1 research outputs found
A Gravitational Theory of the Quantum
The synthesis of quantum and gravitational physics is sought through a
finite, realistic, locally causal theory where gravity plays a vital role not
only during decoherent measurement but also during non-decoherent unitary
evolution. Invariant set theory is built on geometric properties of a compact
fractal-like subset of cosmological state space on which the universe is
assumed to evolve and from which the laws of physics are assumed to derive.
Consistent with the primacy of , a non-Euclidean (and hence non-classical)
state-space metric is defined, related to the -adic metric of number
theory where is a large but finite Pythagorean prime. Uncertain states on
are described using complex Hilbert states, but only if their squared
amplitudes are rational and corresponding complex phase angles are rational
multiples of . Such Hilbert states are necessarily -distant from
states with either irrational squared amplitudes or irrational phase angles.
The gappy fractal nature of accounts for quantum complementarity and is
characterised numerically by a generic number-theoretic incommensurateness
between rational angles and rational cosines of angles. The Bell inequality,
whose violation would be inconsistent with local realism, is shown to be
-distant from all forms of the inequality that are violated in any
finite-precision experiment. The delayed-choice paradox is resolved through the
computational irreducibility of . The Schr\"odinger and Dirac equations
describe evolution on in the singular limit at . By contrast,
an extension of the Einstein field equations on is proposed which reduces
smoothly to general relativity as . Novel proposals for
the dark universe and the elimination of classical space-time singularities are
given and experimental implications outlined