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.
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.
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.
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.