0

Maxwell's equations don't seem to have any delay between changes in electric field and changes in the magnetic field.

So, do Maxwell's equations predict light instantaneously reaches a point one light-year away from the source (I think light takes one year to reach that point).

Or, in other words, do Maxwell's equations predict the speed of causality?

I understand the electromagnetic wave oscillates at the velocity $c = \frac{1}{u_0c_0}$, but Maxwell's theory seems to predict that if I flip on a flashlight and there are no obstructions, the light can immediately be detected one light-year away.

For example, the wave function for the electric field is $g(kx-wt)$ for some function $g$. So, at any time $t$ for all distance $x$ the electric field is changing, which seems to violate the speed of causality.

Perhaps, Maxwell's equations do not predict the speed of casuality, and we need to use more advanced theories (I'm guessing relativity) to predict this. I would like to know if this is the case.

Could anyone tell me (maybe, in the comments) how this is a duplicate question?

Ramchandra Apte
  • 113
  • Not a duplicate (of the indicated question anyway), it's asking about retardation, not how to derive the speed of light. – ProfRob Sep 13 '16 at 09:10
  • I'll answer in a comment. The solns. to Maxwell's equations are a function of $(t - r/c)$, where $r$ is the distance between whatever produces the EM waves and the where the fields are measured. The time $r/c$ is of course the timescale for the propagation of the "disturbance" in the field at the speed of light. See https://en.wikipedia.org/wiki/Retarded_potential – ProfRob Sep 13 '16 at 09:14
  • @RobJeffries thanks, I was reading a bit on retarded time, so if I understood correctly, Maxwell's four equations (that's the form in my book (fundamentals of physics)) aren't sufficient and retardation needs to be incorporated? Or can retarded time be derived from Maxwell's equations? – Ramchandra Apte Sep 13 '16 at 09:19
  • Retardation is a consequence of Maxwell's equations and arises naturally in the case where you have a source of radiation. See https://en.wikipedia.org/wiki/Inhomogeneous_electromagnetic_wave_equation#Solutions_to_the_inhomogeneous_electromagnetic_wave_equation – ProfRob Sep 13 '16 at 11:25

0 Answers0