========================= RELATIVITY AND FTL TRAVEL ========================= Copyright (c) 1995 by John H Kim Faster-than-light travel between star systems is a staple of much science fiction. SF authors thus come up with various pseudo-scientific explanations for it. Consequently, there is a lot of confusion about the Theory of Relativity. This is only natural - it is a very complicated theory which even physicists often have trouble with. Thus I am answering *some* of those questions here. Note: I am a physicist, but I am not an expert in relativity. I will only speak authoritatively about the simpler `Special Theory of Relativity', which is correct as far as we know, but which cannot be used to solve certain problems (in particular, those involving continuous acceleration). For the benefit of those who want to deal with the math, I am giving a summary of some common FTL explanations and what laws they violate. -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- The Explanations ---------------- In general, sci-fi FTL travel results in the possibility of so-called "paradoxes". What this means is that _if_ relativity is true, then the FTL travel will violate the principle of causality: that is, that a cause must precede in time the effect it produces. Lack of causality is known in sci-fi as "time travel", and is even more complicated in theoretical physics than it is in the stories. Specifically, here are some common explanations: -*-*-*- (1) Warp/Stutterwarp Drives These posit starships which are able to bend space or skip through it, resulting in continuous FTL transport through space, even though the ship itself is undergoing no motion - acceleration or decceleration. How good this sounds usually depends on the key words thrown in. However, the lack of actual motion does not prevent the creation of paradoxes. In fact, given the free-moving ship, it should be fairly feasible to make practical use of them: for example, a ship detects an explosion on a distant planet - it then alters its real velocity and "warps" FTL to arrive at the scene before the explosion happened. This is an extreme example, but a lot can be done with "arranged" paradoxes. -*-*-*- (2) Hyperspace/Jump Drives These posit starships able to disappear from an arbitrary point in space, and after some time (hours, days, even weeks later) reappear at another point light-years away. The explanation is usually that the ship has passed through some other dimension - such that the actual motion of the ship was never actually faster than c. The explanation may be fairly scientific-sounding, but this still does not eliminate the possibility of paradox - the phenomena is the same. However, it can be made more difficult for humanity making practical use of the resulting paradoxes. For example, if the jumps are across light-years, and take significant time (days), then it might be more of a major project to create a "usable" paradox (i.e. you have to get up to really significant relativistic speeds). -*-*-*- (3) Stargates/Wormholes These explanations posit special points in space (either "natural" or man-made), at which objects can instantly (or near-instantly) transport to other distant points in space. Thus, a point by our solar system might be linked to a point by a star in the constellation Orion. If "gates" can be freely created or moved - then this can result in the same sort of paradoxes as the other explanations. On the other hand, natural gate-points which are approximately fixed with respect to each other can theoretically be resolved without paradoxes - but this utterly complicates the workings of relativity and will have gravitational consequences as well. Essentially, you can view this as such: Rather than being a form of travel, the gates represent a complex shape of space. The point by our solar system is *physically* next to the point in Orion, in a very real sense. We normally view space as being fairly "flat" - but in fact it is much more convoluted than it appears to be. This explanation can make use of Relativity and causality without paradoxes - but it distorts the current understanding of cosmology. -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- THE BASIC THEORY ================ The essential "paradox" of Relativity is this: two events which are ordered one way in one frame can be ordered opposite in another. The relativistic equations for translation between two frames (which are moving at velocity v in the direction of their z-axes relative to each other) are as follows: x' = x y' = y z' = (gamma)*z - v*(gamma)*t t' = (gamma)*t - ( v/(c^2) )*(gamma)*z 1 where (gamma) = ----------------------- { 1 - (v^2)/(c^2) }^0.5 Note this last term. What is just a matter of *distance* in the unprimed frame can become a change of *time* in the primed frame. You can check this in any appropriate college-level text. -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- Example 1 --------- Imagine that a fast-moving spaceship goes through a short tunnel as it passes by Earth. The tunnel is 60 meters long, while the ship is 40 meters long and moving at 0.87c (gamma ~= 2). Some sick pup on Earth decides to close the spaceship inside that tunnel. Now, the observer on Earth sees the spaceship as being length contracted. So it is just 20 meters long, and can easily fit inside the 60m tunnel. He observes the spaceship's approach vector, then times the front and rear doors to both close simultaneously as soon as the spaceship fully enters the tunnel, trapping the spaceship inside. Earth POV: /------------\ =SS> R F \------------/ Spaceship Tunnel ...........................(time passes)... /------------\ R =SS> F \------------/ However, from the ship's point of view - things are quite different. It is standing still, and the tunnel is moving at it. Further, due to length contraction, the tunnel is only 30 meters long, so there's no way that the ship is going to fit inside. What the ship sees is that the front doors close *first*, then as the ship crashes through them, the rear doors are closed behind it. Spaceship POV: /------\ ===SS==> R F \------/ ...........................(time passes)... /------\ R ===SS==> \------/ Now actually, there is *no* violation of causality in this example. "What?!", you say. Well, you see, in either frame there is no event which precedes the cause. You have to look at it in practical terms. Say, for example, that instead of being timed, the front doors were wired to close only once the rear doors have closed behind the rear of the spaceship as it enters the tunnel. Thus the closing of the front doors is now _caused_ by the closing of the rear doors. The trick here is this: the signal that the rear doors have closed must traverse the length of the tunnel at *lighspeed*. On the timescale of events here, that takes considerable time. In _both_ cases, then, the spaceship has passed through the front of the tunnel before the signal can reach the front doors. When the signal does reach them, the doors close on the same point on the ship: just behind the midpoint. As long as the signal does not go FTL, causality is safe. -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- Example 2 --------- Now having given you a non-FTL example, I can give a typical FTL paradox. Say that a hyperspace-capable spaceship X is sitting still beside Star A. It activates its "jump drive", disappears, and one day later, it appears beside Star B, 1 light-year away. Spaceship POV: =X= \|/ \|/ -A- -----------1 light year------------------------ -B- /|\ /|\ .......................(one day passes).... =X= \|/ \|/ -A- -----------1 light year------------------------ -B- /|\ /|\ But now imagine that another spaceship Y is flying past Star B going at 0.9c away from Star B, so there is considerable dilation effects betweens its view of things and spaceship X. Now, spaceship Y is from a hostile enemy race to spaceship X - and as soon as ship X appears, spaceship Y guesses where it came from. Now, from spaceship Y's point of view, everything is dilated according to the formulas. In *its* reference frame, ship X appeared by Star B *before it disappeared from Star A*. About five months after it appeared by Star B, it disappeared from A (""). =X= \|/ \|/ -A- -----------1 light year------------------------ -B- /|\ /|\ *Y* .......................(five months pass).... \|/ \|/ -A- -----------1 light year------------------------ -B- /|\ /|\ Thus, spaceship Y activates _its_ hyperspace drive, and catches spaceship X by surprise - *before it left Star A*. -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- The Experimental Basis of Relativity ------------------------------------ Relativity is based on two assumptions: 1) All observers see light moving at the same speed. 2) All Galilean frames of reference are valid. You will see the same laws of physics in every frame. The experimental success of Relativity has been extremely successful - from detailed measurements of kinematics at relativistic speeds, to the well-known E=m*c^2, to prediction of the bending of light as it passes by the Sun due to gravitational effects. It could be that one of these assumption is wrong - either a very small error on the observed speed of light; or a "preferred frame" scheme. If so, then Relativity as a whole is invalid. However: whatever theory replaces it must also explain everything which Relativity predicted so accurately. The new theory would undoubtably be more complicated and confusing than Relativity. -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- CONCLUSIONS ----------- My main conclusion is that, if you want to satisfy gung-ho science types, you have a few choices: 1) "Shut up and play!" This is actually the most reasonable, in my mind, and should definitely be considered. Relativity may or may not be given lip service as a theory which works - but no one actually deals with the mechanisms by which it is broken. Develop a set of reasonable, likely sounding rules for FTL (using important keywords like 'quantum tunneling' or 'wormholes'), and ignore the consequences to relativity. 2) "Relativity is *wrong*." There actually are preferred frames - just that our observational techniques here on Earth are too limited to notice them. The effects are large ones across space - which are only noticable if you look on scales larger than the solar system. One version of this was my 'sub-space currents' theory which I posted before. This is 'hoaky' in that relativity has made many darn good predictions, some of which must turn out to be just coincidences in order for this to work. But frankly, you're going to have to do worse than this in any other FTL explanation, as well. 3) "We're violating causality, and we don't care." Relativity is true, time travel *is* possible, and the universe really is a wacky, crazy place. I recommend against this. If you want the universe wacky and crazy, throw out Relativity and use solution #1. Frankly, no one will understand this universe - which has time travel considerably less sensible than that in _Star Trek_ and much more complicated. 4) "The universe is full of holes." This refers to the `fixed stargate' explanation from the beginning, which can in theory be resolved with both Relativity and causality. This is a very limited form of so-called `FTL travel', however, and it may not fit with many sci-fi backgrounds. Further, because of how it messes with cosmology and has strange gravitational effects, it is not neccessarily any more believable to a hard-science player.