I Isn't the speed of light tautologically 299792458 m/s?

[vanhees71]

I don't think so. While it is true that the speed of light is now usually thought of as a historical remnant, like measuring depth in fathoms and distances at sea in nautical miles, the choice of standards is more about how they are realized. When we changed from Amperes to Electron Charge, it wasn't because after a century we finally believed electrons exist: it because charge finally because a better unit than current.

There's of course a difference between the definitions of the units, which now are pretty abstract, i.e., by just defining the numerical values of the "fundamental constants" (of our contemporary best body of knowledge). It's another question, how to realize and with which precision these units. That's why in addition to the pretty short definitions you have entire brochures for "mise en pratique", i.e., how the units are realized by real-world high-precision measurements:

https://www.bipm.org/en/publications/mises-en-pratique

What I find very interesting about discussions like this is the interplay of theory and experiment, i.e., the definition of the units always must depend on some theory.

If one thinks about it the history of the SI units reflects this clearly. E.g., originally the base units were time, distance, and mass, and indeed that was what was needed for Newtonian mechanics. One fundamental law was Newton's universal law of gravitation, and indeed that was used to define the units of time in terms of the motion of the Earth around the Sun and distance in terms of the length of a specific longitude of the Earth and mass via the mass of $1 \, \text{dm}^3$ of water (either at the melting temperature of ice or at the temperature of maximal density):

https://en.wikipedia.org/wiki/Second#History_of_definition
https://en.wikipedia.org/wiki/History_of_the_metre
https://en.wikipedia.org/wiki/Kilogram#Timeline_of_previous_definitions

These definitions have been changed over the time several times. This happens whenever the older standards don't hold up anymore the accuracy one can measure the corresponding quantities due to technological advancements.

 

[hutchphd]

But, what if it wasn't constant in a vacuum? Because of the definition of meter, a statement just cannot be experimentally proven false when it is a tautology.

A system of units is exactly that, no more and no less. If your system defines units of length to be relative to a platinum bar in a vault, how do you know that its length is not "actually" changing when you close the door of vault? The purpose is to allow us to compare measurements over time and space in the most precise and useful way we can apprehend. Apparently one must choose some standard(s) as immutable and constant. The choice is one of utility, not dogma.

 

[pervect]

Isn't the point that the change to unit definitions has changed how we think of distance (at least in the formal sense)? With a physical object as the definition of the meter you're defining distance as a fundamental thing. Coupled with a definition of a time unit, speed is a derived quantity. But in the modern definition, speed and time are the fundamental quantities and length is a derived quantity. In fact, if you track through the definitions, "I'm travelling at 30m/s" actually means "I'm travelling at one ten millionth of $c$", completely independent of the definition of the meter.

Distance is now fundamentally "what radar measures", whereas before it was "what rulets measure".

I suppose distance has changed some, but I view most of the changes in special relativity as being related to how we think about time. Certainly, the inter-relationship between distance and time is new. Changing the standard doesn't seem like as big a deal to me as the conceptual changes related to the unification of space and time.

On the practical side of things, the changes in standardds are a foundation for more precise measurements. The old standards had limitations that were holding back our ability to improve precision - I believe that this is the primary reason that the BIPM changed them. I..e. the changes were made for practical and functional reasons, not ideological ones.

 

[Dale]

I believe that this is the primary reason that the BIPM changed them. I..e. the changes were made for practical and functional reasons, not ideological ones

That is my understanding also. The platinum bar was retired because using the speed of light gave a more reproducible meter.

 

[Vanadium 50]

Ah...PF..where every discussion turns to metrology.

Meter-standard-as-an-artifact ended in the 1960's. It was replaced by a certain spectroscopic line of krypton. The second used to be defined by the earth's average rotation, and was replaced by the atomic clock definition in the 1960's as well. Both were significantly later than the concept of spacetime. The present definition was not because we all suddenly agreed that SR was a good idea. It was because we could measure time far more accurately than distance, and this was likely to remain so for the foreseeable future.

Speaking of which, the OP seems not be participating in this or any of his other threads. I'd call it a drive-by, but don't want to get into a discussion of what the proper velocity standard should be.