# Relativity of Simultaneity

Let's assume there is a light source in the middle of the train and sensors on both sides to detect the light.
From the point of view of an observer inside the train, the two light sensors are the same distance apart, so the light arrives on both sides at the same time.

However, from the point of view of an outside observer, the train is moving at speed $$v$$. Thus, light traveling to the left will arrive first, and light traveling to the right will arrive last. That is, from the standpoint of an outside observer, the two events do not occur at the same time.

Likewise, according to the theory of special relativity, two events that happen simultaneously to one observer may not occur simultaneously to another.
The 'Special theory of relativity' can explain the 'Relativity of simultaneity', and it starts with the following two assumptions.

1. In any inertial system, the laws of physics apply equally.
An 'inertial system' refers to a space with no change in speed, such as a train running at a constant speed.
The laws of physics that apply outside the train (law of inertia, F=ma, action-reaction, (angular) momentum, conservation of energy, etc.) also apply equally inside the train. In fact, even assuming the train is stationary and moving is the scenery outside the train, there is no way to figure it out.
2. The speed of light is the same no matter which inertial system you observe.
Imagine that some light is emitted from a very fast-moving spaceship. If the speed of light observed from the spacecraft is $$c$$ and the speed of the spaceship is $$u$$, the speed of light observed from the outside is likely to be $$u+c$$, but the speed of light is It will still be $$c$$. Even if this light is observed in another inertial system, it is still $$c$$.