5 ms·

This is the problem I have with most discussions of a practical Alcubierre style warp drive. They generally don't address the causality violations that are inhe

This is the problem I have with most discussions of a practical Alcubierre style warp drive. They generally don't address the causality violations that are inherent in ANY form of FTL travel. But if it could be useful as an efficient sub-luminal drive, that would be cool and worth pursuing.

api 6y ago
Based on papers like this, I suspect that some form of sub-FTL "warp" drive may be at least physically possible. Whether it's practical to build any time in the foreseeable future is another question. The energy requirements would be beyond what we can do today and would probably require highly efficient compact fusion.
raattgift 6y ago
Causality violations probably aren't really that much of a problem for mathematical physics. Geroch (a very well known and highly cited relativist) takes a shot at this in a short paper considering a "democracy of causal cones" rather than simply the one that matches light: "All systems, and their cones, are on an equal footing: No one set of fields, or one set of causal cones, has priority over any others." Geroch's argument is that one can still do initial-value-formulation physics even in the presence of causal cones whose width is different -- including wider -- than that of light. https://arxiv.org/abs/1005.1614 https://arxiv.org/abs/1005.1614 -- it is highly technical, but has this as the kicker: "we would then insist that the final field configuration is, not what the observer wills it to be, but rather what follows, evolving these data via [dynamical equations]" Notably, this is backwards from the Alcubierre drive's formulation, which starts with a desired final field configuration, and is trapped by having no "before the bubble existed" initial values surface. The Alcubierre solution is eternal, and offers no way to be stitched into our apparently non-eternal universe (it sure seems to have a beginning, or at least an early hot/dense boundary close to which the presence of an Alcubierre bubble seems even less physically plausible than today). Although it is safe to describe really fantastical configurations of matter very near that early boundary, one has to settle things down in far less than seconds, in order to match several different lines of evidence of about the distribution of the first free-streaming photons (and the earlier free-streaming neutrinos, when we figure out how to build observatories to study them in detail). You could put Alcubierre bubbles everywhere during Cosmic Inflation, for instance, but you have to very quickly and aggressively suppress their observables. Let's turn this on its head: we can in principle construct a spacelike values-surface at time today and let it evolve. A problem we have with this is that the presence of either or both of not-yet-formed or formed-but-eventually-evaporating black holes makes a complete calculation of some far future values-surface impossible in principle, as far as we know, which means in the absence some new fundamental theory of quantum gravity that has yet to be discovered. Putting an Alcubierre drive onto the same today values-surface likewise blocks the complete calculation of the future values-surface, in principle. Dusting the cosmos with lots of Alcubierre drives makes things much worse. But maybe that's OK, because the cosmos appears to be dusted with lots of black holes and configurations of matter (like our own Virgo cluster) that will inevitably mostly settle into giant black holes that may one day evaporate. This means we can't really make a concrete prediction about the far future of our cosmos, in principle. I wouldn't sweat it, because we can't set down much more than the barest approximation of the real values-surface in practice anyway. So since we already have problems with causality thanks to gravitational singularities (or if you prefer, apparent trapping surfaces), and we have excellent evidence of them existing in our universe, an argument that "X poses problems for causality and therefore must be unphysical" is not especially compelling. Instead, the problem grinds down into [a] laying out an initial values surface gets harder, especially if we can't rely on a programme of pushing it further and further back in time so that unusual configurations of matter (black holes, Alcubierre bubbles) have the ability to develop through dynamical laws (which is what we do with physical cosmology, for instance); and [b] writing down the dynamical laws that relate neighbouring values-surfaces (which gets harder because we need more than the Lorentz symmetry group and GL(4). It might be fun to try to make [a] and [b] work in the presence of various FTL mechanisms, and indeed to some extent we do this in very specific settings (cosmic inflation, for instance). However, from the time of the CMB to now there is nothing to suggest a need to account for FTL material (or normal material embedded in a dynamical spacetime that moves it around FTL-style) at any scale, from the cosmological to the laboratory. The theory would undoubtedly be much more complicated than what we already have (which has already evolved and become more complicated as more evidence has become available), so there would not be much point to it. Finally, two extracts from the Geroch paper: "[I]n a similar vein, there exist solutions of Einstein’s equation in general relativity that manifest closed causal curves. But we do not ... allow observers to build time-machines at their pleasure. Instead, we permit observers to construct initial conditions — and then we require that they live with the consequences of those conditions." which is exactly the opposite of Alcubierre's approach in https://arxiv.org/abs/gr-qc/0009013v1 https://arxiv.org/abs/gr-qc/0009013v1 where he starts with a time machine first, and never describes the initial conditions before it exists. One would usually expect that for any artifact such as a spacecraft, there is a time before which it is fully built and switched on. One might compare that with an eternal Schwarzschild black hole and a black hole that forms via gravitational collapse of a massive star (or direct collapse of matter in the early universe). And, "from the present viewpoint the problems associated with superluminal signals do not seem nearly as severe as they did at first glance", a statement that is likely safe should such signals ever be proven.
- rootbear 6y ago
  I've downloaded the Geroch paper and will give it a look, although it's probably over my head. My college physics classes were a long time ago. I nevertheless remain dubious that unrestricted causality violations are possible, but I'm happy to listen to arguments to the contrary.
  - raattgift 6y ago
    The point is that causality violations don't happen just because of FTL, and that a good choice of values-surfaces reveals that. "Preferred" foliations are perfectly fine in relativity when picked out by the matter. Working relativists do it all the time. One just has to be careful about preserving Lorentz-covariance for observers whose time axis is badly misaligned from the "preferred" one, because the (invariant sector of) physics must be identical for them. In particular a good choice of time axis along which to split spacetime values into time-ordered spatial values is a thermodynamic arrow of time that applies to the vast majority of the matter subject to dynamical equations. Example preferred foliations are the cosmological scale factor, and terrestrial atomic time like UTC; they are picked out by the symmetries of the matter (large scale homogeneity and isotropy, near-sphericity and near-rotationlessness, respectively). "Lab frames" for example, are often UTC. That relativity provides mechanism to transform tensor-components as one switches systems of coordinates (or frames) is a great freedom. The point is that in e.g. the cosmological foliation, an FTL (but not instantaneous) traveller will only be at one location on a cosmlogical values surface. Geroch's point is that one should just accept this picture and calculate the evolution of field-values in the presence of objects with causal cones of different widths. There is no causality violation with very gentle assumptions about the spacetime. There are likely to be weird observations though, peculiar to the observers. But we can already have weird stroboscopic effects and so forth for merely very fast (not even relativistic!) travellers thanks to thinks like the persistence of vision or analogues in cameras and detectors. However, an instantaneous traveller (>>>>> FTL, literally infinite speed and causal cones that are infinite in width) may mathematically appear up to infinite times on a single spacelike hypersurface. This does make a mess unless one can extract from the FTL traveller's configuration an equation of motion with enough constraints to make predictions. (For instance, if you have too many copies in the same "slice" of spacetime, does the entire spacetime collapse into a black hole? Can the copies be inside each other? Or only the bosons? And so on.) Finally, a backwards time traveller need not even do FTL. Again, it will appear twice (or more) on well-chosen values surfaces, posing no problems for causality analysis. Here we return to the question of the thermodynamic arrow-of-time. Let's consider a Rocket(with some amount of fuel) accelerating (gently) to the right, leaving an exhaust, that an intertial observer ticking at t watches : t_0 R(10) t_1 eR(9) t_2 eeR(8) t_3 eeeR(7) t_4 eeeeR(6) in this small picture one would pick out a thermodyanmic arrow of time pointing downwards, because the rocket+exhaust's Boltzmann entropy is increasing. The fuel is well-ordered in the rocket's tank, and much more disordered in the exhaust. But the dynamical equations in this arrangement of matter is perfectly reversible. Let's complicate this a bit: t_0 R(10) eeeeeeeeeR(1) t_1 eR(9) eeeeeeeeR(2) t_2 eeR(8) eeeeeeeR(3) t_3 eeeR(7) eeeeeeR(4) t_4 eeeeR(6) eeeeeR(5) Here we have what time travel looks like with this foliation: A rocket behaving normally, and a rocket that is picking up fuel from a hot exhaust, storing it orderly into its tank. R, moving gently through space, sees the thermodynamically-opposite copy out the window in both directions. R believes there is a weird causality violation, because one copy of R sees a copy of itself with less fuel (and wristwatches showing times in the future, but ticking backwards). However, t just sees a time traveller, where the backwards time traveller has an opposite thermodynamic arrow of time. Now we make t the entire cosmic microwave background in its cosmological rest frame, cooling towards the down direction. R can measure the temperature (and dipole redshift from the gentle acceleration) of the CMB and decide whether R is moving forwards or backwards in time relative to the cosmos. This is basically the resolution to (most) time-travel dilemmas in the initial-value/Hamiltonian formulations of General Relativity: equip the spacetime with a distribution of matter (the cosmic microwaves) and nonzero cosmological constant (cosmic expansion or contraction) and use those two features to define a cosmological scale factor that one can use as a principled clock. Physical cosmology is some complications on this picture: we have other fluids as well as the CMB, and they dilute away (in the direction of expansion) differently. There are also of course observers who are moving extremely compared to the slowly-separating galaxy clusters, not just relativistically but at enormous accelerations. These observers are a tiny fraction compared to the cosmological observers. (A bigger problem is that the clumpy observers -- galaxy clusters and things in them -- have to be "stitched in" to the cosmological frame, and that must be a mass-dependent calculation, and is dealt with in various ways including "swiss cheese" models or using thin-shell Israel-Darmois junctions. However the corrections are small and the thermodyanmic arrows of time are still very closely aligned, so occupants of galaxies, even near massive black holes, would still prefer to think of t_n as picking out the difference between forward-time-travelling R and backwards-time-travelling-R). Finally, it is in isolation that the dynamical evolution of R (and e) shows serious causality or closed-system-thermodynamics violations. We would expect to repair that by embedding R (and e) into the wider foliation, which is built out of a block-universe equipped with several spacetime-filling fields. If the block universe contains a pattern like the second diagram above, then the dynamical field equations must obviously allow them. But Geroch's point is the other side if this: let's start with the known dynamical field equations, and see where they take us. They might not take us to a schematic like the one above, and the absence of observations like the picture above weighs heavily towards laying down some initial data (say at t_-1000) and seeing how it evolves. Maybe it can evolve to show t_0 through t_5, maybe it cannot. Relatedly, https://en.wikipedia.org/wiki/One-electron_universe https://en.wikipedia.org/wiki/One-electron_universe where instead of flipping the thermodynamic arrow of time of our backwards-and-forwards time traveller, we are flipping the sign of the electric charge.
avmich 6y ago
> They generally don't address the causality violations So the stated problem with causality violations is that if you went to the past and did something the(n), it's going to change the future from which you started. What if it doesn't? As in, you can't really do anything which changes future, for a reason that an arbitrary numbers of time travelers have already went to past, changed it and had it reflected in the future, so after all those changes the timeline stabilized in an eigenline - that is, the future is robust towards any subsequent changes via the past. In this way there is no causality violation - go ahead, travel to past, try to change anything, the whole world is arranged so that the future won't be affected, one way or another. Roughly speaking, you won't succeed trying to kill your grandfather no matter how'd you try - something will always happen which would prevent it.
- qayxc 6y ago
  > What if it doesn't? As in, you can't really do anything which changes future That's actually a conjecture suggested by Stephen Hawking [1]. [1] https://en.wikipedia.org/wiki/Chronology_protection_conjecture https://en.wikipedia.org/wiki/Chronology_protection_conjectu...

api 6y ago

Based on papers like this, I suspect that some form of sub-FTL "warp" drive may be at least physically possible. Whether it's practical to build any time in the foreseeable future is another question. The energy requirements would be beyond what we can do today and would probably require highly efficient compact fusion.

raattgift 6y ago

Causality violations probably aren't really that much of a problem for mathematical physics. Geroch (a very well known and highly cited relativist) takes a shot at this in a short paper considering a "democracy of causal cones" rather than simply the one that matches light: "All systems, and their cones, are on an equal footing: No one set of fields, or one set of causal cones, has priority over any others." Geroch's argument is that one can still do initial-value-formulation physics even in the presence of causal cones whose width is different -- including wider -- than that of light. https://arxiv.org/abs/1005.1614 https://arxiv.org/abs/1005.1614 -- it is highly technical, but has this as the kicker: "we would then insist that the final field configuration is, not what the observer wills it to be, but rather what follows, evolving these data via [dynamical equations]" Notably, this is backwards from the Alcubierre drive's formulation, which starts with a desired final field configuration, and is trapped by having no "before the bubble existed" initial values surface. The Alcubierre solution is eternal, and offers no way to be stitched into our apparently non-eternal universe (it sure seems to have a beginning, or at least an early hot/dense boundary close to which the presence of an Alcubierre bubble seems even less physically plausible than today). Although it is safe to describe really fantastical configurations of matter very near that early boundary, one has to settle things down in far less than seconds, in order to match several different lines of evidence of about the distribution of the first free-streaming photons (and the earlier free-streaming neutrinos, when we figure out how to build observatories to study them in detail). You could put Alcubierre bubbles everywhere during Cosmic Inflation, for instance, but you have to very quickly and aggressively suppress their observables. Let's turn this on its head: we can in principle construct a spacelike values-surface at time today and let it evolve. A problem we have with this is that the presence of either or both of not-yet-formed or formed-but-eventually-evaporating black holes makes a complete calculation of some far future values-surface impossible in principle, as far as we know, which means in the absence some new fundamental theory of quantum gravity that has yet to be discovered. Putting an Alcubierre drive onto the same today values-surface likewise blocks the complete calculation of the future values-surface, in principle. Dusting the cosmos with lots of Alcubierre drives makes things much worse. But maybe that's OK, because the cosmos appears to be dusted with lots of black holes and configurations of matter (like our own Virgo cluster) that will inevitably mostly settle into giant black holes that may one day evaporate. This means we can't really make a concrete prediction about the far future of our cosmos, in principle. I wouldn't sweat it, because we can't set down much more than the barest approximation of the real values-surface in practice anyway. So since we already have problems with causality thanks to gravitational singularities (or if you prefer, apparent trapping surfaces), and we have excellent evidence of them existing in our universe, an argument that "X poses problems for causality and therefore must be unphysical" is not especially compelling. Instead, the problem grinds down into [a] laying out an initial values surface gets harder, especially if we can't rely on a programme of pushing it further and further back in time so that unusual configurations of matter (black holes, Alcubierre bubbles) have the ability to develop through dynamical laws (which is what we do with physical cosmology, for instance); and [b] writing down the dynamical laws that relate neighbouring values-surfaces (which gets harder because we need more than the Lorentz symmetry group and GL(4). It might be fun to try to make [a] and [b] work in the presence of various FTL mechanisms, and indeed to some extent we do this in very specific settings (cosmic inflation, for instance). However, from the time of the CMB to now there is nothing to suggest a need to account for FTL material (or normal material embedded in a dynamical spacetime that moves it around FTL-style) at any scale, from the cosmological to the laboratory. The theory would undoubtedly be much more complicated than what we already have (which has already evolved and become more complicated as more evidence has become available), so there would not be much point to it. Finally, two extracts from the Geroch paper: "[I]n a similar vein, there exist solutions of Einstein’s equation in general relativity that manifest closed causal curves. But we do not ... allow observers to build time-machines at their pleasure. Instead, we permit observers to construct initial conditions — and then we require that they live with the consequences of those conditions." which is exactly the opposite of Alcubierre's approach in https://arxiv.org/abs/gr-qc/0009013v1 https://arxiv.org/abs/gr-qc/0009013v1 where he starts with a time machine first, and never describes the initial conditions before it exists. One would usually expect that for any artifact such as a spacecraft, there is a time before which it is fully built and switched on. One might compare that with an eternal Schwarzschild black hole and a black hole that forms via gravitational collapse of a massive star (or direct collapse of matter in the early universe). And, "from the present viewpoint the problems associated with superluminal signals do not seem nearly as severe as they did at first glance", a statement that is likely safe should such signals ever be proven.

rootbear 6y ago
I've downloaded the Geroch paper and will give it a look, although it's probably over my head. My college physics classes were a long time ago. I nevertheless remain dubious that unrestricted causality violations are possible, but I'm happy to listen to arguments to the contrary.
- raattgift 6y ago
  The point is that causality violations don't happen just because of FTL, and that a good choice of values-surfaces reveals that. "Preferred" foliations are perfectly fine in relativity when picked out by the matter. Working relativists do it all the time. One just has to be careful about preserving Lorentz-covariance for observers whose time axis is badly misaligned from the "preferred" one, because the (invariant sector of) physics must be identical for them. In particular a good choice of time axis along which to split spacetime values into time-ordered spatial values is a thermodynamic arrow of time that applies to the vast majority of the matter subject to dynamical equations. Example preferred foliations are the cosmological scale factor, and terrestrial atomic time like UTC; they are picked out by the symmetries of the matter (large scale homogeneity and isotropy, near-sphericity and near-rotationlessness, respectively). "Lab frames" for example, are often UTC. That relativity provides mechanism to transform tensor-components as one switches systems of coordinates (or frames) is a great freedom. The point is that in e.g. the cosmological foliation, an FTL (but not instantaneous) traveller will only be at one location on a cosmlogical values surface. Geroch's point is that one should just accept this picture and calculate the evolution of field-values in the presence of objects with causal cones of different widths. There is no causality violation with very gentle assumptions about the spacetime. There are likely to be weird observations though, peculiar to the observers. But we can already have weird stroboscopic effects and so forth for merely very fast (not even relativistic!) travellers thanks to thinks like the persistence of vision or analogues in cameras and detectors. However, an instantaneous traveller (>>>>> FTL, literally infinite speed and causal cones that are infinite in width) may mathematically appear up to infinite times on a single spacelike hypersurface. This does make a mess unless one can extract from the FTL traveller's configuration an equation of motion with enough constraints to make predictions. (For instance, if you have too many copies in the same "slice" of spacetime, does the entire spacetime collapse into a black hole? Can the copies be inside each other? Or only the bosons? And so on.) Finally, a backwards time traveller need not even do FTL. Again, it will appear twice (or more) on well-chosen values surfaces, posing no problems for causality analysis. Here we return to the question of the thermodynamic arrow-of-time. Let's consider a Rocket(with some amount of fuel) accelerating (gently) to the right, leaving an exhaust, that an intertial observer ticking at t watches : t_0 R(10) t_1 eR(9) t_2 eeR(8) t_3 eeeR(7) t_4 eeeeR(6) in this small picture one would pick out a thermodyanmic arrow of time pointing downwards, because the rocket+exhaust's Boltzmann entropy is increasing. The fuel is well-ordered in the rocket's tank, and much more disordered in the exhaust. But the dynamical equations in this arrangement of matter is perfectly reversible. Let's complicate this a bit: t_0 R(10) eeeeeeeeeR(1) t_1 eR(9) eeeeeeeeR(2) t_2 eeR(8) eeeeeeeR(3) t_3 eeeR(7) eeeeeeR(4) t_4 eeeeR(6) eeeeeR(5) Here we have what time travel looks like with this foliation: A rocket behaving normally, and a rocket that is picking up fuel from a hot exhaust, storing it orderly into its tank. R, moving gently through space, sees the thermodynamically-opposite copy out the window in both directions. R believes there is a weird causality violation, because one copy of R sees a copy of itself with less fuel (and wristwatches showing times in the future, but ticking backwards). However, t just sees a time traveller, where the backwards time traveller has an opposite thermodynamic arrow of time. Now we make t the entire cosmic microwave background in its cosmological rest frame, cooling towards the down direction. R can measure the temperature (and dipole redshift from the gentle acceleration) of the CMB and decide whether R is moving forwards or backwards in time relative to the cosmos. This is basically the resolution to (most) time-travel dilemmas in the initial-value/Hamiltonian formulations of General Relativity: equip the spacetime with a distribution of matter (the cosmic microwaves) and nonzero cosmological constant (cosmic expansion or contraction) and use those two features to define a cosmological scale factor that one can use as a principled clock. Physical cosmology is some complications on this picture: we have other fluids as well as the CMB, and they dilute away (in the direction of expansion) differently. There are also of course observers who are moving extremely compared to the slowly-separating galaxy clusters, not just relativistically but at enormous accelerations. These observers are a tiny fraction compared to the cosmological observers. (A bigger problem is that the clumpy observers -- galaxy clusters and things in them -- have to be "stitched in" to the cosmological frame, and that must be a mass-dependent calculation, and is dealt with in various ways including "swiss cheese" models or using thin-shell Israel-Darmois junctions. However the corrections are small and the thermodyanmic arrows of time are still very closely aligned, so occupants of galaxies, even near massive black holes, would still prefer to think of t_n as picking out the difference between forward-time-travelling R and backwards-time-travelling-R). Finally, it is in isolation that the dynamical evolution of R (and e) shows serious causality or closed-system-thermodynamics violations. We would expect to repair that by embedding R (and e) into the wider foliation, which is built out of a block-universe equipped with several spacetime-filling fields. If the block universe contains a pattern like the second diagram above, then the dynamical field equations must obviously allow them. But Geroch's point is the other side if this: let's start with the known dynamical field equations, and see where they take us. They might not take us to a schematic like the one above, and the absence of observations like the picture above weighs heavily towards laying down some initial data (say at t_-1000) and seeing how it evolves. Maybe it can evolve to show t_0 through t_5, maybe it cannot. Relatedly, https://en.wikipedia.org/wiki/One-electron_universe https://en.wikipedia.org/wiki/One-electron_universe where instead of flipping the thermodynamic arrow of time of our backwards-and-forwards time traveller, we are flipping the sign of the electric charge.

avmich 6y ago

> They generally don't address the causality violations So the stated problem with causality violations is that if you went to the past and did something the(n), it's going to change the future from which you started. What if it doesn't? As in, you can't really do anything which changes future, for a reason that an arbitrary numbers of time travelers have already went to past, changed it and had it reflected in the future, so after all those changes the timeline stabilized in an eigenline - that is, the future is robust towards any subsequent changes via the past. In this way there is no causality violation - go ahead, travel to past, try to change anything, the whole world is arranged so that the future won't be affected, one way or another. Roughly speaking, you won't succeed trying to kill your grandfather no matter how'd you try - something will always happen which would prevent it.

qayxc 6y ago
> What if it doesn't? As in, you can't really do anything which changes future That's actually a conjecture suggested by Stephen Hawking [1]. [1] https://en.wikipedia.org/wiki/Chronology_protection_conjecture https://en.wikipedia.org/wiki/Chronology_protection_conjectu...