Variance of the Quantum Coordinates of an Event

Details Variance of the Quantum Coordinates of an Event Variance of the Quantum Coordinates of an Event

1998-07-21

arxiv.org/abs/quant-ph/9807059v1

Int.J.Theor.Phys. 38 (1999) 2015-2028

Physics

Quantum Physics

16 pages, latex, no figures

Scientific paper

We study the variances of the coordinates of an event considered as quantum observables in a Poincare' covariant theory. The starting point is their description in terms of a covariant positive-operator-valued measure on the Minkowski space-time. Besides the usual uncertainty relations, we find stronger inequalities involving the mass and the centre-of-mass angular momentum of the object that defines the event. We suggest that these inequalities may help to clarify some of the arguments which have been given in favour of a gravitational quantum limit to the accuracy of time and space measurements.

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