Built on Facts

A reader writes in with a question about the physics of Star Trek:

When the Enterprise goes into warp speed (which as I take it are multiples of the speed of light, warp 5, 5x the speed of light, etc.) and they show the ship zooming through the cosmos, they always show the stars its passing as elongated. In the special theory of relativity, is it not true that moving near the speed of light objects will appear to actually contract? But then again, according to relativity one can’t go faster than the speed of light, so perhaps there is some other physical phenomena going on here. Or maybe I should just enjoy the show for what it is.


I’m not nearly as conversant in Trek as I am in Star Wars, but I’ll give it a shot.

It’s my understanding that warp speed was originally meant to be polynomial in nature. For a speed of “warp n”, the velocity of the Enterprise was v = c(n^2) or something of that nature. Thus warp 5 is actually 25 times the speed of light. Actually I had better look this up… ok, Wikipedia tells me that in fact the equation is v = c(n^3) so warp 5 is 125 times the speed of light. Which is fast, but still puts travel times between even nearby stars in the region of several days.

Later they changed the formula and now the exponent is 3.333… except for speeds greater than warp 9. That’s an unspecified function with a vertical asymptote so that warp 10 is actually infinite.

Now for relativistic speeds there is length contraction. Objects outside your fast-moving spacecraft will be contracted along your direction of motion in your reference frame. But the Enterprise is moving much faster than light. Special relativity is clearly already out the window because faster-than-light travel is not possible in that theory. The more general version of the theory – general relativity – is a little more lax. You can’t travel faster than light, but theoretically it may be possible to distort space in such a way that the Neutral Zone is only a few million miles away in your reference frame. You can then travel across the distorted space at an normal speed and arrive in a reasonable time.

This is wildly far-fetched and I’m using the word “theoretically” in the loosest possible sense. But it’s TV, so we’ll go with it.

Will it make things appear to be elongated or contracted? I couldn’t say, but there are circumstance in which we actually can directly observe distorted space elongating the appearance of objects. Gravity bends space, and even comparatively modest bending over a long distance can create visually observable effects. If you have a cluster of galaxies between you and some very distant other galaxies, the cluster can act as a gravitational lens. In the picture below you can see the bright galaxy cluster dominating the image, and you can also see background galaxies elongated into distorted arcs by the gravitational distortion on the light moving through the cluster:


Perhaps not exactly the same thing, but certainly in the same spirit. It’s distorted starlight occurring directly from the gravitational warping of space. Close enough for me.


  1. #1 MRW
    March 12, 2009

    My assumption is that the stars aren’t actually stretching, but that the image of them is smearing. Sort of like when long-exposure pictures of car headlights, or a shorter exposure when you are moving the camera quickly. In the Star Trek case, the “camera” (the starship) is moving very quickly, so the streaking effect is large even with a short exposure time.

  2. #3 Romeo Vitelli
    March 12, 2009

    Always remember the immortal words of Lucy Lawless but just substitute “Vulcan” for “wizard”:

    “Frink: “Yes, over here, m-hay, m-hayven… in Episode BF12, you were battling barbarians while riding a winged Appaloosa, yet in the very next scene my dear, you’re clearly atop a winged Arabian! Please do explain it!”

    Lucy Lawless: “Uh, yeah, well, whenever you notice something like that… a wizard did it.”

    Frink: “Yes, alright, yes, in episode AG04—”

    Lucy Lawless: “Wizard!”

    Frink: “Oh, for glavin out loud…”

    — The Simpsons, “Treehouse of Horror X”

  3. #4 ScentOfViolets
    March 12, 2009

    Actually, you don’t even need to be moving faster than light to see objects stretch. A common undergraduate problem is to posit a 100 meter long spaceship launched one from light-year away and traveling towards Earth at 0.99999 c, and then ask the student to calculate how long it will appear to be. The answer is that it will appear to be very long indeed as it approaches and then passes the observer. This has nothing to do with relativity, btw (which is the point of the exercise), and everything to do with simple optics.

  4. #5 Paul Camp
    March 12, 2009

    Pursue the optical angle a little further. Look at the sequence in which photons arrive at the Enterprise from distant stars. Since the Enterprise is outrunning the photons, if you can see the stars at all they SHOULD appear to move from behind the ship to in front of the ship until it slows down again. Then they would all suddenly zip into their proper places as a whole bunch of photons catch up all at once.

    Since this does not appear to be the behavior of stars on Star Trek, we can only conclude that the Enterprise operates primarily in reverse, boldly backing up where no one has ever backed up before.

  5. #6 gpshead
    March 12, 2009

    Warp is not x times to speed of light. It is an exponential function. The wikipedia article is naturally way more up to date with this completely useless trivia from trekkies than I could ever be:


  6. #7 rob
    March 12, 2009

    the stars don’t get stretched out. as you go faster and faster the stars will all get squashed in front of you, even ones that are behind, will look like they are in front. also, the color will get doppler shifted. here is a site that i think is reliable:


  7. #8 Bryan
    March 12, 2009

    I’ve seen the term ‘warp drive spacetime’ thrown around in the literature. There are some nice references in a recent review by Lobo of exotic spacetimes. As far as I know, any spacetime in which superluminal travel is ‘effectively’ possible (such as a wormhole spacetime) counts as a warp drive spacetime. That is, a warp drive spacetime is one in which an observer can travel between two points separated by a very large distance in a very short amount of proper time.

    Unfortunately, all such spacetimes seem to require the existence of exotic matter that doesn’t exist in our Universe. The non-matter-free solutions rudely violate the weak energy condition, and I believe they often violate the other energy conditions as well.

  8. #9 bbbeard
    March 12, 2009

    ScentofViolets: I don’t think that is quite right. First of all, it is not a lengthening, it is a contraction. And maybe you’re being deliberately ambiguous (“calculate how long it will appear to be”), but it *actually* will be 0.44 meters long, or thereabouts, in the Earth frame. That has a specific well-defined meaning: it is the distance (in the Earth frame) between the bow and the stern of the ship at a particular instant of time. However, there is an optical effect (called Penrose-Terrell rotation) which causes a snapshot of the object as it passes to appear as though the object were rotated with its backside tilted toward the observer. Of course, snapshots from the right and left of the object would both show the rotation of the back toward the observer, which illustrates that this really is an optical effect rather than a body rotation. BTW when I was growing up, this rotation was called Fitsgerald rotation but for some reason modern sources cite Penrose and Terrell.

    Paul Camp: actually the more egregious special effect is the Star Wars hyperspace jump blur. As you rightly point out, aberration will cause the apparent distribution of stars to bunch toward the direction of motion, not race toward the back. The Star Trek flight sequences make no sense at all, from a relativistic standpoint, unless you think of it, for example, as the display from a 22nd century imaging device that portrays the true (not apparent) positions of the stars as the starship zooms through a particularly densely populated section of the galaxy.


  9. #10 Aleks
    March 13, 2009

    Guys, guys! Speaking as a SFX tech that actually worked on Star Trek, the Motion Picture, let me tell you candidly – it’s a show! We didn’t consider the physics of anything when designing the fx, but just looked for neat visuals, hence the chromatic shift and streaking of the stars (more easily visible in STMP than in other later shows), the “star burst” when going to warp, etc. I can promise you that neither did anyone working on later movies or tv episodes. Correct physics simply isn’t important to story telling, but having visuals that aid in the story telling process, and that look neat (and beat those guys over at Industrial Light and Magic) was all that counted.
    Didn’t any of you notice that all the shows had sound transmission in space? Didn’t that tip you off to the incorrectness of the science? These weren’t science lessons, they were stories and we looked for the fastest, neatest and best way to further the story telling.
    The stars move because we needed a way to indicate that the Enterprise was moving – so the best way was to have stars peel off and fall back in the distance. That was the solution back in ’66 and we honoured that solution throughout all later versions of the show. It worked, it was neat and all we did from version to version was tweak the visuals a bit – so we did chromatic shifts in the movies, where they could be seen (big screen, you know) and less but equally interesting tweaks for the various tv shows.
    Sorry to stomp a bit on this discussion – I get a kick out of the idea of the physics of Star Trek, and hope that some of what was for us simply neat and completely not-thought-out ideas we used will help stimulate better futures – it already has – some guys, inspired by Dr. McCoy’s medical bed started using scanners and the like in hospital rooms to help monitor patients; now they are routine, but not yet wireless. The MRI, I was told by someone who worked on the earliest versions of that life-saver, came partly out of STMP’s medical bed that could scan and render a 3d image of the body’s insides. Tasers came from ST phasers and stun guns from earlier SF shows. Do you think that cell phones are not inspired by ST? Many models even look like our communicators. And all the gadgets in them come from someone being inspired by Tricorders…..
    I hope other things will be developed because someone was inspired by the work we did and which everyone, down to the lowliest gofer, was proud to be a part of, but I’m sorry to say, there was never a serious discussion of science or physics ever in any of the stuff we did. The formulas for warp were worked out by fans – we never had a guide as to what meant what or how fast it really was, and in every show and movie it swang wildly (in one movie, the Enterprise goes to the centre of our galaxy in a matter of hours or days, and there, instead of encountering a deadly and impenetrable mass of stars bunched so close together that no amount of radiation shielding would have saved the crew’s lives, they encounter a planet and a devil imprisoned there; in the original tv show, the travel time between stars was considerably longer, and perhaps more in line with fan’s calculations). Neat for telling stories, but sorry to say, not much else.
    Poster #2 (Romeo) was right – “wizards” – I was one of them.

  10. #11 Ibid
    March 13, 2009

    A vessel approaching a black hole is supposed to turn to spaghetti. One traveling at relativistic speed is supposed to contract. These changes probably wouldn’t be noticed by the occupants. However, to an outside observer of the ship you’d think you’d be able to see something.

    Roddenberry dealt with the lack of time shifts at those speeds by saying that it warped the space instead of actually traveling through space. I think the Christopher Pike Pilot episode mentioned breaking the time/space barrier… or something to that effect.

    But, if 200 years from now we’re watching the NASCAR races that lap Jupiter’s LaGrange points 50 times you have to wonder what we’ll see. At those speeds would a stationary camera see them at all? If we put cameras on the racers and point them at the others in the race would the others appear to be coneheads or coins or would they just look normal because the camera is also traveling so close to the same speed?

    I’m gonna say that anyone in a position to observe the craft would be unable to see any difference in the shape of the ship.

  11. #12 bbbeard
    March 13, 2009

    Thanks, Aleks, for all the great work on Star Trek over the years.

    But I don’t think the posters here are protesting the lack of scientific rigor in Star Trek. What we are exploring is: what would the correct physics be? It’s a different question. And an interesting one to folks who actually have to do a few relativistic calculations from time to time….


  12. #13 Kevin Bjorke
    March 13, 2009

    Comparing to a stationary observer is a red herring. Clearly, the camera is traveling at speeds close to that of the vehicle. So there’s little need for distortion effects there.

    As repeatedly mentioned on Star Trek, warp travel is not inertial: stop the engine, and the ship quickly drops to sub-warp speeds. Besides the optical effects, I suspect that slight tidal-like variations in the proximal effect of this active warp-drive space distortion are what causes microphones in space near the vehicle to record a low rumble as it passes, and a high-pitched pulsing squeal when phasers are fired. There might not be air to transmit vibration, but the mic elements still vibrate.

  13. #14 sinz54
    March 13, 2009

    In an interview back in the 1960s, Gene Roddenberry admitted that his scientific consultants had told him that the star field would appear to be distorted and contracted at these warp speeds. But that he decided to show the stars zooming by the starship Enterprise, because that would be more familiar to the audience. In other words, artistic license. (cf. “The Making of Star Trek,” by Stephen Witfield)

  14. #15 Aleks
    March 13, 2009

    BBB – I’m just saying don’t go by what we in the FX dept. came up with – we all knew that relativistic distortion would contract the star field in front of the ship, etc (we had endless discussions about what it looked like from side on and from different angles), but instead we opted for the aesthetically pleasing version we used. And thanks for the thanks. I don’t know anyone who wasn’t proud to have worked on the show even if they delivered coffee or spent 5 minutes in the back office. It was real cultural history being made. I’m very proud of my contribution as well.

    By the way, when we asked The Great Bird what he thought it should look like, he said that he sort of thought of the warp engines as distorting space around it and the Enterprise sort of riding the waves. At sub-light it is like surfing and as the speed increases it is like the “tube” grows and closes over the ship, until warp is attained, then it is like a bubble around the ship. Unfortunately, no one knew how to illustrate that and make it look good, so we opted for the effects as they are now established.
    We actually had some trials of the engines “distorting” space around them, but they simply didn’t make any visual sense, so the nacelles glowed blue on the sides instead.

    During one bull session, one of us surmised (I don’t remember who, it could have been me, but we were all consuming copious amounts of various legal and illegal substances at the time) that the warp bubble shrunk the Universe around it, making a short cut through reality. Sort of like if you imagine the universe to be the skin of a balloon, and to get from point A to point B we cut through the inside of the balloon to get there faster. Or the Balloon got “squeezed” was another idea. We actually made some of the navigation controls to reflect this, although it never showed up well on camera, but I heard they used the idea further on a couple of episodes of the Next Generation series.
    One thing we never figured out well was how the navigational shields worked and how they protected the vessel at warp speeds (we do this sort of thinking not because we want to get it right, but imagining something is part of design, and in order to make something that the audience can suspend their disbelief for means creating a world that is consistent within itself.). We finally decided that a warp bubble shielded the ship automatically from anything penetrating it, so when the Enterprise entered the “worm-hole” the warp bubble collapsed and the rock drawn in ahead of the ship into the worm hole could then be a credible threat. Also we decided that space battles were all at sub-light speed, otherwise you couldn’t use phasers or photon torpedoes. The new design of the torpedoes was done to reflect the corona of building release of the explosive, plus the out-gassing of the propellant.
    If anyone can figure out how it should look, I’d be interested to know – I personally think that you’d see contraction of the field in front of the ship up to light-speed, then a sort of grey distortion or a normal field from the ship’s point of view within the bubble and from the camera point of view outside the bubble, the ship would appear distorted and greyed out. But that would look just awful on screen. We did play with an idea of doing that sort of distortion of space as the ship gathered itself to jump to warp, but again, it just didn’t look good. Perhaps if we had CGI of the quality of today at the time we could have done it better. In the second movie they actually DID play at trying to show a distorted star field at the outset of the film, but it never really worked and was more there to give an idea of vertigo inducing bigness, which is actually not what space looks like.
    At least we didn’t do the Kessel run in 12 parsecs. ;-)

  15. #16 erik Remkus
    March 16, 2009

    Warp 10 is not infinite as implied by the episode “All good things” from season 7 of TNG where the Enterprise goes warp 13. It just coincidentally that warp 10 was the technological limit during the series.

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    March 18, 2009

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