Your objection is noted, but it’s not unique to using c to define lengths. The original standard for the meter was a metal bar that was defined to be one meter long (actually the bar was longer but had two marks on it defined to be one meter apart. That is irrelevant to the point, though, so I will refer to this as a meter bar). How did we know the length of the meter bar was 1 meter without measuring it?

The question, while it seems to be a valid question is actually not a legitimate question. The confusion lies in that you seem to think there’s somehow a “true” meter out there that we can use to check our definition of the meter to see if it really is a meter. No such “true” meter exists; we define our standard units any way we find useful. The old meter bar had a length of one meter precisely because we all agreed that it did. There is no deeper meaning than that.

That’s an incredibly important step, though. The agreement upon a standard is what allows measurements in the first place. A measurement is really nothing more than a comparison of an observed quantity to a standard quantity. With our meter bar in hand, we could now go out and measure the lengths of all kinds of stuff. One of the things we wanted to measure is the wavelength of light. We developed ways to measure it very accurately. In fact our measurements got so good, the limiting factor holding us back from making even better measurements was our meter bar. It made sense to scrap the meter bar at that point and define the meter in terms of wavelengths of light. Technically we picked light generated in a particular way and defined its wavelength. How do we know it actually had that wavelength? No better reason than “Because we said so.”

Continuing in similar vein, we used our new standard to measure other lengths. One thing we wanted to measure is c. This isn’t a length, but a velocity. Nonetheless a velocity is just a ratio of length to time, so measuring a velocity involves measuring a length (and a time of course). Again we got good at it, so good that the measurement accuracy was limited by our standard wavelength, so scrap the standard wavelength and define the value of c.

In some regard, this is actually a much better standard. There is no standard length in nature. That is, there’s no phenomenon in nature that always involves the same distance. There is a standard velocity though, namely c. This standard velocity is actually much more fundamental than just being the speed at which photons move. The constant c is a defining constant in the geometry of flat spacetime. It also is involved in the fine structure constant, which gives the strength of the electromagnetic force. Being the speed at which photons move is almost an afterthought regarding the role c plays in physics. In short if c isn’t constant the universe would be a very different place; we’d notice, and it would not be just that the speed of light was different.

This is also the case for other values in nature, such as the quantum of action, given by Planck’s constant, h and also the gravitational constant G, which relates energy to spacetime curvature. Most notably, these constants h,c and G can be mathematically combined to give values with units of mass, time, and length. We could theoretically define our units therefore by simply defining these three constants. These are the true fundamental definitions of our units.

This is a good explanation, thanks.
I still think it is more logical to begin with an absolute measurable physical thing in nature like x wavelenths of light frequency y, and proclaim that length to be one meter. We already determined our time unit of seconds by a naturally occuring oscilliation. So from that we can measure based on frequency, yes?

Thanks for stopping by man.

Didn't we do the same thing with time as we did with distance? Time how long it takes the earth to move x amount and work backwards from there to smaller and smaller time units?

No that was the old way. A second is now defined using the oscillation of caesium radiation, originally set based on how many of those it took for the earth to rotate. But it is now an eternal constant (for the time being), until we find which of those metrics decays in the next eon.

Wavelength of light is not something we can hold a meter stick up to, so I don't think we abandoned the meter stick because it wasn't accurate enough -- perhaps it was useless to begin with (for this particular goal)? Maybe by that point we were well off the path of "measuring" things and "calculating" would be a better word? I could be very, very wrong here Maybe there is a material that leaves streaks when photons pass thru it, and maybe a bloke in kansas used a meter stick to measure it, idk.

https://www.chemedx.org/blog/simple-...velength-light