Gerry- that's a great, deep question. You're right that what units we use sets what number we get for the speed of light. You don't even have to go to another planet to see that. In common U.S. units, it's 186,282 miles per second. In the metric system (first used in France but now used in most of science and engineering) it's 299,792,458
meters per second. In the units often used in parts of physics, it's defined to be 1.0 Planck units.
So is there a more universal way to define it, allowing us to ask some distant extraterrestrials if they get the same value? Yes. There are natural building blocks of matter, atoms, and these come in distinct types. We can define distance units by say the spacing between atoms in a crystal of nickel. We can define time units by say the oscillation period of light from a particular transition of hydrogen atoms between their lowest energy state and their next lowest. Then we can give the speed of light by how many nickel spacings it travels in one hydrogen oscillation period. Something rather like that is actually done in the modern metric system, although not with those specific ingredients. If we assume that the atoms are the same on that distant planet, we can ask the space creatures what they get for the speed of light and see if it agrees with ours.
Now how do we know that they don't actually have different size atoms, with different oscillation frequencies, and a different light speed- but just arranged so that the speed looks the same in their units. That would take a weird coincidence. If we ask them to make a bunch of measurements and they always get numbers that agree with ours, it's far simpler to think that they have the same laws of physics as us than to imagine some tricky way where different laws still make all the numbers match. So far, looking at light and other particles from the rest of the universe agrees with the idea that all the laws are the same throughout. We do have a lot of choices, however, in what particular numbers get used to describe that reality.
(published on 07/26/11)