Physical Warp Drives (2021)

Indeed, if gravity were not described by a QFT at low energies, we would need an extremely convoluted explanation for why quantum effects aren’t always destroyed by the mere existence of gravity. In short, gravitons are the Occam’s razor solution, not having gravitons would be extremely hard to reconcile with the existence of gravity at any scale, and when you dive into the math you see why.

In any case, none of that directly answers your question about gravitoelectromagnetism, which actually is just a way to rewrite the Einstein equations in a particular way that’s valid only sometimes. And that could only be unphysical if Einstein’s equations are unphysical in the same regime. There’s no regime we’ve tested in where the Einstein equations aren’t empirically valid, and they do come naturally as the classical limit of the gravitational QFT (the limit implies there can be small corrections of a particular form, however).

No, it's a real effect and has been measured.

> the equations look similar, but there's no physical justification

Yes, there is; the justification is classical, not quantum, and does not depend on having any quantum theory of gravity. GR is a classical theory, and gravitomagnetism is present in it, similar to the way ordinary magnetism is present in classical electrodynamics. The difference is that electrodynamics is based on a vector field (the 4-potential) while GR is based on a tensor field (the metric); but that difference just changes some particular numerical coefficients in the equations for gravitomagnetism as compared to ordinary magnetism (for example, the gravity analogue to the Lorentz force has a factor of 4 in front of the v x B term). But these are classical fields, not quantum fields.

Not exactly. In the standard cosmology, in an equatorial slicing (cf. slicing a cone with each plane perpendicular to the axis, giving circles) of the expanding universe, space expands very slightly at each point in space as the cosmological time ticks by. If we choose a point (p,t) and some coarsening procedure to reduce the count of points immediately around (p,t) to a finite number, then very soon after at (p,t+\epsilon), and using the same coarsening procedure, there will be more points immediately around p. So, for example, for something (p=const,t_0) we might count seven points in which we could find that something at t_1: {(p,t_1),(p x+1,t_1),(p x-1,t_1), (p y+1, t_1), ...}. But there might be, say, twelve points immediately around (p,t_n), twenty-four around (p,t_{n+n}), etc. The same thinking applies at every point in space with the same value of t. As the universe ages, the numbers of points in space is already enormous and at each of those points in space we add more points.[1]

To that last paragraph we add a system of coordinates where there are cosmological observers[2] "stuck" at a particular spatial coordinate like (x,y,z) at all times, observing more space appearing between them, requiring coordinates in between to label that space. Physically these observers, if already distant, see each other's image becoming smaller, dimmer, and redder, as if they were accelerating away from each other. Physically neither observer detects such an acceleration -- they are in perfect free-fall.

The metric expansion, and accelerated expansion, can be (and is usually treated as) purely local. Nothing interacts superluminally, and there is no need from observation to have large nonuniformities in local expansion in the known universe. That is, at large enough distance scales, the local expansion at any point is well-modelled as constant at all points and at all times: the cosmological constant. (At smaller distance scales, in regions dominated by gravitationally collapsing matter (including dark matter), the local expansion is zero. "Manhattan is not expanding", nor is the rest of the solar system or anything in our galactic cluster as far as we can tell).

In the unknown early universe, various approaches to cosmic inflation essentially generatesa lot more new points around old points than expansion does, and the difference in inflation around any point can be large (loosely, the number-of-points-generated-at-point-p gap between "expanding" and "not expanding" is much narrower than the gap between "inflating" and "inflating less" let alone "not inflating").

> 93-billion light-years wide universe that's only 13 billion years old

There are a lot more points between galaxy clusters in an expanding universe than there is in a non-expanding universe. (Inflation already stopped making new points in space long before the first protons formed, let alone galaxies).

For the most part part galaxy clusters tend to become more compact over time; the matter in them is thick and trending thicker. Expansion doesn't arrest that trend at all. Galaxy clusters shine across the electromagnetic spectrum, and also expel neutrinos and some amount of hot dust and gas. That thin expelled matter does not block expansion very close to it, and so thin matter gets smeared across new points as they appear in its immediate neighbourhood. In the cosmological frame this means stretching their wavelengths or equivalently reducing their kinetic energy or equivalently reducing their temperature adiabatically. However, the expansion is not strong enough to break molecular bonds, so molecules will cool; they won't snap apart because of standard expansion. (Likewise expansion doesn't ionize atoms or fission nuclei; it barely distorts clouds or streams of thick-enough molecular gas that float out of galaxy clusters. The key to turning expansion off is thickness of matter, which may be generated by electromagnetic interactions or even just gravitation).

Now, let's talk about "actual" FTL. There is "local" FTL in which a massive object and a pulse of light starting at the same point ends up with the massive object winning a short race ("short" being e.g. micrometers to kilometres). Our notions of causality arise from the structure of spacetime ("a Lorentzian manifold" gives us a particular <https://en.wikipedia.org/wiki/Causal_structure>), and (if not interfered with, i.e., in vacuum) massless objects (like a pulse of light) move at a particular speed that no massive object can exactly reach. A local FTL event is incompatible with a Lorentzian manifold, but if we see local FTL, out goes the objection that "everything we do strongly supports our idea that the universe is Lorentzian". (<https://en.wikipedia.org/wiki/Modern_searches_for_Lorentz_vi...>)

While reliably observing a local FTL event might seem inconvenient for the theories, relativists could certainly cope with what they would see as a breaking of the global hyperbolicity condition of our universe (which we get from having local Lorentz Invariance everywhere).

Alcubierre-like ideas do not break local Lorentz invariance; there is no local FTL, so it is less disturbing in some ways than tachyons or whatever. Indeed, Alcubierre neatly packaged up his idea into a "bump function" on a perfectly normal Lorentzian spacetime.

The Alcubierre idea essentially just breaks the constant cosmic expansion at points immediately around the "ship", making a lot lot lot more points behind the ship and destroying (or shrinking) a lot of points in front of it. It's a local effect confined to the region around the thin shell of the "warp bubble". The hardest thing is to make the space around the ship relax back to something close to what it was before the bubble zipped through it, and that's the source of many of the objections rooted in properties of as-yet-unobserved matter.

However, if we assume that this is all workable and ship or computer memory chip or whatever goes from A to B faster than light can, our global causal structure cannot be the strongest ones we can get by having local Lorentz invariance everywhere.

In principle we are probably ok climbing down to nearly any rung of the <https://en.wikipedia.org/wiki/Causality_conditions> however for most of those we can't "just" take a set of initial values and evolve them forward, which is everyone's preferred approach to problems in general relativity. The intial value formulation of general relativity came decades after exact solutions like Schwarzschild's and Lemaître, Tolman and Bondi, and perturbations upon all those, so this is a luxury that was not always available to relativists, and at least if future relativists lose global hyperbolicity they will have computers with lots of fast memory.

Examining a warp bubble spacetime that is on a lower rung of the causality ladder essentially requires completely specifying the values of all the fields at all the points in a large region as an "exception" sandwiched between two time-separated "initial" values fields. This requirement was part of Alcubierre's motivation to think about a warp bubble -- he already had an interest in the initial values approach and where it becomes hard to use and where it breaks down (indeed he wrote a textbook that deals with that, <https://academic.oup.com/book/9640)>).

As Alcubierre suggests in the quote you found, global hyperbolicity is what we appear to have in our universe, and there is nothing obviously "enforcing" it. So why isn't there obvious FTL in many places (or even everywhere)? Who knows. There is no "right" answer to that, and it might end up that it's just a feature of our universe like its three spatial and one timelike dimension. (cf. <https://en.wikipedia.org/wiki/Globally_hyperbolic_manifold>).

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[1] This invites a Zeno's paradox view of the metric expansion. At later times there are more steps that one must take between "0" and "1" (and at the same time even more steps between "1" and "2" on the same ruler). One has to visit every mark on the ruler between origin and destination, but the number of marks doubles and re-doubles and re-re-doubles over the course of one's travel.

[2] Experts will recognize that HN is a place for informal descriptions, and that here I flick (without explicit warning) between thinking in terms of comoving coordinates (more space between each coordinate, or more time for a pulse of light to move between two coordinates) and, without saying so, thinking in terms of Fermi coordinates (e.g. <https://link.springer.com/article/10.1007/s00023-011-0080-9>) when taking a more, um, expansive view of Raychaudhri's equations. I apologize if that makes this harder to follow for people familiar with the mathematical details of physical cosmology.

This is a guess, i.e. one possible outcome physicists are considering.

People have proposed alternative outcomes of FTL like the (in my opinion much more sensible) Novikov consistency principle, which roughly proposes that spacetime and the entities it contains (e.g. an observer's wordline) should be looked upon as a whole, in the sense that they need to be self-consistent. Spacetime is not time-dependent and does not evolve, so it does not make much sense to say "something something leads to a [spacetime] paradox".

In short, if I were to instantaneously poof out of existence here on Earth, poof into existence on Mars a second later, grab a rock, poof out of existence again, and poof back into existence back on Earth again another second later and hand you that rock, it doesn't seem reasonable to assert that I traveled backward in time when I clearly traveled forward by two seconds. The whole lecture on that external observer is irrelevant, since there's nothing to observe unless the observer happens to be in my bubble/wormhole/whatever - and even then, one'd only be observing subluminal actions/signals within that region of spacetime.

I have wondered if some of Kafka's writings belong in the science fiction genre.

Maybe space is a bit more emptier than you think, and FTL is a bit slower.

Or maybe it is busy, but we haven't waited long enough. I mean think of a native American in the 1400s. If transoceanic travel is possible, why haven't we seen visitors from other continents yet?

Finally, it is still entirely possible that "they" are already there, and there is a cover up. I don't believe it (Occam's razor), but if FTL turns out to be theoretically possible, than I think I will have to update my beliefs :-)

Not under the Zoo hypothesis: https://en.wikipedia.org/wiki/Zoo_hypothesis

There's plenty of other reasons it's still just a theory, but that isn't one here, if I read it right.

The math can only work (if it even does) in exceptionally constrained circumstances. The main purely-theoretical issue is that the paper's <https://arxiv.org/abs/2102.06824v2> solution is wholly spherically symmetric, and with vacuum everywhere but in the warping region.

"Fig. 1: Asymptotically-flat vacuum background ... general stationary curved region with a spherical topology ... (the warping region) ... flat inner region ... ('passenger' space). ... As we discuss in Section 5, warp drive spacetimes require some form of propulsion in order to accelerate. For this reason, in physical realisations of such spacetimes, the front and rear parts are likely asymmetric". [emphasis mine]

Do the maths fall apart if we deviate from total spherical symmetry, either by changing the front and rear parts, or by breaking the vaccuum condition on the inside and outside of the shell, especially if our matter is not precisely spherically distributed?

They do a review of this, for limited deviations from spherical symmetry, in §4. However, the vaccum condition is what they study, not straying very far from their earlier "if [the warp region] were replaced by Minkowski spacetime, the whole spacetime would be Minkowski space."

The paper declines to answer the question about the distribution of matter (i.e., not-vacuum): "all warp drive spacetimes are asymptotically-flat ... no metric which describes an accelerating warp drive solution has been presented in the literature ... metrics for ... accelerating objects and more general axisymmetric objects which preserve their shape and mass ... remains a subject for future studies". That last part suggests that the inside part might be kept appropriately symmetrical through dynamic reconfiguration of the things inside (i.e., the ship, cargo, fuel, passengers).

But what about outside the warping region? In our solar system, and in our galaxy, we are not in Minkowski space.

The outer part of the warp region, being asymptotically flat, might be amenable to a "thin shell" (Israel/Darmois junction formalism) with the warp bubble far enough away from everything outside that it feels no tidal forces, which for the purposes of the text above is "acceleration". What determines how far is far enough away? The authors don't attempt an answer.

There are plenty of things (stars, most notably) in our part of the galaxy that will induce tides. The solar component of the lunisolar tide in Earth's oceans is substantial at 1 astronomical unit from our sun. That solar component doesn't go away when a space craft is (for example) 2 a.u. away from Earth&Moon on the opposite side of the sun. Can one zip this warp bubble safely past a 1 solar mass star at a distance of 1 au? Ten au? Can the warping region or passenger region be adjusted to allow for close approaches/operation within a star system? All questions for some possible future paper.

Apart from stars, we inhabit a region of space which is dotted with things you can smack into (from the very solid like rocks and iron to the very wispy, stuff will still tend to slow you down when you hit it; deceleration and acceleration are the same issue). Near luminous enough stars, radiation pressure might also induce non-negligible accelerations. Is any of that relevant? If relevant, is it "fixable"? How? Alter the shape of the warping region, or the passenger region, or both? Questions for some possible future paper.

So, even if one accepts for the sake of argument that the maths are flawless and further one just assumes the existence of controllable negative energy densities, this paper's maths are designed for a spacetime which overall isn't very much like what we have within a few hundred lightyears of here. Maybe some future paper will attempt to show that a warp bubble can work in more realistic spacetimes than almost-everywhere-empty-of-matter-and-feeling-no-gravitation setting of this paper. ("Almost-everywhere" means that there is matter and curvature in the warping region, and maybe the passenger region, but nowhere else, not even a destination star a dozen light-years away).

Whether that will provide a way to travel FTL in space time or outside it, we don’t know. But the science is not as settled as it seems even if mere mortals cannot think up a theory to beat the truly incredible power of GR.