How precisely can the speed of light and the metric of space-time be determined $in$ $principle$?

Daniel Braun, Uwe R. Fischer

Published 2015-02-17Version 1

The speed of light in vacuum is one of the most important and most precisely measured natural constants. It determines the metric of flat space-time, presents an upper bound to the speed of all matter and information with respect to any inertial reference frame in the Universe, and plays a crucial role for applications such as satellite-based navigation systems. Its value is fixed by convention to the value $c=299 792 458$ m/s. However, advanced theories predict possible deviations from this universal value, or even quantum fluctuations of $c$. Combining arguments from quantum parameter estimation theory and general relativity, we here establish rigorously the existence of lower bounds on the precision to which the speed of light can be determined $in$ $principle$.