Abstract
We believe one of the main obstacles to unification has been a form of ‘spacetime-matter dualism.' Herein we propose unification based on spacetimematter, finishing Einstein’s dream so to speak. In order to accomplish this, we are proposing two changes to the standard view of fields – having them reside on a graph rather than a differentiable manifold and acknowledging that their dynamical attributes (energy, momentum, mass, etc.) necessarily entail a metric. Specifically, space, time and matter are co-constructed per a global constraint equation using path integrals over graphs in an attempt to derive matter and spacetime geometry ‘at once’ in an interdependent and background independent fashion from something underneath both GR and QFT. The global constraint equation takes the form of a self-consistency criterion (SCC), not a dynamical equation. The use of an SCC implies physics is adynamical and acausal at the fundamental level, in stark contrast to the reigning paradigm of dynamism. Dynamism encompasses three claims: (1) the world, just as appearances and the experience of time suggest, evolves or changes in time in some objective fashion, (2) the best explanation for (1) will be some dynamical law that “governs” the evolution of the system in question, and (3) the fundamental entities in a TOE will themselves be dynamical entities with intrinsic properties evolving in some space however abstract. We believe that general relativity, non-relativistic quantum mechanics, quantum field theory, and the failures of unification generally are giving us clues that all the assumptions of dynamism might be false. In this essay we want to demonstrate how an alternative adynamical approach involving acausal global constraints as fundamental might help solve some longstanding problems. This reboot of unification has potentially profound and sweeping consequences for all of physics including foundational issues in: quantum mechanics, cosmology and astrophysics.
Michael David Silberstein