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Does the Heisenberg uncertainty principle (HUP) apply along the timedimension in the same way it applies along the three space dimensions?Relativity says it should; current practice says no. With recent advances inmeasurement at the attosecond scale it is now possible to decide this questionexperimentally.  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 bemeasurably 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; thencompare. There is -- as expected -- increased uncertainty in thetime-of-arrival if the HUP applies along the time axis. The results are fullyconstrained by Lorentz covariance, therefore uniquely defined, thereforefalsifiable.  So we have an experimental question on our hands. Any definite resolutionwould have significant implications with respect to the role of time in quantummechanics and relativity. A positive result would also have significantpractical applications in the areas of quantum communication, attosecondphysics (e.g. protein folding), and quantum computing.

Does the Heisenberg uncertainty principle apply along the time dimension?