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

The MM experiment pretty much determined that the speed of light was constant. It was not Einstein that postulated it. What Einstein did in his theory of special relativity is combine that fact with the postulate that the laws of physics are invariant (ie. they don’t change based on who observes them) and he made the maths work.

Einstein wasn’t the first to conclude the speed of light was constant irrespective of reference frame. What he did was figure out what that really meant – how things would look to an observer in a relativistic reference frame. This required a complete reimagining of the very notions of space and time. It’s hard to appreciate how groundbreaking this was in the face of centuries of nearly unimpeachable Newtonian mechanics that viewed space as immutable and time as universal. How many times must he have scratched his head and thought, “this can’t be right” before finally becoming convinced without any empirical evidence that he was correct ?

Before Einstein others like George Francis FitzGerald, Hendrik Lorentz (after whom space dilation AKA Lorentz contraction is named), and Henri Poincaré, and others worked on the problem.

In fact, Poincaré submitted a paper a month after Einstein (but a month before Einstein’s paper was published) that had many of the same conclusions and even terminology as Einstein.

In addition to Michelson Morley, the speed of light is directly tied to the Maxwell Equations for the behavior of electromagnetism, which means that there are some uncomfortable implications to a speed of light that depends on the speed of the observer – essentially, the physics governing electromagnetism would have to change depending on how fast you were moving. In general, it has been observed that this is not the case. Physics seems to behave the same regardless of where you are. This means that it’s not a completely crazy idea that the speed of light must be constant in all reference frames.

Back in the 1800s, smart people were working on this problem. One guy (Maxwell) came up with equations that explained how electromagnetic waves propagate. Weirdly enough, the actual velocity given by the equations was just a constant number.

Most people didn’t really think much of this, and figured that light would act exactly as you’d expect. So they designed experiments trying to measure the ‘absolute’ speed of light. They figured that light was similar to sound waves in that it traveled through some medium, and if you travel through that medium in the direction of light, your measurement of the speed of light will change. In other words, if you travel at some fraction of the speed of light, then measure a light beam going past you, you will measure a slower speed of light. However, when they designed experiments to actually measure this (they actually used the speed of Earth in different parts of its orbit, which is neat), nothing worked. They always came up with the exact same number.

The speed of light was constant, no matter how fast you were moving.

This befuddled scientists for decades. Then Einstein comes along and says, “You’re thinking about this wrong. We just need to accept that the speed of light is constant to everyone. If that is true, then our measurements of time and distance *must* disagree with each other if two observers are moving.” This was the key insight. If you accept that speed of light is always constant to any observer, then time dilation (and length contraction) follow.

Let’s talk about time dilation. So what is speed? Well, it is distance per unit time. Now consider the fact that the speed of light is constant. If you have a stick of a known distance, you automatically know the time it takes for light to travel up it (speed is distance per unit time, and we know speed and distance). So this stick is actually a perfect clock! If you can just count how many times a beam of light can bounce up and down this stick, you will have a way of measuring time!

Alright, so you have your clock stick, right. Let’s put you on a train. The train is moving at some speed along the tracks. It doesn’t matter how fast. Inside the train, you look at your clock stick, counting away the seconds. The light goes up the stick. The light goes down the stick. Tick, tock. You don’t notice anything unusual.

Now consider a person standing outside of the train, not moving, watching your clock go up and down your stick. What do they see? Well, since your train is moving, they see the light take a *longer* path to reach the end of the stick. Instead of a straight line up and down, they see the light move in a triangle. The size of the triangle depends on how quickly the train is moving. [Here’s a picture of the path that I’m talking about](https://upload.wikimedia.org/wikipedia/commons/thumb/8/8e/Time-dilation-002-mod.svg/1920px-Time-dilation-002-mod.svg.png).

“So what,” you say? Well, let’s go back to that fundamental law. *The speed of light is always constant.* Let’s say the person outside the train has a clock stick too. When they measure their own time with it, their light travels a shorter distance, so their clock is ticking faster than yours. You disagree on how quickly each second goes by. And when you look outside the train at the person with their clock stick, you see the exact same thing. Theirs appears to form a triangle of light, and is running more slowly that yours.

You both disagree on time. It is relative to your motion. This is time dilation.

And yes, this is measurable and it’s really happening. Because *everything* that happens – inside your body, your brain, your computer, inside a star – happens as information is transferred via electromagnetic interactions. And what is the speed of electromagnetic propagation? It is always the same.

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.

As I understand there were 2 theories that both seemed legit but couldn’t both be true and that was the basis for Einsteins work.

1. Maxwell stating that light always travels at the same speed.

2. Newton with his Laws of Motion. (For example, if a train goes 100 km/h and you throw a ball with 50 km/h in that train then the ball travels with 150 km/h for someone standing still outside of the train.)

If you put a lamp on that train then it’s light should be travelling with the speed of light according to 1 but it should be travelling at the speed of light + 50 km/h according to 2.

Einstein figured out this problem by stating that both can be true if time and space are different for both the train and the person watching outside of it.

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