Hey i was just wondering where Einstein got the idea for his postulates of the speed of light being the same in all reference frames and that there is no preferred frame.
The idea that there is no preferred frame came from Galileo. The idea that the speed of light is the same in all inertial reference frames (note it is not the same in all reference frames) came from Maxwell's equations which worked beautifully with experimental data. Possibly also, the Michelson-Morley experiment's null result. Although I've heard some claim historically Michelson-Morley's experiment didn't really influence Einstein ... it is hard to say directly since his 1905 paper didn't give any references.
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.
Couldn't it be said that the fact that the laws of physics work exactly the same in all inertial frames is a purely empirical induction or observation. That is was first realized by Gallileo through the kinamatics that he observed. I.e. a ball bounced straight down in a uniformly moving platform followed the same down -up down trajectory relative to the platform as a ball bounced on the non-moving ground. relative to the ground. That the observed invariance of physics continued through Newton and right up through Maxwell. That it was empirically verified that the Maxwell equations were invariant and held in electrodynamic systems at differing inertial velocities and the equations called for a constant c . That this not only continued and expanded the observed invariance of the laws of physics but by inference provided an empirical basis for the assumption of the invariance of c. SO the only really speculative part of the 1st and 2nd postulates is the assumption that this observed reality would continue to hold if we had the technology to accelerate a lab to relativistically significant velocities. My memory of reading the history of Gallileo and Maxwell is somewhat hazy so if I have made any errors I hope you and they forgive me.
This page does a pretty good job of it. You can see that c = [itex] \sqrt {\frac 1 {\epsilon_0 \mu_0} }[/itex]
Integral, I think you forgot to include the weblink. It's pretty short, so I'll just type it up here. Maxwell's equations in vacuum: [tex]\nabla \cdot E = 0[/tex] [tex]\nabla \cdot B = 0[/tex] [tex]\nabla \times E = - \frac{\partial}{\partial t} B[/tex] [tex]\nabla \times B = \mu_0 \epsilon_0 \frac{\partial}{\partial t} E[/tex] The trick is to use the vector calc identity, where for an arbitrary vector field A: [tex] \nabla \times \nabla \times A = \nabla (\nabla \cdot A) - \nabla^2 A[/tex] So if we evaluate del x del x B, we get: [tex]\nabla \times \nabla \times B = \nabla (\nabla \cdot B) - \nabla^2 B = \nabla (0) - \nabla^2 B[/tex] as well as [tex]\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 [/tex] putting this together gives: [tex]\nabla^2 B = \mu_0 \epsilon_0 \frac{\partial^2}{\partial t^2} B [/tex] This can be done for the E field as well (start with del x del x E), giving a similar result [tex]\nabla^2 E = \mu_0 \epsilon_0 \frac{\partial^2}{\partial t^2} E [/tex] So waves solution have the speed [tex]v = \frac{1}{\sqrt{\mu_0 \epsilon_0}}[/tex] 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?
I'm not sure I understand this. In what sense `came from'? The proof in 9.37PM seem to me to fall short of implying it - for the equations say nothing about inertial frames: they may be taken to hold only in the frame of the aether, and the quantity v, the velocity, interpreted as referring only to the aether. I understood it to be part of Einstein's contribution to explicitly say that the equations hold strictly in *all* inertial frames, and then show how Newtonian equations have to be modified to make this work. Is my understanding wrong? On MM and Lorentz and FitzGerald, according to Harvey Brown's book `Physical Relativity', FitzGerald seems to be reacting to the MM experiment (Brown 48). He also writes that if it had not been for the prodding of Lorentz and Rayleigh, Michelson may not have performed his experiment with Morley (42). This supports the idea that the experiment was influential in their thinking.
Thanks for the historical info! Eh, I think we may be bordering on debating semantics at this point. The openning post asked where Einstein got the idea for his postulates. Einstein's ideas didn't come out of the blue. In fact, all the essential pieces were already there. Would you be more comfortable if I worded it as: The light postulate was "inspired" by Maxwells equations? Maybe there is yet a better way to word it. But I hope you get now "in what sense" I used that phrase. Basically, to summarize: he took the root of Galileo's belief (physics is the same in all inertial frames), and applied this literally given Maxwell's equations (which as written don't refer explicitly to a medium, so if taken as is, there is a speed all inertial frames must agree on). Previously, everyone struggled with the fact that electrodynamics didn't have Galilean symmetry (although they obviously didn't think of it in those terms at the time). His result "resolved" the galilean symmetry problem, by just realizing it needed to be replaced with Lorentz symmetry. So Lorentz symmetry was no longer a mere coincidence in the equations of electrodynamics (which Lorentz's view seemed to suggest), but was raised to an actual symmetry that relates inertial frames, and thus a symmetry for all physical laws.
In the 1905 paper, after the first paragraph discussing the asymmetry of Maxwell's equations, He says this: On the Electrodynamics of Moving Bodies I note the plural "attempts" and therefore consider it unimportant whether or not he knew of Michaelson-Morley specifically.
In the interest of history of physics the person named Woldemar Voigt is interesting. He worked out the relativistic doppler effect in 1887 but without realizing the paradigm shift. See this document: http://astro1.panet.utoledo.edu/~ljc/voigtc2.pdf
Yes, there were other experiments which related to the motion of the earth or the laboratory through the supposed luminiferous ether, before Michelson-Morley, e.g. observations of stellar aberration and measurements of the speed of light in a moving medium.