Is Warp Drive Possible? If So, How?


Is it possible to build a spaceship which warps the fabric of space and time, as in Star Trek, so that we can travel faster than the speed of light?


Serious physicists do debate this kind of thing. After one such debate, here are:


1.      My bottom line conclusions, in common language

2.      A quick technical summary of my views, for the expert

3.      Some effort to explain the technical position in more detail


The third part will probably evolve in the future as I learn what questions people have.

Perhaps someday I might add a fourth part, to discuss the questions I raise but do not pretend to answer. And maybe I might even divide up the third part into a version for physicists and a version for high school folks; for now, I will try to speak to both at the same time.


Summary of My Present Conclusions


No one on earth really knows whether warp drive is physically possible. Right now, the odds do appear to be against it, but there are serious loopholes in the arguments which say it is impossible. Because it would “open up a whole new world” for the human species (and help us adapt one way or another to the realities of this galaxy, whatever they may be), rationality demands that do what we can to maximize the probability that we do eventually learn how to build a warp drive – as one part of our many other concerns.

            The biggest obstacle to doing this is the tendency of many people today to think of physics as a kind of religion, demanding preaching, faith, formation of fixed opinions about the universe and strict adherence to them,  and solidarity and the stamping out of heresy. There will be no hope at all for warp drive (or for any other major breakthrough), unless we remember that science really is a voyage of exploration, that we still live in a world of uncertainty and mystery and “wildcat drilling,” and that we really need to learn a certain kind of strategic thinking in order to probe the space of possibilities.

Overconfidence, pride and narcissism will not give us warp drive. We need enough self-confidence to ask the big questions, but enough humility to know that we don’t have them yet. It is very sad these days when some adult scientists treat the scientific method the way some Mafia “Catholics” treat the words of Jesus Christ. Everything we know is rooted in experience of some kind – empirical data in the laboratory, or subjective experience. Science demands that we periodically ask ourselves what we really know and what we don’t know, based on shared laboratory experience. (Life is more than science, but to achieve warp drive, we would have to know new things as part of science.) We need to always keep asking what the alternatives are. In sum, we need to remember all that old stuff we learned from the history of science, and from the thinking which led up to Francis Bacon’s proposal for a Scientific Method.

We also need to understand how science has changed, since the mathematics became more difficult and our knowledge became more complicated. We need to aspire to the kind of mathematical thinking that Von Neumann espoused – not handwaving bullshitting with equations (which often reminds me of medieval “proofs” of the existence of God, complete with a thousand angels and renormalizations on the head of a pin), not excessive formalism, but an effective (and strategic) use of logic to try to achieve clear understanding. And now, because physics is even more complicated than it was in the time of Von Neumann, we need to learn how to work together more, by opening ourselves up to the kind of discussions which once could fit within a single brain. And we need to try to listen to a broader community, more than just one discipline.

Quick Summary of Technical Position


First, note that “warp drive” refers to bending space-time around a spaceship. I won’t be talking about wormholes here; they are a different approach to faster than light (FTL) travel.


Years ago, I had the following pessimistic view of warp drive. If we assume time-forwards causality (and think PDE or stochastic PDE), then we face the well-known result in basic mathematics that information cannot propagate faster than the speed of light, under quasilinear PDE. General relativity (GR) can be formulated as just another PDE theory (cf. Weinberg); it is not quasilinear, but at the forward edge of a spaceship-cum-space-warping it still is as close as you like to quasilinear, so forget it. This is similar to the better known heuristic argument from general relativity that any spaceship moving faster than light (FTL) is moving backwards in time, from some viewpoint.

But now I realize that these arguments are not quite airtight (even still assuming GR as the theory of gravity). Under the backwards-time theory of quantum mechanics (as described on my physics web page), we cannot rule out this kind of thing.

And so... forgive me... I did a google on "Alcubierre" yesterday. The Alcubierre solutions are well-known to gravity specialists, but I didn't have reason to look them up before now. It looks to me that the Wikipedia article on Alcubierre solutions is quite good.

At first -- the work of Alcubierre really is quite positive. If we reject time-forwards causality and use the PDE directly to make predictions... it does seem that we can find viable solutions consistent with GR that would allow warp drive, somehow or other. But then... it seems fairly definite that this is possible only if we can create "exotic matter," i.e. regions of space with negative total mass-energy.  This then leaves us with only three serious hopes for warp drive:

(1) Validating an alternative theory of gravity which does not have this restriction;


(2) validating the possibility, and then producing, negative mass-energy "matter" in a confined space.

(3) Or proving the Riemannian physical world is just an illusion ala The Matrix?

Some physicists are enthusiastic about the first route. It is certainly a worthwhile route in principle, but I really doubt we can claim much about it just yet, on an empirical basis. So far as I know (particularly from the recent Harvard astrophysics paper), GR with a cosmological term is still tenable.

I used to feel a lot more encouraged by the hope of negative mass-energy. I would still not rule it out, but I don't see much basis for it in the empirical evidence available to us just yet. A time-symmetric stochastic term can potentially explain a lot of the things I thought we needed negative mass-energy for. Under GR, negative mass-energy stuff would not cluster around galaxies; thus, to the extent that we know dark matter and light-modifying stuff clusters around galaxies... it would have to be something else, and, as such, would seem very speculative.

Maybe it's there, somewhere, but where? How could we learn more, aside from gross theoretical speculation? These are the questions we need to probe more deeply.

Random Bits of Attempted Explanation


I have been asking myself the question: “Do the laws of physics, as we know them today, permit the possibility of warp drive?”


In answering this question, the first problem is that we do not really know the laws of physics today. There are competing opinions, theories and possibilities. One good reason to ask about warp drive is that it may help us probe what we really know and don’t know.


Some people believe that superstring or n-brane theories are the ultimate laws of physics. What do those theories tell us about the possibility of warp drive? I don’t really know. I recently read a first-class science fiction trilogy by Meaney, the Nulaperion chronicles, which I highly recommend. (It is a good idea to read first-class science fiction, giving alternative viewpoints, even if you have a very tight schedule; we always need to remind ourselves that there really are many possible points of view…) He portrays a universe in which n-brane theory and such does make warp drive possible, in some form. But I don’t see any math in the book, or reference to math which makes it possible. So far as I know (without having checked), we have no idea about whether warp drive is really possible or not, in the canonical n-bran theory.


To be honest – I have not explored that issue, because I do not see much of a chance right now that superstring theory is true. I understand that we must keep an open mind, but from a strategic viewpoint, the n-brane effort has other questions to address. Still… if I were an n-brane believer… probably I would try to look at this question. If warp drive did look truly possible under n-brane theory, then proving this mathematically would raise people’s interest in finding out whether n-brane theory is really true. In fact, it might even suggest more realistic ways to try to test whether n-brane theory is true.


But right now, there is not one shred of empirical laboratory evidence that all the beautiful extra dimensions imagined by n-brane theory have any validity at all. The only proper reason to believe this particular choice of theory, out of the enormous universe of possible theories, is that it seems to offer a way to unify the standard model of physics (today’s “official theory” of electromagnetism, nuclear forces and quantum effects) with general relativity (still our best theory of gravity). But there are other ways to achieve such a unification, without inserting quite so many florid novel hypotheses.


Some people are now shifting from superstrings to “quantum loop gravity.” I would view this as one part of the third loophole in the arguments against warp drive. Greg Bear’s terrific science fiction novel Moving Mars exploits this loophole, and discusses how new theories of physics based on “its from bits” may allow this kind of effect. On my physics web page, I have posted a quick discussion of “digital universe” theories, and suggested that someone should explore these further. In fact, one of the world’s top applied mathematicians, Prof. Leon Chua of Berekeley, has followed up on these suggestions, and published a major discussion of some of the possibilities here, in the International Journal of Chaos and Bifurcation.


But for now – I do not see any shred of empirical laboratory evidence yet that the universe has more than the four dimensions that Einstein talked about – three of space and one of time. Furthermore, there are lots of possible ways to unify what we know about quantum theory, nuclear forces, electromagnetism and gravity, without needing to imagine extra dimensions. In order to make real progress, we need to be humble enough to try to make sense of what we can make sense of in Einsteinian space, first.  The first two loopholes in the argument against warp drive can be explored even without a belief in hyperspace.


Here, a very top theoretical physicist would immediately ask: “OK, where is your proposed theory of the universe, which you want to use as an alternative to n-branes and such? If we want to ask whether the theory permits warp drive, where is the theory or theories of the universe that you propose to analyze here?”


Science demands that we make room for different approaches to this kind of question. We need a diversity of efforts, in parallel, which also need to respect each other.


One possible approach is simply to give the theorist what he is asking for directly – a new unified theory of the universe, or a recipe of alternatives and a path to get to such a theory. I have recently posted a new paper which in my view responds to his question as well as possible today. It gives an example of a model Lagrangian which inserts new terms into a Lagrangian previously given by Moshe Carmelli (Classical Fields: General Relativity and Gauge Theory, Wiley 1982) in order to accommodate new work in nuclear physics, and adds a time-symmetric noise term (as justified in my paper on the Q hypothesis, at arXiv:quant-ph/0607096v2. However, more work is needed to carry through the new program, and I have not yet had time to do a deep analysis of what the new Lagrangian says about warp drive. Like the much-debated “zero point energy (ZPE)” hypotheses, this model does contain stochastic terms; however, I do not yet know how close they are to any of the ZPE predictions, or whether they would really allow any of the visionary concepts that ZPE people talk about.


Another approach is simply to assume the validity of general relativity, for now, and try to analyze warp drive on that basis. Since my new Lagrangians, like Carmelli’s, basically start from general relativity, this should give a good starting point in guessing what the new theories imply as well. Since we do not yet have good empirical data on how the universe deviates from general relativity (if it does), this is a reasonable way to try to analyze what we know about the possibility of warp drive today. This approach is what leads directly to the work of Alcubierre which I referred to in the technical summary.


And finally, a third legitimate approach is to probe hard the world of empirical data related to general relativity, and explore alternative theories (such as the theories based on torsion which Einstein explored in later life). Some physicists truly Believe in such alternative theories today. (People like Nash and Sarfatti have become well-known in certain circles.) Belief aside, the physicist Hehl has explored a variety of alternative possible theories very systematically, with reference to empirical data. His 2000 paper, gr-qc 0001010, is the best summary I can find of the status of this line of research. He is following the scientific method far more strictly than do the usual enthusiasts for warp drive, superstrings or even the standard model of physics.


Another important review of the empirical situation on gravity is given at gr-gc 0407113. From a quick read of these two papers, it would seem that we do not yet have any laboratory evidence yet for any of the alternatives to general relativity (leaving aside debates about the cosmological constant, which is essentially just a term within general relativity).  And yet – even the best review papers are sometimes incomplete, and there have been new experiments since those papers were posted. I have not yet asked Yanhua Shih for a detailed account of his own impressive, precise, recent experiments to probe fourth order terms in gravity. Also, I have heard press accounts of a credible experiment at ESA which showed much stronger coupling between gravity and spinning electromagnetic sources than GR predicts; this sounds very similar to what Hehl has been considering.



Hehl has mainly focused on the question of coupling between electromagnetism and gravity (including torsion effects). There is much value in that line of research, because of the experiments they lead to.

But in the long term, coupling between the nuclear strong force and gravity may  be much more interesting, both in terms of unified physics and in terms of technological possibilities not yet foreseen. More energy and force, more possibility for big effects.

It is also interesting to ask how these two streams of work could brought together. Hehl's work suggests, in effect, a kind of coupling very different from the usual kind which Moshe Carmelli discusses. It is then nontrivial (but not necessarily problematic) to ask how such coupling mechanisms could be extended to more unified standard model Lagrangians, like what I propose exploring, and tested. That sounds like a nice mid-sized project, except for the testing, which is bigger.

Unimaginative collider experiments that are essentially random two-particle collisions like what we see in the atmosphere probably are not so dangerous, really. Probably they won't do anything that we haven't seen in cosmic rays in the atmosphere. But really interesting many-body nuclear experiments that truly probe the unknown might best be done in earth orbit.


Hehl himself has written nothing about warp drive, so far as I know. But with an alternate theory of gravity, it should be possible to redo the Alcubierre solutions – and perhaps the result will be more promising.


Warp drive and alternative theories of gravity do sometimes bring out wild and undisciplined thinking and excitement. But this is no excuse for failing to explore the serious questions here in a serious but open-minded way.