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The second is defined as the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom. The metre is the length of the path travelled by light in vacuum during a time interval of 1/299792458 of a second.

With those definitions, we are left with no way to check the invariance of $c$ (the local speed of light in freely falling and non-rotating reference frames). Is there a definition of length which would be independent on anything involving light, and allow to check the invariance of $c$?

I am aware of classical definitions based on pendulum or earth's meridian. I red a definition involving the wavelength of a certain type of radiation, but this again depends on the speed of light. I am wondering it there exists a modern alternative definition of the meter, light independent and usable for precise experimenting.

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  • $\begingroup$ @AlbertAspect the Michelson-Morley experiment only shows that the speed of light is isotropic at the point of measurement in a given reference frame. It doesn't prove that it's the same everywhere or everytime. It still might vary with the expansion of the universe or in super-voids vs. near deep gravity wells. $\endgroup$ – John Dvorak Jan 11 '17 at 16:27
  • $\begingroup$ @Albert Aspect : AFAIK, the Michelson Morley experiment aimed at comparing the speed of light in perpendicular directions. The hypothetical experiment behind my question could be someone wanting to compare the speed of light in a freely falling frame near the earth and a free falling frame near the sun. He could not do that by using the official definition, which by definition would give him the same result. $\endgroup$ – user130529 Jan 11 '17 at 16:28
  • $\begingroup$ Though, tossing an MME into the sun could be a fun project for the next decade. We just have to squeeze it into a tiny amount of space, then hitch a ride with the next cubesat transport to the inner solar system and unfold. $\endgroup$ – John Dvorak Jan 11 '17 at 16:32
  • $\begingroup$ yes, I was wrong $\endgroup$ – user126422 Jan 11 '17 at 16:37
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    $\begingroup$ You don't need to know the length of a meter to do the proposed comparison. You just need to cart the apparatus used in one environment to the other environment. That makes the length you use "$1\,\text{'experimental pathlength}$" in both cases. Problem solved. $\endgroup$ – dmckee Jan 11 '17 at 18:30
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The issue isn't whether we have a definition of the SI base units involving light. The issue is that it is never possible to define empirically whether or not a universal constant is in fact non-constant, except in the case where it's unitless. See Why do universal constants have the values they do? .

dmckee comments:

You don't need to know the length of a meter to do the proposed comparison. You just need to cart the apparatus used in one environment to the other environment. That makes the length you use "1'experimental pathlength" in both cases. Problem solved.

But this doesn't accomplish what the OP wants. The OP wants to test whether or not the speed of light is the same everywhere. Say you have a totally self-contained apparatus that measures $c$ and outputs its result as a number. You move the apparatus somewhere else, and it outputs a different result. One possible explanation is that $c$ varies from point to point. Another possible explanation is that some other universal "constant" has changed. For example, Planck's constant $h$ could have changed. This would change the sizes of atoms in the apparatus, as well as having other effects. We can never say whether $h$ really changed or $c$ really changed. What we would be able to test is whether the fine structure constant changed, because the fine structure constant is unitless.

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