You can take any smooth spacetime manifold you like, plug it into the GR field equation, and get a corresponding stress-energy tensor. "A good many physicists believe that this paradox can only be resolved by the general theory of relativity. Alcubierre recently exhibited a spacetime which, within the framework of general relativity, allows travel at superluminal speeds if matter with a negative energy density can exist, and conjectured that it should be possible to use similar techniques to construct a theory containing closed causal loops and, thus, travel backwards in time. Alcubierre recently exhibited a spacetime which, within the framework of general relativity, allows travel at superluminal speeds if matter with a negative energy density can exist, and conjectured that it should be possible to use similar techniques to construct a theory containing closed causal loops and, thus, travel backwards in time. Note that $\beta^i$ squares up where it's important to maintain sign to maintain a hyperbola. Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. Rindler applied them to the problem of relativistic space travel for the first time in 1960 in a Physical Review article titled "Hyperbolic Motion in Curved Space Time" [1]. Alcubierre isn't done yet, he's still got to find a metric that will fit in a 3+1 spacetime and do what he wants, (provide faster than light propulsion), but if he does, the above property of 3+1 spacetimes will guarantee causality. Dolphus333 mentioned in his answer that Alcubierre demonstrated in his paper that there is no violation of causality in the spacetime he constructed, but I believe this is just for the case of a spacetime containing a single warp bubble--if you have multiple warp bubbles moving in different directions you can indeed violate causality in a manner similar to the tachyonic antitelephone. All you need is to have two of these warp drives going in opposite directions relative to a static observer with intersecting paths. One of the many problems with FTL travel (or signals) is that if any information is sent faster than light, there will exist an inertial frame in which the signal arrives before it is sent, a blatant violation of causality. Should I process the data or add a new constraint to achieve the target? The Alcubierre drive makes use of a supply of negative energy whose gravitation creates a carefully shaped distortion in the space-time of General Relativity, nicknamed a "warp bubble" because Alcubierre was a Star Trek fan. Will they not see the events as being non-causal? causality might kick in in chronology-protection a la Hawking to destabilise the vacuum fields before the CTC is formed. The mechanism described by Alcubierre both invokes an unphysical stress tensor and also violates causality (see point 1). Obviously they can’t observe it at Alpha Centauri five minutes later since they are looking at it 4.3 years ago. A signal arriving "before it's sent" in coordinate time is actually not a problem, because coordinates are arbitrary and meaningless. Every cent of NASA money given to his research has been nothing but a way of defrauding US taxpayers. Why has Pakistan never faced any wrath of the USA similar to other countries in the region especially Iran? But it begs a few questions: It involves expansion and contraction of space, fine, I can see how you can accelerate a bubble of space time faster than light. To see this, all you have to do is zoom out to some scale where the warp drive field becomes a point. SR says that the simultaneity and relative ordering of events is dependent on the relative motion of the observer, but that no matter how it works out, if event A causes event B, no observer will see B first. This makes it more like a FTL railway train than an independent vehicle like a spacecraft. Press question mark to learn the rest of the keyboard shortcuts. What's important here is that $ds^2$ is positive and for real space, $\gamma_{ij}$ is as well. But in this case my question is different and more specific. A large enough gravitational wave, for Now, I'm aware that there are problems with the practicalities (or possibilities) of methods involving exotic matter with negative mass, and that kind of thing has been addressed here: Doesn't Warp theory violate causality? This is stated specifically in the book Time Travel and Warp Drives by Allen Everett (the same physicist I mentioned above) and another physicist, Thomas Roman. Source? General relativity states that no two objects in the same reference frame can go faster that the speed of light relative to each other - which would otherwise cause violations of causality and time travel. a relativistic rocket rather than an Alcubierre drive (since the Alcubierre drive does require exotic matter, and from what I understand it isn't actually accelerating relative to quasi-inertial observers who are far away in the asymptotically flat spacetime of Alcubierre's solution). where $\alpha$ is the lapse function, and is positive, and $\beta$ is the shift vector between spatial foliations. The paper is amazingly well written and folks that have had a grad level general relativity class should be able to easily traipse through it. Or am I correct that FTL claims should be dismissed with extreme prejudice on this basis alone? What with Harold White’s new design for an Alcubierre Drive, it looks like a warp drive may become eventually possible. The Alcubierre drive or Alcubierre warp drive (or Alcubierre metric, referring to metric tensor) is a speculative idea based on a solution of Einstein's field equations in general relativity as proposed by Mexican theoretical physicist Miguel Alcubierre, by which a spacecraft could achieve apparent faster-than-light travel if a configurable energy-density field lower than that of … In doing this, you wind up with a line element that looks like (see erudite comments from @Jerry Schirmer below, I'm playing catchup): $ds^2 = -d\tau^2 = \gamma_{ij}dx^idx^j + 2\beta_i dx^i dt - \left(\alpha^2 - \beta_i\beta^i\right)dt^2$. Alcubierre metric that decrease the negative energy requirements by two orders of magnitude; and introduce a warp drive spacetime in which space capacity and the rate of time can be chosen in a controlled manner. Nevertheless, this does open up some interesting possibilities for futuristic space travel. At the very least, I'll have a set of notes to work from in the future :) This is also the first, broadest, cut at an actual answer regarding causality. For instance, travelling faster than light from a single point of perception this is absolutely possible and for those nay-sayers consider this: Person A heads in one direction at 0.75*c and person B travels in the opposite directs at the same speed, neither is breaking the speed of light but taken from a relative perception of person A, person B has to be travelling at a resultant speed of 1.5*c. That much everyone should agree on. In the case of the Alcubierre drive, however, that's not the trick they're playing. If Person A and Person B both start in a mutual place and go one light year away from the starting point at the same speed and acceleration in opposite directions they are 2 light years away from each other. It is not exactly certain if this means they must be in principle invalid. http://www.washingtonpost.com/news/post-nation/wp/2014/06/11/this-is-the-amazing-design-for-nasas-star-trek-style-space-ship-the-ixs-enterprise/, this series of lecture slides by Alcubierre. No FTL information implies no FTL travel? It's not consistent. The Alcubierre drive, Alcubierre warp drive, or Alcubierre metric (referring to metric tensor) is a speculative idea based on a solution of Einstein's field equations in general relativity as proposed by Mexican theoretical physicist Miguel Alcubierre, by which a spacecraft could achieve apparent faster-than-light travel if a configurable energy-density field lower than that of … curves using a similar idea to the one presented here.". What basically happens is that the alcubierre drive allows an object to seperate it's frame of reference from any object around it aka a "warp bubble". The Alcubierre drive is one of a more general class of spacetimes (Natario 2001), and the metric describing how space curves around it is defined partly by an arbitrary choice of a function $x_s(t)$, from which we get the speed $v_s$ by differentiating: $$v_s=\frac{dx_s(t)}{dt}$$ While there are constraints on certain other parameters of the metric … The expression for the time elapsed on Earth is, $$\mathrm{Earth\ time\ elapsed}= \dfrac{c}{a}\cosh\left(\dfrac{at}{c}\right),$$. Hypnosifl's answer is good but I want to add some context. Is my understanding of GR incomplete and there's something in it that obviates the causality implications of SR? What is the time-travel implications of Alcubierre drive? We need General Relativity to describe this warp drive machine (bends spacetime after all). The explanation that you usually get for how the Alcubierre Drive works, is that you contract space-time in front of you and expand it behind you, which moves you forward. [3]. @innisfree: his spacetime doesnt, because it includes only one of these that doesn't turn around. It utilizes the fact that space-time can be stretched to bypass the speed limit of the universe. That's pretty reasonable I guess. Alcubierre Drive The Alcubierre drive, proposed by Mexican Physicist Miguel Alcubierre in 1994 and derived from the Einstein’s equation describing space and time formulation of the 4 dimensional space-time fabric in the general theory of relativity. So, in essence, all the Alcubierre-drive related metrics provide for ways to violate causality, but suggest there are ways to avoid this. Rev. (Pending a serious replicable experiment showing causality to be breakable. For example, we could appeal to the chronology protection conjecture, which, though very speculative, is better motivated and more likely to be correct than anything in Alcubierre's paper. The mechanism described by Alcubierre both invokes an unphysical stress tensor and also violates causality (see point 1). Anything moving faster than light can be used to communicate with the past, regardless of how it functions. Does an Alcubierre drive(or a variant thereof) violate causality… While the distortion was present one could then make the journey between those stars quickly. The Alcubierre drive or Alcubierre warp drive (or Alcubierre metric, referring to metric tensor) is a speculative idea based on a solution of Einstein's field equations in general relativity as proposed by theoretical physicist Miguel Alcubierre, by which a spacecraft could achieve apparent faster-than-light travel if a configurable energy-density field lower than that of vacuum … Its main problem is that the warped path through spacetime for its trajectory has to be set up before it travels. One good way to check whether or not there are negative particles in the universe is just to take a look around, if during this time the vacuum hasn't changed drastically, then most likely you can forget about negative mass particles. @innisfree: Spacetimes with closed causal curves are forbidden. It's the local geometry of our universe, like it or not. Can we prove absolutely that FTL = causality violation. negative mass) could be created. There is no way around that. This, though, I was told in college was an unavoidable consequence of FTL travel or communication. Would Foucault's pendulum work on the moon? I suspect that when dolphus333 said in his "end edit" that a ship would take 817 years to reach Alpha Centauri for observers on Earth, this comment was falsely assuming that the relationships between time and distance for the Alcubierre drive would be identical to those of a relativistic rocket undergoing uniform proper acceleration in SR. A couple paragraphs before the "end edit" dolphus333 had brought up the case of 'uniform acceleration and no exotic matter whatsoever', i.e. Although time travel would be exciting, there is just never going to be anything that violates special relativity. In physics, it is what is known as the Alcubierre Warp Drive. to 1 light-minute, and this need not take very long. Hence we need to use GR instead. But, wouldn’t it then take years for the spaceship to escape the warp bubble once it got to its … Thats why I said locally the drive is travelling with $v < c$ which implies that something like causality is preserved locally as well. Is it legal to carry a child around in a “close to you” child carrier? So is the conclusion of all this that "exotic matter with negative mass* cannot exist, because if it did, we could use it to build an Alcubierre Drive and violate causality" or "we don't know if causality is an inviolable law, it depends on whether we find any exotic matter"? Is that not a fairly fatal problem? Proto-Indo-European and Proto-Yeniseian paper, Story about a consultant who helps a fleet win a battle their computers thought they could not. Also, you don't get causality for free from the 3+1 formulation, because, in general, 3+1 spacetimes can only evolve over a finite subdomain. But the point is moot because there is no exotic matter that can enable warps or Lorentzian wormoles.. that we know of. Furthermore, the equation for "distance" as a function of acceleration and proper time that dolphus333 gives in the "end edit" is identical to the equation for "d" given on the relativistic rocket page here, and the equation for "Earth time elapsed" that dolphus333 gives is almost identical to the equation for t on that page, except that dolphus333 writes cosh(at/c) where the corresponding relativistic rocket equation has a factor of sinh(at/c)--probably that dolphus333 either misremembered the equation, or made a transcription error when copying it from some other source (if you use the correct equations, then if a ship travels with a uniform acceleration of 188G to Alpha Centauri 4.3 light years away in the Earth's frame, the proper time on the ship would be 14 days just as dolphus333 calculated, but the time in the Earth frame would be 4.32 years, not 817 years).

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