Integral, I think you forgot to include the weblink.
fys iks! said:
Thanks for the reply. Does anyone have a link to a derivation of c from Maxwell's equations?
It's pretty short, so I'll just type it up here.
Maxwell's equations in vacuum:
\nabla \cdot E = 0
\nabla \cdot B = 0
\nabla \times E = - \frac{\partial}{\partial t} B
\nabla \times B = \mu_0 \epsilon_0 \frac{\partial}{\partial t} E
The trick is to use the vector calc identity, where for an arbitrary vector field A:
\nabla \times \nabla \times A = \nabla (\nabla \cdot A) - \nabla^2 A
So if we evaluate del x del x B, we get:
\nabla \times \nabla \times B = \nabla (\nabla \cdot B) - \nabla^2 B = \nabla (0) - \nabla^2 B
as well as
\nabla \times \nabla \times B = \nabla \times (\mu_0 \epsilon_0 \frac{\partial}{\partial t} E) = -\mu_0 \epsilon_0 \frac{\partial^2}{\partial t^2} B
putting this together gives:
\nabla^2 B = \mu_0 \epsilon_0 \frac{\partial^2}{\partial t^2} B
This can be done for the E field as well (start with del x del x E), giving a similar result
\nabla^2 E = \mu_0 \epsilon_0 \frac{\partial^2}{\partial t^2} E
So waves solution have the speed
v = \frac{1}{\sqrt{\mu_0 \epsilon_0}}
bcrowell said:
The issue of whether MM influenced Einstein is complicated. Einstein claimed that he didn't know about MM in 1905, but later evidence showed that he did know about it, and presumably just forgot that he did by the time he made that statement. The thing is, MM as not considered to be conclusive at the time. People did variations of it, motivated by aether theories, well into the 1920's. E.g., someone did a version in a tent on top of a mountain in an attempt to avoid aether entrainment and obtain the "right" result. Since the experimental situation in 1905 was far more muddled than sanitized textbook history would have you believe, it makes sense that Einstein was more heavily influenced by Maxwell's equations than by empirical evidence on this point.
Wow, thanks for the clarification. I knew there was some debate on the issue, but I never knew they later found proof Einstein was aware of it.
Maybe I have my history a bit skewed, but I thought Lorentz's view was the prominent view of the aether by 1905. His view was of a pervading immobile aether. Either way, if the aether was a mobile fluid, Maxwell's equations would have to change.
So I always had the impression that people took MM fairly seriously (such as inspiring Lorentz and Fitzgerald to postulating length contraction, which led to the discovery of Lorentz transformations and Lorentz symmetry in Maxwells equations -- wow, Lorentz was _so_ close). The people obsessed with redoing MM again and again I thought were just the people who rejected Lorentz's view of the aether and considered it a mobile fluid (plus the resistance by some against SR). Miller in particular was quite obsessed with this, as he seemed unwilling to seriously consider light without a tangible medium.
Is that view of history overly revisionist? In particular, did MM actually influence Lorentz and Fitzgerald, or did they have other reasons?
