Updated Math Model for Warp Drives and Classes of Future Warp Drives

There is an update of a mathematical and physical model for a warp drive.

The Alcubierre warp drive is an exotic solution in general relativity. It allows for superluminal travel at the cost of enormous amounts of matter with negative mass density. For this reason, the Alcubierre warp drive has been widely considered unphysical. In this study, we develop a model of a general warp drive spacetime in classical relativity that encloses all existing warp drive definitions and allows for new metrics without the most serious issues present in the Alcubierre solution. We present the first general model for subluminal positive-energy, spherically symmetric warp drives; construct superluminal warpdrive solutions which satisfy quantum inequalities; provide optimizations for the Alcubierre metric that decrease the negative energy requirements by two orders of magnitude; and introduce a warp drive spacetime in which space capacity and the rate of time can be chosen in a controlled manner. Conceptually, we demonstrate that any warp drive, including the Alcubierre drive, is a shell of regular or exotic material moving inertially with a certain velocity. Therefore, any warp drive requires propulsion. We show that a class of subluminal, spherically symmetric warp drive spacetimes, at least in principle, can be constructed based on the physical principles known to humanity today.

Miguel Alcubierre in 1994 require a Jupiter mass of negative energy. Negative energy might not exist and humans cannot produce any negative energy. Bobrick and Martire suggest using regular massive gravitational force to bend space time. They still need a planet-sized mass or something that warps space as much as a planet’s gravity. Planets exist but that level of warping of space is still far, far beyond capabilities and any reasonable development path.

Nextbigfuture reviewed this work in November, 2020.

The researchers propose classifications of future warp drives.

Class I: Mild subluminal warp drives: These would be less than the speed of light. Spacetimes of this class approach the flat Minkowski spacetime in the trivial limit. Non-trivial members of this class contain spacetimes with region Dwarp sufficiently curved, so that tetrads of observers Oin and Oout,co differ significantly from each other, i.e. the observers read off different rates of clocks and lengths of rulers. At the same time, such
spacetimes also contain weak-field solutions corresponding to classical shell-like objects moving with subluminal velocities and weakly modifying the state of the spacetime inside them. Such solutions are possible because the Dwarp region may be set arbitrarily close to being flat, rendering the whole spacetime arbitrarily close to Minkowski spacetime.

Class II: Mild superluminal warp drives: These spacetimes are characterized by the vector field ξ being spacelike or null everywhere. Consequently, such warp drives have luminal or superluminal velocities, i.e., vs ≥ c. These spacetimes also admit a trivial limit, wherein they reduce to flat Minkowski spacetime. Weak-field members of the class correspond to small amounts of ‘superluminal matter’ in the region Dwarp introducing small differences in the measurements of frames Oin, Oout,co. By ‘superluminal matter’ we understand the matter at rest with respect to a space-like reference frame. In the case of the stress-energy tensor for a perfect fluid, such matter violates the dominant energy condition. A general spacetime of this class introduces nontrivial differences between frames Oin and Oout,co. Since superluminal matter cannot be produced from physical matter, and since null or spacelike tetrads cannot be associated with physical observers, the spacetimes of this class have limited interest.

Class III: Extreme superluminal warp drives: These spacetimes are defined by the vector field ξ being timelike in the inner region Din, but null or spacelike in the asymptotic infinity of the outer region Dout. The remote comoving observers in such spacetimes move luminally or superluminally relative to the resting timelike observer Oout, i.e., vs ≥ c. This class of spacetimes does not contain trivial solutions and the warped region Dwarp is sufficiently curved to allow timelike observers Oin to be moving superluminally relative to the timelike observer Oout (and as a consequence, the timelike observer Oin will be travelling back in time from the point of view of yet another remote timelike observer O0 out). At the
same time, the comoving observer Oout,co is formally superluminal; in other words, remote timelike observers cannot be comoving with a warp drive of this class.

Class IV: ‘Extreme’ subluminal warp drives: Spacetimes of this class are defined by the vector field ξ being null or spacelike in the inner region Din, but timelike at the asymptotic infinity of the outer region Dout. Since the comoving observer Oout,co is timelike, such spacetimes are subluminal, i.e. vs < c. Since the Killing vector is spacelike in the inner region Din, no timelike internal observers can be at rest relative to the inner boundary of the drive ∂Din. This property bears similarity to black hole spacetimes, except for that the inner region Din for this class of spacetimes is flat everywhere. A necessary condition for spacetimes of this class to be physical is that the Killing horizon coincides with the boundary of the inner region, ∂Din. Otherwise, some fraction of matter in the region Dwarp will be superluminal.

For subluminal velocities, the Alcubierre drive belongs to Class I, mild subluminal warp drives. For superluminal velocities it belongs to Class III, extreme superluminal warp drives.

The math model suggest the most optimal way of reducing the total energy, as measured by Eulerian observers, is by flattening the shape of the warp drive.

The flattening of the warped region may be adjusted with velocity so that the drive preserves the same total energy.

Superluminal solutions can be constructed which satisfy the quantum inequalities.

Written by Brian Wang, Nextbigfuture.com

25 thoughts on “Updated Math Model for Warp Drives and Classes of Future Warp Drives”

  1. FTL is a big no. Not going to happen. Ever.

    If you want to know what the future of human space travel is, google "The StarLost". Think generational ships. Arks. 10,000 year voyages. Yeah, I know its not sexy, but then reality never is.

  2. If I am understanding you correctly, it is really a time machine for moving into the future (if it worked). If you went on a "circular" trip, just traveling away from the earth and back again, you would arrive far in the future. If you arrived back again 10k, 20k or 50k+ years in the future you would not likely need to inhabit another star system. Either humanity would have wiped itself out by then and left you a planet to inhabit we know works for humans, or you would have access to tens of thousands of years of technologies in an extremely advanced society.
    You could tool it from a few hundred years to great amounts of time depending on your goals. To receive advances in biological sciences like life extension, make it just a few hundred years for a relatively simple trip with todays technology. You could take it to the extremes of the lifetime of the human species, and maybe your genetic code itself will be valuable to a society that has suffered from genetic manipulation and/or degradation. Really we would just be limited by our tech.
    Interesting possibilities either way.

  3. Interestingly they say that you need a massive gravitational body to produce this. Like planet-scale. But that isn't the only thing that warps space-time. Energy does the same thing ( I mean, technically that may be why mass is warping it, but you get me).

    So maybe a big enough energy field could do it. Maybe a miniature blackhole's Hawking radiation?

  4. Can you expand on why going faster than 0.9C is deadly? 

    And how does one determine such a speed? My understanding is that you can only have a velocity relative to something else. And Earth is already traveling at well above 0.9C relative to the most distant observable galaxies.

  5. Maybe so, if the change from procaryote to eucaryote is as unlikely as people speculate. However, no matter how unlikely, there are probably closing on an infinite number of situations in which it could happen..

  6. What can I say, this is so cool I can't contain myself… That said, since we can't generate the huge energies (yet) to according to the current theory, how about a compromise? Say we use the mass of a large stellar object, like Jupiter, and use it to translate our momentum into gravity, Think of a top that you make spin on top of a desk (work with me here, because I am making this up as I go). Once you impart "spin" it has a value of embedded inertia.

    The same mass, now moving very quickly, can create (or direct) a great deal of energy. How to capture that energy? First thing that comes to mind is a flywheel. That spinning top on a desk? Now think >1,000 order of magnitude. And perhaps 10,000x expensive, depending on the defense contractor who gets such a contract. Hey, when Ike warned us about the military-industrial complex in 1960, notice he never said they were cheap?

  7. That assumes life isn't rare. We don't know that.

    It seems it's hardy and contagious, once it emerges, but the problem could be for it to start in the first place.

    It won't surprise me if the Solar System was infected with bacterial life from the many exchanges of material between the planets, but at the same time, we'll eventually figure out the galaxy overall is rather empty.

  8. If true, this ability to move on and on in our short lifetimes means the galaxy has already been totally settled.

    But no sign of it so far.

  9. I've given up on doubting that there might be a way to achieve FTL. Too many unexplored, artificially declared limits on scientifically proven "reality".

  10. Despite not making the real trip any shorter or you any faster, it would still be a game changer.

    If you can send something at modest sub-relativistic speeds to another star (something an Orion, a laser sail or a fusion rocket could do), you could also send people on a one way trip there and arrive with the same crew, just with the parts outside the warp shell a bit older.

    The mission would require a good, long lasting power supply, but you wouldn't lose any skills on your crew nor have other ethical and societal problems coming from a long confinement. The same people going would be the ones arriving (if nobody drops dead mid flight), nothing of sending unborn kids to grow and die on a tin can without their choice. Also, much less catastrophic collision risks while going at a more leisurely pace.

    Also, if the warp shell can be switched on and off, they could schedule turning it off every so many real years, to do regular checkups and maintenance, and getting up to date on the latest news from the increasingly faraway Earth.

    The fact you'd be losing everyone you knew can't be avoided, but people going to settle another star aren't planning to see again anyone contemporary to them anyway, except those making the trip along with them.

    Some schemes including ISRU and replenishing energy (e.g. hydrogen and antimatter mining from other planets) would allow practically endless missions, slowly roaming from star to star.

  11. They mentioned the STL warp shell still needs to be pushed by a conventional thruster.

    So it seems you could indeed get to 0.99c, but you'd be spending as much energy as pushing any regular lump of matter while doing it.

    The difference the STL warp drive brings seems to be the time ratio inside the bubble and outside can be very different.

    The trip inside the STL bubble could look shorter, arbitrarily so, as per their description.

    So in practice, you could take the STL warp drive ship, push it with any thruster like a chemical rocket, turn the STL warp drive on and travel to another star at slightly above solar escape speeds, taking millennia to arrive, but inside the warp bubble you could perceive the trip took very little!

    So it could act more like time dilation at slow speeds, or like a hibernation pod than a Star Trek warp drive, but it would still solve two of the biggest problems of interstellar travel (supplies and perceived trip duration). I assume you'd still need energy for the warp shell across the trip though.

    With it, you could travel to another star with whatever technology you have allowing solar escape speeds, and do the whole trip, seeing the end of it yourself, but you'd be leaving everything you knew behind.

    Of course, the need of a power supply would make you want to minimize the trip duration, going as fast as you can, but you could do crewed interstellar trips with a starship going at 1%-2% c, if your power supply can survive a few centuries.

  12. If one could use warp drive to move without anything other than the compression of space time, then it’s a game changer even without superluminal velocity. All of a sudden you dispense with the need for reaction mass, needing only the fuel to power your warp drive. Not only that, but since everything inside the bubble remains stationary and isolated from the universe then acceleration and deceleration do not affect the occupants nor does impacts from molecules and dust which otherwise would vaporise a very fast vehicle. In short, with an adequate power supply and working warp drive of up to a significant fraction of c and the entire solar system becomes fully accessible and nearby stars reachable for human exploration and settlement.

  13. The Alcubierrie warp drive falls into Classes I and III on this list.
    How fast are we talking when it comes to subliminal drive? Could we achieve 0.99c like the Enterprise does with impulse engines?

    And if time dilation still effects the occupants of the space craft, then there are many other cans of worms still open. I'm certain that going this fast would kill you. You're basically becoming input mass for the supercollider. By my napkin estimates (lost the napkin years ago) anything over 0.9c is death, and that's assuming there aren't other nasty surprises before that speed.
    Can we block outside influences so that normal or normal-ish space-time is achieved within the bubble?

  14. I hate to throw cold water on these things, but . . .

    Given that space-time itself may actually be a wave, with its origin at the Big Bang Event, and the universe expanding with each wavelength it propagates (at the cost of magnitude, i.e. entropy), and wavelengths do not change without outside interference, I really don't see much hope that we can reduce or increase the rate at which it propagates on any scale, local or universal, other than on a purely relative basis related to what we think of as the rate of time.

  15. Ok, thanks, will do. In return I will recommend the Mars trilogy by Robinson. It's a hard sci-fi about the colonization of Mars. It's so real and well founded in science that, in my mind, it doesn't even feel like fiction. But the story is also pretty good.

  16. I would.

    Larry Niven and Jerry Pournelle (who worked together sometimes) are both good writers and have a solid grasp of modern space oriented science. Yes, they are prepared to throw a couple of "magic" things in there, because otherwise you just can't travel to other stars while your story is happening, but otherwise they are pretty solid.

  17. So, the STL warp drive could actually be like Larry Niven's "Known Space" Slaver Stasis fields?

    Those fields made time go much slower inside the volume of effect, resulting in practically invulnerable "force fields" that simply stopped time for whatever was inside.

  18. Even STL warp would be quite useful. Think about it: the main thing that's hard about colonizing other star systems is the speed required. But with STL warp, as long as you're willing to leave everyone and everything you've ever known behind, you could experience a thousands-of-years trip in an arbitrarily short subjective time. This means that the delta-v required is not that much more than the escape velocity of the Sun.

    EDIT: Nvm, I meant the solar escape velocity from Earth orbit.

  19. To the extent I understood the paper, no, they claim that STL warps are possible without negative energy/mass, but FTL always requires it.

    They also established an important point: You still need something pushing the warp around, it doesn't move on its own. All the warp gets you is the ability to go faster. Maybe only subjectively?

  20. Are they claiming FTL travel without the negative energy density? Or do they have the same problem as Alcubierre in that respect?

    The abstract says Alcubierre requires negative energy density and goes superluminal. Then they say that this new result allows SUBluminal with positive energy density. And they say another version of it allows SUPERluminal. But it doesn't say whether the superluminal version of it requires negative energy or not. That's a pretty important detail to leave out!

Comments are closed.