Michael , Silberstein
(2011)
Relational Blockworld: A Path Integral Based Interpretation of Quantum Field
Theory.
In: UNSPECIFIED.
Abstract
We propose a new path integral based interpretation of quantum field theory (QFT). In
our interpretation, QFT is the continuous approximation of a more fundamental, discrete
graph theory (theory X) whereby the transition amplitude Z is not viewed as a sum over
all paths in configuration space, but measures the symmetry of the differential operator
and source vector of the discrete graphical action. We propose that the differential
operator and source vector of theory X are related via a self-consistency criterion (SCC)
based on the identity that underwrites divergence-free sources in classical field theory,
i.e., the boundary of a boundary principle. In this approach, the SCC ensures the source
vector is divergence-free and resides in the row space of the differential operator.
Accordingly, the differential operator will necessarily have a non-trivial eigenvector with
eigenvalue zero, so the SCC is the origin of gauge invariance. Factors of infinity
associated with gauge groups of infinite volume are excluded in our approach, since Z is
restricted to the row space of the differential operator and source vector. We show it is
possible that the underlying theory X, despite being discrete, is the basis for exact
Poincaré invariance. Using this formalism, we obtain the two-source transition amplitude
over a (1+1)-dimensional graph with N vertices fundamental to the scalar Gaussian
theory and interpret it in the context of the twin-slit experiment to provide a unified
account of the Aharonov-Bohm effect and quantum non-separability (superposition and
entanglement) that illustrates our ontic structural realist alternative to problematic particle
and field ontologies. Our account also explains the need for regularization and
renormalization, explains gauge invariance and largely discharges the problems of
inequivalent representations and Haag’s theorem. This view suggests corrections to
general relativity via modifications to its graphical counterpart, Regge calculus. We
conclude by presenting the results of our modified Regge calculus approach to Einsteinde
Sitter cosmology where we produced a fit to the Union2 Compilation data for type Ia
supernovae rivaling that of the concordance model (ΛCDM), but without having to
invoke dark energy or accelerated expansion.
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