RK1992 said:
Is there ever going to be an ultimate asnwer? We can keep asking "why?" but is there a time when such questions become worthless and we have to accept it as it is? For me (an A level student), it seems like a question for philosophy because physics usually asks "what happens?" as far as I can tell.
You definitely make some good points. Still, thinking as physicists, we can be hopeful that a theory may one day be developed that is general enough to predict the value of c. Many of our theories can't exactly predict numbers like universal constants, or masses/charges of fundamental particles, and we are forced to determine them experimentally. However, this is not proof that it is impossible to do so eventually.
As an example, one can use quantum field theory to predict the size of a proton. This value seems to agree with previous experimental values. However, recently we see some data that shows the proton might be a little smaller. So, is the theory wrong, or was the calculation done incorrectly, or is the new experimental technique flawed? Not being an expert, I don't know, but I can look at this as an example of how a theory might predict numbers that were previously only given by experiment. A theory that is correct and very general, might give accurate numerical predictions for universal constants.
An interesting thing, which falls short of the goal here, can be found in classical electromagnetic theory. We can do simple electrostatic experiments and find a value of permitivity of free space \epsilon_0, then we can do a magnetostatic experiment to find the permeablity of free space \mu_0. Then, we can use Maxwell's equations to derive a wave equation which predicts the number for c as {{1}\over{\sqrt{\epsilon_0 \mu_0}}}. This is quite profound because some simple static measurements that anybody can do in their basement, can let us calculate an important universal constant related to a universal theory of electrodynamics, relativity and gravity. This still falls short of the goal, because we have just substituted a different universal constant for c. A deep analsysis reveals that permitivity and permeability are related based on choice of units and the required rules of coordinate transformations of the components of the electromagnetic field tensor. However, even though the ratio of them is known theoretically, the product of these constants can not be predicted by any physics theory. In effect, we can determine any two of the three constants, \mu_0, \epsilon_0, c, once the third is given to us by experiment. Development of a theory that can predict all three values, as required by a universal law, would be a major achievment in physics.
and yes it does bring other parts of the universe. I wasn't implying otherwise. I was only pointing out that the new definition of the meter forces a fixed number to be assigned to the value of c in meters/second. So the number used to describe c in m/s itself does not relate physically to any of the parts of the universe and no physical change would change the number. You could redefine the second to be an hour and the number we get for c in m/s would be exactly the same. No matter how you change the fine structure constant (if you could change it) it would not change the number used to describe c, using the new definition of the meter. However, a change in the fine structure constant would drive real physical changes in the speed of light, even though the number would not change.
