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  1. Since the unit of distance is defined in terms of speed of light in vacuum, if the speed of light in vacuum were to change by "magic", what experiment would be able to detect that?

  2. Is there a theory which says that the speed of light is not a function of time (in the same medium)?

edit. people voting for close, please see my comment

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marked as duplicate by Kyle Kanos, John Rennie, ACuriousMind, Brandon Enright, Carl Witthoft Jul 24 '14 at 14:18

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There are several possibilities to measure the speed of light. For instance, if you know the distance to the moon, you could send a laser pulse there, and wait for its reflection. You could also measure wavelength and frequency of monochromatic light (in vacuum) and its speed will be the product of the two.

If you set up such an experiment and perform it on a regular basis, you will get a rather constant curve. If at some point in time the measurements begin to diverge consistently, you will have detected such a "magic" change.

On a funny side note: the speed of light in meters per second would not change in that event, because since 1983 the meter is defined as the distance light travels in vacuum in 1/299,792,458th of a second (Source: Wikipedia). So, if the speed of light were to change, it would change our measure for length.

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