Faster than light

From what I've heard, special relativity doesn't forbid faster than light travel, it only forbids travelling at the speed of light. I often hear people say that if one was to travel faster than light, one would go backwards in time. Where does this assertion come from? To me, it seems like that rather than going backwards in time, one would move in a sort of imaginary time dimension. What am I missing here?

Originally posted by amolv06
From what I've heard, special relativity doesn't forbid faster than light travel, it only forbids travelling at the speed of light. I often hear people say that if one was to travel faster than light, one would go backwards in time. Where does this assertion come from? To me, it seems like that rather than going backwards in time, one would move in a sort of imaginary time dimension. What am I missing here?

Interesting thought. I'm sure someone better versed in physics will come along and lay the smack down on me, but my boneheaded algebra approach seems consistent with your assertion that superluminal velocities do not, in fact, imply travel backwards through time.

Suppose v>c. Then let v = c+k, where k>0. Using the time dilation formula, we have:

dt* = dt / SQRT(1-(v/c)^2)

= dt / SQRT(1-((c+k)/c)^2)

= dt / SQRT((c^2 - c^2 - 2ck - k^2)/c^2)

= dt / SQRT((-2ck - k^2)/c^2)

= (1/i) * dt / SQRT((2ck + k^2)/c^2)

Now, using the fact that (1/i) = -i, we have:

dt* = -i * dt / SQRT((2ck + k^2/c^2)

This expression is an imaginary number with real part Re(dt*) = 0, and imaginary part Im(dt*) = -dt / SQRT((2ck + k^2/c^2). As amolv06 suggests, a preliminary reading of this result would indicate that at superluminal velocities the component of travel in "normal time" would be 0, while there would be some negative component of travel in "imaginary time", whatever that means. It doesn't seem to indicate travel backwards through time at all. So, as amolv06 asked, where does this assumption that superluminal velocity does imply travel backwards through time come from? Is it strictly sci-fi, or is there some physical basis for it?

Another interesting result of this sort of algebraic manipulation is that anything that moves at superluminal speeds must have an imaginary rest mass to have a real mass when measured in our reference frame!

Originally posted by amolv06
What am I missing here?

I am just guessing, but it is probably based on the following 'logic':
As a particle speeds up its time dilates. When it reaches light speed, it takes no time at all. When it goes faster than light speed, it must be going back in time!

But is this logic coming from science or science fiction? Because if it's coming from science, I would appreciate if you can expound on that idea.

The equation states that it is impossible to go at speed of light (SOL). Nothing says it's impossible to go faster than SOL, but since you cannot traverse the SOL, then it doesn't matter if it is possibel to go beyond SOLor not.

Nothing says that the time goes backward in faster than light (FTL) speeds. It mustn't do anything, it doesn't have to obey our logic or intuition. But even if time went backwards, even your brain would go backwards, so you would not notice anything.

If you want to go FTL, then you have to solve the problem how to accellerate from sub light speed to super light speed without going in light speed any time. Like jumping from sub to suer without ever hitting SOL. When you've solved that, then FTL transportation is solved.

A special kind (theoretical, not yet observed) of particle, called tachyons, travel actually in FTL speeds. How is this possible? Answer: They are born (or created, or always been there) in FLT speeds. They have an immaginary mass. Not only they fly in FTL velocities, but they demand energy to slow down. The lower energy they have, the faster will they go.

So in FTL speeds, every mass has an immaginary component in it. Like you way 60 kg and another sqrt(-1) times a factor of 1 kg too. When I explain this to scientists, they shake their heads and plainly say: "Nature doesn't like imaginary values of any kind."

Would we ever fly FTL? Then we have gained access to some kind of hyper space, with (almost) instantaneously acess to every corner in the universe. Star Trek is only science fiction, it doesn't work that way.

So these tachyons -- how do they traverse through time?

Originally posted by amolv06
So these tachyons -- how do they traverse through time?

Don't know.

See http://en.wikipedia.org/wiki/Tachyon

Originally posted by amolv06
From what I've heard, special relativity doesn't forbid faster than light travel, it only forbids travelling at the speed of light. I often hear people say that if one was to travel faster than light, one would go backwards in time. Where does this assertion come from? To me, it seems like that rather than going backwards in time, one would move in a sort of imaginary time dimension. What am I missing here?

Special relativity doesn't forbid massive particles of moving with speeds that are greater than c. What it does forbid is for a massive particle to achive c if it starts with a speed less than c.
So if you start with v>c you're off the hook.

As for traveling back in time. The idea is scientific but it isn't an absolute. Some observers might see the particles moving back in time and others might see the particle moving forward in time.

Originally posted by PBE6
Interesting thought. I'm sure someone better versed in physics will come along and lay the smack down on me, but my boneheaded algebra approach seems consistent with your assertion that superluminal velocities do not, in fact, imply travel backwards through time.

Suppose v>c. Then let v = c+k, where k>0. Using the time dilation formula, we have:

dt* = ...[text shortened]... ds through time come from? Is it strictly sci-fi, or is there some physical basis for it?

Dude, you got it (almost) right. Tyhe fact that you noticed that a tachyon proper time is imaginary is great ut you can't stop your analysis there. If you continue you'll see that to some observers the motion of a particle that has a speed that is greater than the speed of light does appear to be backwards in time. But it isn't so for all observers.

Did you know the Star Trek Warp Drive was invented by a Mexican - and that it's not necessarily fictional?

http://en.wikipedia.org/wiki/Alcubierre_drive

Originally posted by AThousandYoung
Did you know the Star Trek Warp Drive was invented by a Mexican - and that it's not necessarily fictional?

http://en.wikipedia.org/wiki/Alcubierre_drive

I don't think Star Trekkers are using this method at all. The Alcubierre drive is using distorted space. Star Trekkers are using hyper space (?), a fictive space outside our 3 spatial dimensions. Our space is just a subset to this superdimensional space.

As far as I understand it (and that might not be far enough, granted) wouldn't a particle become infinitely massive if it was accelerated up to the speed of light?

You are correct, but here I am not concerned with how the particle attained superluminal speeds. I am only interested in the theoretical implications of a particle travelling at such speeds.