If it was possible to travel faster than the speed of light, would time reverse itself (like backwards time travel) or just not exist?

Asked by: Nicole

Answer

Your question is a very interesting one, and it is great to see that you are thinking about
Professor Einstein's theory in this way, but unfortunately, you're probably not going to
like the response. When you assume that it's possible to travel faster than the speed of
light, you're taking the laws of physics and punching them in the stomach and throwing them
down the stairs.

The problem is that you can't say, 'Hey, what would happen if you could go faster than the
speed of light?' because that's totally physically impossible. It's not possible to go
faster than the speed of light, so the laws of physics can't possibly say what would happen
if you imagine things that way in some hypothetical universe. Physics is a complete
package: once you decide to ignore one physical law, you're ignoring them all.

You run into a similar problem when you ask 'What if I could divide by zero?' or 'What if I
could build a perpetual motion machine?' or 'What if I went back in time and killed my
grandfather before I was born?' There's no answer, because the question doesn't make any
sense.

Of course, this doesn't bother the writers of Star Trek. They go faster than the speed of
light every show and travel into the past like it's a trip to Disneyland. This brings up
an interesting point, however: The idea of a space-warping engine is NOT entirely a bad
one! Warping space would allow you to travel as if you were moving faster than light by
changing the structure of the universe, at least temporarily. You would end up in a
certain location much faster than if you travelled there the 'normal way,' kind of like a
secret passage. Happily for relativity, you would STILL not actually be travelling faster
than the speed of light in local space, so Einstein's 'speed limit' still holds.

The point is that though it's fun to think about and enjoy in science fiction, truly going
faster than the speed of light is a violation of the laws of physics and therefore can not
really be discussed by physics. I can't say time would reverse itself or not exist or
anything because those aren't even options. It's like if I invited you out to dinner and
you told me you absolutely couldn't come, but then I asked you whether you were going to
have the soup or the salad!
Answered by: Steve Healey, Physics student, Rutgers University, New Jersey

One of the reasons that prevent any object with a mass going at or faster than the speed of light is that the mass is not constant - it increases with velocity and it goes to infinity at the speed of light. So that eventually you need infinite amounts of energy to accelerate infinite mass past the speed of light mark! (and as far as I know we have yet to find an infinite source of energy :-)

However if you would still like to choose if you are having the soup or the salad at the dinner you will not attend here is a thought.

We really do not know what would happen to time when an object passes the speed of light. The only thing we have to rely on is the Special Theory of Relativity (Einstein 1905) and according to it time in a moving reference frame (say your space ship) goes slower as compared to a stationary frame (say Earth) the faster you go. In fact the equation that governs this so called time dilation is given below:

So you see when you start off - at zero speed (0% of speed of light) your time is just regular i.e. the time slowing factor (xt) is equal to 1. As you speed up your time runs slower by the factor shown on the y-axis. As you are approaching 100% of the speed of light your time slows more and more until it is infinitely slowed down. (You should realize that everything slows down including your heart beats, your thoughts, etc.) So for an example if your ship goes at 98% of the speed of light and you take a one year journey, when you return to Earth five years have gone by.

This region of speeds below 100% of the speed of light is the region of our regular time or Real Time.

Now say somehow you were able to go faster than the speed of light (i.e. the v in the above equation is now greater than c the speed of light). The equation will then give us a square root of a negative number on the right hand side (which is an imaginary number.) Well I can factor out the imaginary unit number (i or the square root of minus one) and plot the result on the same graph. This region I call Imaginary Time since it is some weird time with an imaginary unit attached to it (so I don't really know what this time means.)

However you see that time in this imaginary region will speed up from infinity to the regular time speed of 1 and continue speeding up. At 140% or higher speed of light, time slowdown factor is less than one, i.e. time will go faster than in the stationary frame! So for an example if your ship goes at 200% of the speed of light and you take a one year journey, when you return to Earth only about 7 months have gone by. However I need to stress again that this is just a crazy thought experiment which produces some weird imaginary time and has no physical meaning.
Answered by: Anton Skorucak, M.S. Physics, PhysLink.com Editor

'I thank You God for this most amazing day; for the leaping greenly spirits of trees and a blue true dream of sky; and for everything which is natural which is infinite.'