Topic Editors

Department of Mathematics and Geosciences, University of Trieste, 34100 Trieste, Italy
Research Center for Theoretical Physics and Astrophysics, Institute of Physics, Silesian University in Opava, Bezručovo nám.13, CZ-74601 Opava, Czech Republic

Covariance, Objectivity and Evolution Equations in Either Classical or Quantum Gravity and Quantum Mechanics

Abstract submission deadline
20 August 2024
Manuscript submission deadline
20 October 2024
Viewed by
4505

Topic Information

Dear Colleagues,

Covariance, objectivity, and evolution equations are key aspects of classical gravity, quantum gravity (CG and QG), and quantum mechanics (QM) alike. In fact, it is generally agreed that any physical theory underlying discrete or continuum systems should have an intrinsic, either classical or quantum, Hamiltonian structure. On the other hand, that same structure should have an objective character, i.e., it should hold—in principle—in a coordinate-independent setting. This means that, correspondingly, all theories should have an objective character as well, i.e., be independent of the observer. For relativistic theories, such a property is fulfilled provided all classical and quantum observables are set in terms of 4 tensors, i.e., they are manifestly covariant. Manifest covariance is therefore the property that warrants validity of the principle of general covariance in all the aforementioned physical contexts.

However, besides manifest covariance, further common crucial aspects arise. They include the following relevant issues:

a) Analogies between QM and QG;

b) The construction of classical and quantum variational principles;

c) Implications of manifest covariance in CG, QG and QM.

In particular, further related specialized topics, of special interest both for QM and QG, include:

d) The evolution form of the quantum-wave equations;

e) The conditions of validity of the Born identity;

f) The conditions of validity of generalized Heisenberg uncertainty principles;

g) The conditions of validity of quantum logic;

i) The problem of quantum regularization.

Properly understanding these issues becomes increasingly urgent and meaningful. Nevertheless, the identification of the relevant quantum phenomenology depends very much on the precise choice of the model of quantum gravity to be adopted as well as the theory of quantum mechanics implemented for the description of discrete systems. Therefore, the choices of quantum gravity and quantum mechanics models become crucial by themselves. The goal of this Special Issue is to offer a privileged stage for a specialized debate on the subject, with the purpose of advancing tentative answers to these fundamental questions. For this purpose, review articles, as well as original research works, are welcome to be presented.

Prof. Dr. Massimo Tessarotto
Dr. Claudio Cremaschini
Topic Editors

Keywords

  • classical and quantum gravity
  • variational principles
  • Hamiltonian theory
  • covariance and manifest covariance
  • quantum regularization of singular solutions
  • Born rule
  • Heisenberg uncertainty principle
  • quantum wave equation
  • quantum logic in QM and QG
  • stochastic effects in QM and QG
  • quantum trajectories in QM and QG

Participating Journals

Journal Name Impact Factor CiteScore Launched Year First Decision (median) APC
Entropy
entropy
2.7 4.7 1999 20.8 Days CHF 2600 Submit
Galaxies
galaxies
2.5 4.1 2013 21 Days CHF 1400 Submit
Quantum Reports
quantumrep
- 3.3 2019 18.7 Days CHF 1400 Submit
Symmetry
symmetry
2.7 4.9 2009 16.2 Days CHF 2400 Submit
Universe
universe
2.9 3.6 2015 20.6 Days CHF 2400 Submit

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Published Papers (3 papers)

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11 pages, 495 KiB  
Article
The 1932 Majorana Equation: A Forgotten but Surprisingly Modern Particle Theory
by Luca Nanni
Universe 2024, 10(4), 167; https://doi.org/10.3390/universe10040167 - 1 Apr 2024
Viewed by 796
Abstract
The Standard Model is an up-to-date theory that best summarizes current knowledge in particle physics. Although some problems still remain open, it represents the leading model which all physicists refer to. One of the pillars which underpin the Standard Model is represented by [...] Read more.
The Standard Model is an up-to-date theory that best summarizes current knowledge in particle physics. Although some problems still remain open, it represents the leading model which all physicists refer to. One of the pillars which underpin the Standard Model is represented by the Lorentz invariance of the equations that form its backbone. These equations made it possible to predict the existence of particles and phenomena that experimental physics had not yet been able to detect. The first hint of formulating a fundamental theory of particles can be found in the 1932 Majorana equation, formulated when electrons and protons were the only known particles. Today we know that parts of the hypotheses set by Majorana were not correct, but his equation hid concepts that are found in the Standard Model. In this study, the Majorana equation is revisited and solved for free particles. The time-like, light-like and space-like solutions, represented by infinite-component wave functions, are discussed. Full article
16 pages, 296 KiB  
Essay
On the Hole Argument and the Physical Interpretation of General Relativity
by Jaume de Haro
Universe 2024, 10(2), 91; https://doi.org/10.3390/universe10020091 - 14 Feb 2024
Viewed by 977
Abstract
Einstein presented the Hole Argument against General Covariance, understood as invariance with respect to a change in coordinates, as a consequence of his initial failure to obtain covariant equations that, in the weak static limit, contain Newton’s law. Fortunately, about two years later, [...] Read more.
Einstein presented the Hole Argument against General Covariance, understood as invariance with respect to a change in coordinates, as a consequence of his initial failure to obtain covariant equations that, in the weak static limit, contain Newton’s law. Fortunately, about two years later, Einstein returned to General Covariance, and found these famous equations of gravity. However, the rejection of his Hole Argument carries a totally different vision of space-time. Its substantivalism notion, which is an essential ingredient in Newtonian theory and also in his special theory of relativity, has to be replaced, following Descartes and Leibniz’s relationalism, by a set of “point-coincidences”. Full article
27 pages, 363 KiB  
Article
Unconstrained Lagrangian Variational Principles for the Einstein Field Equations
by Claudio Cremaschini and Massimo Tessarotto
Entropy 2023, 25(2), 337; https://doi.org/10.3390/e25020337 - 12 Feb 2023
Cited by 2 | Viewed by 1266
Abstract
This paper deals with the problem of establishing a systematic theoretical formulation of variational principles for the continuum gravitational field dynamics of classical General Relativity (GR). In this reference, the existence of multiple Lagrangian functions underlying the Einstein field equations (EFE) but having [...] Read more.
This paper deals with the problem of establishing a systematic theoretical formulation of variational principles for the continuum gravitational field dynamics of classical General Relativity (GR). In this reference, the existence of multiple Lagrangian functions underlying the Einstein field equations (EFE) but having different physical connotations is pointed out. Given validity of the Principle of Manifest Covariance (PMC), a set of corresponding variational principles can be constructed. These are classified in two categories, respectively, referred to as constrained and unconstrained Lagrangian principles. They differ for the normalization properties required to be satisfied by the variational fields with respect to the analogous conditions holding for the extremal fields. However, it is proved that only the unconstrained framework correctly reproduces EFE as extremal equations. Remarkably, the synchronous variational principle recently discovered belongs to this category. Instead, the constrained class can reproduce the Hilbert–Einstein formulation, although its validity demands unavoidably violation of PMC. In view of the mathematical structure of GR based on tensor representation and its conceptual meaning, it is therefore concluded that the unconstrained variational setting should be regarded as the natural and more fundamental framework for the establishment of the variational theory of EFE and the consequent formulation of consistent Hamiltonian and quantum gravity theories. Full article
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