Schwarzschild vs vs Alcubierre & Time Dilation

[Prierin]

Let me begin with the fact I am a rube in the field of Quantum Physics. I seem to have an innate grasp of certain concepts but if it comes to proving theory with math, I’m out. That being said, I am completely fascinating with Miguel Alcubierre’s theory on collapsing, or “warping”, space between two points as to move a physical object across an impossible distance nearly instantly. This is stupendous as I have always theorized that speed is NOT the answer when it came to interstellar travel. Let’s face it, even if we could somehow manage to move at even .99c it would take over 4 years at a constant speed to reach Proxima Centauri, let alone “into the beyond”. With the Alcubierre Drive speed, it seems, is no longer a limiting factor.

However, this raises a question regarding time dilation as the common derivative of the Schwarzschild metric, t = t0/(1-v2/c2)1/2, seems not to really apply at all as v (the speed of the moving object) is no longer a key factor. Everything is now relates to, I would imagine, the gravitational effect on space-time. Different pockets of space are affected by different pulls of gravity which in turn affects the rate of time. So what would the new equation look like?As an example, let’s say a ship equipped with a functioning Alcubierre Drive traveled a distance of 16.73 LY and back again. The entire (33.46 LY) trip took less than three hours. I can’t imagine the same three hours the crew of the ship experienced would have been experiences back on Earth but the question is, how much time (t0) has passed in relation to the observers own frame of reference (Earth) to the crew of the ship?

 

[Orodruin]

The warp solution would bend space-time and so would require GR and not SR. As such, you cannot expect to simply plug in some velocity and get a gamma factor.

It should be noted that the warp drive solution would require new forms of matter which we do not know if they exist. It would also allow time travel.

 

[Matterwave]

It would also allow time travel.

I believe Alcubierre explicitly calculates in his original paper that no closed time like curves exist, and that the space-time is in fact is globally hyperbolic and so time travel is not allowed in the Alcubierre solution.

 

[Orodruin]

You may be right. I was not thinking of Alcubierre in particular and imagining something looking more like Minkowski space globally.

 

[Matterwave]

Ah, Alcubierre's solution is the only "warp solution" I know of. At the least it shows not all "warp solutions" feature time travel. :)

 

[georgir]

Ah, Alcubierre's solution is the only "warp solution" I know of. At the least it shows not all "warp solutions" feature time travel. :)

No, it does not exclude time travel. You can still theoretically get a time-travel effect by doing two FTL trips. The only way to rule out time travel from it would be if the space curvature you created for your first trip somehow prevents you from making the second trip, which sort of makes sense if you imagine you are effectively trying to warp the same bits of spacetime in two different ways. But it is hard to argue that the required trips really need to affect the same bits of spacetime - especially if you split it into three trips that form a triangle-like shape in space.

 

[Matterwave]

No, it does not exclude time travel. You can still theoretically get a time-travel effect by doing two FTL trips. The only way to rule out time travel from it would be if the space curvature you created for your first trip somehow prevents you from making the second trip, which sort of makes sense if you imagine you are effectively trying to warp the same bits of spacetime in two different ways. But it is hard to argue that the required trips really need to affect the same bits of spacetime - especially if you split it into three trips that form a triangle-like shape in space.

I did not say "exclude time travel", I said "not all warp solutions feature time travel". There may be "warp solutions" which do have CTC's and therefore allow time travel.

 

[PeterDonis]

the common derivative of the Schwarzschild metric, t = t0/(1-v2/c2)1/2

This is not the Schwarzschild metric; it's just the time dilation formula from Special Relativity, where there is no gravity. The metric used in SR is

$$
ds^2 = - dt^2 + dx^2 + dy^2 + dz^2
$$

what would the new equation look like?

The metric for the Alcubierre drive is given here:

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

how much time (t0) has passed in relation to the observers own frame of reference (Earth) to the crew of the ship?

Do you mean, how much time does the crew experience, given that observers on Earth see them completing the round trip in three hours? I believe it will be the same as for the Earth observers, i.e., three hours. But I have not done an actual calculation.

 

[kochanskij]

I just want to point out a complication with the Alcubierre Warp Drive that is often overlooked. Besides requiring large amounts of negative energy, devices would have to be placed in space along the flight path and timed to automatically trigger space contraction in each one's local area. There is no way for a freely flying ship to force space ahead of it to contract before it get there. This warp drive spaceship would work more like a train running on tracks than Star Trek's Enterprise.