Physics question

[silverpig]

Originally posted by: Born2bwire

Originally posted by: miketheidiot
why is the speed of light the speed of light?

why isn't the speed of light some other speed?

can the speed of light be derived from some constant? why is it the speed that it is?

Speed of light is the constant. You don't derive it, you define it. Now, if you want some real fun, try deriving the fine structure constant from first principles.

You define the NUMBER, but you can derive the speed of light from electromagnetism.

c^2 = 1/(E_0*u_0)

You can get derive that relationship, but at some point you have to set some units.

 

[Born2bwire]

Originally posted by: silverpig

Originally posted by: Born2bwire

Originally posted by: miketheidiot
why is the speed of light the speed of light?

why isn't the speed of light some other speed?

can the speed of light be derived from some constant? why is it the speed that it is?

Speed of light is the constant. You don't derive it, you define it. Now, if you want some real fun, try deriving the fine structure constant from first principles.

You define the NUMBER, but you can derive the speed of light from electromagnetism.

c^2 = 1/(E_0*u_0)

You can get derive that relationship, but at some point you have to set some units.

To the best of my knowledge though, there isn't a way to derive \epsilon_0 from first principles. \mu_0 is defined exactly by convention and \epsilon_0 is defined by it's relationship with c. Maxwell's equations dictate the speed of light from the choice of the wave number, but the wave number was chosen from experimental (and since the redefinition of the meter, defined) values. The setting of the speed of light in a vacuum is about as basic as you get in relativity and classical electromagnetism. With a defined value of c, you can use Maxwell's Equations to derive any relationship of electromagnetism and the various electrostatic formulas to derive the remaining electrostatic phenomena. So when you get down to it, you still need to know the value of \epsilon_0, or c by extension, to be able to derive classical EM. To the best of my knowledge, QED and QM do not have a means of deriving \epsilon_0, just like QM does not have a means of deriving the fine structure constant from first principles (though that doesn't stop Griffiths from asking you to try in a homework problem, cruel bastard).