Is there a reason that c has that particular value?
Is there a reason that it should have some other value?
Because it was created to have that value, with 1 meter.
It seems to be a fundemental built in property of our universe.
The value comes out of maxwell's equations from the permeability and permativity of free space - although in practice it's easier to measure the speed of light and calcualte the permeability and permativity from that.
In practical terms the experimental value of the speed of light is so well known that it is fixed and the length of the meter changes as new measurements are made.
Or in other words, "The reason c has the value it does is because the BIPM says so"
I may have not been clear. I was looking for why c is a particular speed (?) not how the measurement scale is calibrated.
It seems to be an unknown as to why light travels at the speed it does.
In theory, how do we come up with the permeability and permativity of free space?
I think the question is why is it that the universe chose 3E8 m/s seemingly arbitrarily as the speed limit of the universe as apposed to so 4E8 or something even larger (or presumably smaller). So what makes that speed more special than another?
I don't think that there can be an answer to that question. It is just an axiom of nature.
In this question it is not c but the meter and the second that are arbitrary. In fact they have always been recognised as very arbitrary. You can have physical things that are less arbitrary however. A resonant frequency of the Cs atom for instance for time. (Then that is multiplied by a number that gives a time near that of the old second). As for m , well meters are defined by how far light travels in a second! (multiplied by a number to give something like the old meter).
Now for the theory of these less arbitrary things, it is e.g. the resonant frequency of Cs that is the less fundamental and is explained by some theory in terms of c and other fundamental constants, not the other way round!
So really for explanation of c, barring surprises, all it makes sense to ask is whether it can be explained in terms of other fundamental constants like h or you might hope one day, mathematical ones like pi or sqrt(5).
That is the philosophical (epistomological) part; for the answer to this reformulated question I would have to turn you over a physicist who knows what he is talking about, but AFAIK the question is sometimes asked but has never yet been answered.
no. All of these things are contrived. I don't think that the question is about applying some sort of measurement to it but rather something more abstract. Let me try and phrase it this way:
The speed of light is not infinite. It does in fact have a finite speed. That being said, it can only have one finite speed. Why choose the speed that it did? If the speed was different, wouldn't everything else just change in relation to that?
If light has a definite "maximum" speed than the magnitude of the number simply depends on our choice of units that we use to measure it. In other words, the speed of light is only "3 x10^8" if we measure the speed in meter/seconds. In fact, the maximum speed of light CAN be any "number" we wish it to be if we just decide on new units to use to measure length and time. So there is no significance to the "number" of 3x10^8 itself other than that the speed of light happens to come out to that when we decide to measure length with a meter and time with a second. I think a few other people in this thread mentioned this point already but just didn't go into it.
Another question is why does light have any finite maximum speed at all? Or does it in fact have a finite maximum speed might be another question? Apparently some calculations in QED when light is diffracted for example do not give correct answers unless small probabilities are taken into account for light going slightly faster than 3x10^8 m/s.
The number of the speed of light obviously depends on the units we use. Slightly complicated because for practical reasons the metre is now defined in terms of the speed of light.
The speed of light does have a 'natural' value in terms of other fundemental constants such as permeativity/permeability which link things like the charge on the electron to the units of length and time. It might be possible that in a different universe the speed of light was different and all these other constants were also changed to the new value - of course this might mean that there is no difference to this universe - all the changes cancel out if you like!
It is likely that you could not have a different speed of light with the other constants being the same - the result would likely be that atoms couldn't form or instance. This gets into the anthropic arguement that the reason for the current constants is that it's the only set of values which allow us to exist and measure them.
Separate names with a comma.