arXiv subjects

W. M. Stuckey

Publications and source records attributed to W. M. Stuckey.

27 records · Page 2Linked to original sources

arXiv2008

Unification per the Relational Blockworld

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.

quant-ph↗

arXiv2007

Reconciling Spacetime and the Quantum: Relational Blockworld and the Quantum Liar Paradox

The Relational Blockworld (RBW) interpretation of non-relativistic quantum mechanics (NRQM) is introduced. Accordingly, the spacetime of NRQM is a relational, non-separable blockworld whereby spatial distance is only defined between interacting trans-temporal objects. RBW is shown to provide a novel statistical interpretation of the wavefunction that deflates the measurement problem, as well as a geometric account of quantum entanglement and non-separability that satisfies locality per special relativity and is free of interpretative mystery. We present RBW's acausal and adynamical resolution of the so-called "quantum liar paradox," an experimental set-up alleged to be problematic for a spacetime conception of reality, and conclude by speculating on RBW's implications for quantum gravity.

quant-ph↗

arXiv2007

Implications for a spatially discrete transition amplitude in the twin-slit experiment

A discrete path integral formalism is used to obtain the transition amplitude between 'sources' (slits and detector) in the twin-slit experiment of quantum mechanics. This method explicates the normally tacit construct of dynamic entities with temporal duration. The resulting amplitude is compared to that of Schrodinger dynamics in order to relate 'source' dynamics and spatial separation. The implied metric embodies non-separability, in stark contrast to the metric of general relativity. Thus, this approach may have implications for quantum gravity.

quant-ph↗

arXiv2006

Quantum to Classical Transition per the Relational Blockworld

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.

quant-ph↗

arXiv2006

An Argument for 4D Blockworld from a Geometric Interpretation of Non-relativistic Quantum Mechanics

We use a new distinctly "geometrical" interpretation of non-relativistic quantum mechanics (NRQM) to argue for the fundamentality of the 4D blockworld ontology. Our interpretation rests on two formal results: Kaiser, Bohr & Ulfbeck and Anandan showed independently that the Heisenberg commutation relations of NRQM follow from the relativity of simultaneity (RoS) per the Poincare Lie algebra, and Bohr, Ulfbeck & Mottelson showed that the density matrix for a particular NRQM experimental outcome may be obtained from the spacetime symmetry group of the experimental configuration. Together these formal results imply that contrary to accepted wisdom, NRQM, the measurement problem and so-called quantum non-locality do not provide reasons to abandon the 4D blockworld implication of RoS. After discussing the full philosophical implications of these formal results, we motivate and derive the Born rule in the context of our ontology of spacetime relations via Anandan. Finally, we apply our explanatory and descriptive methodology to a particular experimental set-up (the so-called "quantum liar experiment") and thereby show how the blockworld view is not only consistent with NRQM, not only an implication of our geometrical interpretation of NRQM, but it is necessary in a non-trivial way for explaining quantum interference and "non-locality" from the spacetime perspective.

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arXiv2005

Deflating Quantum Mysteries via the Relational Blockworld

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."

quant-ph↗

arXiv2002

On a Pregeometric Origin for Spacetime Dimensionality and Metric Structure

Motivated by Wheeler's bottom up pregeometry, we introduce a pregeometric approach that does not assume Wheeler's probability amplitudes for establishing spacetime neighborhoods. Rather, a non-trivial metric is produced via the concept of a uniformity base, which is generated with discrete topological groups over some arbitrary fundamental, denumerable set. We show how the concept of entourage multiplication for the elements of our uniformity base mirrors the underlying group structure. This fact is then exploited to create entourage sequences of maximal length, whence a fine metric structure. The resulting metric structure is, for certain group structures, consistent with E4-embeddable graphs. Examples over Z2 x Z4, D4, Z6, D3, Z8, and Z5 are provided. Euclidean embeddability over Z7 and Q8 is discussed. Unlike the statistical approaches typical of graph theory, this method generates dimensionality over low-order sets. Possible applications to the pregeometric modeling of quantum stochasticity and non-locality/non-separability, wave function collapse, and the M4 structure of spacetime are provided in the context of Z2 x Z2 x Z4.

gr-qc↗

arXiv2001

Metric structure and dimensionality over a Borel set via uniform spaces

We introduce a pregeometry that provides a metric and dimensionality over a Borel set (Wheeler's "bucket of dust") without assuming probability amplitudes for adjacency. Rather, a non-trivial metric is produced over a Borel set X per a uniformity base generated via the discrete topological group structures over X. We show that entourage multiplication in this uniformity base mirrors the underlying group structure. One may exploit this fact to create an entourage sequence of maximal length whence a fine metric structure. Unlike the statistical approaches of graph theory, this method can suggest dimensionality over low-order sets. An example over Z2 x Z4 produces 3-dimensional polyhedra embedded in E4.

gr-qc↗

arXiv2001

Uniform Spaces in the Pregeometric Modeling of Quantum Non-Separability

We introduce a pregeometry employing uniform spaces over the denumerable set X of spacetime events. The discrete uniformity D_X over X is used to obtain a pregeometric model of macroscopic spacetime neighborhoods. We then use a uniformity base generated by a topological group structure over X to provide a pregeometric model of microscopic spacetime neighborhoods. Accordingly, quantum non-separability as it pertains to non-locality is understood pregeometrically as a contrast between microscopic spacetime neighborhoods and macroscopic spacetime neighborhoods. A nexus between this pregeometry and conventional spacetime physics is implied per the metric induced by D_X. A metric over the topological group Z2 x ... x Z2 is so generated. Implications for quantum gravity are enumerated.

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