what actually paradoxs of theory of relativity is ?

Answer 1

There are several. One that comes to mind is the dilation of time.
If it is caused by speed, both observers, the one traveling and the one at "rest," will perceive that it is the other guy's clock that is running slower. On the other hand, if you are at the top of a tower, your clock will run faster than one on the ground, and the observer on the ground will agree that it is indeed your clock that's running faster.
The "twin paradox" is probably the most widely known. If your twin speeds of into space at a fraction of the speed of light and he's gone for awhile, when he returns, he will be younger than his twin who stayed behind.

Answer 2

Well. The easiest one is called the train paradox (sometimes called the ladder paradox; where the train is replaced by a ladder). As you probably know; when something speeds up its apparent length; that is its length seen from a stationary observer seems to be contracted; Meaning smaller then the original length. Keep in mind that only to a stationary observer would a speeding object’s length seem smaller then the original. If a person is going at the same speed as the speeding object, he would see the original length.
Now; suppose if a train is going at speed close to C. Its apparent length would've been considerably smaller. Suppose the train has to enter a tunnel. But the tunnel is slightly smaller then the length of the train. Since there's apparent length contraction, a stationary person would see the train smaller then its original length, so that person would believe the train is inside the tunnel even though the tunnel is smaller then the train’s original length. To the person on the train; the length of the train is as if it’s original since he’s moving with train.
So to the person out side it would appear as if the train is in side the tunnel via length contraction. To the person inside the train the tunnel would be too short and would believe that some part of the train is still out side of the tunnel. So contemporarily; the stationary observer sees that the train is inside the tunnel because it’s of its contracted apparent length; while the person inside the train believes that some of the train is still outside the tunnel. Imagine if u were to close the tunnel’s door, believing that the train is inside; because u only see its apparent length. But that doesn’t make sense. The person in the train sees some parts of the train out side of the tunnel. Is the door going to close or not. Now there’s a paradox.

Answer 3

Albert Einstein's idea was that, theoretically, the closer we come to traveling at the speed of light (186,000 miles per second), the more time would appear to slow down for us from the perspective of someone who, in relation to us, was not moving. He called the slowing of time due to motion time dilation.

For a more detailed explanation and example that Einstein used to illustrate this, see the following link:

Answer 4

Einstein's solution to the paradox is that Cerulean's spacetime is skewed compared to Vermilion's.

The thing to notice in the diagram is that Cerulean is in the centre of the lightcone, according to the way Cerulean perceives space and time.

Vermilion remains at the centre of the lightcone according to the way Vermilion perceives space and time.

In the diagram Vermilion and her space are drawn at one `tick' of her clock past the point of emission, and likewise Cerulean and his space are drawn at one `tick' of his identical clock past the point of emission.