faster than lightspeed

[bored_teen]

why would it matter? it seems people think that you can go back in time by exceeding the speed of light. why? wouldn't you just arrive at your location faster than the light would? as far as my logic goes, the only difference is that it'd be dark when you stopped.

 

and if going faster than light does enable us to go back in time, shouldn't we also de-age? if we age going slower than lightspeed, shouldn't we stop aging at lightspeed, and de-age if we exceed lightspeed?

[iNow]

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

 

Faster-than-light communication is, by Einstein's theory of relativity, equivalent to time travel. According to Einstein's theory of special relativity, what we measure as the speed of light in a vacuum is actually the fundamental physical constant c. This means that all observers, regardless of their relative velocity, will always measure zero-mass particles such as photons traveling at c in a vacuum. This result means that measurements of time and velocity in different frames are no longer related simply by constant shifts, but are instead related by Poincaré transformations. These transformations have important implications:

 

• The relativistic momentum of a particle would increase with speed in such a way that at the speed of light an object would have infinite momentum.
  
• To accelerate an object of non-zero rest mass to c would require infinite time with any finite acceleration, or infinite acceleration for a finite amount of time.
  
• Either way, such acceleration requires infinite energy. Going beyond the speed of light in a homogeneous space would hence require more than infinite energy, which is not generally considered to be a sensible notion.
  
• Some observers with sub-light relative motion will disagree about which occurs first of any two events that are separated by a space-like interval.[5] In other words, any travel that is faster-than-light will be seen as traveling backwards in time in some other, equally valid, frames of reference. Therefore any theory which permits "true" FTL also has to cope with time travel and all its associated paradoxes.[6]
  

Albert Einstein elaborated that faster-than-light travel is impossible.

[bored_teen]

In other words, any travel that is faster-than-light will be seen as traveling backwards in time in some other, equally valid, frames of reference.

 

what i'm getting from that is that faster-than-light will be seen as moving back in time. how so? if it is viewed as going back in time, does that mean you would pop up (let's say) yesterday? why is that? just because you're going ridiculously fast doesn't mean that you should be able to return to before you started. unless light defines/governs time...

[iNow]

I'm going to use resources that say it better than I could. If my responses aren't good enough, hopefully another member will respond. Be well.

 

 

http://everything2.com/e2node/Why%2520faster%2520than%2520light%2520implies%2520back%2520in%2520time

The reason that sending a superluminal signal enables you to send a signal back in time is that the events connected by a faster than light worldline have a spacelike separation. Suppose Alice is sitting in her lab on her space station, and she sends out a superluminal signal. Let's call the event of sending the signal event A. Alice sends the signal to Bob, who is out on a space ship, and he receives it at event B. Because the signal is superluminal, events A and B have a spacelike separation, Δx > cΔt. As a result, they have a different order in time in different frames of reference, as is discussed in the light cone node. That means that, although according to Alice event A clearly happens before event B (the signal is sent before it's received), there are some reference frames in which event B happens at an earlier time than event A, so the signal is received before it is sent according to such observers. Thus, we've already found that it looks like the signal is being sent to an earlier time, and we have to begin to question our ideas of causality.

[Radical Edward]

what i'm getting from that is that faster-than-light will be seen as moving back in time. how so? if it is viewed as going back in time, does that mean you would pop up (let's say) yesterday? why is that? just because you're going ridiculously fast doesn't mean that you should be able to return to before you started. unless light defines/governs time...

 

the thing to look at here is the Lorentz Transforms, which are deduced from simple geometrical considerations, where the speed of light in vacuum © for all observers is a constant. (It is a constant because the permittivity and permeability of free space are invariant with velocity, leading to Einstein's extending Galilean relativity to include electromagnetics)

 

for a more detailed look, the Lorentz Transforms

 

but here they are anyway:

 

 

 

looking at the top one, we can get the time dilation:

 

 

on the right hand side, the delta_t is the time between two events for one observer, and on the left hand side, delta_t' is the measured time between those same two events for another observer travelling at velocity v with respect to the first.

 

now if we make delta_t=1 for simplicity, and make v=sqrt(2)*c, then on the right hand side you get

 

delta_t' = 1/sqrt(-1)

 

which is 1/(+/-)i seconds.

 

and that doesn't make alot of sense.

 

the real core of all this lies in the fact that we're all travelling at c, but through spacetime. in a rest frame, we see all of our velocity in the t direction, but as two objects move relative to one another, some of the velocity gets transferred out of the t direction into one of the spatial directions. light however has all of its velocity in the spatial directions, and none in t.

[bored_teen]

the thing to look at here is the Lorentz Transforms, which are deduced from simple geometrical considerations, where the speed of light in vacuum © for all observers is a constant. (It is a constant because the permittivity and permeability of free space are invariant with velocity, leading to Einstein's extending Galilean relativity to include electromagnetics)

 

for a more detailed look, the Lorentz Transforms

 

but here they are anyway:

 

 

 

looking at the top one, we can get the time dilation:

 

 

on the right hand side, the delta_t is the time between two events for one observer, and on the left hand side, delta_t' is the measured time between those same two events for another observer travelling at velocity v with respect to the first.

 

now if we make delta_t=1 for simplicity, and make v=sqrt(2)*c, then on the right hand side you get

 

delta_t' = 1/sqrt(-1)

 

which is 1/(+/-)i seconds.

 

and that doesn't make alot of sense.

 

the real core of all this lies in the fact that we're all travelling at c, but through spacetime. in a rest frame, we see all of our velocity in the t direction, but as two objects move relative to one another, some of the velocity gets transferred out of the t direction into one of the spatial directions. light however has all of its velocity in the spatial directions, and none in t.

 

so, in essence, what would be time travel in my frame of reference would only be time dilation in yours? doesn't that mean that true time travel (transporting yourself into the past) is impossible?

[swansont]

It has some nasty repercussions that are more easily seen if a third person/frame is involved, like sending a message, having a second party see the result of that message and being able to tell you not to send the message before you sent it. If you want causality, you can't have superluminal information transfer.

[Radical Edward]

so, in essence, what would be time travel in my frame of reference would only be time dilation in yours? doesn't that mean that true time travel (transporting yourself into the past) is impossible?

 

erm, no. the time dilation goes so far it turns inside out. think about scaling an object by -1 in the x direction, you end up with a mirror image.

[bored_teen]

erm, no. the time dilation goes so far it turns inside out. think about scaling an object by -1 in the x direction, you end up with a mirror image.

 

so what would be the overall effect as viewed by both parties? in this case, let's assume i'm observing you, and you're going faster than lightspeed. what would i see? what would you experience?