It’s been hypothesized that you could travel faster than light by creating a bubble of space that moved faster than light while the ship remained stationary inside it. But according to Special Relativity, for **any** reference frame in which faster than light travel happens, there’s another reference frame where that is traveling back in time. So are these hypothetical warp drives also potential time machines?

I don’t think the bubble of space moves faster than light in a warp drive, it merely is a bubble around which space is warped (as in reshaped). Nothing is travelling faster than light, the distances between points are being altered. So if I were to warp to New York from London, I would create a bubble of normal space around me, and then alter the distance between NY and London and then merely step over to New York. To an outside observer it would appear as if I had travelled really fast, but in truth I have not.

At least that’s how I understand it. Could be wrong though.

In a word, yup. Anything that lets you get from A to B in a shorter time than light takes to traverse the distance, also lets you travel in time.

Why’s that?

Speed of light: 299,792,458 m/s

Light takes 8 minutes and 19 seconds to reach Earth. If I could travel at twice the speed of light it would still take me 4 minutes and 9 seconds to make the same trip. How does that relate to going back in time?

Special relativity: Say two spaceships meet each other at time t[sub]0[/sub]. They travel at a relative speed of 0.87c. On both spaceships, there’s an instantaneous transmitter, i.e. a device that transmits information at ‘infinite’ speed (this works for any speed greater than c, but the math gets more complicated for finite speeds). Now, say, a minute after the meeting, people on ship A notice that ship B’s back light is broken, so they instantaneously send a message to ship B informing them of their gross violation of intergalactic traffic codes, which as everybody knows are enforced with extreme rigidity. However, since ship B moves at a speed of 0.87c relatively to ship A, it is subject to time dilation, and thus, only thirty seconds have elapsed since the two ships met.

So far, so good. The engineer on ship B, being of the swift sort, fixes the back light, mumbles something about how he cannae change th’ laws o’ physics, Captain, and then sends back a thanks, at about 45 seconds after the ships met. However, again, since ship A is moving at 0.87c relatively to ship B, it is subject to time dilation; thus, if 45 seconds have elapsed on ship B, only 22.5 seconds have elapsed on ship A. Thus, the thank you arrives on ship A 22.5 seconds after the ships have met, and thus, 37.5 seconds before ship A ever sent its message to ship B, which of course, seeing as how the problem’s already fixed, they now don’t have to.

Or, with more detail, see the story here.

Warp drives are scientific nonsense. You can’t fit them into a universe that follows the laws of relativity. Don’t try.

[nerd hat]

Star Trek warp drives at least posit the existence of ‘subspace’. Essentially another dimension ‘below’ normal space/time. So anything you do there has no effect on normal space because it isn’t taking place there. Except it sometimes makes the Holodeck go haywire in which case you have to use a reverse polarity Tachyon pulse…

I was referring to Alcubierre et al proposed FTL schemes, not Star Trek. Maybe impossible but not absurd, at least superficially. Mainly I was wondering if the General Relativity provisions of curved space somehow overrode the FTL=Time Travel aspect of Special Relativity.

Thank you! I’d always wanted that explained to me in terms no more complicated than that.

Thank you. I am going to devour that in detail later tonight.

Lumpy, no, there is no possible scheme of any sort in a universe where general relativity holds in an exact form in which it’s possible to have a warp drive. Warp drives of any sort violate general relativity. Of course, it’s possible that in the future we may discover that general relativity and quantum mechanics are not exactly true, just like in the early twentieth century we discovered that Newtonian physics was not exactly true. It’s possible that a new overarching theory may be discovered which includes general relativity and quantum mechanics as limiting cases, just as general relativity and quantum mechanics were shown to be overarching theories for Newtonian physics in which it was just a limiting case. But that’s what it would take - a complete overhaul of physics. In physics as it stands now, it’s not possible to have warp drive of any sort.

I don’t think that is true. The Alcubierre drive - Wikipedia features a space-time metric that satisfies the equations of general relativity, and so do other “warp drive” metrics. They generally do not satisfy various energy conditions http://en.wikipedia.org/wiki/Energy_conditions often used to make solving problems in general relativity easier, but it is known that the energy conditions are not always satisfied in the real universe. It is possible (some would say probable) that additions to general relativity would involve additional restrictions that would make warp drives impossible, but based on what’s currently known (as far as I know), warp drives of the Alcubierre type can’t be ruled out.

P.S. If “no time travel” turns out to be a law of physics, then warp drives are impossible.

That doesn’t make any sense! If ship A sends the message at 1 minute into flight from their reference frame (which is the same as 30 seconds into flight from the reference frame of ship B), and ship B sends a reply two seconds later (from ship B’s frame of reference), why wouldn’t ship A receive the reply at 1 minute and 4 seconds into flight (from ship A’s frame of reference)? 32 seconds have passed for ship B, and 1 minute 4 seconds have passed for ship A. Causality = unaffected.

Here is an article on the Alcubierre drive by a physicist (John Cramer) describing it as consistent with GR Alternate View Column AV-81

Wrong. Alcubierre warp drive works within the laws of general relativity. See Alcubierre drive - Wikipedia

But special relativity = broken. Your proposal would introduce a special, absolute frame of reference specifying the ‘true’ time: while wrt ship A, the time on ship B runs slower, wrt ship B, the time on ship a runs faster (since when 32 seconds have elapsed on B, 64 have elapsed on A according to your scheme). But each of the two ships has equal reason to consider itself ‘at rest’, and the other as moving, and in a moving frame of reference, time runs slower. So, from ship A’s perspective, time runs half as fast on ship B, but equally well, from ship B’s perspective, time runs half as fast on ship A. This seems contradictory, but as long as we’re limited to speed of light signals, the story is always consistent; it is only once we exceed that limit that paradoxes arise.

In fact, with only a minute amount of math, we can express this without any ‘jumping’ from one frame to the other. Let A be the sender, and B be the receiver. If A sends at t[sub]0[/sub] a signal to B, received there at t[sub]1[/sub], then the time it takes to get there is Δt = t[sub]1[/sub] - t[sub]0[/sub] = (B - A)/s, if s is the signal’s speed.

Now let’s view this from a frame moving at a certain velocity v. Then, all times get Lorentz-transformed: t’ = γ(t - xv/c²). Thus:

Δt’ = t’[sub]1[/sub] - t’[sub]0[/sub] = γ(t[sub]1[/sub] - Bv/c²) - γ(t[sub]0[/sub] - Av/c²) = γ(1 - sv/c²)Δt

But (1 - sv/c²) is not constrained to be positive; in fact, it will be negative if sv > c². Thus, since in special relativity, all v < c are allowed, if s exceeds c only by a smidgen, from some frame of reference, Δt’ will be smaller than 0, and the signal will be received before it is sent.

OK, so I guess my question is "has anyone addressed the subject of Alcubierre (et al) warp drives leading to time travel?

As Cramer points out in his essay on the Alcubierre Drive, a spacecraft inside the warp is isolated from the effects of relativity, so you might think that it would also be immune from the effects of reversed causality. A spaceship inside a warp bubble experiences no time dilation, for example.

But **Half Man Half Wit**’s thought experiment still holds. You could use a spaceship inside a warp bubble as a near-instantaneous message delivery system between two relativistic spacecraft, and the results would be the same.

In short, if you travel faster than light, there are frames of reference in which you also travel backwards in time. Most of the time this wouldn’t be a problem- but if (for instance) you try to communicate with something travelling very rapidly you could end up communicating with something in your own past light cone.

The Rietdijk–Putnam argument is a paritcularly mindbending example of this effect.

Rietdijk–Putnam argument - Wikipedia

I think that the end result of all these paradoxes and unlikelihoods is the same; warp drives can’t be physically real.

The answer is “yes”; it was done in a paper in 1996 by Allen Everett, a year or two after Alcubierre’s original paper. Here’s a link, though it’s highly technical. Basically, Everett’s argument was to show that using spacetimes that expand & contract in a way much like Alcubierre’s does, you can construct a spacetime that contains a “closed timelike curve”. A “closed timelike curve” is basically a path in spacetime that you could follow, going “forward in time” at all points along your path, and end up at the same place & time that you started at.

As noted above, this presents issues for causality. It’s not a priori impossible that time travel would cause paradoxes; if the timeline is perfectly self-consistent à la *12 Monkeys* or *Primer*[sup]1[/sup], with effects and causes making a nice little loop, then there’s not really a problem. But it does mean that we can’t, say, set up an experiment any way we want to in such a spacetime; somehow we would be constrained to set things up so that whatever objects we were dealing with came back to their original configuration after a certain amount of (subjective) time had elapsed. This runs contrary to both our experience from science and our notions of free will, which is a big hairy mess that most scientists prefer to stay far away from.

[sup]1[/sup]At least, I assume that *Primer* is self-consistent. I still don’t quite understand it.

If a rock is sent back in time from TimePoint A to TimePoint B, is there suddenly more energy/matter in the universe at TimePoint B then there was previous to the jump? From the point of view of those at Timepoint B, has matter been created?