Special relativity and Light Speed

Question

can somebody explain me how did einstein come up with the idea that the speed of light had to be constant,that it doesn't depend on the state of motion of the observer? I mean cuz I've always heard that as a fact,and i know it is,but exactly what line of thinking led him to deduce that?

It's ok if you have to get into advance maths and physics in order to explain me that, I'll try to understand as much as possible.

PS: Dont tell me that it was because of the michelson- morley experiment.Einstein himself always said he knew nothing about that experiment when he came to the conclusion that the speed of light was absolute,so he somehow managed to get to that conclusion using nothing but his brain.

Answer 1

Maxwell's Equations imply that the speed of light is constant in the frame in which it is valid. The problem is that the equations are not invariant (valid) if you change frames (observer velocity) according to the Galilean Transformation assumed in Newtonian Mechanics. That's where one simply subtracts the relative frame velocity from the velocity of the object (like a photon) in the initial frame to get the velocity in the new frame. Einstein thought intuitively that the laws of physics (like Maxwell's Equations) should not depend on one's frame, so he simply assumed that they do not (he was like that), and pursued its implications (Special Relativity).

Answer 2

Once Maxwell gave us the speed of light and M/M provided inconsistencies, Einstein attempted to find a set of transformations that preserved energy and momentum and a constant speed of light c, in any inertial frame.

The Lorentz transformations, which already existed, were seen to fit these criteria, and were used to derive relativistic energy and momentum. I was taught that the Lorentz transformations were found by Einstein, essentially as a result of his looking for them, or something like them, until he did!

There is a very well researched and detailed article on the history of SRT at: http://www.aip.org/history/einstein/essa...

(It actually reveals that we don't know exactly what Einsteins process was)

There is a quick read on the Lorentz transformations and their effects at: http://hyperphysics.phy-astr.gsu.edu/hba...

Lastly, here are the expressions for relativistic dynamics: http://hyperphysics.phy-astr.gsu.edu/hba...

I could not find a detailed derivation for you (mine are in print) but the last link does give a brief one.

Hope this helps...

Answer 3

Maxwell's equations give us the speed of light.  Before Einstein, everyone thought that the equations applied in some special reference frame--the luminiferous ether.  But M&M failed to find any relative velocity to the ether.  Einstein postulated that Maxwell's equations (and hence the speed of light) hold in ALL reference frames, so length and time have to stretch to accomodate that.

I don't think you are corect that Einstein didn't know about the M&M negative results though.  They were published almost 20 years before, and anyone even moderately engaged in the subject (and Einstein was, despite being a bit out of the academic loop) would have known that.

http://www.fourmilab.ch/etexts/einstein/...

Read the second paragraph of the prologue--Einstein was clearly aware of M&M.  And he was also aware of (and cited) the work of Lorentz, who had already done the math for length contractions and time dilations, but interpreted the contractions/dilations as stretching of objects moving through the ether rather than stretching of space and time themselves.

Answer 4

You are absolutely correct.

The speed of light through space can be calculated from the properties of space using Maxwell's equations for electromagnetism.

Einstein started from the position that the laws of nature can't depend on how fast you're moving.  So the properties of space can't depend on how fast you're moving. So the speed of light that you observe will be absolute.