Which objects reference my ViewController strongly?

What explanation does Theory of Relativity offer for time dilation experienced by two objects, when each is observed taking the other as the frame of reference?

• Let's assume there are two particles A and B, A is stationary w.r.t  earth and B moves at a velocity c/2 w.r.t earth. According to theory of relativity, time for B should move at √3/2 times as that of A. If the time difference is taken into consideration, the velocity of A w.r.t B is around 0.43 times c. So, from the frame of reference of B, time for A should move around 0.9 times as that of B. Doesn't it seem paradoxical?

• Answer:

  It's paradoxical until you realize that the relationship between A-time and B-time isn't a simple proportionality. They also use different standards for judging simultaneity across space (per the second term in the Lorentz transformation for time) and this turns out to make everything symmetrical. It's bit like the A clock sits in London and  the B clock runs slow but is traveling at a large fraction of a time zone per hour towards New York and being compared to local solar time wherever it is. Because it's being compared to clocks that are set earlier and earlier (midday London is 7 am New York), the B observer claims it's actually running fast. Now of course this particular example breaks down because it's easy to travel east to west at more than one time zone per hour and thus travel backwards in local solar time. But that's where the speed of light limit come in. The maximum difference that relativity uses is set by the mysterious xv/c^2 term in the Lorentz equation for time. Since v can't be more than c, different observers don't disagree by more than 1/c seconds per meter of separation, and you can't out run that because you can't go faster than c meters per second.