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arXiv:0903.2642

Relational Blockworld: Towards a Discrete Graph Theoretic Foundation of Quantum Mechanics

W. M. Stuckey, Timothy J. McDevitt, Michael Silberstein

Published Mar 15, 2009• 0 citations
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Abstract

We propose a discrete path integral formalism over graphs fundamental to quantum mechanics (QM) based on our interpretation of QM called Relational Blockworld (RBW). In our approach, the transition amplitude is not viewed as a sum over all field configurations, but is a mathematical machine for measuring the symmetry of the discrete differential operator and source vector of the discrete action. Therefore, we restrict the path integral to the row space of the discrete differential operator, which also contains the discrete source vector, in order to avoid singularities. In this fashion we obtain the two-source transition amplitude over a "ladder" graph with N vertices. We interpret this solution in the context of the twin-slit experiment.

DOI
10.48550/arxiv.0903.2642

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We propose a discrete path integral formalism over graphs fundamental to quantum mechanics (QM) based on our interpretation of QM called Relational Blockworld (RBW). In our approach, the transition amplitude is not viewed as a sum over all field configurations, but is a mathematical machine for measuring the symmetry of the discrete differential operator and source vector of the discrete action. Therefore, we restrict the path integral to the row space of the discrete differential operator, which also contains the discrete source vector, in order to avoid singularities. In this fashion we obtain the two-source transition amplitude over a "ladder" graph with N vertices. We interpret this solution in the context of the twin-slit experiment.
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We propose an adynamical interpretation of quantum theory called Relational Blockworld (RBW) where the fundamental ontological element is a 4D graphical amalgam of space, time and sources called a “spacetimesource element.” These are fundamental elements of space, time and sources, not source elements in space and time. The transition amplitude for a spacetimesource element is computed using a path integral with discrete graphical action. The action for a spacetimesource element is constructed from a difference matrix K and source vector J on the graph, as in lattice gauge theory. K is constructed from graphical field gradients so that it contains a non-trivial null space and J is then restricted to the row space of K, so that it is divergence-free and represents a conserved exchange of energy–momentum. This construct of K and J represents an adynamical global constraint between sources, the spacetime metric and the energy–momentum content of the spacetimesource element, rather than a dynamical law for time-evolved entities. To illustrate this interpretation, we explain the simple EPR-Bell and twin-slit experiments. This interpretation of quantum mechanics constitutes a realist, psi-epistemic model that might underwrite certain information-theoretic accounts of the quantum.
The transition from the quantum realm to the classical realm is described in the context of the Relational Blockworld (RBW) interpretation of non-relativistic quantum mechanics. We first introduce RBW, discuss its philosophical implications and provide an example of its explanatory methodology via the so-called "quantum liar experiment." We then provide a simple example of a quantum to classical transition in this context using a gedanken twin-slit experiment. We conclude by speculating on the extrapolation of RBW to quantum field theory, suggesting the need for a new principle of physics based in spatiotemporal relationalism. Accordingly, RBW suggests a novel approach to new physics which supplies a means for its falsification.
The main thread of chapter 4 introduces some of the major mysteries and interpretational issues of quantum mechanics (QM). These mysteries and issues include: quantum superposition, quantum nonlocality, Bell’s inequality, entanglement, delayed choice, the measurement problem, and the lack of counterfactual definiteness. All these mysteries and interpretational issues of QM result from dynamical explanation in the mechanical universe and are dispatched using the authors’ adynamical explanation in the block universe, called Relational Blockworld (RBW). A possible link between RBW and quantum information theory is provided. The metaphysical underpinnings of RBW, such as contextual emergence, spatiotemporal ontological contextuality, and adynamical global constraints, are provided in Philosophy of Physics for Chapter 4. That is also where RBW is situated with respect to retrocausal accounts and it is shown that RBW is a realist, psi-epistemic account of QM. All the relevant formalism for this chapter is provided in Foundational Physics for Chapter 4.