Hacker News Reader

But one thing I could not really figure out is whether this so-called FTL travel has the potential to violate causality, because I don't fully understand how causality and FTL are related.

The relationship is that FTL in one reference frame is travel backwards in time in another.

If you're able to travel FTL in 2 different inertial reference frames, then you should be able to travel backwards in time and violate causality. Note that the "should" here is important - I can think of lots of possibilities for how that should could be prevented.

That said, I'd be much more optimistic about the plausibility of a proposed warp technology that only lets you go FTL relative to the implicit reference frame of the distant stars. Because that avoids any possibility of causality violation.

>That said, I'd be much more optimistic about the plausibility of a proposed warp technology that only lets you go FTL relative to the implicit reference frame of the distant stars. Because that avoids any possibility of causality violation.

I don't understand what you're getting at. It would be trivial for someone close by to match that reference frame, and then what?

I don't understand what you're getting at. It would be trivial for someone close by to match that reference frame, and then what?

And then nothing. :-)

My point is that being able to go FTL relative to distant stars does not allow time travel relative to distant stars, which means that there is no possibility of causality violation.

Being able to go FTL in 2 arbitrary reference frames leads to potential causality violation.

It's still not at all clear to me what you're saying.

Feel free to express yourself in more technically/mathematically: while GR is certainly not my field, I took classes in grad school that covered the material.

This is a point about SR, not GR.

In SR, if A and B are two events and B is outside of the light cone of A, then reference frames can be found where A happens before B, A and B happen at the same time, and A happens after B. Therefore FTL travel in one reference frame is traveling backwards in time in another.

The ability to travel FTL in a single preferred reference frame is not sufficient to cause causality violations. That is because all trips move me forward in time according to the preferred reference frame, so I can't wind up at the same time and place that I (in my personal history) was at before. But if I can travel FTL in my choice of reference frame, in my choice of direction, then I can plan a trip from A to B which is FTL in one reference frame, then switch and travel from B to A FTL in a different reference frame. From the original reference frame I first traveled FTL, then backwards in time. In the second reference frame I first traveled backwards in time, then FTL. But both agree that two copies of me wound up at the same place at the same time, and I can try to violate causality.

Suppose that you go from SR to GR but are dealing with a large region that is approximately described by SR though locally it may look different. In my "warp drive" there is no local FTL. But the observations about SR, reference frames, and simultaneity still hold between two distant locations. The ability to warp as fast as I like but only relative to one "approximate SR reference frame" does not let me violate causality. But the ability to do it in any direction relative to any reference frame that I like, gives me the ability to construct "closed time-like loops". Which is what is required to try to violate causality.

Note that I say "try". It is possible that a unified theory of GR and QM could allow for closed timelike loops, but (thanks to quantum decoherence) would not allow you any meaningful interaction with the previous copy of you.

>It would be trivial for someone close by to match that reference frame, and then what?

all the machinery of the SR is valid only on the background of the fixed spacetime. Once you start to massage the spacetime itself, the SR is only approximation which is good only to the extent of how good fixed spacetime model is approximation of your real spacetime.

>I'd be much more optimistic about the plausibility of a proposed warp technology that only lets you go FTL relative to the implicit reference frame of the distant stars.

That sounds like a stationary ether; where there is some 'true' reference frame in the universe. The main intuition behind relativity is that there is no preferred reference frame.

My point is that the laws of physics can be have symmetries that do not exist in practice. For instance in the Standard Model there is nothing to say that protons need to be heavier than electrons. But thanks to the Higgs field, they are different everywhere that we see.

In the case of general relativity, even when there is no preferred reference frame in the theory, there is an obvious one that is still special. See http://en.wikipedia.org/wiki/Mach%27s_principle for more on that.

Causality in our universe is much more complex than A->B->C->...

Quantum causal relations: A causes B causes A

http://www.eurekalert.org/pub_releases/2012-10/uov-qcr100212...

Reading the linked press release, it does not seem like they are claiming A->B->A. Rather, they are claiming a suppersistion of two states, (A->B) and (B->A). In the same way quantum mechanics allows a particle to be in two states at the same time, it allows the ordering of events to be two states at the same time.

Either way you end up in a causal loop.

But no worse of one than virtual particles traveling backwards in time in a Feynman diagram.

Your third paragraph is a nice way to think about FTL. Actually it causes quite interesting problems to define FTL, since nothing special happens locally.

> But one thing I could not really figure out is whether this so-called FTL travel has the potential to violate causality, because I don't fully understand how causality and FTL are related.

They are not directly related, as I wrote above, nothing special happens except you find a 'shortcut.' So at every point there is still a nice lightcone ( locally) and every event is caused by events in its past lightcone. However, you can have global causality violation, that is closed timelike curves, a fancy way to talk about timetravel. The idea is, that you travel always forward in time and you reach the same space time point at which you started. Much in the same way that you can travel always forward on a tire (torus) and still reach your starting point. Something like this may or may not happen on a metric which permits FTL, for example the Alcubierre metric does not permit travel on such curves. [1] But it would actually be easy to perform the same analysis on a Godel solution [2], which would permit closed timelike curves.

Edith: Added the comment about the Godel solution.

[1] Alcubierre, 2000 http://arxiv.org/pdf/gr-qc/0009013v1.pdf

[2] https://en.wikipedia.org/wiki/G%C3%B6del_metric

I don't see how this can avoid violating causality. When analyzing this sort of thing, the method by which one travels faster than light doesn't matter at all. Warp drives, hyperspace, or magic carpet, it's all the same. The mere fact that one can do it is sufficient to violate causality. With any method, any method at all, that transmits information or objects faster than light, one can construct a scenario in which Event A precedes Event B in one reference frame but B precedes A in another reference frame. I'm sorry I don't have a brief example to post here, but everything I've ever read about this supports this view. I'd love to be wrong. I grew up looking at the stars from my back yard, watching Star Trek on its first run, and hoping that the stars would be in reach in my lifetime. But the Universe isn't here to please me and if FTL is really impossible, well, I'll live.

You are confusing special relativity and general relativity. In special relativity you are ( sort of) right. In general relativity you can find shortcuts in the way we measure distances. The trick is, that speed can either denote a local property, as measured by your speedometer, or a global property, that is distance traveled divided by time. And the light speed limit only applies to the local property. So if you can find a spacetime that contains a shortcut, then you can increase the distance traveled faster than the speed of light. ( And there is nothing in general relativity to stop you, since it only requires you to move locally slower than the speed of light.) An example for this would be a expanding universe ( and for simplicity let me assume that the expansion only starts a some time t1.) So you travel from t0 to t1 with constant velocity v < c. And you are then at some point x=v(t1-t0). Then you stop and expansion sets in. You stay in place at x, as measured relative to some point nearby, but the distance to your original starting point increases, since space itself is expanding. And there is nothing to stop this increase to be faster than the speed of light.

The other thing is the "sort of" parenthesis, the Lorentz transformation is directly linked to the causal structure of special relativity. A statement like "if* you could go faster than the speed of light, then you could violate causality" is somewhat nonesensical, since if you could go faster than the speed of light, then you would break local Lorentz invariance and therefore you break your very definition of causality.

Thank you for explaining the GR vs SR aspect of this. I was somewhat aware that the no-FTL rule was different in GR but I didn't really understand how. I'll have to look into this more and now I know where to start. I'm not sure I follow the second part, about Lorentz invariance, but my physics is decades old, so that's not surprising. Time to do more reading.

Sorry for the botched formatting (HN is for some reason not showing me a edit link :/ )

A quite interesting paper on the topic is McMonigal & al. [1], it is a bit technical but they discuss the Alcubierre warp drive quite nicely.

To elaborate on the second paragraph about special relativity, one way to define Lorentz transformations is, that they are the transformations which preserve the causal structure of Minkowsky space. On the other hand, the speed limit is a direct consequence of the Lorentz transformations. So the causal structure and the speed limit are directly related. To look again at the argument that a velocity larger than the speed of light implies causality violation: The moment you argue that a speed faster than the speed of light is possible, you implicitly change the meaning of causality. Then you use the Lorentz transformations to conclude that in on frame of reference event A precedes B and that event B precedes A in another. So you first deny the special status of the Lorentz transformation, just to go on and use Lorentz transformations. And my take on this is a strong maybe, the moment you start talking about local Lorentz invariance violation, anything goes. Perhaps there is causality violation, perhaps not, but this depends on your specific meaning of 'causality' and 'faster than light' and not very much on special relativity.

[1] http://arxiv.org/abs/1202.5708

Nobody seems to have poked any holes in the math since Alcubierre first published, and it's not for lack of attention.

I'm not sure what they say about causality, but there's been some work suggesting causality doesn't have to be absolute. Imagine a billiard table, with a wormhole that curves and goes three seconds backward in time. You aim a billiard ball through the wormhole, such that it will emerge earlier and knock itself off the path, never entering the wormhole, and creating a paradox.

But what actually happens is, the ball emerges on a slightly altered trajectory, striking itself a glancing blow, and the ball enters the wormhole.

And why did it emerge with an altered trajectory? Because it was struck a glancing blow.

Physicists have worked out some math on this, and haven't managed to find any scenario that results in inconsistency.

http://en.wikipedia.org/wiki/Novikov_self-consistency_princi...

There is a really good book called Time Travel in Einstein's Universe by Richard J. Gott (http://www.amazon.com/books/dp/B003L1ZYKG) that explores different concepts of time travel and violations of causality without violating Einstein's principles of relativity.