Nov 30 2012

Faster-than-light travel using spacetime distortions

The speed of light is the biggest barrier to the dream of intergalactic travel and the chance that we might ever encounter extraterrestrial intelligent beings. Faster than light travel has been the Holy Grail of scientists and science fiction writers and indeed of anyone who dreams of visiting distant stars and galaxies. After the recent unfortunate premature hype over the claims of faster-than-light neutrinos, I thought that we would not hear of such claims for some time. But it appears that scientists at NASA have been working on an idea that would enable faster-than-light travel.

The idea is based on a 1994 paper by Miguel Alcubierre and you can see the abstract of it here. The full paper is available by subscription only but I took a look at it and this article aimed at a general audience (obtained via Machines Like Us) gives a pretty good description of the basic physics and adds more information.

What is interesting is that the proposed idea does not violate any existing laws and lies within the framework of relativity theory and does not require exotic topologies like wormholes, the usual device suggested for getting around the light-speed limit.

What the author points out is that relativity only prohibits an object from travelling locally faster than the speed of light, i.e., it must stay within its local light cone. But by expanding spacetime behind a spaceship and contracting spacetime in front of it, you can propel the spaceship using spacetime itself and thus get motion greater than the speed of light when viewed by an observer who is outside the distorted region of spacetime. The popular idea that most closely resembles this is the ‘warp drive’ of science fiction. (Recall that there are also no limits to the speed with which space itself can expand, which is why distant galaxies are receding from us with speeds greater than that of light, ‘propelled’ by the expansion of space.)

Albucierre does a calculation in which a spaceship leaves Earth and moves towards a star in normal flat spacetime under normal propulsion for a short distance d. It then comes to rest and is then rapidly accelerated by spacetime distortions until it reaches the halfway point of its journey, whereupon the distortions are reversed to slow it down and bring it to rest at a distance d from the star. It then completes the final distance with normal propulsion in flat spacetime again. If the distance d is much less than the total distance to the star D, and the magnitude of the spacetime acceleration/deceleration is a, then the total time for the journal is given by 2√(D/a). By making a suitably large, we can make the time of travel as small as possible. In theory, wee could make a day trip to another galaxy!

Is there a catch? Unfortunately yes. There is always a catch. To get the required spacetime distortions one needs energy densities that are negative. But all the matter-energy forms we are aware of (ordinary matter, anti-matter, dark matter, and dark energy) all produce positive energy densities. Thus it may look hopeless but quantum mechanics comes to the rescue. It turns out that while the vacuum has zero energy density, this is true only for the average energy density and it may be possible to ‘squeeze’ the vacuum to create localized regions of positive and negative energy density such that the average is still zero.

The other major catch is that to produce faster-than-light speeds that can make intergalactic travel feasible requires a large value of a which in turn requires a large negative energy density. What NASA scientists are working on is tweaking Alcubierre’s model by varying the geometry of the spacetime distortions to try and overcome these hurdles and try and produce such motion in the laboratory. If they manage to exceed the speed of light by even a tiny amount, that would be a huge breakthrough in showing the feasibility of the idea. This paper by NASA scientist Harold White describes the attempts to achieve this.

Engineers are ingenious. They tend not to want to waste their time with speculative ideas but once you have shown them that an idea works in practice, however tiny the effect, that provides them with a huge incentive and motivation to begin working on making it workable on a large scale, and once they set their minds to it, they often achieve amazing things.


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  1. 1

    I recall seeing this come up in a TV special William Shatner hosted about Star Trek’s inspired effects on real-world technology.

    If memory serves, they interviewed Miguel Alcubierre about his warping spacetime paper.

    One of the other obstacles that came up, IIRC, was the enormous amount of energy required to make this method work.

  2. 2
    Kevin, 友好火猫 (Friendly Fire Cat)

    Cubert: I understand how the engines work now. It came to me in a dream. The engines don’t move the ship at all. The ship stays where it is, and the engines move the universe around it.

    Bender: That’s a complete load!

    Cubert: Nothing’s a complete load! Not if you can imagine it. That’s what being a scientist is all about.

  3. 3

    I’ve also read an article that said that the warping would produce so much directed and focused radiation that traveling to a planet would sterilize it. So you better point the ship away from your actual target.

  4. 4
    The Lorax

    Can’t travel faster than the speed of light? Re-shape reality itself until you can.

    No wonder the Doctor admires humans.

  5. 5
    Paul W.

    Hmmm. Negative energy density.

    The main things that reminds me of is Guth’s inflationary theory of the early moments of the big bang, where negative energy density causes exponential expansion (“inflation”).

    Could our expanding universe be the wake of somebody’s FTL warp drive, or something like that?

    I’m no physicist, and I have no idea if that actually makes any sense whatsoever… just making a superficial connection.

  6. 6

    I think there is another, co.ceptual problem that i find is severe:
    From all ive heard about their idea, the spacetime away from the traveller will be approximately Minkowski in these scenarios, i.e. flat with no weird topology. This means that from far away this travel will be equivalent to an object moving with v greater c through approx. minkowski space. there will be unavoidable time travel paradoxes. Ive looked at the sn neutrinos in some depth back in the day, and when you start allowing for negative energy densities this is kind of a generic problem. I.o.w., if you really build this thing, the big news is not the speed …

  7. 7
    Paul W.

    Does this kind of FTL warp drive manage to avoid time paradoxes by preserving the topology of spacetime, or something like that?

  8. 8
    Mano Singham

    In Guth’s inflationary model, the energy density is still positive but it exerts a negative pressure, and that is what causes the expansion.

  9. 9


    The cosmological constant + the proposed inflaton generate negative pressure, yes, but where have you heard that they involve negative energy density?

  10. 10
    Paul W.

    Oops… hadn’t seen AlexK’s comment about time paradoxes before posting mine.

  11. 11
    Paul W.


    I may have misremembered what was supposed to have been negative in the inflationary period, but before I posted I googled up the Wikipedia article on Energy Density, which says this (emphasis added):

    Some believe[who?] that vacuum energy might be the “dark energy” (also called Quintessence) associated with the cosmological constant in general relativity, thought to be similar to a negative force of gravity (or antigravity).[citation needed] Observations that the expanding universe appears to be accelerating seem to support the cosmic inflation theory—first proposed by Alan Guth in 1981—in which the nascent universe passed through a phase of exponential expansion driven by a negative vacuum energy density (positive vacuum pressure).

    I dunno if it’s right.

  12. 12
    Paul W.

    And I hadn’t seen Mano’s reply to the other comment about energy density being positive but pressure being negative when I posted the above.

    I guess the Wikipedia article writer got it backwards too.

  13. 13

    Sounds about right. Quintessence is a bit like inflation but slow+ for later times in order to get varying dark energy. In popular books and talks people often use “antigravity” to describe the unintuitive fact that in GR, the presence ofpositive but constant energy density makes space expand. This is a bit misleading . The confusion stems maybe from the fact that the effect of dark energy is not sensibly described by objects repelling each other. space itself is expanding.

  14. 14

    Mano do you agree with my assessment? I really don’t see a way around it although I really would like to ;)
    The other issue one would have to consider is the effect on the proper time of the traveller and how much unruh/ hawking radiation this contraption would dump on her

  15. 15
    Mano Singham

    I went into that page and corrected it. Thanks for alerting me to it.

  16. 16
    Mano Singham

    These are good questions and I don’t know the answers off-hand. I am not sure what form the time travel paradoxes would take in this case. Do you recall where you read about this?

  17. 17

    Wouldn’t this violate causality?

    I’m not an ideologue, so that’s not enough to make me reject it completely, but I do think it makes it highly unlikely to ever work.

  18. 18

    IIRC, the production of wormholes also requires negative energy density regions or materials. So your ‘does not require exotic geometries like wormholes’ thing is a bit of a sleight of hand, as the FTL drive hypothesized here would require the same exotic power source that a wormhole-sustaining generator would.

    Though I think my comment may be converging with Alex’s: if you create a negative energy density material/region in order to build your star drive, the star drive is not the big news item.

  19. 19
    Paul W.

    Doesn’t the creation of useful wormholes (e.g., to someplace you’d want to go, and that are actually much shorter paths) require stronger assumptions than just being able to create a region of negative energy density?

    The negative energy thing may be the killer in either case, but I would think that wormhole solutions would be harder in other ways.

  20. 20
    Kevin K

    Funny. I had this idea a while back. Don’t know if I had scanned this article or heard about it somehow; but it pretty much matches what I thought would be the likeliest way to achieve “warp” speeds.

    But not being a physicist, I chalked it up to just science fictiony thinking. If I ever write my sci-fi opus, that’ll be my propulsion mechanism.

  21. 21


    Thats more or less what i meant by time travel paradox.

    My thinking was simply that using the time coordinates of the asymptotic minkowski space, if something travels faster than c, there is a reference frame (related to say the earth frame by a lorentz transformation of the coordinates) in which the arrival is before the launch. I assume that this drive cannot alter the asymptotic geometry of space so much that these asymptotic time coordinates are not sensible any more. ( otherwise this drive would basically change the entire causal structure of the universe.) Since the superluminal capabilities of the vessel do not depend on its relative motion to an arbitrary reference frame like the earths, you can go back with another of these !this is enough to send i.formation to the past.

  22. 22
    Ms. Anthrope

    Actually, a PDF of the article is available if you use google scholar to search for the title.

  23. 23

    Incidentally, I take slight issue with this:

    The speed of light is the biggest barrier to the dream of intergalactic travel and the chance that we might ever encounter extraterrestrial intelligent beings

    Arguably the opposite is true: relativity gives us the stars, it doesn’t take them away – because of time dilation. Normal acceleration + newtonian physics would mean you’d get to local stars in a few years, and distant stars centuries after you die. And you’d have to carry lifetime supplies with you. And your ships would suffer years of wear and tear. Space is just too big; the only way to cover the distances in human life times is some form of relativity, where going fast changes local time.

    As an example, Alpha Centauri is 4.2 light years from earth. With relativity, traveling there at 0.999c would take 2 months local time. At 0.99999r, its about 6 local days. Covering the same distance at the same velocity in a newtonian universe would take 4 years. Relativistic time dilation is, in some ways, the star drive you’re looking for.

  24. 24
    Francisco Bacopa

    Maybe someone can explain something to me here: How can energy ever take a negative value? Energy is a scalar quantity. I don’t think scalars can ever have a negative value, as opposed to vectors which often do and sometimes and can be given negative values with impunity by changing coordinate systems.

    Am I just missing something here? In general it seems to me that negative energy makes no sense.

  25. 25
    Mano Singham

    In physics a scalar, roughly speaking, is a quantity that is independent of the coordinate system that is used. So mass is a scalar. An object’s mass remains the same if we shift or rotate the coordinate system. A scalar can be specified by one number, but that number can be positive or negative. For mass, that number is positive, but that need not be the case for all scalars.

    The total mechanical energy of a system (=kinetic plus potential) can also be positive or negative, depending on the baseline we take for zero potential energy. The non-relativistic kinetic energy is always positive because it is defined as (1/2)mv2, and those are all positive numbers. But the value of the potential energy can range anywhere from +(large number) to -(large number) depending on our choice of where to fix the zero point.

    If we take the vacuum as the zero total energy baseline (as is usually the case) and ignore quantum fluctuations of the vacuum, then all energy of matter and radiation is positive. But when you have those fluctuations, then you can have localized regions of negative energy.

    It’s weird, I know, but the effect is independent of whether something is a scalar or not.

  26. 26

    The effect being of course that many years will pass outside of your reference frame.

    For a great sci-fi take on that see Dan Simmons’s Hyperion universe where people incur “time debt” through starship travel. In of the stories in the first book is about a space traveler who periodically visits a planet ans falls in love with a woman there. Each visit he is only a little older while around a decade passes for her.

  27. 27

    Oh indeed, I missed the bit about negative energy density when i read the paragraph before. Yes that bit was just wrong

  28. 28
    Vote for Pedro

    This reminds me of a lecture point Dr. Singham made in a class of his I took some years ago about reification. In fact, energy was his prime example, if I recall correctly.

    Reification is the process of treating an abstract idea as if it is concrete (has physical form/reality/”is a thing”). When we treat energy as if it’s equivalent to our everyday experience of warmth or as if it works like gasoline, rather than as an abstract concept used for physics bookkeeping, that’s reification. I’m not criticizing – I think it’s actually pretty interesting that our brains work that way – but it is something to watch for.

    I think that’s why the idea of negative energy seems odd at face value: when we think it’s odd, it’s because we’re reifying energy instead of treating it like the tool it is. Or “abstract idea we find useful to describe situations mathematically” rather than tool, since “tool” gets us into the same mess!

  29. 29
    Mano Singham

    You are absolutely right.

    You have no idea how gratifying it is to have something that I taught many years ago still be remembered!

  30. 30

    Unfortuantely Alcubierre drives are unstable to Hawking radiation.

    Semiclassical instability of dynamical warp drives

    A popular science level explanation of the Alcubierre warp drive and its instability podcast : http://titaniumphysicists.brachiolopemedia.com/2012/02/20/episode-9-warp-drives-with-zach-weinersmith/

  31. 31

    Linkety link to the full (free) paper. Arxiv is your friend.

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