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Holographic quantum mechanics

Vitaly Kuyukov

Published Oct 27, 2019• 0 citations
Publisher

Abstract

In this paper, we consider the interpretation of quantum mechanics based on the holographic principle. A simple analysis gives the following result. Particle energy is proportional to the density of holographic information in space. The particle momentum is proportional to the flow of holographic information. The density of holographic information reflects the wave properties of the particle.

DOI
10.31219/osf.io/nxtgq

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In this paper, we consider the interpretation of quantum mechanics based on the holographic principle. A simple analysis gives the following result. Particle energy is proportional to the density of holographic information in space. The particle momentum is proportional to the flow of holographic information. The density of holographic information reflects the wave properties of the particle.
Photons, the fundamental quanta of light, are widely recognized as carriers of energy and mediators of electromagnetic interactions. This paper proposes that photons also encode the "address" of quantum interactions within the holographic plane, providing a mechanism for coordinating quantum phenomena across space time. Building on the framework presented in Emergent Universe from Many Unreal World Interpretation, this hypothesis suggests that photons function as messengers of spatial and informational coordinates, offering new interpretations of wave function collapse, quantum entanglement, and delayed-choice experiments. This approach integrates the holographic principle with quantum mechanics, potentially bridging two foundational theories of modern physics. Keywords Photons; Quanta of light; Energy carriers; Electromagnetic interactions; Quantum interactions
Quantum mechanics does not provide any ready recipe for defining energy density in space, since the energy and coordinate do not commute. To find a well-motivated energy density, we start from a possibly fundamental, relativistic description for a spin- 12 particle: Dirac's equation. Employing its energy-momentum tensor and going to the non-relativistic limit we find a locally conserved non-relativistic energy density that is defined via the Terletsky-Margenau-Hill quasiprobability (which is hence selected among other options). It coincides with the weak value of energy, and also with the hydrodynamic energy in the Madelung representation of quantum dynamics, which includes the quantum potential. Moreover, we find a new form of spin-related energy that is finite in the non-relativistic limit, emerges from the rest energy, and is (separately) locally conserved, though it does not contribute to the global energy budget. This form of energy has a holographic character, i.e., its value for a given volume is expressed via the surface of this volume. Our results apply to situations where local energy representation is essential; e.g. we show that the energy transfer velocity for a large class of free wave-packets (including Gaussian and Airy wave-packets) is larger than its group (i.e. coordinate-transfer) velocity.
We propose six principles as the fundamental principles of quantum mechanics: principle of space and time, Galilean principle of relativity, Hamilton's principle, wave principle, probability principle, and principle of indestructibility and increatiblity of particles. We deductively develop the formalism of quantum mechanics on the basis of them: we determine the form of the Lagrangian that satisfies requirements of these principles, and obtain the Schroedinger equation from the Lagrangian. We also derive the canonical commutation relations. Then we adopt the following four guide lines. First, we do not premise the relations between dynamical variables in classical mechanics. Second, we define energy, momentum, and angular momentum as the constants of motion that are derived from homogeneity and isotropy in space and time on the basis of principle of space and time. Since energy and momentum are quantitatively defined in classical mechanics, we define them in quantum mechanics so that the corresponding conservation laws are satisfied in a coupling system of a quantum particle and a classical particle. Third, we define Planck's constant and the mass of a particle as proportionality constants between energy and frequency due to one of Einstein-de Broglie formulas and between momentum and velocity, respectively. We shall obtain the canonical commutation relations and the Schroedinger equation for a particle in an external field in the definitive form. We shall also prove that relations between dynamical variables in quantum mechanics have the same forms for those in classical mechanics.
Through studying we investigate the sense of the wave function of the mass and charge the density distributions of the quantum system. According to the protective calculation, a charged quantum system has effective distribution of mass and charging density in space, proportional to the square of the absolute value of its wave function. In a practical interpretation a wave function of the quantum system can be taken as a definition of either a physical field or the ergodic motion of a particle. The main distinction among the ergodic movement of a sphere and a cell lies in the concurrent property a sphere occurs simultaneously in space, while the agosic movement of a cell is spatially separated in time. If the wave function is a physical force, then the mass and charging density are simultaneously distributed in space to the charged quantum system and thus to the gravitational and electrostatic self-interactions of its wave function. This not only contradicts the superposition principle of quantum mechanics but also contradicts the findings of the experiments. Therefore, wave function is not a definition of a physical area, but rather a transient phase of a material.Each moment has a single localized particle with mass and charge, so the wave function is not auto-introduced. Therefore, it has been argued that the classical ergodic model may not correspond to quantum mechanics for determining constant motion of the particles. Based on the negative result, we say the wave function is a random and unsatisfactory explanation of the particles' quantum motion in nature.In this view, the square of the absolute value of the wave function not only gives the particles' potential in certain locations but also the potential where the cell is. The proposed Latest wave-function description offers a natural practical other than orthodox interpretation, and also suggests that the Broglie-Bohm theory and the interpretation of many worlds are incorrect, and the theories of dynamic collapse They are heading in the right direction by accepting collapse of wave function.