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12/7/04


Re: Acoustic Metrics, and the OPERA neutrino result
Posted:
Feb 15, 2012 8:59 PM


On 14/02/2012 18:54, Rock Brentwood wrote: > But how do you propose to do that? It would be a lot like getting > partisans on the Conservative and Liberal side of the aisle to quietly > shack up together.
Well, I think they may have accidentally already done it ... or at least, "rogue elements" may have already done a key part of it.
I don't think that the relativity community appreciated just how much leeway the quantum gravity guys were given to explore alternative structures. They were given a wider remit, on the understanding that it was acknowledged that some of the systems that the QG guys would be working on were strictly temporary, and that they were therefore able to be explored and mapped out even if they didn't necessarily agree with special relativity.
Acoustic metrics are fascinating (IMO), but nobody from the core relativity community was able to study them (or even ask the questions that led to them), for about half a century because of the deeplyheld belief that anything that didn't agree with SR was automatically not credible, and not worth investigating, let alone publishing. It was a nonsubject.
I mean, it was /literally/ a nonsubject, there was even a slightly selfserving clause in Misner, Thorne and Wheeler's "Gravitation" that went as far as defining a metric theory as being "a theory that had a metric and reduced to special relativity". ... So a metric theory founded on an acoustic metric supposedly /wasn't/ a metric theory. It wasn't anything. If you thought "rigorously" using MTW definitions, then the very /idea/ of an acoustic metric theory was literally "unthinkable", in the Orwellian sense. The language was too customised to support the current system to allow even the concept of a serious alternative, and an entire field of math and physics research was eliminated by our hacking the definitions to make alternative approaches impossible "by definition".
... until the late 1990s.
What the guys studying acoustic metrics did with their "acoustic black hole" models was to study how the statistical behaviour of Hawking radiation seemed to agree with the statistical behaviours of a system in which special relativity's rules weren't the ones in operation. With an "acoustic" black hole, the horizon isn't a starting point, a limit that you draw on your map that nothing can cross. It's an "emergent" end result. It's more like the effect that you get when you use a laser to project a line onto the surface of a rippling lake. You never get to see a "naked singularity" section of line with an exposed dead end, but you /do/ get loops of line that constantly bud off from the main line and return. The geometry of the lineboundary appears to fluctuate acausally according to the description produced by the projection, but there's an additional dimension at work, and that the horizon represented by the line isn't a fundamental barrier, but a crosssection between a projected limit and classical wave behaviour. The projected line shows discontinuouslydisconnecting and reconnecting loops, but the physics of the water surface is entirely classical. The "quantum" behaviour is "visibly" real, but you're essentially dealing with projective artefacts.
It's like when you see someone walking behind a tree and reemerging at the other side ... it's not that they're disappearing from the universe and reemerging from "nowhere" (although that's how it appears in a 2D projected view of the situation), it's more that we simply don't have a complete set of data, and don't get to see what behind the tree. We can deduce what's behind the tree by assuming a deeper continuity, or by making use of indirect signalling, which in QM terms counts as making use of virtual particles, which again brings us back to the language that QM adopts for Hawking radiation, in describing particles whose presence can only be sensed indirectly.
The significance here of the "acoustic horizon" description is that it allows the horizon surface to fluctuate in response to events that occur behind it (the unseen person behind the tree is capable of shaking the tree, so that we see the shaking). Information leaks out.
It's also analogous (if you want to take a big crosssubject leap) to the behaviour of a cosmological horizon. A "cosmological" horizon is noisy, leaky, and emits the analogue of Hawking radiation entirely classically. If an object nominally behind the horizon accelerates towards us, it can warp the local geometry and make the effective horizon surface "jump" to a new location that's behind it. In terms of a GR1915style geometrical description, the object has discontinuously "tunnelled" from behind the horizon to in front of it, but in the cosmological case, it's actually the effective horizon's position that has jumped backwards to behind the object, rather then the object physically jumping forwards.
So cosmological horizons are actually acoustic horizons, and obey the rules of acoustic metrics rather than those of SRbased theory. If we can then use topology to map the laws of cosmological horizons onto gravitational problems, then we get the same sort of description of leaky, fluctuating limits, and a classical explanation of how objects with gravitational horizons can give off indirect radiation.
This didn't get done because we were originally convinced that black holes /couldn't/ radiate, because this violated GR1916. If we unified the descriptions of "cosmological" curved spacetime and "gravitational" curved spacetime, we'd have had to say that there was a classical mechanism for indirect radiation from black holes, which couldn't be explained by the current version of general relativity ... and we couldn't modify general relativity to include that behaviour without then invalidating special relativity's concept of how a lightspeed barrier was supposed to work, which GR kinda inherited though the proviso that gravitational physics was supposed to reduce to SR physics.
SR's lightspeed barrier, like GE1916's gravitational horizon, is prescriptive rather than emergent. To allow gravitational horizons to wobble and "warp", and leak information classically from behind r=2M meant that we'd have to also allow the SRstyle lightspeed barrier (which could be described as a form of horizon) to wobble and warp, to allow physicallyaccelerated particles to be able to advance forwards of the main wavefront, due to local warpage produced by the acceleration.
And that behaviour appears to correspond with what now /seems/ to have been spotted at OPERA.
To me, the "cosmological" case provides an apparently unavoidable example of "acoustic metric" physics appearing to be physically correct in real life. The question then seems to me to be: does the universe support multiple types of physics with different laws and rules for different types of curvature ... or does it have a single set of geometrical rules that apply everywhere? If we're applying Occam's Razor ruthlessly, we could argue that if acoustic metrics apply in cosmology, and if quantum mechanics' descriptions of black holes seem to be indistinguishable from what we'd expect if the same "acoustic" laws applied to gravitation, then perhaps we really do have a single set of laws for both situations, which then have to apply to the sorts of problems that we typically try to describe using special relativity, too.
Cosmology provides a theoretical proofofconcept that this logic appears to be physically real, quantum mechanics appears to prevent us from arguing that black holes don't obey the same "acoustic" laws, and the OPERA result ... maybe ... could turn out to be the third corner of our triangle, showing the same "acoustic" behaviour in particle physics.
Eric Baird



