Quantization, Relativity, and Fields

The intrinsic unification of the quantum theory and relativity has been discussed here in the light of the last developments. Such development is possible only on the way of the serious deviation from traditional assumptions about a priori spacetime structure and the Yang-Mills generalization of the well known U (1) Abelian gauge symmetry of the classical electrodynamics. In fact, more general gauge theory should be constructed. Formally we deal with the quantum version of the gauge theory of the deformable bodies-the gauge theory of the deformable quantum state. More physically this means that the distance between quantum states is strictly defined value whereas the distance between bodies (particle) is an approximate value, at best. Thereby, all well known solid frames and clocks even with corrections of special relativity should be replaced by the flexible and anholo-nomic quantum setup. Then Yang-Mills arguments about the spacetime coordinate dependence of the gauge unitary rotations should be reversed on the dependence of the spacetime structure on the gauge transformations of the flexible quantum setup. One needs to build " inverse representation " of the unitary transformations by the intrinsic dynamical spacetime transformations. In order to achieve such generalization one needs the general footing for gauge fields and for " matter fields ". Only fundamental pure quantum degrees of freedom like spin, charge, hyper-charges, etc., obey this requirement. One may assume that they correspond some fundamental quantum motions in the manifold of the unlocated quantum states (UQS's). Then " elementary particles " will be represented as a dynamical process keeping non-linear coherent superposition of these fundamental quantum motions.

International Journal of Theoretical Physics, 1996

2024

1996

We put forward a framework, inspired by recent axiomatic and opera- tional approaches to generalized quantum theories, wherein we investigate the possibility of unifying quantum theories and relativity theories. The framework concentrates on a detailed analysis of a general construction of reality, that can be used in both, quantum and relativity theories. By means of this construction of reality we clarify some well known conceptual problems that stand in the way for a conceptual uniflcation of quantum and relativity theories on a more profound physical level than the purely mathematical algebraic level on which now uniflcation attempts are in- vestigated. More speciflcally we concentrate on the problem of 'what is physical reality' in quantum and relativity theories.

infohost.nmt.edu

Quantum field theory (QFT) is a theory of relativistic fields for describing the properties of elementary particles and their interaction.

arXiv (Cornell University), 2021

Quantum information theorists have created axiomatic reconstructions of quantum mechanics (QM) that are very successful at identifying precisely what distinguishes quantum probability theory from classical and more general probability theories in terms of information-theoretic principles. Herein, we show how one such principle, Information Invariance & Continuity, at the foundation of those axiomatic reconstructions maps to "no preferred reference frame" (NPRF, aka "the relativity principle") as it pertains to the invariant measurement of Planck's constant h for Stern-Gerlach (SG) spin measurements. This is in exact analogy to the relativity principle as it pertains to the invariant measurement of the speed of light c at the foundation of special relativity (SR). Essentially, quantum information theorists have extended Einstein's use of NPRF from the boost invariance of measurements of c to include the SO(3) invariance of measurements of h between different reference frames of mutually complementary spin measurements via the principle of Information Invariance & Continuity. Consequently, the "mystery" of the Bell states that is responsible for the Tsirelson bound and the exclusion of the no-signalling, "superquantum" Popescu-Rohrlich joint probabilities is understood to result from conservation per Information Invariance & Continuity between different reference frames of mutually complementary qubit measurements, and this maps to conservation per NPRF in spacetime. If one falsely conflates the relativity principle with the classical theory of SR, then it may seem impossible that the relativity principle resides at the foundation of non-relativisitic QM. In fact, there is nothing inherently classical or quantum about NPRF. Thus, the axiomatic reconstructions of QM have succeeded in producing a principle account of QM that reveals as much about Nature as the postulates of SR.

Studies in History and Philosophy of Modern Physics, 1995

From a human perspective a considerable portion of all known physical phenomena can, with reasonable precision, be accounted for in terms of what we misleadingly call non-relativistic physical theory. In the framework of such theory the relativity principle that holds is Galilean Invariance, as opposed to Lorentz Invariance which holds in what we call special relativistic theory. In the Galilean Invariant case the simultaneity of spatially separated events is independent of any reference frame, and any velocity can be transformed into any other velocity by Galilean transformations between equivalent reference frames. Consequently, no limits can be placed on the speed of propagation of causal influences, and, in the absence of a medium, relative to which an influence could propagate, instantaneous actions at a distance can hold. Famously, they were assumed to hold in Newton's theory of gravity and the early accounts of electric and magnetic forces. But actions at a distance run the risk of jeopardizing the legitimacy of one of our basic conceptual inclinations. That is the inclination to grant preferred status, as causal agents acting on a physical system, to those physical systems which are spatially proximate to the given system. To the extent that one can render conceptually precise this sense of preferred status (e.g. the effects of the agent occur more quickly or are more intense, etc.), complexes of systems which allow this inclination to be satisfied are regarded as local in their causal structure. This inclination can be mollified, despite action at a distance, provided that the actions diminish in their effects with the distance over which they act. But without that feature, and especially in the presence of some

Eprint Arxiv Gr Qc 0009052, 2000

A local conception (in the sense of the equivalence principle) is proposed to reconcile quantum theory with general relativity, which allows one to avoid some difficulties-as e.g. vacuum catastrophe-of the global approach. All nonlocal aspects of quantum theory, including EPR paradox, remain intact. 1 A slghtly improved version of the paper arXiv:gr-qc0009052.

2010

I will argue that the proposal of establishing operational foundations of Quantum Theory should have top-priority, and that the Lucien Hardy's program on Quantum Gravity should be paralleled by an analogous program on Quantum Field Theory (QFT), which needs to be reformulated, notwithstanding its experimental success. In this paper, after reviewing recently suggested operational "principles of the quantumness", I address the problem on whether Quantum Theory and Special Relativity are unrelated theories, or instead, if the one implies the other. I show how Special Relativity can be indeed derived from causality of Quantum Theory, within the computational paradigm "the universe is a huge quantum computer", reformulating QFT as a Quantum-Computational Field Theory (QCFT). In QCFT Special Relativity emerges from the fabric of the computational network, which also naturally embeds gauge invariance. In this scheme even the quantization rule and the Planck constant can in principle be derived as emergent from the underlying causal tapestry of space-time. In this way Quantum Theory remains the only theory operating the huge computer of the universe.

2008

In this article, the axioms presented in the first one are reformulated according to the special theory of relativity. Using these axioms, quantum mechanic’s relativistic equations are obtained in the presence of electromagnetic fields for both the density function and the probability amplitude. It is shown that, within the present theory’s scope, Dirac’s second order equation should be considered the fundamental one in spite of the first order equation. A relativistic expression is obtained for the statistical potential. Axioms are again altered and made compatible with the general theory of relativity. These postulates, together with the idea of the statistical potential, allow us to obtain a general relativistic quantum theory for ensembles composed of single particle systems. 1