Quantum Mechanics of Classical Fields

Amnon Katz

B. K. Agarwal

Andrei Yu. Khrennikov

The similarity between classical wave mechanics and quantum mechanics (QM) played an important role in the development of QM (starting with works of De Broglie, Schrödinger, "late Einstein", Lamb, Lande, Mandel, Marshall, Santos, Boyer, and many others). We present a new wave-type approach, so called prequantum classical statistical field theory (PCSFT). PCSFT explores an analogy between some quantum phenomena and classical theory of random fields. Quantum systems are interpreted as symbolic representations of such fields (not only for photons, cf. Lande and Lamb, but even for massive particles). All quantum averages and correlations (including composite systems in entangled states) can be represented as averages and correlations for classical random fields. In this paper PCSFT is used to provide a classical signal representation of bunching and anti-bunching. At least the latter is typically considered as essentially quantum (nonclassical) phenomenon.

Andrei Yu. Khrennikov

Albert Einstein did not believe in completeness of QM. He dreamed of creation of prequantum classical statistical mechanics such that QM will be reproduced as its approximation. He also dreamed of total exclusion of corpuscules from the future model. Reality of Einstein's dream was pure fields' reality. Recently I made his dream come true in the form of so called prequantum classical statistical field theory (PCSFT). In this approach quantum systems are described by classical random fields, e.g., electromagnetic field (instead of photon), electron field or neutron field. In this paper we generalize PCSFT to composite quantum system. It is well known that in QM, unlike classical mechanics, the state of a composite system is described by the tensor product of state spaces for its subsystems. In PCSFT one can still use Cartesian product, but state spaces are spaces of classical fields (not particles). In particular, entanglement is nothing else than correlation of classical random fields, cf. again Einstein. Thus entanglement was finally demystified.

N. Rosen