Andreka and her colleagues have described various geometrically inspired first-order theories of special and general relativity, while Szekely's PhD dissertation focuses on an intermediate logic of accelerated observers. In this paper we will attempt to incorporate a model of quantum theoretical trajectories that can reasonably claim to be physically meaningful into those theories.
We have recently shown that a model of quantum trajectories, based on discrete finitary motion, is logically equivalent to Feynman's path-integral formulation when spacetime is assumed to be Euclidean. In this paper we argue that relativistic observers are subject to the same quantum illusions as in the Euclidean case: even though motion is discrete and respects no built-in 'arrow of time', observers have no choice but to perceive particle trajectories as continuous paths in spacetime.
Whereas the relativistic theories presuppose continuous paths as part of their axioms, the illusion of continuity allows us to replace this axiom with a lower-level quantum-inspired axiom concerning discrete jumps in spacetime. We investigate the nature of these jumps, and how far they can be tied to the underlying geometric structure of spacetime. In particular, we consider hops which preserve features of the underlying number field, and investigate the extent to which all hops can be restricted to be of this form.
We conclude that hop-based motion can also be regarded as an illusion, one caused by modelling physics in the 'wrong' number system.
Deviation of trajectories in nonrelativistic and relativistic cases and Shirokov effect
Institute for Problems in Mechanical Engineering of Russian Academy of Sciences（俄罗斯科学院机械问题研究所）；Petersburg Nuclear Physics Institute named by B. P. Konstantinov of National Research Centre “Kurchatov Institute”（国立库尔恰托夫研究所鲍·彼·康斯坦丁诺夫命名圣彼得堡核物理研究所）
Modelling the delayed shock-breakout emission following jet-launching binary neutron star mergers via relativistic magnetohydrodynamic simulations simulations
INAF, Osservatorio Astronomico di Padova（意大利国家天体物理研究所帕多瓦天文台）；INFN, Sezione di Padova（意大利国家核物理研究所帕多瓦分部）
