Fundamental classical and quantum dynamical theory

Danko Dimchev Georgiev

Quantum physics provides a good candidate for a mathematical entity, namely, the quantum state vector in the Hilbert space. The causal potency problem originates from determinism: In classical physical theories there are fundamental constituents entering in the mathematical description of the physical laws that govern deterministically the dynamics of physical systems. Since only these fundamental constituents are causally potent to affect the deterministic behavior of physical systems, consciousness has to appear as a fundamental constituent of the physical theory as well. Existentialism clashes seriously with determinism. Classical deterministic physics allows no free will and no objective morality. Classically, functionalism leads to epiphenomenalism because the generated conscious experiences are unable to change the already predetermined future dynamics of the brain. In quantum physics, however, the quantum indeterminism in the dynamics of quantum systems provides a multitude of possible outcomes from the measurement process.

M. Blagojević

Classical dynamics is usually considered to be the first level in the development of our understanding of the physical laws in Nature, which today is based on quantum theory. Despite the many successes of quantum theory in describing basic physical phenomena, it is continually running into difficulties in some specific physical situations. Thus, all attempts to quantize the theory of gravity have encountered serious difficulties. In order to find a solution to these problems, it seems to be useful to reconsider the fundamental principles of classical dynamics. In this context, the principles of Hamiltonian dynamics are seen to be of great importance not only for a basic understanding of classical theory, but also for its quantization.

A. Carati, L. Galgani

Antoine Tilloy

This note derives the stochastic differential equations and partial differential equation of general hybrid quantum–classical dynamics from the theory of continuous measurement and general (non-Markovian) feedback. The advantage of this approach is an explicit parameterization, without additional positivity constraints. The construction also neatly separates the different effects: how the quantum influences the classical and how the classical influences the quantum. This modular presentation gives a better intuition of what to expect from hybrid dynamics, especially when used to construct possibly fundamental theories.

Maciej Zworski