Does the Heisenberg uncertainty principle apply along the time dimension?

TL;DR

This paper investigates whether the Heisenberg uncertainty principle applies to the time dimension in quantum mechanics by proposing an experimental test involving time-of-arrival measurements, with implications for physics and technology.

Contribution

It develops a metric for time-of-arrival in quantum systems and proposes an experimental test to determine if the HUP applies along the time axis, constrained by Lorentz covariance.

Findings

Increased uncertainty in time-of-arrival if HUP applies in time

Experimental framework fully constrained by Lorentz covariance

Potential implications for quantum communication and attosecond physics

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.