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arXiv:1909.09133

Can We Derive Quantum Mechanics as an Emergent Theory from a Modified Relativity

Jeffrey Alloy Q. Abanto

Published Sep 19, 2019• 0 citations
arXivHTMLPDF

Abstract

A new model of Deformed Special Relativity (DSR) was proposed to derive a modified General Relativity at the sub-quantum level towards the Planck scale. This was used as a basis for a new approach to Emergent Quantum Mechanics from which the standard mathematical formalism of Relativistic Quantum Mechanics was derived. Lastly, a new interpretation for the so-called quantum wave was suggested.

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A new model of Deformed Special Relativity (DSR) was proposed to derive a modified General Relativity at the sub-quantum level towards the Planck scale. This was used as a basis for a new approach to Emergent Quantum Mechanics from which the standard mathematical formalism of Relativistic Quantum Mechanics was derived. Lastly, a new interpretation for the so-called quantum wave was suggested.
In this paper, the deformed Special Relativity, which leads to an essentially new theoretical context of quantum mechanics, is presented. The formulation of the theory arises from a straightforward analogy with the Special Relativity, but its foundations are laid through the hypothesis on breakdown of the velocity-momentum parallelism which affects onto the Einstein equivalence principle between mass and energy of a relativistic particle. Furthermore, the derivation is based on the technique of an eikonal equation whose well-confirmed physical role lays the foundations of both optics and quantum mechanics. As a result, we receive the angular deformation of Special Relativity which clearly depicts the new deformation-based theoretical foundations of physics, and, moreover, offers both constructive and consistent phenomenological discussion of the theoretical issues such like imaginary mass and formal superluminal motion predicted in Special Relativity for this case. In the context of the relativistic theory, presence of deformation does not break the Poincaré invariance, in particular the Lorentz symmetry, and provides essential modifications of both bosons described through the Klein-Gordon equation and fermions satisfying the Dirac equation. On the other hand, on the level of discussion of quantum theory, there arises the concept of emergent deformed space-time, wherein the presence of angular deformation elucidates a certain new insight into the nature of spin, as well as both the Heisenberg uncertainty principle and the Schrödinger wave equation.
The old dilemma of quantum mechanics versus the theory of relativity is reconsidered via a first principles relativistically invariant theory. By analytic extension of quantum mechanics into the complex plane one may (i) include dynamical features such as time‐ and length‐scales and (ii) examine the possibility and flexibility of so‐called general Jordan block formations. The present viewpoint asks for a new perspective on the age‐old problem of quantum mechanics versus the theory of relativity. To bring these ideas together, we will establish the relation with the Klein‐Gordon‐Dirac relativistic theory and confirm some dynamical features of both the special and the general relativity theory.
This paper provides an examination of the de Broglie relation, tracing its historical development from the quantum hypotheses proposed by Planck and Einstein to its covariant relativistic derivation. The discussion begins by situating de Broglie's seminal insight within the early framework of quantum theory. We then reconstruct his original heuristic derivation. The primary focus of this work, however, is the derivation of the de Broglie relation directly from the principles of special relativity, employing the four-momentum formalism. A comparative analysis between the heuristic and relativistic approaches underscores the universality and conceptual coherence of the latter. The paper concludes by highlighting the significance of relativistic mechanics in establishing a consistent foundation for wave-particle duality, further reinforcing this through a quantum field theoretical perspective.
On the basis of the results of some experiments dealing with the violation of Local Lorentz Invariance (LLI) and on the formalism of the Deformed Special Relativity (DSR), we examine the connections between the local geometrical structure of space-time and the foundation of Quantum Mechanics. We show that Quantum Mechanics, beside being an axiomatic theory, can be considered also a deductive physical theory, deducted from the primary physical principle of Relativistic Correlation. This principle is synonym of LLI and of a rigid and at minkowskian space-time. The results of the experiments mentioned above show the breakdown of LLI and hence the violation of the principle of Relativistic Correlation. The formalism of DSR allows to highlight the deep meaning of LLI breakdown in terms of the geometrical structure of local space-time which, far from being rigid and at, is deformed by the energy of the physical phenomena that take place and in this sense it has an active part in the dynamics of the whole physical process. This perspective has a far reaching physical meaning that extends its consequences to the foundations of Quantum Mechanics according to the interpretation of Copenhagen. It provides a 'real' explanation and description of quantum phenomena enriching, by the concept of deformed space-time, the realistic interpretation in terms of pilot wave and hence it uncovers the reality hidden below the probabilistic interpretation and dualistic nature of quantum objects.
In the last years, many different primeval quantization theories on the Planck scale have been developed. Their goal is to provide a vacuum model able to ground the research beyond the Standard Model. Despite their goal is quite ambitious and aims toward particle physics, a necessary and notable consequence is we can read Quantum Mechanics from an emergent viewpoint. Different hypotheses on elementary cells are possible. We will focus here on the conceptual features of G. ’t Hooft and F.Winterberg theories with a special attention for the emerging of non-local correlations. These theories define a new style in the interpretation of Quantum Mechanics.
The task of quantizing general relativity raises serious questions about the meaning of the present formulation and interpretation of quantum mechanics when applied to so fundamental a structure as the space-time geometry itself. This paper seeks to clarify the foundations of quantum mechanics. It presents a reformulation of quantum theory in a form believed suitable for application to general relativity. The aim is not to deny or contradict the conventional formulation of quantum theory, which has demonstrated its usefulness in an overwhelming variety of problems, but rather to supply a new, more general and complete formulation, from which the conventional interpretation can be deduced. The relationship of this new formulation to the older formulation is therefore that of a metatheory to a theory, that is, it is an underlying theory in which the nature and consistency, as well as the realm of applicability, of the older theory can be investigated and clarified.