Formulation of causality-preserving quantum time of arrival theory
- URL: http://arxiv.org/abs/2304.06949v1
- Date: Fri, 14 Apr 2023 06:27:45 GMT
- Title: Formulation of causality-preserving quantum time of arrival theory
- Authors: Denny Lane B. Sombillo and Neris I. Sombillo
- Abstract summary: We revisit the quantum correction to the classical time of arrival to address the unphysical instantaneous arrival in the limit of zero initial momentum.
We show that the vanishing of arrival time is due to the contamination of the causality-violating component of the initial wave packet.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We revisit the quantum correction to the classical time of arrival to address
the unphysical instantaneous arrival in the limit of zero initial momentum. In
this study, we show that the vanishing of arrival time is due to the
contamination of the causality-violating component of the initial wave packet.
Motivated by this observation, we propose to update the temporal collapse
mechanism in [Galapon E. A. 2009, Proc. R. Soc. A.46571-86] to incorporate the
removal of causality-violating spectra of the arrival time operator. We found
that the quantum correction to the classical arrival time is still observed.
Thus, our analysis validates that the correction is an inherent consequence of
quantizing a time observable and is not just some mathematical artifact of the
theory. We also discuss the possible application of the theory in describing
point interactions in particle physics and provide a possible explanation to
the observed neutron's lifetime anomaly.
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