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
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.
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