I don't know what aug-hbar is - is it the noise the gun makes?
Bob Todd whee,
Tue 8 Dec 2009, 20:20,
archived)
I dunnoSounds quantum mechanical to me.
Someone please kill me :(
(Someone please kill me :(
boris the spider,
Tue 8 Dec 2009, 20:22,
archived)
Are you suggestingthat the Dirac constant is some sort of mediator to an uncertainty relationship between position and momentum operators as they are non-commutative? That's madness. Pure madness.
(,
Tue 8 Dec 2009, 20:38,
archived)
I am so sorry
Edit: Fuck GIMP and its habit of adding random glitches because it doesn't optimise GIFs well enough to actually save the actual changes between frames. Also I should have got rid of the i not the hbar. Then it'd only be another diffusion equation. Hahaha TAKE THAT SCHROEDINGER YOU DEAD CAT-HATING WOMANISING CUNT. But it's too late now. :(
boris the spider,
Tue 8 Dec 2009, 20:42,
archived)
I've never gone near FlashI've heard bad things. One time my friend told me it raped his mum :( With big, black tentacles. :((
( boris the spider,
Tue 8 Dec 2009, 20:58,
archived)
hang on a minute,that Lagrangian isn't Lorentz covariant.
(
Moon Girl Technologies horrendous beanbag,
Tue 8 Dec 2009, 21:02,
archived)
Nope, not in the slightestIt's a Lagrangian that produces the Gross-Pitaevskii equation, which is more or less the Schroedinger equation for a Bose-Einstein condensate of weakly-coupled atoms. (It's basically just a mildly-nonlinear Schroedinger equation; the coupling term is just the first-order expansion in the energy.)
The Schroedinger equation isn't at all Lorentz-covariant. Though, entertainingly, if you take that Lagrangian and linearise it, the system you get can be cast as a relativistic wave equation. The phonons propagate on an effective Schwarzschild spacetime, complete with event horizon and Hawking radiation. Fascinating shit, on which I can be a TOTAL BORE.
(The Schroedinger equation isn't at all Lorentz-covariant. Though, entertainingly, if you take that Lagrangian and linearise it, the system you get can be cast as a relativistic wave equation. The phonons propagate on an effective Schwarzschild spacetime, complete with event horizon and Hawking radiation. Fascinating shit, on which I can be a TOTAL BORE.
boris the spider,
Tue 8 Dec 2009, 21:06,
archived)
the laser cooling and condensed matter group used to come out with that kind of stuff,not my bag, I'm all for Dirac myself.
( Moon Girl Technologies horrendous beanbag,
Tue 8 Dec 2009, 21:10,
archived)
Not sure about thisbut I don't think you get acoustic black holes out of a linearised Dirac system. Neither do you get one from a linearised Klein-Gordon system.
What I did like was a paper a few years back that clearly started as a really nerdy joke -- a couple of guys who put a condensate around a black hole and found that you can have an acoustic black hole orbiting a gravitational black hole. Oh, how we laughed.
They've made an acoustic hole in the lab now, a couple of months back. I almost jizzed my pants.*
* May not have almost jizzed my pants.
(What I did like was a paper a few years back that clearly started as a really nerdy joke -- a couple of guys who put a condensate around a black hole and found that you can have an acoustic black hole orbiting a gravitational black hole. Oh, how we laughed.
They've made an acoustic hole in the lab now, a couple of months back. I almost jizzed my pants.*
* May not have almost jizzed my pants.
boris the spider,
Tue 8 Dec 2009, 21:12,
archived)
In all honesty I don't know what an acoustic black hole is,but what does it tell us about the fundamental nature of the universe?
The Schrodinger Equation pops out of the Dirac Equation in the non-relativistic limit, so I'm sure you could wangle an acoustic black hole out of it if you were so inclined and knew what you were doing.
(The Schrodinger Equation pops out of the Dirac Equation in the non-relativistic limit, so I'm sure you could wangle an acoustic black hole out of it if you were so inclined and knew what you were doing.
Moon Girl Technologies horrendous beanbag,
Tue 8 Dec 2009, 21:16,
archived)
It tells us whether the arguments Hawking made are validThe dynamics of an acoustic hole are the same as a gravitational one -- so the sound waves act around an acoustic hole exactly as light waves do around a (uncharged, non-rotating) gravitational black hole. If Hawking's arguments, which are still basically the only result we've got marrying gravity and quantum mechanics together, are valid then we'll see Hawking radiation from an acoustic black hole. Since it's pretty impossible to make a black hole in the lab (and, yeah, that includes the LHC, the theories that would produce black holes there are pretty speculative stuff), this is more or less our only concrete and cheap way of testing the interaction of gravity with quantum effects.
The thing I'd add is that an acoustic black hole is like a normal black hole except it only works on sound waves. The easiest way of imagining one is to get a tube and wrap it on itself and send water through at just below the speed of sound. In the direction of the flow, as viewed from the lab, the sound waves are moving at almost, but not quite, twice the speed of sound. Opposing the flow, they're almost stationary. If you now squeeze the tube then the flow goes supersonic at that point. In the supersonic patch sound waves can't travel against the flow -- they're swept along regardless, like sperm trying to swim up the Niagara Falls. At the point where the flow goes supersonic you've got an acoustic event horizon, while at the point it goes subsonic again you'd have another horizon (that one would correspond to a white hole).
Interesting stuff. Not actually that *useful* but if I wanted to be any use to humanity I wouldn't have done theoretical physics and then sat about on B3ta drawing magenta cocks onto Snoopy cartoons.
(The thing I'd add is that an acoustic black hole is like a normal black hole except it only works on sound waves. The easiest way of imagining one is to get a tube and wrap it on itself and send water through at just below the speed of sound. In the direction of the flow, as viewed from the lab, the sound waves are moving at almost, but not quite, twice the speed of sound. Opposing the flow, they're almost stationary. If you now squeeze the tube then the flow goes supersonic at that point. In the supersonic patch sound waves can't travel against the flow -- they're swept along regardless, like sperm trying to swim up the Niagara Falls. At the point where the flow goes supersonic you've got an acoustic event horizon, while at the point it goes subsonic again you'd have another horizon (that one would correspond to a white hole).
Interesting stuff. Not actually that *useful* but if I wanted to be any use to humanity I wouldn't have done theoretical physics and then sat about on B3ta drawing magenta cocks onto Snoopy cartoons.
boris the spider,
Tue 8 Dec 2009, 21:23,
archived)
curious.I'm not convinced they're an exact analogy but they might shed some light on things, so to speak.
( Moon Girl Technologies horrendous beanbag,
Tue 8 Dec 2009, 21:34,
archived)
The analogy isn't at all exactI got the words the wrong way round, but it's the kinematics that are analogous. The dynamics are totally fucked. Meaning that the geodesics are the same (so Hawking's arguments are safe; they didn't rely on the Einstein equations) but the Einstein equations coupling them to matter are totally different. In relativity that's just the Einstein equations in their horrible non-linear glory. In acoustic holes it's pure non-relativistic wave equations -- you don't need to look at quantum fluids to get acoustic holes, you can build them in any perfect fluid. So the dynamics are governed by Newtonian mechanics.
Still, it is an interesting curiosity. There's a small but entertaining group of physicists trying to use these arguments to get a totally different picture on quantum gravity and the standard model by getting it from emergent systems in condensed matter. If you're actually interested, Volovik put up "The Universe in a Helium Droplet" on his website for free download a few years back; he basically found pretty mucha ll the symmetries of the standard model and of relativity emerging from perturbations in superfluid Helium II. The dynamics were totally wrong again, but the symmetries were all there. If someone can find a system where the symmetries *and* the dynamics emerge, then the conventional picture of finding unification by pushing to ever-higher energies and adding symmetry after symmetry will be overturned.
Which would be nice.
(Still, it is an interesting curiosity. There's a small but entertaining group of physicists trying to use these arguments to get a totally different picture on quantum gravity and the standard model by getting it from emergent systems in condensed matter. If you're actually interested, Volovik put up "The Universe in a Helium Droplet" on his website for free download a few years back; he basically found pretty mucha ll the symmetries of the standard model and of relativity emerging from perturbations in superfluid Helium II. The dynamics were totally wrong again, but the symmetries were all there. If someone can find a system where the symmetries *and* the dynamics emerge, then the conventional picture of finding unification by pushing to ever-higher energies and adding symmetry after symmetry will be overturned.
Which would be nice.
boris the spider,
Tue 8 Dec 2009, 21:47,
archived)
You know what,that is simultaneously both surprising and not surprising, somehow.
( Moon Girl Technologies horrendous beanbag,
Tue 8 Dec 2009, 21:53,
archived)
Bloody physicistsAn uncharged non-rotating black hole?
What good is that in the real world, I ask you?
(What good is that in the real world, I ask you?
littlefish I like cheese,
Tue 8 Dec 2009, 22:16,
archived)
ABSOLUTELY NONEREAL black holes are like REAL men. Errr, spinning around and round and with a healthy electric field, and emitting a constant stream of radiation. In men that's called "farting". Also, they've got another universe hidden inside them. Through the ring.
I'm going to shut up now. I think that would be a good idea.
(I'm going to shut up now. I think that would be a good idea.
boris the spider,
Tue 8 Dec 2009, 22:31,
archived)
alsodon't think you'd get an acoustic hole out -- it relies on the equations being hyperbolic. the schroedinger equation is hyperbolic but i don't think the dirac equation is.
i may very well, however, be dead wrong because it's now about seven years since i looked at the classification of differential equations. if the dirac equation *is* hyperbolic then it's possible we'd get an acoustic hole. i may look into that actually. it'll while away the long winter evenings...
(i may very well, however, be dead wrong because it's now about seven years since i looked at the classification of differential equations. if the dirac equation *is* hyperbolic then it's possible we'd get an acoustic hole. i may look into that actually. it'll while away the long winter evenings...
boris the spider,
Tue 8 Dec 2009, 21:25,
archived)
well as I say,the Schrodinger equation IS the Dirac equation in the non-relativistic limit, so any solution the former has, the latter ought to have as well. I don't know how you'd get a self-interaction term to work though, but there must be some Lorentz covariant form of it, because if it isn't Lorentz covariant, it can't be true, otherwise Special Relativity isn't true.
( Moon Girl Technologies horrendous beanbag,
Tue 8 Dec 2009, 21:32,
archived)
Doesn't necessarily followThing is the acoustic hole comes along because of the behaviour of fluctuations; at low energies this is fine, but at high energies there's no immediate reason to believe that there isn't something influencing the fluctuations (indeed, there will be) that changes their behaviour enough that now they don't look like they act on a Schwarzschild spacetime. I'd not be surprised to find that you can't write an effective spacetime at all for the high-energy general case, and only at low energies.
The self-interaction term is just coming from a Taylor expansion of the Gibbs free energy. Or it may be the Helmholtz free energy. One of the two. It's also actually not quite a Schroedinger equation because that psi isn't a wavefunction so much as the product of the individual wavefunctions of the atoms in the condensate. So if you follow the kind of arguments made for the low-energy case and put it at high energies you could doubtless write a modification to the Dirac Lagrangian that included an interaction. Just that it would be a bit odd to consider a high-energy Bose-Einstein condensate...
(The self-interaction term is just coming from a Taylor expansion of the Gibbs free energy. Or it may be the Helmholtz free energy. One of the two. It's also actually not quite a Schroedinger equation because that psi isn't a wavefunction so much as the product of the individual wavefunctions of the atoms in the condensate. So if you follow the kind of arguments made for the low-energy case and put it at high energies you could doubtless write a modification to the Dirac Lagrangian that included an interaction. Just that it would be a bit odd to consider a high-energy Bose-Einstein condensate...
boris the spider,
Tue 8 Dec 2009, 21:38,
archived)
I think Special Relativity relies on Lorentz covariance,in fact I believe the two are pretty much the same thing. Having said that, the general case is often difficult and not particularly useful. I couldn't honestly tell you if the Dirac equation has any real world applications outside of particle accelerators. It's just, kind of... nice.
( Moon Girl Technologies horrendous beanbag,
Tue 8 Dec 2009, 21:58,
archived)
yeahlorentz invariance underpins special relativity -- and general, since special relativity is recovered from general in the flat limit. there'll certainly be real-world applications of it; it's the equation governing the behaviour of relativistic electrons, and if it doesn't have some application somewhere in semiconductor physics that has a bearing on modern computers i'd be quite surprised...
( boris the spider,
Tue 8 Dec 2009, 22:05,
archived)
who knows what's going to happenwhen they move on to the 32nm process. Even still, electron drift velocities may be very low even though the signal speed approaches the speed of light.
( Moon Girl Technologies horrendous beanbag,
Tue 8 Dec 2009, 22:11,
archived)
very trueeven so, i'd be surprised if they didn't have to take relativity into account at some point. though i should maybe prepare to be surprised.
( boris the spider,
Tue 8 Dec 2009, 22:17,
archived)
THANK YOUHAVE A PICTURE TO MAKE UP FOR THE PHYSICS IN THIS THREAD
MORE PHYSICS. SPUNKING.
(MORE PHYSICS. SPUNKING.
boris the spider,
Tue 8 Dec 2009, 22:33,
archived)