Question

Can someone explain the theory of relativity in the simplest form?

Answer 1

Things that happen, ie events, can be labelled by their coordinates in a given reference frame, for example (x,y,z,t).

Now suppose that there are two inertial reference frames S and S', in coincidence at t=0, but S' is moving in the common x direction with a constant speed v with respect to S.
An event can be labelled by its coordinates in S, (x,y,z,t) or just as well by its coordinates in S', namely (x', y', z', t').
Special relativity tells you how to obtain the S' coordinates of an event if you know the S coordinates (and vice versa), with some equations known as the Lorentz transformation.

If you consider two events and look at the difference in their coordinates, dx dy dz dt, it is found that the quantity\[c^2t^2-x^2-y^2-z^2\] is the same, regardless of which set of coordinates you use to evaluate it. It is called the spacetime interval between the events.

In the jargon of special relativity, the spacetime interval is invariant under a Lorentz transformation. More generally, things that transform in the same way as the spacetime interval are known as fourvectors.

The law of motion F = dp/dt still holds but the momentum looks slightly different than in Newtonian mechanics\[p=\frac{ mv }{ \sqrt{1-v^2/c^2} }\]

I suppose I've given more of a brief summary than an explanation - a very good book that explores these ideas in more detail is 'Spacetime physics' by Taylor and Wheeler, if you can find a copy.

Answer 2

Thanks man!

Answer 3

You're welcome.

Correction - the spacetime interval should have been written as
\[c^2dt^2-dx^2-dy^2-dz^2\]

Answer 4

Yea actually i saw a documetary on einstein where it was written this way.