Classical mechanics, quantum mechanics, field theory

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.

B. K. Agarwal

Andrei Yu. Khrennikov

This paper is a contribution to the project "emergent quantum mechanics" unifying a variety of attempts to treat quantum mechanics (QMs) as emergent from other theories pretending on finer descriptions of quantum phenomena. More concretely it is about an attempt to model detection probabilities predicted by QM for single photon states by using classical random fields interacting with detectors of the threshold type. Continuous field model, prequantum classical statistical field theory (PCSFT), was developed in recent years and its predictions about probabilities and correlations match well with QM. The main problem is to develop the corresponding measurement theory which would describe the transition from continuous fields to discrete events, "clicks of detectors". Some success was achieved and the click-probabilities for quantum observables can be derived from PCSFT by modeling interaction of fields with the threshold type detectors. However, already for the coefficient of second-order coherence g2(0) calculations are too complicated and only an estimation of g2(0) was obtained. In this paper, we present results of numerical simulation based on PCSFT and modeling of interaction with threshold type detectors. The "prequantum random field" interacting with a detector is modeled as the Brownian motion in the space of classical fields (Wiener process in complex Hilbert space). Simulation for g2(0) shows that this coefficient approaches zero with increase of the number of detections.

Abhinav Tr

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.