Towards special relativity

 

When everything seemed fine, newton laws explained the motion of stars and cars and everything around us, Maxwell laws accounted for electromagnetism and electromagnetic spectrum was understood there comes a theory, which changed our understanding of the universe.

Conflict between two of the most important yet basics laws or principle, which led us to a completely new chapter in the field of physics “The Special theory of relativity”. It all starts with a thought “what is it like to travel along side of a light ray?” every child knows that the light travels at 300,000 Km/sec. And there is also a principle of relativity, which says that all natural phenomenon are identical irrespective of the reference body. You would see an apple falling down from tree so does your friend. There is no contradiction between your observation of an apple falling and your friend`s observation (given your friend is not freefalling).Now so does the law of propagation of light should be identical to you and to your friend. Right? Where is the conflict? Let me show you.

Imagine you are at a railway junction standing on a platform in front you have a railway track, a train is approaching with uniform velocity along with it is a ray of light at a speed of c the train does not stop but continue to move along the light ray with a uniform velocity v. Your friend is seated in a compartment both you and you friend measure the speed the light. For you it is c but for your friend who is himself travelling with speed v.

We were to calculate the relative speed of light with that of your friend according to Newtonian mechanics it would come out to be

w (speed of light relative to your friend ) = c –v

Which is somewhat less that the speed of light. But for you it was c and clearly your friend in not accelerating then why does the results does not comply with the very basic definition of principle of relativity?

Consider you see two lightning bolts struck ground 100 m apart at same time at points A and B from railway platform you observe both of them simultaneously but your friend at the mid-point of AB in railway compartment moving towards one and away from other will counter the lightning at A first and B later!

How the two of you experience the same event differently?
Time is not absolute!

It is because of two unjustifiable hypotheses from classical mechanics; these are

Time is independent of motion of bodies.

The space (distance) between two points of rigid body is independent of motion of bodies

We discard these two considerations and our problem disappears.

In fact, there is a length contraction of moving bodies! An interesting topic for some other day.
To prove the above points and the consistency of speed of light we have a set of equations known as “Lorentz transformation”.

Let your co-ordinates be x,y,z,t and your friend`s co-ordinates be x` ,y`,z`,t`. Light ray follows the path of a straight line with equation x=ct We substitute for x the value ct in equation first and fourth we get:

Divide both and we get:
x`=ct`
Which immediately follows. It is referred to your friend. For him speed of light is also c without time being absolute.
This is the founding idea behind special relativity although Galilean relativity existed before Albert Einstein but Einstein revised the relativity principle and changed the course of physics.