Michael Silberstein

We propose a path integral over graphs approach to quantum gravity and unification that requires a modification and reinterpretation of both general relativity and quantum field theory via their graphical instantiations, Regge calculus and lattice gauge theory, respectively. As we outline below, the spacetime metric and the matter and gauge field gradients on the graph are co-determining, so there is no “background spacetime” connoting existence independent of matter-energy-momentum, and the graphical action can be characterized geometrically via graphical boundary operators.

We propose a new path integral based interpretation of quantum field theory. In our interpretation, QFT is the continuous approximation of a more fundamental, discrete graph theory 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 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 -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 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, but without having to invoke dark energy or accelerated expansion.

Nonreductive physicalism is the conjunction of the following three statements. Firstly, mental properties are real. Secondly, mental properties are neither reducible to nor identifiable with physical properties, and thirdly, mental properties are causally efficacious with respect to physical properties. Nonreductive physicalists hold these assumptions to be true not only for mental properties but all special science and macrophysical properties. I will defend the following three theses: first, if certain widely held assumptions are true e.g., no downward causation, microdetermination or, the doctrine that motivates these assumptions is true namely, microphysical determinism then nonreductive physicalism must fail i.e., the three statements can not jointly be true. Therefore, we must accept that reductionism, epiphenomenalism or eliminativism is unavoidable not only for mental properties, but for all but the most basic physical properties. Second, certain quantum mechanical phenomena show that in fact all the trouble making assumptions are false. Thirdly, a true picture of the physical world not only opens up the possibility of mental causation and higher-order causation in general, but also offers an empirical example of a kind of "emergentism" or holism that could provide us with a model for explaining the nature of the mental and its causal role.