Comment by captainmuon | Hacker News Reader

Comment by captainmuon | Hacker News Reader

I always find these kind of papers interesting. It seems like they found a more general "warp drive" metric. But after skimming it, I don't understand how they want to create it in reality.

The best shot I think we have at metric engineering - unless you want to build something crazy like moving spheres and rings of ultra dense matter - is to look into materials with interesting spin-gravity coupling.

We know that rotating bodies have additional gravitational interactions. The effect is tiny, but measurable in experiments (e.g. Gravity Probe B). We also know that atomic spin is not just an abstract quantum number but actual angular momentum. So there should be some kind of spin-gravity interaction, even though it would be incredibly weak. But even though the absolute force is small, if we manage to make it time dependent we could amplify the effect. Just like a changing magetic field creates an electric field, a changing "gravitomagnetic" field would create a gravitational field. This is basically the insight that took us from compasses and static electricity to the whole of electrical engineering.

I am not sure such materials could even exist. And even though I have a PhD in Physics, I have no idea how one would approach this theoretically. The treatment of particle spin seems to be very rare in GR, and then you would have to marry this to solid state physics and somehow calculate how the situation changes when the spin density changes and so on... The furthest I got was to open a thread on stackexchange about it :-) but who knows, maybe someday somebody looks into this stuff:

https://physics.stackexchange.com/questions/46099/materials-...

Warning: lots of jargon ahead.

I really wish I understood this better, but the sense I've gotten is that intrinsic spin needs to couple to gravitation through torsion rather than through the usual curvature we study in GR. Most GR courses and textbooks barely mention torsion at all: IIRC Wald for example specifies "torsion free" as a condition on derivative operators and basically doesn't ever explore the alternative (I think there's a homework problem on it). The torsion free condition is what guarantees that Christoffel symbols are symmetric in their lower indices. Once upon a time while trying to understand all this back in grad school, I wrote up a set of notes extending Wald's calculations of curvature to include the possibility of torsion. I never tried to publish them anywhere, since of course it's nothing new or groundbreaking, but they're on my website here: http://www.slimy.com/~steuard/teaching/tutorials/GRtorsion.p...

Those notes do not discuss the connection to spin, because I was only halfway aware of it at the time and because I didn't have the time to delve into it enough to figure it out. (I also didn't know at the time that this is often called "Einstein-Cartan theory".) One notable thing about torsion is that it's a non-propagating field: as I recall, it's only non-zero inside the material with spin. I'm not entirely sure what the effects of all that might be. This 1976 review article has been lurking at the back of my to-read pile for ages: https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.48....

I have no idea whatsoever whether any of that is useful for making warp drives or for metric engineering. But I figured I'd share, since it seemed relevant.

I was with you until the analogy to electromagnetism and time dependency. I admittedly don't have a PhD in physics (undergrad astrophysics), so I possibly won't understand your answer, but isn't gravitomagnetism more of a useful fiction than anything people actually believe models reality? I mean the equations look similar, but there's no physical justification: gravity is not a field in the QFT sense.

I guess I'm asking why you'd expect there to be an analog to the interaction between electrical and magnetic fields, when the nature of the thing is so different?

Gravity (more precisely, a dynamical metric) is absolutely a field in the QFT sense. The problem is that its unrenormalizable. That’s a technical term that roughly means the theory doesn’t make predictions to arbitrarily high energies. As a result the QFT describing gravity cannot be used to answer the interesting questions about black holes and Planck-scale physics. Historically this has meant that a new physical mechanism has been ignored that becomes relevant only at large energies, such as stringy physics in string theories or discrete spacetime in LQG. That’s part of why critics argue about the falsifiability of string theory (unfortunately the same critics don’t make the obvious conclusion that unfalsifiability in this sense implies to all models of quantum gravity, not just strings—-and that’s a funding motivated lie by omission. This has to be true since by their own framework, if LQG predicts something and string theory predicts nothing, the experiment distinguishing them could falsify string theory by validating that prediction).

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).

> isn't gravitomagnetism more of a useful fiction than anything people actually believe models reality?

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.

> after skimming it, I don't understand how they want to create it in reality

That's because nobody knows how to do that, and statements in papers like these that claim it can be done are basically hand-waving.

Unfortunately, different quantum spin orientations don't appear to evade the weak equivalence principle. Dropping Bose-Einstein condensates in vacuum drop towers is a popular experiment. An example, "Tests of the Universality of Free Fall with Atoms in Different Spin Orientations", 2016, <http://dx.doi.org/10.1103/PhysRevLett.117.023001> which is the published version of <https://arxiv.org/abs/1503.00433v1>. Likewise, one would not expect a ferromagnet and a ferroic glass to fall differently in a drop tower.

Quantum spin is relevant in post-Newtonian (GR-compatible) gravitation, though.

Rough argument: let's represent perturbations of the metric (gravitational waves) as a massless spin-2 boson field on top of some sourceless background geometry; this is essentially the programme of perturbative quantum gravity. (’t Hooft, <https://dspace.library.uu.nl/bitstream/1874/4708/2/16331.pdf> corresponding to DOI10.1142/9789812796653 (_0007).) This is almost General Relativity. GR's "no prior geometry" (MTW §17.6) axiom puts paid to the idea of obtaining a compatible theory by inserting some force into a static background, and ultimately this idea that spacetime is dynamic is what causes PQG to be a poor theory for strong gravitational interactions ('t Hooft ut supra, 2nd paragraph of §4).

Spin-2 interactions are attractive for the same charge. As far as we know, physicality demands PQG treat everything (including the gravitons) in the universe as possessing the same sign of gravitational charge. We can't (quasi-)neutralize with matter or vast collections of gravitons, so we can't charge screen in the sense of <https://en.wikipedia.org/wiki/Electric-field_screening> as opposed to having things like Lagrange points in Newtonian gravitation.

There is a family of theoretical approaches involves appreciable amounts of matter with opposite gravitational charges from everything else or introducing two "opposite" metrics and coupling most matter to our familiar one and a minority of matter to the other. Informally, we make gravitational and inertial masses unequal for some matter, breaking the weak equivalence principle (unlike in my first paragraph). Evidence takes us away from these approaches.

Additionally, opposite rank-2 tensor charges repel, so it's hard to imagine engineering up a scheme that uses any "anti-gravitating" matter with a single metric tensor, and theoreticians would have to imagine some cutoff to prevent runaway acceleration of an anti-gravitating particle let loose inside the solar system; Bondi, 1957, <https://doi.org/10.1103/RevModPhys.29.423>

One sketch of this sort of idea off the top of my head is Hossenfelder's "Antigravitation", <https://arxiv.org/abs/gr-qc/0508013>, which is per the author a toy idea (each Standard Model particle has a gravitational-anti particle) that makes a simplifying assumption that takes one away from general curved spacetimes (ibid., §4 and the para below eq. 17, which is suggestive of Bondi's runaway).

Instead, we might try to contrive a universe with a complement of fun things like pp-waves (which maybe one can get with your spheres and rings). It's unlikely that this can be done without going outside the limits of linearized gravity (GEM and so forth), and such exotic things tend to cause gravitational collapses. (E.g. Bondi & Pirani XIII <https://royalsocietypublishing.org/doi/10.1098/rspa.1989.001...> aka <https://doi.org/10.1098/rspa.1989.0016> which is on scy hob if you need that) Because of B&P, it occurs to me that if we have a line of galaxies in an expanding Robertson-Walker spacetime, perturbing that with a caustic wave might keep (the remnants of) the galaxies from exiting each others' Hubble volumes, which maybe you can sort of think of as effective FTL, or perhaps related to the "FTL" of the most distant galaxies disappearing from view).

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Universality of free fall / Galilean gravity treat: https://en.wikipedia.org/wiki/File:Apollo_15_feather_and_ham...

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