Understanding Einstein's Discovery: The Constant Speed of Light

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how exactly did Einstein come to the conclusion that light travels at the same speed regardless of the observers own speed?
 
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It's not really a concusion it'sthe starting point.
There is a much earlier principle of relativity that says the laws of physics are the same for any moving body - so your physics test doesn't give different answers in the summer and winter when we are moving in opposite directions around the sun.
But Maxwell's laws give a fixed speed for light.
This would destroy the earier principle, because we could use a measurement of light speed to say how we were moving.

Einstein said 'what would we have to do to make the first principle work?' = the speed of light would have to be the same for everyone.
From this postulate (=claim) all the effects of special relativity follow.
 
Also a number of experiments, in particular the Michaelson-Morely experiment, showed that light could NOT be used to determine an "absolute" speed.
 
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