Not the language, the velocity. My car goes the speed it does based on such factors as how much gas I’m giving it, whether it’s going up or downhill, etc. A thing falls at terminal velocity because of its shape, the density of the air it’s falling through, and such. But what is it about wave properties that make light go c in a vacuum? Or is it something about the nature of spacetime? Or the nature of a vacuum? Or something else?
I would say that c is a property of the universe in general, similar to pi or e. Otherwise, would there be any reason for it to appear in formulae for things that do not seem to involve velocity (most famously e=mc^2)?
I see that I mis-read the question. :smack:
It is c because that is the speed at which moving electric fields generate moving magnetic fields and visa versa. Its hard wired into Maxwell’s equations. Faraday suspected as much before hand, but didn’t have the math skills to show it.
More generally, c is the velocity at which cause-and-effect spreads, and the velocity that is constant with respect to reference frames. Light is one of a number of things that propagate at c, which is a more fundamental thing than electromagnitism. It is just a historical curiosity that we think of c as “the speed of light”.
Well, it’s not just a “historical curiosity”; the special properties of light–the only massless particle that interacts via the electromagnetic force and can therefore be readily observed on everyday scales–results in it being characteristically identified with c. We hypothesize that other massless particles also travel at c, but the gravitational interaction of hypothetical gravitons is too weak to measure discretely, gluons (massless bosons which regulate the strong interaction via exchange between bound quarks) don’t last long enough to observe and aren’t found outside of their confined state in normal conditions, and other massless particles (exotic or supersymmetric particles) are highly speculative.
However, as Napier notes, there are deeper implications to c as a universal speed limit besides giving us a singular and invariant value for the speed of light. It is the absolute rate of causality along any space-like or time-like path; that is to say, it defines the boundaries of your past and future personal universe, the so-called light cone of your existence, and barring any warp drives or open loop space-like paths through time or whatever (which we have good, or at least comfortable, reasons to believe don’t exist for any practical purposes) you’ll never see any event that occurs outside that possible range of future positions.
This all falls out of Maxwell’s Equations and Special Relativity, and c ends up as this common constant about which other parameters vary. Now, if the question is why is c=299,792,458 m/s (that’s an exact value, by the way, not an approximation, on the basis that the meter is defined in terms of a set number of wavelengths of a particular frequency of light) then the answer is “Uh-oh-no.” We just don’t know why c is what it is any more than we know what’s in the case.
Here’s some reading for you from older threads covering the topic:
[thread=327045]Why c squared?[/thread]
[thread=311975]Why do light, radio and electricity all travel at the same speed?[/thread]
[thread=313761]Help With E=MC Squared[/thread]
It was still a worthy contribution regarding an obscure nomenclature. Now explain “j”.
Stranger
Great reading. Thanks, Stranger. The most helpful post to me was this one.
One thing I’d like to add is that Einstein’s deductive work makes sense to me since I have some grounding in logic. I am concerned, though, about one of his premises for both relativity theories — namely, that physical law is everywhere the same. Correct me if I’m wrong, but we know now that that is not the case in certain places (like black holes, for instance). Typically, when a premise is found to be wrong, an argument loses its soundness (though it retains its validity). Has anyone amended the theories to say that their conclusions apply ONLY where physical law is as it is where we are?
One of the common methods to challenging Special or General Relativity is to challenge this postulate (the equivalence principle) and it is, indeed, an assumption, albeit one we’ve found (from our single viewpoint in the haystack of the universe) no evidence to undermine.
Singularities and higher dimensional flaws are places where, in simple terms, the math no longer works, but that doesn’t invalidate equivalence elsewhere; it doesn’t mean that the fabric of spacetime is any different there, but just that these are places where the sheets have gotten knotted. From a quantum mechanic point of view, a black hole is just a giant composite quantum particle with “no hair” or distinguishing characteristics; you could swap it with another of the same mass, angular momentum, and charge, and no one would be the wiser.
Still, there’s no absolute way of proving this underlying postulate, and if we discover it to be untrue, most or all of relativity theory would have to be rewritten. It’s not the sort of thing that keeps most physicists up at night, though.
Stranger
Not to worry. If it could be proved true, it wouldn’t be a postulate; it would be a conclusion. 
Funny thing is, that link actually says it was probably first c for “constant”…
To be precise, we don’t know what happens in a black hole. Much more serious is that relativity theory appears to be incompatible with quantum mechanics. One governs the large (anything we can see and a good deal smaller, down roughly to atomic distances) and the other the small. Some physicists (Freeman Dyson being the best known example) are content with that situation. As well as I understand Dyson’s position, physics is around to allow us to calculate events and if we need different theories at different scales, that doesn’t bother him. Others (like me, but then I am a mathematician) want a theory with explanatory value, not just the ability to calculate.
Now relativity, both general and special, does have explanatory value. If you understand that the speed (NOT velocity) of light is constant in any inertial frame, then certain things follow. That is special relativity. General relativity explains that all bodies just follow geodesics, but bodies with mass warp space, so the geodesics don’t look straight. (I don’t then understand why we need gravitons, though).
The more speculative modern theories (e.g. string theory) are an attempt to resolve the contradiction and, perhaps, come to a fundamental understanding of why things are the way they are.
This is it. Really, if you use the most natural units, c is 1. We just don’t see it that way because we find it convenient, for various reasons, to measure space and time in different units. But really, 3e8 meters of space (actually a hair less, but I don’t feel like bothering with all the digits) is, in some sense, the same thing as 1 second of time. It’s like if we had a piece of graph paper, with the vertical scale marked in centimeters, and the horizontal scale marked in inches. If I drew a diagonal line at 45 degrees on that paper, I might then measure it as having a slope of 2.54 cm/inch. I could ask what the significance is of the slope 2.54 cm/inch, but really, the significance is just that 2.54 cm/inch = 1. So it is with c, as well.
– Ambrose Bierce, the Devil’s Dictionary
Being brung up in physics, instead of EE, I use i for the square root of minus one. Or the Square Root of Myna’s Sex.
It seems to me backwards to ask the question that way. I think it is better to ask, “Why did we decide to define the meter and the second to be such that light in a vacuum traverses 299,792,458 of the former in one of the latter?” Which is not to dismiss the issue as mere convention. It is equivalent to asking, “Why do we live at a scale where it is convenient to define the meter and the second in the way that we do?”
>Well, it’s not just a “historical curiosity”; the special properties of light–the only massless particle that interacts via the electromagnetic force and can therefore be readily observed on everyday scales–results in it being characteristically identified with c.
I’d even debate this one. Photons are the only massless particle that interacts via electromagnetism, but light usually means visible photons, or those specially named according to their relationship to visibility, like infrared or ultraviolet.
It’s certainly plausible to me that we might have made much more progress with radio waves than with visible or nearly visible light, and referred to c as the speed of radio. Not that this ought to have been more likely, just, that the reason people associate c with light has to do with the history of our understanding, and not with anything intrinsic to c.
>the so-called light cone of your existence
When I studied cosmology, I heard this issue described more by “world lines”, which better suggest the idea of worlds with apparently no possibility of interacting because their world lines were exclusive.
>Really, if you use the most natural units, c is 1.
An interesting point. At least, this is one version of a natural unit system.
>“Why did we decide to define the meter and the second to be such that light in a vacuum traverses 299,792,458 of the former in one of the latter?”
Now, that one really is pretty much just history, and maybe not very inspired history. We have the semi base 60 system for angles and time from antiquity, and the meter as 1/10000 of the distance from equator to pole. Of course, fixing a recent best estimate of c at a defined value and then changing the definition of a meter to match that forever is a nice improvement over the scribed bars.
And, actually, since the standard wavelength is a visible orange light, in that sense c is more clearly defined as “light speed” than as the underlying constant of the universe.