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[Background note: I'm a physics professor with a background in string theory and relativity.] You're raising a sensible point, and most of the objections raise

by Steuard 14y ago

[Background note: I'm a physics professor with a background in string theory and relativity.] You're raising a sensible point, and most of the objections raised here are invalid. But it nevertheless turns out (surprisingly, to me!) that your argument doesn't work. This topic came up a lot during the short-lived superluminal neutrino excitement last year, and one good discussion of it by Sean Carroll can be found at: http://blogs.discovermagazine.com/cosmicvariance/2011/09/24/can-neutrinos-kill-their-own-grandfathers/ http://blogs.discovermagazine.com/cosmicvariance/2011/09/24/... That post includes a link to a paper by Bob Geroch that goes into the topic in detail. The very short summary is that there is no mathematical necessity for "causality" to be defined just by relativity: the union of the relativistic definition and some other well-defined causal theory can work just as well, even if that theory involved faster-than-light travel. So thank you for raising a very good point about this topic, even if it wasn't quite accurate. And to those who've objected here: unless your objection explicitly quoted Geroch, odds are very good that they're wrong.

Steuard 14y ago
That being said, I'm not certain whether there's any way to avoid causality violation if the hypothetical FTL travel results entirely from within relativity itself. (Geroch's argument, as I understand it, is based entirely on combining two different theoretical structures.)
nessus42 14y ago
I would certainly defer to your much superior knowledge of physics. Mine is only that of an MIT student who was thoroughly indoctrinated with Special Relativity as part of MIT's general science education, and who sat in on an undergrad course on GR taught by cosmologist Max Tegmark. If I understand Bob Geroch properly (much of his paper is Sanskrit to me, but I think I understand the parts that are in English), he acknowledges that FTL particles would seem to allow you to set up "closed causal curves" (i.e., violate causality in a way that would allow you to try to generate a time paradox), but he asserts that you would never actually be able to achieve this goal due to something like the "Novikov self-consistency principle", although he doesn't mention this principle by name. This is similar to the position that many physicist think about the existence of closed time-like loops in GR. Sure, in some sense they are possible, since GR shows you how to set them up, but something like the Novikov principle would either prevent you from setting one up or from doing anything nefarious with one. So, if I understand things correctly, Geroch's claim doesn't really different too much from assertions that I made elsewhere in this thread, that sure you might be able to build an FTL drive, but if the universe lets you do this, it's not going to let you make good use of one, like, for instance, creating an FTL space-liner fleet, because if it did, you'd generate a time paradox soon enough. Or if the universe were so kind as to let us do that, we'd end up finding ourselves in a very strange world where Novikov's principle was mucking with our daily affairs in a very creepy manner.
- Steuard 14y ago
  I've admittedly not worked through Geroch's paper thoroughly myself, so I won't make strong claims here. But based on my understanding, I'd say that his assertion is a bit stronger than what you're suggesting here. He's not just giving a sort of meta-argument that "the space-time manifold of the universe must be consistent, so some mysterious effect will always stop you from killing grandpa". Rather, his point is that your second theory (the one that you're adding to standard relativistic physics) has already been assumed to be causal when taken on its own (it must have a well-defined initial value formulation: that's one of his postulates). What he demonstrates is that putting the two causal theories together will still preserve causality. So when he says that you won't be able to use standard SR tricks to create closed causal curves, he really honestly means that any possible arrangement of the matter/energy content that could do that would be forbidden by the fundamental laws of the theories you're using. (Not just that it "wouldn't happen to work out".) To phrase it yet another way, Geroch would say that you could not build a time machine in such a theory, not just that you couldn't use it to change the past in a meaningful way.
michael_nielsen 14y ago
The issue is addressed explicitly in Alcubierre's paper where he mentions (at least twice) that there are no closed causal loops in his metric. So there's no violation of causality, and the standard intuitions from special relativity don't apply. Pretty remarkable! The lack of closed causal loops apparently follows immediately from standard results about the sort of metric construction he uses. There's no need to invoke Geroch.
- Steuard 14y ago
  I'm not surprised that Alcubierre addressed this point, though I'm glad to hear that for certain. (I've done little more than glance at his original paper... I never have enough time for all the cool stuff.) But my understanding is that his metric is "eternal", in the sense that the warp bubble exists into the infinite past and future. That's obviously not practical for any actual application of the idea (as you'd need in a "warp drive" as discussed in this original article). Instead, people want to find a way of creating a similar warp bubble where one did not exist before (presumably analogous to the way that stellar collapse creates a black hole that eventually approaches the Schwarzschild solution). So my question is, if someone does eventually find a GR solution that "creates" a warp bubble, would it be possible to patch multiple such solutions together in a way that allowed closed causal curves? (I'm imagining sending a warp "pulse" from Earth to a distant star, then having the recipient boost into a different rest frame, and then send a new warp "pulse" back to Earth, for instance.) The answer may still be a clear "no", mind you. But it's not obvious to me what arguments you'd use to show that (particularly since we don't know what form a "warp bubble creation" metric would take, assuming it's possible at all).

by Steuard 14y ago

Steuard 14y ago

That being said, I'm not certain whether there's any way to avoid causality violation if the hypothetical FTL travel results entirely from within relativity itself. (Geroch's argument, as I understand it, is based entirely on combining two different theoretical structures.)

nessus42 14y ago

I would certainly defer to your much superior knowledge of physics. Mine is only that of an MIT student who was thoroughly indoctrinated with Special Relativity as part of MIT's general science education, and who sat in on an undergrad course on GR taught by cosmologist Max Tegmark. If I understand Bob Geroch properly (much of his paper is Sanskrit to me, but I think I understand the parts that are in English), he acknowledges that FTL particles would seem to allow you to set up "closed causal curves" (i.e., violate causality in a way that would allow you to try to generate a time paradox), but he asserts that you would never actually be able to achieve this goal due to something like the "Novikov self-consistency principle", although he doesn't mention this principle by name. This is similar to the position that many physicist think about the existence of closed time-like loops in GR. Sure, in some sense they are possible, since GR shows you how to set them up, but something like the Novikov principle would either prevent you from setting one up or from doing anything nefarious with one. So, if I understand things correctly, Geroch's claim doesn't really different too much from assertions that I made elsewhere in this thread, that sure you might be able to build an FTL drive, but if the universe lets you do this, it's not going to let you make good use of one, like, for instance, creating an FTL space-liner fleet, because if it did, you'd generate a time paradox soon enough. Or if the universe were so kind as to let us do that, we'd end up finding ourselves in a very strange world where Novikov's principle was mucking with our daily affairs in a very creepy manner.

Steuard 14y ago
I've admittedly not worked through Geroch's paper thoroughly myself, so I won't make strong claims here. But based on my understanding, I'd say that his assertion is a bit stronger than what you're suggesting here. He's not just giving a sort of meta-argument that "the space-time manifold of the universe must be consistent, so some mysterious effect will always stop you from killing grandpa". Rather, his point is that your second theory (the one that you're adding to standard relativistic physics) has already been assumed to be causal when taken on its own (it must have a well-defined initial value formulation: that's one of his postulates). What he demonstrates is that putting the two causal theories together will still preserve causality. So when he says that you won't be able to use standard SR tricks to create closed causal curves, he really honestly means that any possible arrangement of the matter/energy content that could do that would be forbidden by the fundamental laws of the theories you're using. (Not just that it "wouldn't happen to work out".) To phrase it yet another way, Geroch would say that you could not build a time machine in such a theory, not just that you couldn't use it to change the past in a meaningful way.

michael_nielsen 14y ago

The issue is addressed explicitly in Alcubierre's paper where he mentions (at least twice) that there are no closed causal loops in his metric. So there's no violation of causality, and the standard intuitions from special relativity don't apply. Pretty remarkable! The lack of closed causal loops apparently follows immediately from standard results about the sort of metric construction he uses. There's no need to invoke Geroch.

Steuard 14y ago
I'm not surprised that Alcubierre addressed this point, though I'm glad to hear that for certain. (I've done little more than glance at his original paper... I never have enough time for all the cool stuff.) But my understanding is that his metric is "eternal", in the sense that the warp bubble exists into the infinite past and future. That's obviously not practical for any actual application of the idea (as you'd need in a "warp drive" as discussed in this original article). Instead, people want to find a way of creating a similar warp bubble where one did not exist before (presumably analogous to the way that stellar collapse creates a black hole that eventually approaches the Schwarzschild solution). So my question is, if someone does eventually find a GR solution that "creates" a warp bubble, would it be possible to patch multiple such solutions together in a way that allowed closed causal curves? (I'm imagining sending a warp "pulse" from Earth to a distant star, then having the recipient boost into a different rest frame, and then send a new warp "pulse" back to Earth, for instance.) The answer may still be a clear "no", mind you. But it's not obvious to me what arguments you'd use to show that (particularly since we don't know what form a "warp bubble creation" metric would take, assuming it's possible at all).