From my patchy understanding of relativity, the speed of light being same to all observers is the key ‘hypothesis’ that leads to other consequences like time dilation, relativity etc.
But how did Einstein come to this ‘hypothesis’? Was it just a moment of extraordinary inspiration or were there other ‘hints’ that lead to this? I mean Michelson Morley experiment ( [https://en.wikipedia.org/wiki/Michelson%E2%80%93Morley\_experiment](https://en.wikipedia.org/wiki/Michelson%E2%80%93Morley_experiment) ) was well over a decade earlier. So how come nobody else thought of the idea of speed of light being a constant to everyone?
Follow up question: from this hypothesis, is the space-time continuum also an obvious conclusion? Or did it require another inspired genius moment?
(I use hypothesis in quotes to illustrate that it was indeed a hypothesis when proposed).
In: Physics
When we teach Special Relativity today we tend to start with the two key postulates; “the laws of physics are the same for all inertial observers” (the relativity part) and “the speed *c* is the same for all inertial observers” (the special part). And that is how Einstein sets out the first half of his famous 1905 paper. But that wasn’t how it was developed.
[The paper itself](https://users.physics.ox.ac.uk/~rtaylor/teaching/specrel.pdf) is titled “On the electrodynamics of moving bodies” (when translated), and begins:
> It is known that Maxwell’s electrodynamics—as usually understood at the present time—when applied to moving bodies, leads to asymmetries which do not appear to be inherent in the phenomena. Take, for example, the reciprocal electrodynamic action of a magnet and a conductor…
The motivation behind the paper wasn’t Einstein saying “hmm, what if the speed of light is the same for all inertial observers”, but Einstein trying to find a solution to some major problems in early 20th century electrodynamics – problems many other people were working on at the same time.
This goes back to Maxwell’s equations, over 30 years earlier (although even then Maxwell was building on over a century of work by others, including Ampere, Volta, Watt, Coulomb, Gauss – people who are household names even if we don’t realise it). His work suggested light was a self-propelling wave in the electromagnetic field, and that it should move at a fixed speed, *c*. But that led to the question “fixed speed compared with what?” – speeds are relative. There were several proposed solutions to this – including the idea of an aether, which the Michelson-Morley had tried and failed to find.
Meanwhile various other problems fell out of Maxwell’s work (the “asymmetries” Einstein talked about) – situations where two people can look at the same thing, but get different results. So some physicists were working on that angle – finding out why the numbers didn’t add up.
By the time Einstein published his paper people had figured out most of the maths they needed to “fix” those problems (including the “Lorentz transformations” – which Lorentz had figured out). They just didn’t understand why they needed these equations or where they came from – they had reverse-engineered them from the problems in electrodynamics.
What Einstein did was show that if you started with just those two postulates (relativity – which had been around for hundreds of years – and the constancy of the speed of light) – and did a bunch of work – you could derive the maths that others (including Lorentz) had already figured out.
He connected the different parts of the puzzle, showed that by fixing one issue you also fixed all the others.
And he wasn’t the only one – others were working on this at the same time, they just weren’t quite as fast as he was.
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