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Hi! Could the formulas to calculate time dilation in the theory of relativity be modified in a way as to be able to calculate how "far" an object would travel into the past given that the object has a certain velocity that is greater than the speed of light? (In the same way that the current formulas allow one to calculate how "far" an object would go into the "future" given that the object has a velocity that is very near the speed of light) If so, what is the modified formula for time dilation (into the "past") due to an object's velocity (greater than c) and gravitational time dilation (that would allow an object to "move" backward in time)? I would assume that the modified gravitational time dilation formula would pertian to super-high gravities such as those in black holes, which may (theoretically)allow an object that is experiencing those gravitational effects to move backward in time (gravity slows time, maybe a super-high gravitational field would reverse time?)? Thank you so much for your help, your answers are GREATLY appreciated!
Question Date: 2010-01-31
Answer 1:

The equation to measure relativistic time dilation is
t = T * (1 - v2/c2)(1/2), where t is time on board the spaceship or whatever, T is the time measured by the observer, v is the velocity, and c is the speed of light. Notice what happens if v is greater than c: the expression inside of the parentheses becomes negative, so when you take the square root of that (1/2 power), the entire expression becomes an imaginary number.

I don't think anybody can really evaluate what the universe would look like with imaginary as well as real dimensions. The same equations that indicate that your tachyon would experience imaginary, rather than real, time, would also cause it to experience imaginary space as well. These are so far out of our ability to observe them that it's very difficult to test any speculations we might have.

Answer 2:

Unfortunately no, the formulas used to calculate time dilation in the theory of relativity cannot be used to calculate how far an object could travel back in time were it somehow able to travel faster than the speed of light.

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