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arXiv:1004.2933

Completely local interpretation of quantum field theory

Roman Sverdlov

Published Apr 16, 2010• 2 citations
arXivHTMLPDF

Abstract

The purpose of this paper is to come up with a framework that "converts" existing concepts from configuration space to ordinary one. This is done by modeling our universe as a big "computer" that simulates configuration space. If that "computer" exists in ordinary space and is ran by "classical" laws, our theory becomes "classical" by default. We have first applied this concept to a version of quantum field theory in which elementary particles have size (that is, a theory that does not yet exists). After that, we have also done the same with Pilot Wave model of discrete jumps, due to Dürr et el.

DOI
10.48550/arxiv.1004.2933

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The purpose of this paper is to come up with a framework that "converts" existing concepts from configuration space to ordinary one. This is done by modeling our universe as a big "computer" that simulates configuration space. If that "computer" exists in ordinary space and is ran by "classical" laws, our theory becomes "classical" by default. We have first applied this concept to a version of quantum field theory in which elementary particles have size (that is, a theory that does not yet exists). After that, we have also done the same with Pilot Wave model of discrete jumps, due to Dürr et el.
An interpretation and re-formulation of modern physics which removes the presumption of the space-time continuum, and bases physical theory on a small number of rational and empirical principles. After briefly describing the philosophical principles underlying the theory, we rigorously construct a discrete model of quantum mechanics. Kets are names, or labels which categorise states of matter but do not directly describe them. The principle of superposition is seen as a definitional truism in the categorisation of states. This resolves the measurement problem of quantum mechanics by attributing the collapse of the wave function to information. The probability interpretation has a natural meaning in which the configuration of interacting particles plays the role of a hidden variable. The model supports a form of relativistic quantum field theory which does not depend on quantisation or second quantisation from classical mechanics. Continuous laws of wave mechanics are found in a discrete metaphysic which does not involve waves. Classical law is the expected behaviour of many elementary particles. The constraints on the theory are sufficient to establish that particles are point-like entities with specific properties found in nature. Newton's first law and conservation of momentum are established from the principle of homogeneity. Maxwell's equations are derived from the simple interaction in which a Dirac particle emits or absorbs a photon. Feynman rules are calculated for the discrete theory and differ from the standard rules by the removal of the ultraviolet divergence and the use of proper loop integrals. They give finite and unambiguous results.
I propose a local, realist interpretation of quantum mechanics based on a physical scalar wave field in ordinary three-dimensional space. Each fundamental particle (electron, photon, proton, etc.) possesses its own wave field. The field is fundamental — it is not emitted by the particle, nor does it draw energy from the particle’s motion. The particle is guided by the phase gradient of its own wave via a Bohmian guidance law. The wave evolves according to a linear Klein-Gordon equation. For a single particle this reproduces the full empirical success of quantum mechanics, including the hydrogen spectrum and the double-slit interference pattern. For multiple particles, each particle retains its own local 3D wave; no configuration space is needed. Entanglement is rejected as a fundamental physical phenomenon: the correlations observed in Bell-type experiments are interpreted as ordinary statistical correlations arising from common past interactions, not as evidence of non-locality or of a non-separable quantum state. The quantum mechanical wave function in configuration space is regarded as a mathematical tool, not a physical field. The theory is local, realist, and fully three-dimensional.
The goal of this paper is to re-express QFT in terms of two "classical" fields living in ordinary space with single extra dimension. The role of the first classical field is to set up an injection from the set of values of extra dimension into the set of functions, and then said injection will be used in order to convert the second field into a coarse grained functional, thereby approximating QFT state. It turns out that this work also has a side-benefit of modeling ensemble of states in terms of one single state which, in turn, is interpretted in the above way. It is important to clarify that by "classical" we mean functions over ordinary space rather than configuration, Fock or function space. The "classical" theory that we propose is still non-local.
States in quantum field theory (QFT) are represented by many-particle wave functions, such that a state describing n particles depends on n space–time positions. Since a general state is a superposition of states with different numbers of particles, the wave function lives in the configuration space identified with a product of an infinite number of four-dimensional Minkowski space–times. The squared absolute value of the wave function is interpreted as the probability density in the configuration space, from which the standard probabilistic predictions of QFT can be recovered. Such a formulation and probabilistic interpretation of QFT allows one to interpret the wave function as a pilot wave that describes deterministic particle trajectories, which automatically includes a deterministic and continuous description of particle creation and destruction. In particular, when the conditional wave function associated with a quantum measurement ceases to depend on one of the space–time coordinates, then the 4-velocity of the corresponding particle vanishes, describing a trajectory that stops at a particular point in space–time. In a more general situation a dependence on this space–time coordinate is negligibly small but not strictly zero, in which case the trajectory does not stop but the measuring apparatus still behaves as if this particle has been destroyed.
The central motivating idea behind the development of this work is the concept of prespace, a hypothetical structure that is postulated by some physicists to underlie the fabric of space or space-time. I consider how such a structure could relate to space and space-time, and the rest of reality as we know it, and the implications of the existence of this structure for quantum theory. Understanding how this structure could relate to space and to the rest of reality requires, I believe, that we consider how space itself relates to reality, and how other so-called “spaces” used in physics relate to reality. In the first chapter I compare space and space-time to other spaces used in physics, such as configuration space, phase space and Hilbert space. I support what is known as the “property view” of space, opposing both the traditional views of space and space-time, substantivalism and relationism. I argue that all these spaces are property spaces. After examining the relationships of these spaces to causality, I argue that configuration space has, due to its role in quantum mechanics, a special status in the microscopic world similar to the status of position space in the macroscopic world. In chapter two prespace itself is considered. One way of approaching this structure is through the comparison of the prespace structure with a computational system, in particular to a cellular automaton, in which space or space-time and all other physical quantities are broken down into discrete units. I suggest that one way open for a prespace metaphysics can be found if physics is made fully discrete in this way. I suggest as a heuristic principle that the physical laws of our world are such that the computational cost of implementing those laws on an arbitrary computational system is minimized, adapting a heuristic principle of this type proposed by Feynman (1982). In the final chapter some of the ideas of the previous chapters are applied in an examination of the physics and metaphysics of quantum theory. I first discuss the “measurement problem” of quantum mechanics: this problem and its proposed solution are the primary subjects of the final chapter. It turns out that considering how quantum theory could be made fully discrete leads naturally to a suggestion of how standard linear quantum mechanics could be modified to give rise to a solution to the measurement problem. The computational heuristic principle reinforces the same solution. I call the modified quantum mechanics Critical Complexity Quantum Mechanics (CCQM). I compare CCQM with some of the other proposed solutions to the measurement problem, in particular the spontaneous localization model of Ghirardi, Rimini and Weber (1986). Finally I argue that the measure of complexity of quantum mechanical states I introduce in CCQM also provides a new definition of entropy for quantum mechanics, and suggests a solution to the problem of providing an objective foundation for statistical mechanics, thermodynamics, and the arrow of time.