Testing trajectory-based determinism via time probability distributions

• URL: http://arxiv.org/abs/2404.09684v2
• Date: Tue, 23 Sep 2025 12:38:29 GMT
• Title: Testing trajectory-based determinism via time probability distributions
• Authors: Matheus V. Scherer, Alexandre D. Ribeiro, Renato M. Angelo,
• Abstract summary: We introduce a prescription for constructing an arrival-time probability distribution within generic trajectory-equipped theories.<n>We derive a conditional probability distribution that is unreachable by quantum mechanics.<n>Our results can be tested experimentally, thereby assessing the validity of trajectory-based determinism.
• Score: 41.99844472131922
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: It is notorious that quantum mechanics cannot predict well-defined values for all physical quantities. Less well-known, however, is the fact that quantum mechanics is unable to furnish -- without additional assumptions -- probabilistic predictions even in emblematic scenarios such as the double-slit experiment. In contrast, trajectory-equipped theories naturally have more predictive power. This work formalizes the aforementioned assertions and illustrates them through three case studies: (i) free particle, (ii) free fall under a uniform gravitational field, and (iii) the double-slit experiment. Specifically, we introduce a prescription for constructing an arrival-time probability distribution within generic trajectory-equipped theories and then derive a conditional probability distribution that is unreachable by quantum mechanics. Our results can, in principle, be tested experimentally, thereby assessing the validity of trajectory-based determinism without the need for experiments involving the direct measurement of arrival time.

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