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arXiv:0712.2778

Unification per the Relational Blockworld

W. M. Stuckey, Michael Silberstein

Published Dec 17, 2007• 2 citations
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Abstract

We use the Relational Blockworld (RBW) interpretation of quantum mechanics to resolve the foundational problems therein. As predicted by Smolin, the resolution of these problems is not independent of the problem of unification and the nature of time. Specifically, RBW requires a theory fundamental to quantum physics in which one must explicitly construct dynamical/diachronic entities (objects obtained via trans-temporal identification) from 'relations'. We use discrete graph theory to propose heuristically the nature of this underlying theory, which is based on a self-consistency criterion for the mutual construct of dynamical/diachronic entities, space and time whence a spatiotemporally discrete action fundamental to the path integral approach to quantum and classical physics. The proposed unification scheme suggests a novel approach to quantum gravity.

DOI
10.48550/arxiv.0712.2778

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We use the Relational Blockworld (RBW) interpretation of quantum mechanics to resolve the foundational problems therein. As predicted by Smolin, the resolution of these problems is not independent of the problem of unification and the nature of time. Specifically, RBW requires a theory fundamental to quantum physics in which one must explicitly construct dynamical/diachronic entities (objects obtained via trans-temporal identification) from 'relations'. We use discrete graph theory to propose heuristically the nature of this underlying theory, which is based on a self-consistency criterion for the mutual construct of dynamical/diachronic entities, space and time whence a spatiotemporally discrete action fundamental to the path integral approach to quantum and classical physics. The proposed unification scheme suggests a novel approach to quantum gravity.
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.
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.
We introduce the Relational Blockworld (RBW) as a paradigm for deflating the mysteries associated with quantum non-separability/non-locality and the measurement problem. We begin by describing how the relativity of simultaneity implies the blockworld, which has an explanatory potential subsuming both dynamical and relational explanations. It is then shown how the canonical commutation relations fundamental to non-relativistic quantum mechanics follow from the relativity of simultaneity. Therefore, quantum mechanics has at its disposal the full explanatory power of the blockworld. Quantum mechanics exploits this expanded explanatory capability since event distributions among detectors per the density matrix follow from spacetime relations (symmetry group) alone. Thus, the event distributions of non-relativistic quantum mechanics follow from a blockworld wherein spacetime relations are fundamental. Per RBW "quantum mysteries" are deflated and the implications for consciousness and the perception of temporal flow and absolute becoming are explored. We conclude that given RBW, consciousness is no less fundamental than any "physical" feature of the world such as brain states. Further, active consciousness is needed to explain the illusion that it is a dynamical world and consciousness in its most fundamental state is relational and non-local.
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.
We present a perspective that can resolve most of the tensions between non-relativistic quantum mechanics (QM) and special relativity while deflating "quantum mysteries." All of this is achieved using spacetime symmetries as fundamental in a blockworld setting, i.e., by interpreting spacetime relations as fundamental to relata. To justify this "Relational Blockworld" (RBW), we adopt a result due to G. Kaiser whereby the relativity of simultaneity, stemming from the Poincare algebra, is responsible for the canonical commutation relations of QM. And, we incorporate a result due to A. Bohr, B. Mottelson and O. Ulfbeck whereby the density matrix for a given experimental situation is obtained from its spacetime symmetry group. We provide an example to illustrate the explanatory nature of RBW and conclude by showing how RBW deflates "quantum mysteries" on geometric grounds.
We present a spacetime setting for non-relativistic quantum mechanics that deflates "quantum mysteries" and relates non-relativistic quantum mechanics to special relativity. This is achieved by assuming spacetime symmetries are fundamental in a blockworld setting, i.e., by interpreting spacetime relations as fundamental to relata. To justify this Relational Blockworld (RBW), we adopt a result due to G. Kaiser whereby the relativity of simultaneity, stemming from the Poincare algebra of special relativity, is responsible for the canonical commutation relations of non-relativistic quantum mechanics. And, we incorporate a result due to A. Bohr, B. Mottelson and O. Ulfbeck whereby the density matrix for a given experimental situation is obtained from its spacetime symmetry group. We provide an example to illustrate the explanatory nature of RBW and conclude by explaining how RBW deflates "quantum mysteries."