Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math.independent

Topic: Acoustic Metrics, and the OPERA neutrino result
Replies: 5   Last Post: Feb 16, 2012 11:15 AM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
united

Posts: 4
Registered: 12/7/04
Re: Acoustic Metrics, and the OPERA neutrino result
Posted: Feb 15, 2012 8:59 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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 deeply-held
belief that anything that didn't agree with SR was automatically not
credible, and not worth investigating, let alone publishing. It was a
non-subject.

I mean, it was /literally/ a non-subject, there was even a slightly
self-serving 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 line-boundary 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 cross-section between a
projected limit and classical wave behaviour.
The projected line shows discontinuously-disconnecting 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 cross-subject 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
GR1915-style 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 SR-based 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 SR-style lightspeed barrier
(which could be described as a form of horizon) to wobble and warp, to
allow physically-accelerated 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 proof-of-concept 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




Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.