If the metre is now defined as the distance light travels in vacuum in $1/299\,792\,458^{\textrm{th}}$ of a second and the speed of light is accepted to be $299\,792\,458\ \textrm{m}\,{\rm s}^{-1}$, doesn't this seem like the chicken and egg problem?
I remember reading somewhere (in the context of uncertainity principles):
…the more precisely one property is measured, the less precisely the other can be measured.
So how, then, do physicists claim to have accurately measured the speed of light? Does this mean the definition of the metre is dependent on our ability to accurately measure the speed of light?
After all, to determine speed (distance traveled/time taken) you must first choose some standards of distance and time, and so different choices can give different answers?
What about so many other factors that affect these measurements? I do not claim to understand the theories of relativity entirely, but what about the chosen frame of reference? Spacetime curvature?
Does this mean that our measurements are only relative and not absolute?
Best Answer
There are three relevant quantities involved here: the length of a meter, the duration of one second, and the speed of light. You only need to absolutely measure one of them, after which the other two can be defined in terms of the one that is measured.
For technological reasons, we have chosen to make the measured reference quantity the length of one second, which is defined in terms of the number of oscillations of radiation associated with the transition between the hyperfine ground states in cesium (specifically, it's 9,192,631,770 oscillations of that light). This is basically because there are experimental techniques that allow incredibly precise measurements of the frequency of radiation, at a level that really can't be matched by length or speed measurements. (The best frequency measurements in the world use trapped aluminum ions as the "clock," and are good to something like one part in $10^{18}$.)
Having defined the second in terms of some physically measurable quantity, we are then free to define the speed of light as having some particular value in meters/second, and then define the meter in terms of the distance traveled by light in one second. The size of a meter is merely a matter of convention, not anything fixed in the physical world, so as long as we have anchored the second to something fundamental, we can make the meter be whatever we want.
The particular values of the meter and the speed of light that we choose are based on older measurements using a meter defined in terms of the circumference of the Earth. We've chosen to keep that value, because it would be a hassle to make a wholesale change.