Nonlinear nonlocal classical field theory of quantum phenomena

Seif Randjbar-Daemi

Andrei Yu. Khrennikov

We developed a purely field model of microphenomena—prequantum classical statistical field theory (PCSFT). This model not only reproduces important probabilistic predictions of quantum mechanics (QM) including correlations for entangled systems, but also gives a possibility to go beyond QM, i.e. to make predictions of phenomena that could be observed at the subquantum level. In this paper, we discuss one such prediction—the existence of nonlocal correlations between prequantum random fields corresponding to all quantum systems. (And by PCSFT, quantum systems are represented by classical Gaussian random fields and quantum observables by quadratic forms of these fields.) The source of these correlations is the common background field. Thus all prequantum random fields are 'entangled', but in the sense of classical signal theory. On the one hand, PCSFT demystifies quantum nonlocality by reducing it to nonlocal classical correlations based on the common random background. On the other hand, it demonstrates total generality of such correlations. They exist even for distinguishable quantum systems in factorizable states (by PCSFT terminology—for Gaussian random fields with covariance operators corresponding to factorizable quantum states).

Andrei Yu. Khrennikov

In a series of previous papers we developed a purely field model of microphenomena, so called prequantum classical statistical field theory (PCSFT). This model not only reproduces important probabilistic predictions of QM including correlations for entangled systems, but it also gives a possibility to go beyond quantum mechanics (QM), i.e., to make predictions of phenomena which could be observed at the subquantum level. In this paper we discuss one of such predictions - existence of nonlocal correlations between prequantum random fields corresponding to {\it all} quantum systems. (And by PCSFT quantum systems are represented by classical Gaussian random fields and quantum observables by quadratic forms of these fields.) The source of these correlations is the common background field. Thus all prequantum random fields are "entangled", but in the sense of classical signal theory. On one hand, PCSFT demystifies quantum nonlocality by reducing it to nonlocal classical correlations based on the common random background. On the other hand, it demonstrates total generality of such correlations. They exist even for distinguishable quantum systems in factorizable states (by PCSFT terminology - for Gaussian random fields with covariance operators corresponding to factorizable quantum states).

W. David Wick

In the 1980's and 90's, A. O Barut and colleagues developed a nonperturbative approach to electrodynamics eschewing so-called ``second-quantization". Based on incorporation of self-energy terms, the resulting nonlinear and nonlocal theory explained many well-known phenomena of atomic and radiation physics. In 2017, this author introduced a nonlinear, nonlocal theory with the intent of resolving the Measurement Problem. Barut also suggested that his theory resolved such paradoxes. Here I compare the two theories with special attention to That Dot on the Screen.

H. Muirhead