Relativity...Part 6

Albert Einstein

 After understanding that time is not what we think and it is completely different and has lost his absolute character just because of constant nature of speed of light. Now we have to learn that to maintain constant nature of speed of light not only time but space also changes. So today we are going to see the difference between Newtonian space and Einsteinian space. According to Newton as he clear wrote in his famous book "The Principia" that "Absolute space, in its own nature, without regard to anything external, remains similar and immovable".

In Einstein's relativity space also lose its absolute character to keep the speed of light constant for both the observers who are in motion and who are not.

Transverse lengths

Two sprinters running opposite to each other having metersticks

Imagine 2 sprinters A and B are having a meterstick having a thin knife blade attached to the top end. They run towards each other at a high relative speed, holding the sticks perpendicular to direction of motion. If the stick are equally long, then the knives should hit each other. But if one stick is longer than other, it will be sliced off by the knife on the shorter stick.

Suppose B's stick is shorter than 1metre according to A. Then B's knife will slice off the top of A's stick. This fact does not depend on who is observing it. It is definitely A's stick that has been cut off. Now this cannot happen , according to Einstein's first postulate, because it would mean that there is a priori reason for preferring one reference frame over other. In such an originally symmetric experiment, with the laws of physics the same for both A and B, everything that happens to A should also happen to B. The one possibility remaining, that the knives hit one another is a symmetrical result showing that to either observer the metersticks have the same length. It means transverse lengths are unaffected by motion.

Longitudinal lengths

According to Einstein the body which are in motion their lengths get contracted. And it is given by the same factor Gamma that we have learnt in previous parts.

Length contraction

To understand this let us take a very simple example that will again blow our mind. Imagine there is stick of length "D" which is at rest in our frame of reference. A clock moving along side the right of stick with velocity "v". According to our frame of reference the time it take to reach right hand of length is 

     
   T=D/v
and we also know that it is going to take less time for moving clocks.

Now look at the same experiment with clock's frame of reference then the clock is at rest and it is the stick which is moving so what should be the time elapsed according to clock's frame it should be again D/v yes, but in reality from clock's frame of reference it is 

        

       T'=(D/v)(√1-(v/c)²

  

It again breaks our understanding of reality. Now why this happened is because-in order to maintain constant nature of speed of light according to  Albert Einstein space also have got changed that is length of moving stick is not as same as length of stick which is at rest. It means length of stick is going to be less than original length and this length is given by "d" which is

     d=D(√1-(v/c)²

Contraction in length of stick

And this also explains why time elapsed is different and this is called contraction of longitudinal lengths. In next part we will discuss more about weird things that takes place in space and remember is all because of constant nature of speed of light.