TITLE:
Quantum Local Causality in Non-Metric Space
AUTHORS:
Fosco Ruzzene
KEYWORDS:
Quantum Foundations, Heisenberg Gedanken Experiments, Error-Disturbance Relations, Quantum Locality, Non-Metric Space
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.6 No.6,
June
14,
2018
ABSTRACT: The possibility that quantum mechanics is founded on
non-metric space has been previously introduced as an alternative consequence
of Bell inequalities violation. This work develops the concept further by an
analysis of the iconic Heisenberg gedanken experiment. No lower bound is found
in the gedanken uncertainly relation for a non-metric spatial background. This
result has the fundamental consequence that the quantum particle trajectory is
retained in non-metric space and time. Assignment of measurement number-values
to unmeasured incompatible variables is found to be mathematically incorrect.
The current disagreement between different formulations of the empirically
verified error-disturbance relations can be explained as a consequence of the
structure of space. Quantum contextuality can likewise be explained
geometrically. An alternative analysis of the extendedEPRperfect anti-correlation configuration is given. The consensus that local
causality is the sole assumption is found to be incorrect. There is also the
additional assumption of orientation independence. Inequalities violation does
not therefore mandate rejection of local causality. Violation of the assumption
of orientation independence implies rejection of metric, non-contextual
variables algebraically representing physical quantities.