system can be as well represented as classical correlations. In particular, it can be done for entangled systems. Creation of such classical field representation demystifies quantum entanglement. In this paper we show that quantum dynamics (given by Schrödinger’s equation) of entangled systems can be represented as the stochastic dynamics of classical random fields. The “effect of entanglement” is produced by classical correlations which were present at the initial moment of time, cf. views of Albert Einstein.

[1]  Andrei Khrennikov,et al.  Generalizations of Quantum Mechanics Induced by Classical Statistical Field Theory , 2005 .

[2]  Timothy H. Boyer,et al.  A Brief Survey of Stochastic Electrodynamics , 1980 .

[3]  H. Elze.  Is there a relativistic nonlinear generalization of quantum mechanics? , 2007, 0704.2559.

[4]  A. Barut,et al.  Foundations of radiation theory and quantum electrodynamics , 1980 .

[5]  H. Elze.  Does quantum mechanics tell an atomistic spacetime , 2009, 0906.1101.

[6]  Luis de la Peña,et al.  The quantum dice : an introduction to stochastic electrodynamics , 1996 .

[7]  Quantization in classical mechanics and reality of Bohm's psi-field , 2009, 0906.1723.

[8]  Andrei Khrennikov,et al.  A pre-quantum classical statistical model with infinite-dimensional phase space , 2005, quant-ph/0505228.

[9]  Andrei Khrennikov,et al.  To quantum averages through asymptotic expansion of classical averages on infinite-dimensional space , 2007 .

[10]  Andrei Khrennikov.  On the problem of hidden variables for quantum field theory , 2006 .

[11]  Andrei Khrennikov.  Nonlinear Schrödinger equations from prequantum classical statistical field theory , 2006 .

[12]  J. Neumann.  Mathematical Foundations of Quantum Mechanics , 1955 .

[13]  A quantum-classical bracket from p-mechanics , 2005, quant-ph/0506122.

[14]  H. Elze.  The Attractor and the Quantum States , 2008, 0806.3408.

[15]  Andrei Khrennikov.  Description of Composite Quantum Systems by Means of Classical Random Fields , 2010 .

[16]  Andrei Khrennikov,et al.  Prequantum Classical Statistical Field Theory: Complex Representation, Hamilton-Schrödinger Equation, and Interpretation of Stationary States , 2006 .

[17]  Andrei Khrennikov.  Born's rule from classical random fields , 2008 .