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Your not getting what invariant means.mirrormirror said:i think that what i fail to grasp is WHY ( that is, for what practical reasons ) the light beams will reach the MOVING box doors at the same time, like all of you said. The way i think of it, exactly due to the fact that c is constant and invariant, it will take it more time to reach the front clock than the rear one, because the front one is moving away from it and the back moving towards it. The observer inside the box doesn't know this, but he will notice it when he he sees the front clock stopped at 12:00:11 and the back clock stopped at 12:00:10.
Here's an example. You have two clocks, At first we look them from the perspective of someone at rest with respect to the clocks. A flash of light is emitted from a point halfway between them. It expands outward at c equally in all directions, strikes the clocks and starts them running. They remain in sync
Now we consider the same clocks and the same light flash from the perspective from someone to which the clocks are moving left to right. Again, the flash is emitted from midway between the two clocks and again expands outward at c equally in all directions. This is what 'invariant' means; All inertial frames measure light as moving at c with respect to themselves.
As a result, in this frame, the light hits the left clock before hitting the right clock.
The left clock starts first and then the right clock. The clocks are not in sync. Let me repeat these are the same clocks and the same light flash as in the first example, just considered from a different inertial frame.
As to why this is the case, it is because this is how time and space relate to each other.
I'll try to use an analogy. Absolute time and space, like you are proposing are like the directions North-South and East-West. If you ask someone how far North and far West Chicago is from Miami, everyone gives the same answer.
However, what we have found that time and space aren't like North-South and East-West. They are more like Left-right and forward-backward. If you ask two people how far to the left and how far forward Chicago is from Miami, they will give you different answers if they are facing in different directions relative to each other. And you can't say which one is "really" correct, because the whole concept of Left and Right are dependent of the person.
In the same way, time and space are frame dependent. One frame can say that two events are simultaneous and another will say that they are not in the same way that one person facing one direction will say that two objects are directly to the right and left of each other, while another person facing in a different direction will say that they are not, and that one object is forward of the other.