Saturday, November 21, 2020

Warp Drive News. Seriously!

[This is a transcript of the video embedded below.]

As many others, I became interested in physics by reading too much science fiction. Teleportation, levitation, wormholes, time-travel, warp drives, and all that, I thought was super-fascinating. But of course the depressing part of science fiction is that you know it’s not real. So, to some extent, I became a physicist to find out which science fiction technologies have a chance to one day become real technologies. Today I want to talk about warp drives because I think on the spectrum from fiction to science, warp drives are on the more scientific end. And just a few weeks ago, a new paper appeared about warp drives that puts the idea on a much more solid basis.

But first of all, what is a warp drive? In the science fiction literature, a warp drive is a technology that allows you to travel faster than the speed of light or “superluminally” by “warping” or deforming space-time. The idea is that by warping space-time, you can beat the speed of light barrier. This is not entirely crazy, for the following reason.

Einstein’s theory of general relativity says you cannot accelerate objects from below to above the speed of light because that would take an infinite amount of energy. However, this restriction applies to objects in space-time, not to space-time itself. Space-time can bend, expand, or warp at any speed. Indeed, physicists think that the universe expanded faster than the speed of light in its very early phase. General Relativity does not forbid this.

There are two points I want to highlight here: First, it is a really common misunderstanding, but Einstein’s theories of special and general relativity do NOT forbid faster-than-light motion. You can very well have objects in these theories that move faster than the speed of light. Neither does this faster-than light travel necessarily lead to causality paradoxes. I explained this in an earlier video. Instead, the problem is that, according to Einstein, you cannot accelerate from below to above the speed of light. So the problem is really crossing the speed of light barrier, not being above it.

The second point I want to emphasize is that the term “warp drive” refers to a propulsion system that relies on the warping of space-time, but just because you are using a warp drive does not mean you have to go faster than light. You can also have slower-than-light warp drives. I know that sounds somewhat disappointing, but I think it would be pretty cool to move around by warping spacetime at any speed.

Warp drives were a fairly vague idea until in 1994, Miguel Alcubierre found a way to make them work in General Relativity. His idea is now called the Alcubierre Drive. The explanation that you usually get for how the Alcubierre Drive works, is that you contract space-time in front of you and expand it behind you, which moves you forward.

That didn’t make sense to you? Just among us, it never made sense to me either. Because why would this allow you to break the speed of light barrier? Indeed, if you look at Alcubierre’s mathematics, it does not explain how this is supposed to work. Instead, his equations say that this warp drive requires large amounts of negative energy.

This is bad. It’s bad because, well, there isn’t any such thing as negative energy. And even if you had this negative energy that would not explain how you break the speed of light barrier. So how does it work? A few weeks ago, someone sent me a paper that beautifully sorts out the confusion surrounding warp drives.

To understand my problem with the Alcubierre Drive, I have to tell you briefly how General Relativity works. General Relativity works by solving Einstein’s field equations. Here they are. I know this looks somewhat intimidating, but the overall structure is fairly easy to understand. It helps if you try to ignore all these small Greek indices, because they really just say that there is an equation for each combination of directions in space-time. More important is that on the left side you have these R’s. The R’s quantify the curvature of space-time. And on the right side you have T. T is called the stress-energy tensor and it collects all kinds of energy densities and mass densities. That includes pressure and momentum flux and so on. Einstein’s equations then tell you that the distribution of different types of energy determines the curvature, and the curvature in return determines the how the distribution of the stress-energy changes.

The way you normally solve these equations is to use a distribution of energies and masses at some initial time. Then you can calculate what the curvature is at that initial time, and you can calculate how the energies and masses will move around and how the curvature changes with that.

So this is what physicists usually mean by a solution of General Relativity. It is a solution for a distribution of mass and energy.

But. You can instead just take any space-time, put it into the left side of Einstein’s equations, and then the equations will tell you what the distribution of mass and energy would have to be to create this space-time.

On a purely technical level, these space-times will then indeed be “solutions” to the equations for whatever is the stress energy tensor you get. The problem is that in this case, the energy distribution which is required to get a particular space-time is in general entirely unphysical.

And that’s the problem with the Alcubierre Drive. It is a solution to a General Relativity, but in and by itself, this is a completely meaningless statement. Any space-time will solve the equations of General Relativity, provided you assume that you have a suitable distribution of masses and energies to create it. The real question is therefore not whether a space-time solves Einstein’s equations, but whether the distribution of mass and energy required to make it a solution to the equations is physically reasonable.

And for the Alcubierre drive the answer is multiple no’s. First, as I already said, it requires negative energy. Second, it requires a huge amount of that. Third, the energy is not conserved. Instead, what you actually do when you write down the Alcubierre space-time, is that you just assume you have something that accelerates it beyond the speed of light barrier. That it’s beyond the barrier is why you need negative energies. And that it accelerates is why you need to feed energy into the system. Please check the info below the video for a technical comment about just what I mean by “energy conservation” here.

Let me then get to the new paper. The new paper is titled “Introducing Physical Warp Drives” and was written by Alexey Bobrick and Gianni Martire. I have to warn you that this paper has not yet been peer reviewed. But I have read it and I am pretty confident it will make it through peer review.

In this paper, Bobrick and Martire describe the geometry of a general warp-drive space time. The warp-drive geometry is basically a bubble. It has an inside region, which they call the “passenger area”. In the passenger area, space-time is flat, so there are no gravitational forces. Then the warp drive has a wall of some sort of material that surrounds the passenger area. And then it has an outside region. This outside region has the gravitational field of the warp-drive itself, but the gravitational field falls off and in the far distance one has normal, flat space-time. This is important so you can embed this solution into our actual universe.

What makes this fairly general construction a warp drive is that the passage of time inside of the passenger area can be different from that outside of it. That’s what you need if you have normal objects, like your warp drive passengers, and want to move them faster than the speed of light. You cannot break the speed of light barrier for the passengers themselves relative to space-time. So instead, you keep them moving normally in the bubble, but then you move the bubble itself superluminally.

As I explained earlier, the relevant question is then, what does the wall of the passenger area have to be made of? Is this a physically possible distribution of mass and energy? Bobrick and Martire explain that if you want superluminal motion, you need negative energy densities. If you want acceleration, you need to feed energy and momentum into the system. And the only reason the Alcubierre Drive moves faster than the speed of light is that one simply assumed it does. Suddenly it all makes sense!

I really like this new paper because to me it has really demystified warp drives. Now, you may find this somewhat of a downer because really it says that we still do not know how to accelerate to superluminal speeds. But I think this is a big step forward because now we have a much better mathematical basis to study warp drives.

For example, once you know how the warped space-time looks like, the question comes down to how much energy do you need to achieve a certain acceleration. Bobrick and Martire show that for the Alcubiere drive you can decrease the amount of energy by seating passengers next to each other instead of behind each other, because the amount of energy required depends on the shape of the bubble. The flatter it is in the direction of travel, the less energy you need. For other warp-drives, other geometries may work better. This is the kind of question you can really only address if you have the mathematics in place.

Another reason I find this exciting is that, while it may look now like you can’t do superluminal warp drives, this is only correct if General Relativity is correct. And maybe it is not. Astrophysicists have introduced dark matter and dark energy to explain what they observe, but it is also possible that General Relativity is ultimately not the correct theory for space-time. What does this mean for warp drives? We don’t know. But now we know we have the mathematics to study this question.

So, I think this is a really neat paper, but it also shows that research is a double-edged sword. Sometimes, if you look closer at a really exciting idea, it turns out to be not so exciting. And maybe you’d rather not have known. But I think the only way to make progress is to not be afraid of learning more. 

Note: This paper has not appeared yet. I will post a link here once I have a reference.

You can join the chat on this video on Saturday 11/21 at 12PM EST / 6PM CET or on Sunday 11/22 at 2PM EST / 8PM CET.

We will also have a chat on Black Hole Information loss on Tuesday 11/24 at 8PM EST / 2AM CET and on Wednesday 11/25 at 2PM EST / 8PM CET.


  1. The classic case of a warp drive is by Miguel Alcubierre. This is a spacetime that is a sort of stretch carpet; if your foot scoots the carpet forwards the carpet in the leading region ahead of your foot compresses while the trailing region is stretched out. Where your foot steps is the flat region internal to the warp bubble that you want to place your spaceship. This compressing of the region in front has the effect of reducing the effective distance the ship travels. If there is this region of compressing that reduces by 10 the distance between points of space, then travel to alpha Centuri 4.3 light years away is reduced in effective distance to .43 light years. It is a neat trick and using logarithms we can consider the factor of 10 "warp factor one." Thus, warp factor 9, I think the usual limit on Star Trek, is a reduction of distance to a billionth. The effective distance to alpha Centuri is then reduced from about 45 trillion kilometer to just 45,000 km.

    There are some people out there really pounding on this. I know one guy who is knowledgeable in physics, PhD and the rest, who is quite adamant about this. My skeptical cup runneth over though. This is not to say I think this research is worthless, quite the opposite. However, I do not think NASA, ESA, Roscosmos, JAXA or anyone is going to ever see so much as warp factor ε. The warp drive spacetime is a bubble, that if it is made small enough is a sort of tachyon. The tachyon is the first excited state of the bosonic string. The relationship between the warp drive and flat or de Sitter spacetime can then tell us things about the foundations of physics. In particular I think that relationship is a spacetime variant of mixing oil and water.

    I have this Catalogue of Spacetimes, which can be found on the arxiv [ arXiv:0904.4184v3 [gr-qc] ] that is very useful. Anyone who has done GR calculations knows these can be tedious. This metric is

    ds^2 = -(1 - β_xβ^x)dt^2 + 2β_idx^i + dx_idx^i

    where the velocity term β_x = v_xf(r(t)) along the x direction. This function f(r(t)) is this "top hat function "

    f(r(t)) = ½{tanh(σ(r + R) - tanh(σ(r - R))}/tanh(σR)

    where sig and R define the scale of the warp bubble. I will not trouble you with the calculations, for they get a bit wooly. The result though is that the curvature of this spacetime gives

    R_{00} - ½Rg_{00} = -{v_x^2(y^2 + z^2)/4det(g)^2r^2}×(df/dr)^2.

    This is negative which means the mass-energy density that is the source of this gravitational field is negative. This means the Hawking-Penrose weak energy condition, which is the most general, that T_{00} > 0 is violated. This means all types of terrible things can happen, such as closed timelike curves, time travel etc. Other spacetimes such as wormholes and Krasnykov tubes have these properties as well.

    1. I have to say I never believed the idea that one may travel from one point in spacetime to another by condensing the spacetime in front and stretching spacetime behind the ‘bubble’. There’s a flaw in thinking that would actually mean real movement. It is zero movement relative to the spacetime around the bubble.

      Comparable to two black ink points on a balloon. Squeezing the rubber of the balloon between the points does seem to move them towards each other, but the amount of material between them always stays the same. The points don’t move, it only looks as if they would.

      I’m afraid the bubble would not move (i.e. to A. Centauri) at all, and the distance would only be distorted, not changed.

    2. Your point is well taken, but perhaps instead of dots we should imagine one of them to be say, an ant. If the object within the bubble is moving by thrust it can then take advantage of the spatial contraction. Frankly too I question the necessity of an artificially expanding space behind the craft.

    3. Point taken, but I doubt the analogy of the ant hits the point. The ant crawls 'over' the rubber. In spacetime, the craft wouldn't just 'dive and crawl' parallel to spacetime, at least if we leave star trek aside.

      I doubt that objects can escape their spacetime environment, and I doubt that condensing spacetime changes anything in that regard. Objects coming close to a black hole are being accelerated towards it, in ever inscreasing density of spacetime, becoming subject to time dilation as they fall into the hole. Although they are 'close', it takes them increasingly longer, eventually eternally, to reach it.

      I assume the same would apply to the craft that condenses spacetime in front of it. It may come 'close' to the Alpha Centauri, from an outside perspective, but it never reaches it within its own frame of reference.

  2. continued due to character limit:

    Susskind et al have been touting this ER = EPR that entanglement and black hole Einstein-Rosen bridges are equivalent. This means with the standard Penrose conformal diagram there are analogues between the black hole top triangle and the white hole bottom triangle with a and a^†. For a quantum black hole there is then this sort of “winking” between being a black hole and a white hole, the raising and lowering of superposed states, which is a sort of wormhole. These spacetimes then on a quantum mechanical level may transition between each other, and a dS spacetime may on a quantum level have a superposition with AdS where there are tachyons. So, quantum mechanically it is not unreasonable to think that a quantum fluctuation can correspond to a tachyon as maybe a shadow state. As a result, there is some plausible theoretical utility to the warp drive.

    I do though think quantum states of gravitation form entanglement tensor networks that are “hard.” In contrast to standard entanglements that are brittle, it is possible that entanglements that stitch together spacetime are hard. This has to do with the effective negative heat capacity of spacetime. As a result, large macroscopic spacetime configurations such as the warp drive are, I think, extremely unstable and effectively do not exist. I think it is extremely unlikely there will be starship Enterprise ready to warp drive to other stars.

  3. Concerning "What makes this fairly general construction a warp drive is that the passage of time inside of the passenger area can be different from that outside of it."
    That sound a little worrying. It wouldn't be very useful to "warp" to a far distant destination in just 10 minutes but to come out and find the rest of the universe had aged 10 000 years!

    1. I would have to perform some integrations, but if the warp drive compresses space then it makes some plausible sense time is distorted as well.

  4. Your article brought to mind an interesting corollary I read a while ago concerning said Alucbierre drive. Apparently, just travelling with it, then breaking will have disastrous consequences for anything in the direction of travel, at least based on the work of the university of Sydney. The article mentioning these results can be found here.

    1. Their conception seems to assume a flat 'bow' with even compression. I think that rather than a blast, the craft would leave a trailing wake.

  5. If warp drives are possible it certainly makes the Fermi paradox more pointed.

  6. CI Pig,
    If warp drives are possible it certainly makes the Fermi paradox more poignant.

  7. Energy is a relative quantity. You can set its sign by defining the zero potential.

    Even Higgs might be antipodal and have positive and negative phases in relation to nonorientation.

    So, its madness to deal with invariant (in a way) "negative energy".

    I think we should very tightly consider spacetime as the description of interactions, not as background canvas like mammals to survive in food chain.

  8. Seriously indeed. My money's on the Jarnell Intersplit.

  9. As I posted previously and that has been shown in experiments by Lief Holmlid, it may be possible to create an electroweak black hole where a bubble of self-amplifying energy is initiated when the quantity of metallic hydrogen is irradiated by light. Additional energy feedstock could be provided by in falling matter gathered from space as per the Bussard ramjet process.

    The material that can carry this reaction is metallic hydrogen that has been activated using light; a chain reaction where electrons are converted to polaritons via light matter entanglement supports an ever increasing Bose condensate of polaritons where its energy content eventually reaches grand unification of forces levels.

    A magnetic bottle would form the activated metallic hydrogen envelope that surrounds the passenger area.

    To evaluate the curvature of space produced by the envelope, the relativistic equations can be evaluated assuming the energy density of the envelope approaches grand unification of forces values

  10. Hi Sabine (and also Lawrence),

    I have a question: Can the Einstein field equations also be used to describe what would happen to space-time in a 'warp-core' breech? I would imagine that the "breech" part could all be described as taking place on the T_{mu,nu} side of the Einstein equation.


    1. The term core breech or warp-core breech is a Star Trek term. There were a number of episodes where that term occurred.

      The warp bubble is not really controllable. From the perspective of the observer in the center the perimeter region where the exotic matter would exist is not in their future light cone. This means turning it on and off are not possible.

      It is then not clear what would happen if the warp bubble would by some means decay. It is also not clear how generating the warp bubble is possible. The metric is in a sense "eternal." Ford and Penning showed the solution has stability issues. In generating the negative energy to construct the warp bubble there is positive energy that has to be removed to "elsewhere," and even this requires more energy. This is an energy interest problem, as they term it, and the "energy hole" you dig is not stable and gets filled in with positive energy. There are Hawking-like radiation physics involved with this.

  11. In the discussion tomorrow it would be good I think if we could avoid topics such as UFOs and the rest. The discussion today in the last 15 minutes I was there got mired in that.

    Think about it folks. Earth has been here for 4.5 billion years, life for 3.7 billion and complex life for .5 billion. There is no evidence of there ever having been an alien visitation of Earth. At least no evidence of any ET coming here to use resources. Any ET capable of warp drive technology would be very energy and resource hungry. If warp drives were possible they would not come at all cheap.

    UFOs are not in any way evidence of faster than light travel. It seems very unlikely ETs are traveling many light years just to check us out. Claims of such are extremely extraordinary.

    1. @Lawrence Crowell: What do you think of what Dr. M. B. Paranjape said about the issue of negative mass, which I quoted below in a posting at 8:03 PM, November 21, 2020? I was sort of hoping that maybe the prohibition on the presence of negative mass, (or possibly just negative energy density?), wasn't entirely ironclad in our de Sitter space. Another consideration are vacuum fluctuations, where energy is borrowed from a nearby region of space such that for a brief time there are two adjacent regions one with negative energy density the other positive energy density. In Kip Thorne’s “Black Holes & Time Warps”, on pages 291-294 he describes “gravitational vacuum fluctuations”. But these are on an unimaginably tiny scale of 10^-55 cm. (a Planck-Wheeler length), where these fluctuations become a “froth of quantum foam”. An idea he broaches in this book is that a super advanced civilization might “pull” these fluctuations up from the vacuum, expanding them to usable size for a wormhole.

    2. Negative mass can occur in condensed matter. A Brilloin zone defines a type of vacuum energy and this can renormalize the mass of an electron so it is negative. That is a bit bizarre, and it mean a force in one direction results in an acceleration in the opposite direction. However, in the free vacuum of the observable universe the vacuum energy obeys the Hawking-Penrose energy condition T^{00} ≥ 0. So negative mass does not happen in free space.

      Anomalous dispersion of microcavity trion-polaritons

      “Note that the fundamental difference between the earlier observation of negative polariton mass and this work is that many-body interactions result in an anomalous trion-polariton dispersion, resulting in charged cavity polaritons exhibiting negative mass in the neighbourhood of kǁ = 0.”

      This main stream research was published in Nature Physics.

      Polaritons can produce negative mass as per experimental results documented Nature physics.

      Metallic hydrogen demonstrates an open ended condensed matter structure that will support the cavity dynamics necessity to stabilize, maintain, grow and accumulate the polariton condensation that generates the negative mass necessary to implement a warp drive.

    4. I have explained here that the term "negative mass" in condensed matter physics does NOT mean actual negative mass. It is an unfortunate and misleading technical term. Please discontinue repeating the incorrect claim that research has shown negative mass can be created.

    5. As you have stated previously that negative mass does not exist in general relativity and the Higgs mechanism, but as a quasi-property of and analogous duel system, will the nature of this behavior be an effective substitute in the engineering of a warp drive?

      Polariton condensation has been shown to mimic identically mathematically real general relativist behavior such as the production of Hawking radiation which has been seen to exist experimentally together with other black hole like behaviors.

      "We propose a new system for the study of event horizons and black holes - a Bose-Einstein condensate of exciton-polaritons. Hawking radiation from a closed horizon in 2D is observed in numerical experiments. We simulate inter-Universe and intra-Universe wormholes capitalizing on the spinor nature of polariton condensates and on the spin dependence of polariton-polariton interactions."

      Observation of self-amplifying Hawking radiation in an analogue black-hole laser

      If the entire math structure is the same and the actions and behavior of the duel is the same, is this analogous duel good enough to produce the same engineering effects and provide a substitute for the real thing, even if the real thing does not exist.

    6. I agree! The word effective is important. This is similar to the case when you accelerate a car, a helium filled balloon goes forward. A normal (positive) mass object in the car like your head would go backward. So sometimes people say the balloon has effective negative mass!

    7. A polariton is an photon or optical phonon the couples to an exciton of electric or magnetic dipole. This results in the loss of level degeneracy and an avoided crossing. If this energy gap is positive then the polariton will have negative energy or mass.

      Yet it must be stressed, this is not in the free vacuum state of the spacetime we live in. It is not possible in free space or source-free vacuum to have T^{00} < 0.

    8. The negative mass in solid state systems is a renormalization of the mass. One can think of the ordinary mass of the electron being taken up in the Brillouin zone with additional mass so there is an effective negative mass.

  12. presented in 2019 at the Time Machine Factory Conference in Turin.

    1. "Technically, you would only need one time traveler convention." - From Cat and Girl, Feb 11, 2003.

  13. I was really looking forward to this video, being a fan of Star Trek and having a long time fascination with UFOs, that presumably are coming across interstellar space. I found it intriguing that a configuration that is more flat in the direction of travel, as in the Bobrick-Martire warp drive metric, was more energy efficient. This may be a trivial observation, but in the early days, and still today, the physical shape of UFOs is often that of a relatively flat disc. When they accelerated, it was typically reported that it was along the flat face of the disc.

    On the issue of negative energy densities that violate various energy conditions, Dr. M. B. Paranjape in a 24 May 2017 article in Physics Today, titled: “Don’t dismiss negative mass”, stated: “If there is a backreaction on the production of these [positive-negative mass] pairs on the background cosmological energy, the production of negative mass should drive that energy density to zero, thus terminating the possibility of its production and quenching any instability”. If he’s right in that assessment then maybe negative energy density isn’t ruled out.

    But I’m not quite sure how to interpret what he’s saying. It sounds like as soon as a negative energy particle appears in a region of space its negative energy is neutralized by the all permeating (positive energy) cosmological constant, or dark energy, preventing an endless replication of positive-negative particle pairs. But if the negative energy particle had the mass (negative mass) of an electron, and was of similar dimensions it presumably would have vastly greater (negative) energy density than the cosmological constant in the same volume of space. So it seems that for that process to be viable the negative energy electron would have to soak up the positive cosmological constant energy of a fair sized volume of space before it disappeared. But then there’s the problem of lepton number and spin violation, assuming a positive-negative energy pair of electrons was initially formed in which these quantities cancelled.

    1. To carry on with this. Corda and I [ ]worked on how the near coalescence condition of two black holes results in a sort of Casimir effect. The spacetime in between these BHs is a form of anti-de Sitter spacetime. So just as with the ordinary Casimir experiment, where two conducting plates can define a confined vacuum of lower energy, the same happens here. There is a form of negative energy vacuum. There is the excitation of quantum states, which have closer correlation with string theory. So maybe, the tachyon state of the bosonic string is possible there.

      Now I do not know about you, but the last place I would want to be is between two near colliding black holes. Also in what we did this becomes most relevant when the black hole horizons are within the Compton wavelength of elementary particles.

      I would then still maintain that negative mass particles in free space do not exist. It will never be possible to harvest the quantum hair excited by near colliding black holes. The most we can do is observe gravitational memory effects from this quantum information.

      Some solids have a mass renormalization of the electron so it is negative. Similarly this process with near colliding black holes can have analogues in condensed matter. We may then be able to fashion new types of superconducting materials this way. So there are technological applications, but not exactly the sort of thing that will send giant spaceships with people warping off to the stars.

    2. @Lawrence Crowell: I downloaded the pdf of your joint paper with Christian Corda, and visually scanned through it. Like all such deep technical papers it was way over my head. But I did glean a few things. If I’m not mistaken, this configuration of near merging black holes could be a test for quantum gravity in the sense of creating the quanta of the gravitational field – copious numbers of gravitons. Now, sorry if I’m going off on a tangent, but I understand that really strong spatial curvature like near a black hole would generate gravitons (assuming they exist), particularly if disturbed, based on earlier readings from the likes of Kip Thorne. There’s a 1978 paper by Kovacs and Thorne titled “The Generation of Gravitational Waves, Bremsstrahlung”, where they describe the disturbance/distortion of the gravity fields of two passing stars which changes their mutual trajectories and generates gravitational waves of low frequency just as happened in the several black hole merger detections by LIGO. And, as has been pointed out on previous blogposts here, and in the 1978 paper these waves can be thought of as coherent states of gravitons.

      In that 1978 paper Kovacs and Thorne describe this graviton generation process as the gravitational analogue to electromagnetic bremsstrahlung radiation emitted when a charged particle (electron) is deflected in its trajectory by the electric field of a nucleus. Now I kind of wondered if such gravitational bremsstrahlung was taking place on a microscopic scale in superconductors on hearing about acceleration signals emanating from superconductor condensates subjected to varying degrees of acceleration via either mechanical or electromotive means: e. g. Martin Tajmar et al 2003-2006, and others. Now, obviously, this would entail new physics, as there are no known strong gravity-like forces in nature at atomic scales that would be needed to produce such robust signals tens of magnitudes larger than classical gravity allows. But I had a ludicrously simple idea that links these signals to a microscopic Alcubierre like warp. The bugaboo is that it would require negative energy density for its realization so presumably not viable, unless there’s some loophole in the no-go theorem that you mentioned. However, this idea also ties into some thoughts on UFOs to be discussed in the next section, if it shows up.

      This other section may be in violation of the rules, even though others have presented ideas here. But in those cases they were clearly of a professional grade in contrast to the entirely amateur speculations in the next section.

    3. David wrote:"If I’m not mistaken, this configuration of near merging black holes could be a test for quantum gravity in the sense of creating the quanta of the gravitational field – copious numbers of gravitons." Yes that is an upshot of this. The tiny fraction of a second before the actual merger is a sort of Casimir vacuum configuration that is being "pumped." This should manifest itself in gravitational memory or BMS symmetry transformation of the metric.

      Generating gravitational waves has analogues with EM wave generation. The main difference is you must have quadrupole or higher momments. A dipole transition would be mdv/dt that violates momentum conservation. So in general gravitational waves are generated by bodies in elliptical orbits with some quadrupole moment. There are analogues with Bremsstrahlung raidation.

  14. Have you done or could you make a video about the possibility of reaction-less drives? I've lost interest in FTL travel years ago upon realizing the likelihood of enormous "sun"-lit worlds that can be constructed, making future space travel even more exciting, with enough materials between the stars to build trillions of habitats. (If interested, YouTube's Isaac Arthur made a 30 minute video "Continent-Sized Rotating Space Habitats", a realistic depiction of how that's possible, even likely) No FTL speeds necessary, however...
    I would be very interested in your take on reactionless drives, thank you!

  15. You say this new preprint demystifies warp drives, but after reading your description of it, I can't see how. It sounds like it's a rehash of Alcubierre's original paper, which I thought was well written and clear enough already, plus a bit of additional material that you can already learn from the "Alcubierre drive" Wikipedia article.

    "In this paper, Bobrick and Martire describe the geometry of a general warp-drive space time. The warp-drive geometry is basically a bubble. It has an inside region [and] wall [and] an outside region." Even without my elisions, this sounds just like Alcubierre's construction and I thought it was clear in the original paper.

    "You cannot break the speed of light barrier for the passengers themselves relative to space-time. So instead, you keep them moving normally in the bubble, but then you move the bubble itself superluminally." That was clear in the original paper; it was the entire point.

    "Bobrick and Martire explain that if you want superluminal motion, you need negative energy densities." That's true because whatever the details of your warp bubble generator, as long as it's localizable in a Minkowski background, you can arrange a few boosted copies of it to make a tachyonic antitelephone setup with closed causal loops, and there's a theorem that a spacetime with closed causal loops has to violate one of the energy conditions. I think the real story is the unavoidable closed causal loops, not the energy condition violation.

    "[T]he only reason the Alcubierre Drive moves faster than the speed of light is that one simply assumed it does." I thought that was clear in the original paper, where the motion is described by an arbitrary function x_s(t) and there's no dynamics relating that function to anything else. It isn't possible even in principle for the passengers to affect the function (e.g. to turn off the "drive") since part of the bubble wall is spacelike separated from them.

    "Bobrick and Martire show that for the Alcubiere drive [...] [t]he flatter [the bubble] is in the direction of travel, the less energy you need." Alcubierre didn't talk about that, as far as I can remember, but it's not new; there are published papers talking about relative energy requirements of different warp bubble shapes and I think some of them date to shortly after Alcubierre's paper.

    My own opinion is that the hype about Alcubierre's paper is due almost entirely to the vast majority of people not reading much of it except the title. Because the words "warp drive" appear there, they assume that somewhere in the body of the paper is a way to build a Star-Trek-like warp drive, and the only problems are details like where to get "exotic matter" to put in the warp nacelles. If this new preprint dispels some of that illusion, then perhaps it'll be a useful addition to the literature. But if that's their goal, they'll have to change the title to something other than "Introducing Physical Warp Drives", because that's the only part of the paper that most people are going to read.

    1. The metric term g_{tt} = 1 - v_x^2f(r) indicates there is this distortion of the "time-time" part of the metric given by a velocity v_x. The function is this complicated top hat function. See above of my post yesterday to see this. This is though a bizarre thing. For this velocity v_x in the x direction is relative to a frame. In the frame of this bubble v_x' = 0. This metric term also says there is a compression of spacetime by this factor. This defines a warp factor as a measure by how much g_{00} deviates from unity.

      If the velocity is small then this warp factor can compress the effective distance travelled, but in this metric it is slower than light. If v_x approaches the speed of light then this warp factor means this bubble is moving faster than light. So how does one set this in motion? If you do so within your frame then v_x = 0. How to establish this metric is a puzzle, and it looks to be a sort of mechanical conveyance that "always runs" and has not controls.

      The warp drive is realistically a spacetime mathematical gadget that can be used to understand better some theoretical problems. I think the prospects for this to become a real system are almost infinitesimal.

    2. Continued: As a 14 year old, ages ago, I was struck by reports of disc shaped UFO’s undergoing fantastic accelerations along the flat face of the disc; so inefficient aerodynamically. then, in a aha moment I thought maybe they are generating a dipole, super strong gravity field that neutralized accelerations on the occupants. As an eighth grader, knowing basic electromagnetics, this analogy to a dipole magnetic field generated by a circulating electric current in a loop of wire came naturally. From that point on I puzzled how one could conceptualize an exact gravitational analogue to an electromagnetic field (not like the feeble Lens-Thirring effect that I learned about years later). In a sudden 1996 epiphany the apparent answer popped into mind. In a gravity field two quantities vary as a function of the field’s strength – length scales and the rate of temporal passage. So, presto, assign one of these variables as the equivalent of the electric field and the other for the magnetic field. I chose the length variable for the equivalent of an E field and thus the time variable becomes equivalent to the M field in the electromagnetic (EM) analogy. The corresponding ‘charges’ would then be ‘spatial’ charges (length in 3D) and ‘time’ charges, analogous to electric charges and (hypothetical) magnetic monopole charges in EM.

      I dubbed this hypothetical (vector) field associated with these particles the “spatiochronetic” (SC) field, which effectively would be a consequence of an S-duality between electromagnetism and gravity. It’s then assumed this field’s strength matches the EM field strength. And, just as the electric and magnetic components of an electromagnetic (EM) wave oscillate between positive and negative potentials for the former, and north and south polarities for the latter, so the SC field would have equivalent excursions. Without going into detail it was easy to see that a stationary observer monitoring the passage of an SC wave, would perceive the volume of space bounded by the SC wave to alternately exhibit positive and negative energy states of the vacuum. Replace the ‘observer’ with an electron and entrain it at a nodal point between a negative vacuum-state region (to its posterior), and positive vacuum-state region (to its anterior), and you have the topology of an Alcubierre warp in which the electron follows a (localized) geodesic, while the overall disturbance is subject to acceleration from the global perspective.

      By assuming the SC field/waves match the strength of the Coulomb force binding electrons to their nuclei, and are one and the same as de Broglie waves, you now have an explanation for the absence of synchrotron radiation, and thus stability, of atoms. With electrons being subject to angular accelerations up to 10^22 g’s, the extraordinarily large (10^-5 g’s) acceleration signals, detected by the Tajmar group in an angularly spun-up superconductor ring, might make sense as a consequence of gravitational bremsstrahlung radiation from trillions of disturbed micro-warps, magnified by large scale coherence. And, as for those pesky aliens cavorting about our skies, maybe they figured out how to synthesize these speculative spatial quanta in great abundance. Circulate those in some kind of coil in the outer circumference of the disc (or tic-tac), and bingo by Maxwell’s laws you generate a bipolar temporal field. Or vice versa, circulate speculative temporal quanta and generate a dipole spatial field.

      But, alas, with the Hawking-Penrose energy condition prohibiting negative energy density, these wild and wooly ideas are fit only for a sci-fi plot.

    3. "As a 14 year old, ages ago, I was struck by reports of disc shaped UFO’s undergoing fantastic accelerations along the flat face of the disc; so inefficient aerodynamically."

      Yeah, no:

      Kenneth Arnold: ""the objects moved like saucers skipping across the water."

    4. When I was around the ages of 11 to 14 the idea of UFOs as alien spacecraft was some source of wonder. Later these things faded away. As my understanding of reality improved these things seemed less important.

      I suspect humans will never venture outside the solar system. Our probes and robots might, but I doubt that flesh and blood humans will ever venture out there. I wrote a book meant to introduce basis physics of mechanics and relativity on sending probes to other stars. Just doing this will be a huge venture. Sending humans to other stars would be many orders of magnitude more difficult.

      I suspect space aliens face much the same. Even if by some improbability there is some ETI around a star a few 10s of light years away, I suspect they too would never come here. Further, I doubt there are more than maybe one ETI per galaxy in any period of time.

    5. Lawrence Crowell: Way back in the 90’s when I concocted the (unworkable, due to unphysical negative energy) S-duality idea of a role exchange between electromagnetism and gravity, yielding a gravity-emulating, length-time Maxwell field on the one hand, and a ‘metric’ mimicking our space-time with electric and magnetic parameters, or an electric-magnetic continuum (a la Minkowski), I had been wondering if there might be some connection to superstring theory. Back then Ed Witten’s M-Theory was all the sensation, spawning an avalanche of new papers. I noted that the graphic depiction of M-theory, like a stretched tent (seen from above) with ‘pegs’ holding the six ‘corners’ down, embodied S-dualities and T-dualities between the six ‘pegs’, or individual sub-theories. So, a natural thought was; could that EM/GR duality be embraced within a larger duality framework involving all the forces of nature, and could this be the real physical meaning of M-theory?

      That larger, more complex, framework envisioned dividing the Standard Model into three sort of equivalent elements – strong force (QCD), electroweak force, and gravity (possibly in conjunction with the Higg’s field), that would have crystallized out after the big-bang, and before reaching our current electroweak symmetry breaking temperature. Now with three elements, by the permutation rule (N!, where N = 3), there are six possible transpositions, which might correspond to the six sub-theories in Witten’s M-Theory, where presumably one corresponds to our Universe. A few years after Witten had his remarkable idea, Randall and Sundrum startled the physics community with their brane model, where our Standard Model resides on its own 4D brane within an infinite 5D space. Naturally, this led to the thought that maybe the other five possible sub-theories of M-Theory might reside on their own branes, distinct from ours, having crystallized out differently following the big-bang.

      To be honest I don’t really understand M-Theory, and concepts like the AdS/CFT correspondence at even remotely the level professional do, so these laymen-level ruminations are for sure not tenable, not to mention the unphysical energy problem. But, I’ve incorporated the imaginary EM/GR duality as a plot device in a sci-fi novel, set 300 years in the future, when humankind is on the threshold of developing its first warp drive to reach the stars.

    6. Some of what you say is a bit outside theoretical constructs. So it is hard to comment. M-theory is the observation that various string types can be transformed into each other by STU correspondences. These correspondences are not really symmetry transformations in the standard sense. The S-duality is based on the Montenen-Olive duality that is just a correspondence between electric and magnetic monopole strengths. There is T-duality that is based on linear fractional transformations so that the increased tension on elongating a string is dual to a reciprocal of that for the winding number of a string. U-duality is a sort of hybrid. What is unknown is what is the full symmetry transformation between the various string types.

    7. Lawrence Crowell stated 6:11 AM, November 24, 2020: “I suspect humans will never venture outside the solar system”.


      I followed basically an opposite tack to you re the UFO subject in early life. At the age of 14 I was a skeptic, assuming all such reports were misidentified aircraft, meteors, etc. Then my twin brother took out two books on the subject from our local Teaneck, New Jersey library and I was hooked. In those early years of my exposure to this subject it became increasingly apparent that a significant percentage of eyewitness accounts stood out from the background ‘noise’ by exhibiting a narrow range of behavior that clearly seemed to distinguished genuine UFO reports from misidentified natural and manmade phenomena. In short, I treated this filtered set of reports as empirical evidence for possibly novel technology.

      Of special interest are manifestation of phenomena that might be construed as evidence for a warp drive capability, aside from the more indirect observations of high-g accelerations/decelerations pointing in that direction. A case that especially stands out, but it is by no means unique in the literature is the experience of Sgt. Ben Thompson of the Wanaque, New Jersey reservoir police force. He was on patrol on a night in January, 1966 when he spotted an intensely bright auto sized object approaching the reservoir at low elevation. In his own words as he was being interviewed: “No. The water was pulled up. It was sucked upward. But not off its bed. The flying object would just raise a whole big area of water – I don’t know – for maybe two hundred and fifty feet. As far as I could see. The object would just pull at the water and I could plainly see the water rising. And when this thing flew away from the area, the water would just settle right down again.” He further elaborated that the water was lifted 2 to 3 feet off its bed.

      Watching it move low over a nearby hillside Sgt. Thompson stated: “And that object just pulled the trees right together. Each tree just mingled in with the other one. They came together just as smoothly as could be. It wasn’t a violent motion. It didn’t break the trees or anything like that. It would be just like somebody took a big rope and circled it around four or five hundred trees and then ran it through a chain-block and started pulling those trees together. And they’d come together nice and slow.” Since it was night time he was able to observe these phenomena due to the extremely intense light the object gave off, which illuminated the surrounding area to quite a distance.

      Granted, such a report is quite incredible but taken at face value suggests that the local space is being powerfully warped in a contraction sense as in the forward region of an Alcubierre warp drive. If some kind of particle exists in nature’s stable which affects space or time at an intrinsic strength comparable to the electromagnetic field, it might serve as the basis for such a technology. Unfortunately, the spatiochronetic field idea previously enumerated is ruled out due to unphysical energy requirements. Nonetheless, I’ve been thinking of trying to calculate how much of a current of the imaginary spatial charges in that model would be needed to produce the observed effects in this report.

    8. Lawrence,

      In the previous comment I meant to say “how much of a current of the imaginary temporal charges”, as that would generate a bipolar spatial field – contracting length scales on one side and expanding them on the other side. Of course I realize this idea is not viable due to the need for negative energy density. But as a thought exercise it would be fun to try to figure out. This, of course, would differ from the normal situation where both time and space are affected by ponderable masses. I’m a bit groggy this AM to do any deep thinking, but as a starting point I was thinking of the tides the moon raises at a distance of 384, 400 kilometers and a mass of 7.35 x 10^22 kg. But again that’s with general relativity and the curving of space-time. But maybe I can get an approximation for length contraction only, assuming a field equal in strength to electromagnetism.

  16. Just being pedantic but this part

    "The way you normally solve these equations is to use a distribution of energies and masses at some initial time. Then you can calculate what the curvature is at that initial time, and you can calculate how the energies and masses will move around and how the curvature changes with that. "

    isn't accurate even at the level of precision of the post. You also need to specify a Riemannian metric and a two tensor, which will be the restriction of the Lorentzian metric and the second fundamental form of this time slice.

    1. When I say "curvature" I mean the curvature tensor. I assure you it's totally accurate "at the level of precision of the post" which is for people who have no idea what a metric, a signature, or a two tensor is.

    2. But as written, it gives the impression that the specification of the stress-energy tensor at a time determines the solution. That is far from true. There are infinitely many solutions with the same T, say vacuum solutions.

  17. Where is the link to this paper?

    1. There isn't one. It hasn't appeared yet.

    2. Paper can wait. Is there any evidence that anything cannot go faster than the speed of light under different circumstances? Moreover, is taken into account that the speed of light is endogenous and "warp drive" exogenous?

  18. Warp Drive is purely fictional, abstract device.
    There is EM-Drive which is made of metal. Is it works? How it works?

    1. The warp drive is FAPP a mathematical gadget. The EM drive is an actual device, but nobody has concluded it does much of anything but send EM waves out an antenna horn.

  19. What a lot of fun this was to read and think about about. Perhaps a much, much, much slower than speed of light experimental warp drive can be developed someday to begin to test it out. Even that would be an unimaginable advance in getting around the solar system and beyond, or at the very least get us a step closer to toward proof of concept.

  20. "Another reason I find this exciting is that, while it may look now like you can’t do superluminal warp drives, this is only correct if General Relativity is correct. And maybe it is not. Astrophysicists have introduced dark matter and dark energy to explain what they observe, but it is also possible that General Relativity is ultimately not the correct theory for space-time."

    In other words, one can explain some observations by introducing additional sources, or by modifying GR. The "dark matter versus modified gravity" is one aspect of that. (The fact that Mercury's perihelion procession is explained by GR and not by Vulcan was a case when modified gravity was the answer and not dark matter.) However, although I am sure that Sabine agrees with me here, some people (e.g. David Merritt) think that dark matter and dark energy are some sort of extensions to GR. So don't misread what Sabine wrote: GR is correct and dark matter and dark energy are additional sources OR GR is incorrect (or, of course, both).

    Of course, even if GR is incorrect, that does not imply that some sort of practical warp drive is possible. :-|

    1. Dark energy is just a cosmological constant. Much of the main physics can be found with just Newtonian physics. What makes this a puzzle is that if this is quantum zero point energy then how it is so small is unknown.

      Dark matter is a complete unknown. At least with dark energy we have a connection to general relativity and FLRW or de Sitter spacetimes. Dark matter is unknown and the WIMP hypothesis for DM is moribund at this time.

    2. Certainly if Dark Energy is a cosmological constant it makes much more sense as an extension of GR than as a source. You'd have to be really weird to have a constant as your stress tensor (and you'd expect to have fluctuations around that constant, which we don't see), but it's perfectly reasonable looking plopped into the Einstein Hilbert action.

    3. Not only is dark energy a bad name (as Sean Carroll wrote, everything has energy and many things are dark), but using the term can seem to imply that something more complicated than the cosmological constant is needed. However, there is no observational indication that something more complicated than a cosmological constant is needed.

    4. Dark matter might be unknown, but the alternative is to assume that we should somehow magically know the contents of the Universe. Linnaeus came up with his classification scheme even though other species were discovered afterwards.

      Certainly not everyone believes that the small value of the cosmological constant is a problem.

    5. Phillip Helbig: Thanks, that was an interesting paper.

  21. Lawrence Crowell1:42 PM, November 25, 2020

    "Dark energy is just a cosmological constant. ... how it is so small is unknown."
    We've been through all this many times. It is not known to be "so small". It is just not known why the value is what it is - same for the speed of light and any other "fundamental" constant.

    "Phillip Helbig1:00 AM, November 26, 2020

    "Certainly not everyone believes that the small value of the cosmological constant is a problem."

    Clearly it is not a problem - it is physical reality. The measured value is the measured value. And it is not a question of belief. It is simply a question of what the empirical facts are. Everything else is just speculation.

    How's that paper coming along? It's taking an awfully long time. Are you fine-tuning it?

    1. While I (along with Rovelli, so I am in good company) disagree with the standard answer, you seem to have not understood (what is widely perceived to be) the problem.

    2. Phillip Helbig3:55 PM, November 28, 2020

      It is not about the company you keep, it is about empirical evidence. There is some empirical evidence that the universal expansion is accelerating, as you convinced me. Dark energy is obviously a complete speculation (it is what it says on the tin, unobserved), and even relying on a CC in the Einstein equations to describe the acceleration is possibly suspect as the current gravity model can't even correctly describe the motion of orbiting stars in a galaxy. Cosmologists should focus on fixing this real problem instead of sprinkling things not known to exist like dark energy, dark matter and inflation into their models to force a fit and publishing CUP books about baby Jesus.

      **** Based on completely basic logic, though, if there is a CC and it is measured to be 10^-57 or 10^-1 sextillion or whatever, that contributes zero evidence to the fine-tuning hypothesis. ****

      Do you agree? If the Great Rovelli told you, would you agree?

  22. I'm reminded of, perhaps apocryphal, letter written to Einstein accusing him of setting a speed limit to the universe. It amused me, as it demonstrated a lack of understanding of what physics is. It looks like warp drives can get round that 'speed limit' so long as we can find that dratten negative energy!

  23. Sabine, you say:
    " … this is only correct if General Relativity is correct. And maybe it is not. Astrophysicists have introduced dark matter and dark energy to explain what they observe, but it is also possible that General Relativity is ultimately not the correct theory for space-time."

    Several problems in cosmology can be explained if we assume that General Relativity is not correct. For instance dark energy. Question now can be, to which extend we have to change GR to have a solution for such problem. And to concretize an example: would it really spoil Einstein’s formalism for GR if we assume that speed of light c was different in former times?

    A. Albrecht and J. Magueijo have shown (in 1999) that several problems can be solved with this assumption; without leading to logical conflicts. To take an example here: if we assume that c was slightly greater some billion years ago, the problem of dark energy is immediately gone. Because with a greater c a certain red shift will yield a higher speed for the radiating object. And so, if the speed of supernovae I was if fact higher at former times, there is no acceleration and so no need for dark energy.

    If c was much greater in former times, the case of cosmological inflation is also explained.

    Now one could ask the question, why and in which way c changes. It is not too difficult to find a physical model for that.

    1. More possible way is that the principles of GR are very correct but we have not understood them deeply enough.

    2. If GR would be very correct, why do we have these cases like dark matter, dark energy, and inflation? And why does no one of main stream have an idea how to progress?

    3. An example. Now we understand quite well dipole matter, normal matter. Gravitational interactions are quadrupole waves. If only there are exotic (dark) matter structures that can be formed for quadrupolic measures, not for dipolic...

      Still, the normal matter structure with quarks might be modelled even as octopole oscillator.

      Then we know the deep connection between the dynamics of geodesics and the energy of matter structure. What if dark exotic matter is the very larger structures than atomic? In specific constraints the quantum logic could be the same as with atomic but delays are looong and uncertainties by statistical data merely not observable in human measuring scale directly...

      That's the way of thinking i'm considering an intuitive manner to find out new physics.

    4. Eusa:

      Is my information correct that these particles, which interact by dipolar or quadrupolar fields, have never be seen up to now?

      I feel very sure that such particles will not be found in future. It is a search for the wrong subject. The investigations should address the theory (or the theories) of gravity themselves.

    5. Electromagnetism has dipole and normal matter oscillates as dipolar field. We can observer normal matter daily, cannot we?

      Who gess, the dark matter can oscillate as quadrupolar field and self-interact just like normal normal matter dipolarly...

  24. General relativity is full of surprises. I remember Jack Wisdom's 2003 paper in Science on "swimming" through space time. He came up with a scheme for a partially rigid body to move by cyclically changing its shape. This sounds like something a cat would do to land on its feet. Apparently, it takes advantage of the curvature of space time.

    He admits that it doesn't move one far. A one meter object making order of one meter moves only advances 10^-23 meters per stroke, but with higher curvatures ...

  25. Dr. Hossenfelder;

    A very enlightening piece, thank you for this post, and for some of the personal insight. For me your timing for this post is very good as I am sorting through some of my own thoughts on what else physics can tell us. I tend to follow your position on fundamental physics. That is look at what we have discovered and ask questions and dig into what we do not understand about what we have discovered so far. Don't chase the unknown until we really understand and have answered all of the questions about what is known.

    If I may be so bold as to offer a philosophical thought that is inline with your post;

    There is no experiment anywhere that can be used to test string theory, parts of SUSY and/or explain why unification of quantum and relativity is necessary.

    Since the beginning of recorded history millions upon millions of people have provided information and evidence about UFOs/ETs and Spirits/Beings (paranormal)

    Todays scientist will tell me/us that string theory, SUSY and unification are real but UFOs/ET and Spirits/Beings are not.


  26. I’m puzzled as to why one needs to be enclosed in a “bubble”. The “warp” that is envisioned is really a self-replicating gravitational field that a spaceship would be attracted to. The ship and its occupants would be in a constant state of free-fall until the field was shut down. Stopping should only require the pilot to reverse the direction of the field so that the warp trails the craft until one reaches a velocity more amenable to maneuvering.

  27. Could these drives enable time travel to the past?
    (If we live in a closed Gödel universe)

  28. This is entirely too much speculation for a paper nobody can even see to read



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