Covariance, Multiverse, and Stochastic Effects in Classical Electrodynamics, Quantum Mechanics, and Quantum Gravity

Dear Colleagues,

The objectivity and covariance properties of the relevant stochastic and multiverse representations of an abstract Hamiltonian structure, as well the validity of the Heisenberg uncertainty principle, are key aspects of quantum mechanics (QM) and quantum gravity (QG) alike. In fact, it is generally agreed that any quantum theories of both matter and space–time systems should exhibit both an objective, intrinsic Hamiltonian and a corresponding Hilbert space structure. The question, however, is whether and how the Hamiltonian structures are preserved (or otherwise) when non-local coordinate frames are adopted, as it can happen in curved space–time.

However, the following questions arise:

1. The first question has a preparatory character towards QG and QG. It concerns classical electrodynamics (CE) in curved space–time. In fact, questions as to whether the Hamiltonian structure of the equations of CE is generally preserved (or not) in curved space–time, as well as how the covariance property is actually realized, have arisen and should be addressed. For this purpose, examples of exact non-linear (and non-local) CE problems should be investigated.
2. Another related key issue is the formulation of non-relativistic QM in curved space–time. The crucial question to consider is whether non-commutative effects can arise or not in the case of curved space–time.
3. A relevant issue pertaining to both QM and QM concerns the construction of stochastic representations for QM and QG theories and the identification of the consequent multiverse representations of QM and QG.
4. Regarding the multiverse representation of QM and QG the question arises of their possibly related phenomenology and of possible experimental tests and/or Gedanken experiments to ascertain their actual physical existence.
5. A related key question concerns the possible relationships between the Boolean and/or quantum logic for QM and QG and Gödel’s undecidability theorems.
6. Finally, the possible occurrence of different characteristic lengths arising in QG and QM is another area of interest.

Properly understanding these issues has become increasingly urgent and meaningful. Nevertheless, the identification of the relevant quantum phenomenology very much depends on the precise choice of the quantum gravity model adopted, as well as the theory of quantum mechanics implemented for the description of particle systems. Therefore, the choices of quantum gravity and quantum mechanics models are exceptionally significant.

The goal of this Special Issue is to offer a platform for specialized debate on the subject, with the purpose of advancing tentative answers to these fundamental questions. In light of this, original research works and review articles that are relevant to the above-mentioned fields are welcome.

Prof. Dr. Massimo Tessarotto
Guest Editor

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