Maxwell's Eqns & Einstein on Speed of Light

[Phymath]

what about maxwell's equations/theroy states that the speed of light is constant in all refrence frames? (how'd enstien figure that to be true)

 

[brentd49]

It was by experiment, i.e. michelson-morley, that determined that the speed of light is constant in all inertial reference frames. But most people thought this was impossible, they thought Maxwell's equations must be wrong. You would too, if Newton's laws had been around for hundreds of years and Maxwell's only a decade or two. So Einstein just assumed Maxwell was right, by using Lortenz Transformations (which are just the Galeian transformations rederived with the speed of light constant) to describe relativity. Interesting enough Lortenz was the first to right down the equations for special relativity, but he didn't see in those equations the global picture that Einstein saw. Einstein saw the physical effects of when the speed of light is constant not just some equations that seemed to interpret a particular experiment.

 

[Integral]

When Maxwell's equations are cast in the form of the wave equation, the term $\frac 1 {\sqrt \mu_0 \epsilon_0}$ shows up as the speed of electromagnetic waves. Maxwell did this in about 1867, when he computed the value of that constant, he was amazed to see that it equaled the current (for 1867) value of the speed of light. This was the first real evidence that light was electro magnetic in nature. No one, including Maxwell, was very happy with that result. Most assumed that there was an error somewhere, and waited for Maxwell to resolve what came to be known as Maxwell's Conundrum. Then in 1887 (A.E. was ~8yrs old) came the Michelson Morley experiment, which was intended to show experimentally that Maxwell had made a mistake. M&M failed to prove Maxwell wrong, indeed their experiment verified Maxwell's prediction at this point the great schism of Physics was an ugly fact.

Einstein, using his 2 basic postulates was able to DERIVE Lorentz's equations. His method was not restricted to E&M but applied to all physical bodies, His derivation was elegant and simple, requiring only basic calculus to understand. It may well have been the simplicity of his derivation which earned him the respect of his peers. And why that respect remains intact even a century later. Einstein was able to POSTULATE the constancy of c because it was an established fact though the work of Maxwell and Michelson & Morley. He did not pull it out of the air, but simply stated a fact that was well known to all Physic st of the late 19th century.

 

[brentd49]

lol, my answer was just a back of the envelope approximation. I think you said more about it than my book.