Does the Heisenberg uncertainty principle apply along the time dimension?
arXiv:2101.10512 · doi:10.1088/1742-6596/1956/1/012014
Abstract
Does the Heisenberg uncertainty principle (HUP) apply along the time dimension in the same way it applies along the three space dimensions? Relativity says it should; current practice says no. With recent advances in measurement at the attosecond scale it is now possible to decide this question experimentally. The most direct test is to measure the time-of-arrival of a quantum particle: if the HUP applies in time, then the dispersion in the time-of-arrival will be measurably increased. We develop an appropriate metric of time-of-arrival in the standard case; extend this to include the case where there is uncertainty in time; then compare. There is -- as expected -- increased uncertainty in the time-of-arrival if the HUP applies along the time axis. The results are fully constrained by Lorentz covariance, therefore uniquely defined, therefore falsifiable. So we have an experimental question on our hands. Any definite resolution would have significant implications with respect to the role of time in quantum mechanics and relativity. A positive result would also have significant practical applications in the areas of quantum communication, attosecond physics (e.g. protein folding), and quantum computing.
arXiv commentPresented as a talk at International Association for Relativistic Dynamics 2020 Conference; accepted for Journal of Physics: Conference Series: Proceedings of IARD 2020. 38 pages, 7 figures, 94 references. This is third revision, revised in response to reviewer comments
References in corpus (13)
- Experimental loophole-free violation of a Bell inequality using entangled electron spins separated by 1.3 km
- Phase shift in atom interferometry due to spacetime curvature
- Time-of-arrival probabilities and quantum measurements
- Niels Bohr as Philosopher of Experiment: Does Decoherence Theory Challenge Bohr's Doctrine of Classical Concepts?
- On the significance of a recent experiment demonstrating quantum interference in time
- A Path Intergal Approach to Current
- Quantum Arrival and Dwell Times via Idealised Clocks
- An Elementary Canonical Classical and Quantum Dynamics for General Relativity
- Feynman Integrals with Absorbing Boundaries
- Exact Energy-Time Uncertainty Relation for Arrival Time by Absorption
- A self-adjoint arrival time operator inspired by measurement models
- Times of arrival: Bohm beats Kijowski
- Feynman's Decoherence