Faster than the speed of light?

[Nikola Mitic]

If we use the basic relativity equations on the speed faster than light we would get(in calculating differences in time on the Earth and on the spacecraft )an imaginary number.So does that mean that maybe by traveling faster than a light we would end back in the past,or that would just mean bigger difference in time?Or just the Einstein equations would be wrong.Of course than it's impossible to travel faster than light,this is just a mind experiment.
Sorry for my English

 

[zhermes]

Generally, one hears that going faster than light (which is impossible) would take you back in time---personally, I'm entirely unconvinced about this, but some rigorous work has been done on the subject (do a search for "Tachyons").

Otherwise, I think the question is pretty much unanswerable: the in-exceed-ability of the speed of light is such a fundamental, basic assumption of all of our physics that none of our intuitions/techniques would apply if you could exceed the speed of light.

 

[JesseM]

Generally, one hears that going faster than light (which is impossible) would take you back in time---personally, I'm entirely unconvinced about this, but some rigorous work has been done on the subject (do a search for "Tachyons").

What are you unconvinced about? Because of the relativity of simultaneity, anything going faster than light in one frame would be going backward in time in another--i.e. if there's one frame where the event of the tachyon signal being received happens after the event of it being sent, there's another frame where the signal is received at an earlier time than it's sent, this follows in a simple way from the Lorentz transformation. And if tachyons respect the first postulate of relativity, then if it's possible to send signals backwards in time in one frame, it's possible to do it in all frames, which means if you and I are moving apart at sublight speeds, I can send you a tachyon signal which moves FTL in my frame and backwards-in-time in yours, then you can send a reply which moves FTL in your frame but backwards-in-time in mine, with the net result that I receive your reply before I sent the original message (see the spacetime diagrams here).

 

[zhermes]

That is a very clear and reasonable explanation---It did elucidate the point for me.

But...

What are you unconvinced about?

The proper time interval is imaginary, as in the particles energy; thus the stress-energy tensor would be negative... etc etc; I just think 'going backwards in time' is far too neat of a solution...

 

[JesseM]

The proper time interval is imaginary

True, but the tachyon's proper time would only be relevant if you wanted to somehow figure out how the tachyon itself experiences time, in what order it experiences different events on its worldline and so forth. When people say that tachyons go back in time, they're just analyzing their external behavior in the frames of slower-than-light observers, specifically the fact that different frames must disagree about whether the event of the tachyon being emitted or the event of the tachyon being received happened at an earlier time.

as in the particles energy

The idea is that a tachyon would have imaginary rest mass, so that all the tachyon's measurable qualities like momentum and energy would be real-valued...see here. There are apparently good quantum-mechanical reasons to think they don't exist though, even aside from the implausibility of causality violations.

 

[Nikola Mitic]

Thanks for the ansewrs.