Wormholes are connections of different points in space-time which occur due to bending of the space time geometry. Like a piece of paper can be folded and a hole can be created to connect two points on the paper, which causes the distance between those two points to reduce to zero by creating a pathway directly from one point to another point. There are no experimental evidences to prove the existence of wormholes, however there are some theoretical solutions for wormholes.
I will describe a thought experiment which questions the existence of wormholes. I haven’t yet found out the flaw in the thought experiment or proper explanation other than that wormholes can’t exist. It would be great if I can get suggestions regarding the matter.
The idea goes thus:
Suppose two twins Howard and Raj are at the same point A in space-time. One day Howard gets the chance to travel in space (Basically the same setup as in the twin paradox). Howard boards a spaceship and starts moving away from point A in a straight line at a speed comparable to the speed of light. When he reaches point B in his journey (still travelling) the statements recorded by both of them are:
Raj: Howard has reached point B and time on my clock is 5 hours and time on Howard’s clock must be 3 hours (assume that Howard is moving with velocity corresponding to the above time intervals). So he is younger than me. Howard: Raj is moving away from me and hence he is younger than me. Howard is still moving at constant speed and hence both the frames are inertial. This is a paradoxical situation that who is correct and who is wrong. But on closer observation we find that there is no paradox. The two statements are not simultaneous according to relativity of simultaneity. Suppose event P is the event when Raj’s clock ticks 5 hours and event Q be the event in which Howard reaches point B. These two events are simultaneous in reference frame of Raj, but they are not simultaneous in Howard’s reference frame i.e. when Raj’s clock ticks 5 hours according to Howard, he is not at point B.
Now comes the main part of this thought experiment. Suppose if there is a wormhole at point B which connects directly to point A. Now Howard reaches the same point in space-time where Raj is, and still moving with constant velocity so that his frame is still inertial. Now what happens? Both of them again give the same statement that the other one is younger than me. As they have reached the same point in space-time the two statements must be simultaneous!
If we consider that wormhole connects two points only through space and not through time, than who is younger? If wormholes connects two points through both space & time, does that mean they have time travelled with respect to one another?