Q: Hyperspace, warp drives, and faster than light travel: why not?

Physicist: Firstly: no.  But, if you’re really set on it: maybe.  The essential problems are that moving faster than light (FTL) requires impossible acceleration (not difficult but impossible in a “doesn’t make sense to talk about” kind of way), and FTL violates causality in some weird ways (for example, it allows travel backward in time).

This needs a little background, so pack a lunch.

Differently moving observers see events happen in different places.  For example, if you’re in a car, everything you do seems to be happening in more or less the same place, while for someone on the side of the road all the things that you do are strung out along the car’s route.

Perspectives that are moving with respect to each other are said to be in different “frames”.  So everyone in the car are in one frame, everyone waiting at a bus stop are in another frame, and everyone in an airplane overhead are in yet another frame.  There’s nothing more to frames than that.  So, something like “move to a different frame” just means “change speed”.

Alice (red) and Bob (blue) are moving with respect to each other. For no particularly good reason Alice sets off two firecrackers (green crosses). In Alice's frame (left) the explosions happen in the same place, one after the other. In Bob's frame (right) the explosions happen in different places. In all of the diagrams in this post, time is up and space is right/left.

Galileo (the famous one) recognized that in different frames the same events happen in different places (picture above).  More than that, he realized that all of the physics that he knew of worked the same regardless of the frame (moving / not moving), and with remarkable humility he named that realization “Galilean Equivalence”.

In 1905 the ‘Stein introduced a theory about relative movement that took Galilean Equivalence (physical laws are the same in all frames) and added invariance of light speed in all frames.  This is the corner-stone of relativity, and it’s called the “Einstein Equivalence Principle”.  The first big result of the EEP, is that not only do different frames disagree on where events happen, but also when.  It’s a bit much to go into, so if you’re interested in why, there’s an “explanation” in this post.

Different frames (red and blue) disagree on, among other things, what "now" is. The time that an event occurs, and even the order of events, can be changed by moving from one frame to another. The dashed lines are a single moment in time, (which are different) from each frame's perspective.

In the world according to Galileo (pre-relativity) any event could be moved relative to any other just by moving very fast.  For example if two events happen in the same place, but one hour apart according to Alice, then Bob can make the second event happen 60 miles away from the first by moving at 60 miles per hour relative to Alice.  Sadly, questions about “who’s right?” aren’t valid.  The universe has no “preferred frame”.

In Galileo’s old-timey world view there are some restrictions to how events can be rearranged from one frame to another.  Namely, the time when an event occurs never changes, and the future is always the future, and the past is always the past.

With the advent of relativity that was no longer the case, however, new restrictions popped up.  A pair of events can be separated in three ways: timelike, lightlike, and spacelike.

For a given event (center, black) all other events fall into one of three categories: timelike, lightlike, or spacelike separated. The yellow lines represent the path that light takes through the given event. The spacelike event can move around in its area on the right (even allowing it to occur before or after the center event), and the timelike event can move around in its area on the top.

Timelike separation means that there’s some frame in which the two events happen in the same place.  That is, if you move fast enough (slower than light) you can be present at both.  Timelike separated events always happen in an order: no matter what frame you’re in, everyone will agree which event happened first and which happened second.  Every event you’ve ever personally experienced has been “timelike separated” from every other.

Lightlike separation means that to be present at both events you’d have to be traveling at light speed.

Spacelike separated means that there’s no way to be present at both events, even travelling at the speed of light.  Things that are happening in Alpha Centauri “right now” are spacelike separated from us (right now).  There is always some frame in which spacelike separated events happen at the same time, but never in the same place.  Even weirder, spacelike separated events don’t have an order.  Different frames will disagree on which happens first.

So, finally: here’s the issue.  If you accelerate like crazy, get a huge rocket or whatever, the highest speed you can get up to is almost the speed of light.  The “start” and “stop” events of your journey will always be timelike separated, regardless of how high your acceleration, or how long you accelerate for.  Traveling faster than light means that your start and stop events are spacelike separated, and there is no physically real acceleration that can get you to move like that.  Most people are willing to forgive that, and say: “Dude, wormholes and warp drives!  S’cool!”.  But those brave souls still need to contend with the second issue: causality.

A ship with some kind of FTL drive races a beam of light. Left: The ship engages the drive (green cross), simply moves faster than light for a while, then disengages the drive (red cross). Right: The exact same situation as viewed from a different frame.

Say you’ve got the Enterprise (NCC-1701) and it works just like you’d expect: it cruises around at sub-light speeds until it engages its warp drive, which allows it to move at FTL speeds.  It moves from one star system to another, then eventually disengages the drive and “drops out of warp”, no harm no foul.  However!  When viewed from a different frame, the same situation can be very strange.

The engage and disengage events are spacelike separated, so they don’t actually have an order.  From (any one of) the proper frames, the disengage event can happen first (right half of the image above).  When that’s the case you find that:

-First there’s one ship, traveling slower than light.

-Then suddenly, and without cause of any kind, two new copies of the ship appear at a place some distance away.  One is traveling faster than light, and the other is traveling slower.  This event corresponds with the drive being shut down.

-The FTL version travels backward until it contacts the original ship, at which point they both disappear at the moment that the original engages its drive.

Now, sure, ships coming into existence and popping out again may seem bad enough, but the big problem is that FTL travel opens the door to backward time travel (forward is fine: you’re doing it now).

By taking a couple spacelike paths that end earlier than they started you can zig-zag back in time and find yourself in the same place you started, but earlier than the time when you originally left (in the example on the right side of the picture above the route gets you back to before you left, but in a different location).

Time traveling zig-zag: If you can get into the past somewhere else once, then why not do it twice and get into your own past?

There are a lot of problems with time travel (see: “Time Cop” and “Back to the Future”).  But, paradoxes and amazing one-liners aside, it seems to be very impossible.  There is no indication, direct or indirect, that the future can affect the past at all (except for psychics, obviously), let alone that anything can physically move from the future to the past.  So; case closed.  As long as the future follows the past, nothing can travel faster than light.

Spacetime diagrams for some sci-fi ideas about FTL (from left to right, then top to bottom): Star Trek or Star Wars, Battlestar Galactica, Babylon 5, and Dr. Who. Dashed lines are connections, not traversed distance. Click to enlarge.

But wait!  Despite their romantic prospects, physicists are consummate, rarely-say-die, optimists.  In that vein they’ve come up with several scenarios that (if real) would allow for FTL travel, but circumvent the whole time-travel thing.

The quickest way is to alter one of the basic assumptions of relativity; namely that all frames are equivalent.  Just declare that FTL travel is possible, but only in one direction.  That prevents things from zig-zagging into the past, but it also makes space travel kinda boring.  Sure you can explore stuff, but you can never get home.

Alternatively, you can declare that there exists one unique frame such that no paths into the past are possible.  Although other frames still get weird effects (disappearing ships, and causeless events, and whatnot), nothing can to loop back into its own past.  I think this is the idea that most sci-fi shows and books are working with, but that’s meeting them more than half way.

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16 Responses to Q: Hyperspace, warp drives, and faster than light travel: why not?

  1. Idran says:

    Relating to the “fictional universe” thing, can you elaborate on the last paragraph a little? If I understand right, basically what you’re saying is if you had a universe that did possess a preferred frame of reference, then this aspect of FTL wouldn’t exist?

  2. The Physicist The Physicist says:

    You wouldn’t have to worry in general about things going into their own past (which is what causes problems and paradoxes).
    In a nutshell, the last paragraph is about establishing an absolute ordering of the events that any object can experience. That is, if you see an “effect” at some point, there’s no way that you can travel such that later (for you) you’ll see the “cause”.
    I’m not sure that be-clears or be-murkys.

  3. Serpentia says:

    I remember reading in some book that logically considered the physics in Star Trek and explained the impossibilities and circumventions, and there was something that I *probably* didn’t understand properly, but seems relevant here.

    The author did a bit of work describing that, while it would need an astronomical amount of energy, it’s still physically possible to travel distances faster than light would, by shrinking the space between you and the destination. Your ship never moves faster than light, and you still arrive a thousand years faster than you normally would.

    Thoughts?

  4. The Physicist The Physicist says:

    I was worrying about that. That’s why I was careful to talk about “starting” and “ending” events while ignoring everything in between.
    The exact method used to get from one place to another isn’t terribly important. In Star Trek the warp drive makes the acceleration “real”, but the “causality problems” remain.
    So, while locally, the ship never moves faster than light it does still move faster than light globally, and that’s what causes problems.
    Confused readers should read about the “Alcubierre Drive” which is (frankly) the result of a physicist watching too much Star Trek.

  5. Michael Piper says:

    Have you seen the experiment on light that moves faster than light by moving backwards? http://rochester.edu/news/show.php?id=2544

  6. The Physicist The Physicist says:

    It’s not as exciting as it sounds (unfortunately). They’re basically doing this again.

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  9. Ron says:

    Are there really causality problems with FTL?? My understanding of the equations for time v. speed is that time isn’t negative with FTL, but complex. I tend to think that is fundamentally different.

    Mass is the same way. Sure, C is impossible for anything with mass, but close to it on either side isn’t. Given the interesting reports on neutrinos lately (still unconfirmed) I wasn’t all that shocked! In fact, I had generally wondered why anything with mass would consistently travel near the speed of light for any reasonable length of time. However, if they are traveling faster than light, it makes perfect sense! They can never slow down to the speed of light because of the infinite mass problem.

  10. The Physicist The Physicist says:

    Fair enough!
    That’s why I was careful not to talk too much about how the FTL object experiences time, and just tried to stick to where/when it ends up from the perspective of other reference frames, which is where the real problems crop up.

  11. Ron says:

    By complex, I meant that it was in the form of a mathematically complex number, that is a+bi and not a straight forward negative number.

    Also, another error that I think many people make is to think that if it were actually a straight forward negative number, that would mean that they would travel backwards in the time of a stationary observer. In reality, It would mean they age in a negative direction to include the causality issue of arriving at there destination at the age of 20years old prior to deciding to leave for it at the age of 40.

    If it can be shown that neutrinos, or anything for that matter, do travel FTL(I’m not saying that they do. I’m going to wait for the experimental data to come in..), we are definitely going to have to wrap our minds around what a+bi actually implies in terms of relativity.

    Doesn’t hurt to get a head start…alas though, it makes my brain hurt. uhg! lol I hate complex numbers!

  12. The Physicist The Physicist says:

    Complex; I dig.
    It sounds like you’re talking about the spacetime interval, L, which for other people reading this, is defined as L^2 = ct^2-x^2-y^2-z^2, which is equal to the amount of time (times c) experienced by an object traveling along a given path. But the important thing about L^2 is that it’s consistent in all frames. The sign of L, or even whether L is real or complex, is pretty unimportant.
    In fact, as often as not, L^2 is defined with the opposite sign! That said, our description of relativity is defined and described entirely from “this side” of the speed of light. FTL travel seems like it should make sense, intuitively (I mean, it’s just faster, right?), but the math stops making sense. We can’t say too many conclusive things about what an FTL object would experience.
    Probably not “backwards aging”. Time (in every example) will always “feel” like it’s moving forward from anything’s point of view.

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  14. DC Ambrose says:

    Traveling faster than light means that your start and stop events are space-like separated? I thought you said traveling at light-speed means that the start and stop events are light-like separated. Could you mean that light like separation is infinite (since one’s mass would become infinite at light-speed), faster than light would be the causality problem due to individuals in different frames (people on a starship in normal space would be perceiving a space-like separation start-stop event occurring in random locations, while the people on board the trans-light vessel would be perceiving it as if it were them going to their destination? I’m trying to wrap my head around this but say an anti-gravity flux between star cores aided in the directional accuracy at which a starship “jumped” along a theoretical jump “line” of anti-gravitational flux? Thus it could use the stars as way-points, and the jump-points at these anti-gravity wells in various locations within star systems (getting into fiction a bit I know, but I’m trying to come up with a legitimate explanation for rapid interstellar travel involving other dimensions coiled up and the effects of anti-gravity and anti-matter have on these dimensions. :P)

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