# A mostly inaccurate story on Relativity

How did Einstein discover his famous theories of relativity? And what is the difference between the two theories, the special and general theories of relativity? Essentially, the difference is Gravity. The special theory doesn’t take into account Gravity. For that reason, it is specialised to inertial references systems (systems with no acceleration and no breaking).

## Special Relativity

So what is this first theory, the special relativity? At the time of Einstein, a “principle of relativity” was already existing. So what he did was transforming a principle into a theory. What does the principle of relativity says? It says:

The laws of Nature shall remain the same for you,
wether you are standing still or travelling in continous rectilinear translation.

By law of nature, we essentially means laws of movemements. Imagine that you are eating a soup at the restaurant of a train station. The special relativity theory says that you could eat the soup exactly the same way than if you were on a train (moving in continous rectiliar translation). Eating the soup with reference to the train is the same as eating the soup with reference to the station: you apply the same movements with the spoon for the same results. No soup should be spilled.

This seems all good, however another law was also already known and verified at the time:

Whatever the referential, the speed of light is a constant.

Let’s imagine the following experience: you set up a lamp on the platform of the station, emitting photons parrallel to the train. At the other end of the platform, you set up a receiver, able to measure the speed of the photons received. Reading the measurements, you would find c, the speed of light. Good.

However, if you fixed the receiver on the side of a train going at velocity V, what would you measure? ‘c - V’? Or c + V if the train would go the other direction? Wrong, the measure is still c. If your train could go at the speed of light, you would open the window and measure the speed of the photons passing by: still c. How is it possible?

The answer is that the time and distances that you measure on board a moving train are different than measured from the platform. Onboard the train, the time passes slower with respect to the station, and the distances measured are also smaller. If you are on a train going very fast and looking outside, it will seems to you that people are thinner, and moving slower. This modification of space-time allows to always obtain the same speed for the photon, even when measure from a moving object.

Of course everything is relative: people on the platform will see you thinner and moving slower inside the train. In special relativity, your own clock is always the fastest.

Would Headlights Work at Light Speed? (click for video)

## General Relativity

Let’s come back to our soup. You’re comfortably seated at the wagon bar, with your soup in front of you. The windows blind is closed: you are completely oblivious of the world outside the train. For you, their is only one reference: the train itself. You start eating, and suddenly something incomprehensible happens: the soup, previously fixed with respect to the train, jumps on your laps.

The apparent explaination is simple: the train accelerated. For example, it started turning with respect to the earth. So it seems that the earth is a better candidate to be a reference system. But this doesn’t seem to be fair: why some systems are equivalent reference systems (for example a train moving straight at a regular speed is equivalent to the station) and some others are not (trains turning, for instance)?

The answer is not so easy to understand. The trick is that, when the train is turning, something equivalent to a gravity field is created inside it. As explained in the video under, the gravity and the space-time are the same thing. A bended space-time can have the same effect than a force. When the train is turning, its own spacetime is deformed, and that makes the soup to want to jump on your lap.

The main finding of General Relativity is that the inertial forces and the gravity force are of the same nature.

General Relativity : Einstein vs. Newton (click for video)