But the view of a 'wavefunction' relies on a strong interpretation of QMand Schroedinger QM doesn't really apply here. For one thing it's non-relativistic (and so observationally wrong at high energies) and it's single quantised. QFT doesn't really rely on wavefunctions in the same way. In QFT (QED, say) it makes about as much sense to talk about a point particle as not talk about a point particle -- or that's my view of it, from my rusty memories of actually doing any QFT.
Anyway, regardless, I don't know of a theory that can actually make predictions (or many that don't, including string theory) that don't implicitly or explicitly employ a spacetime. Typically it's set as Minkowski (like in QED, QCD etc) or Minkowski + perturbations (like in string theory). Trying to extend the predictions of such theories -- regardless of whether you can employ a wavefunction interpretation or not -- to arbitrarily small scales or high energies is therefore going to grow problematic without a quantum theory of gravity.
(Also I'm philosophically ill-inclined to look at a Fock space and say 'that's the reality'. It's not, it's just a Fock space.)
(Anyway, regardless, I don't know of a theory that can actually make predictions (or many that don't, including string theory) that don't implicitly or explicitly employ a spacetime. Typically it's set as Minkowski (like in QED, QCD etc) or Minkowski + perturbations (like in string theory). Trying to extend the predictions of such theories -- regardless of whether you can employ a wavefunction interpretation or not -- to arbitrarily small scales or high energies is therefore going to grow problematic without a quantum theory of gravity.
(Also I'm philosophically ill-inclined to look at a Fock space and say 'that's the reality'. It's not, it's just a Fock space.)
boris the spider,
Mon 24 May 2010, 16:18,
archived)
We need a quantum theory of gravity for various reasons,but not for explaining why electrons aren't black holes! That's just a funny idea to introduce to the unwary.
I'm not just thinking of the Schrodinger wavefunction here, although it suffices for the explanation. The relativistic Dirac equation has a wavefunction - a Spinor wavefunction. Maxwell's Equations have a wavefunction in the form of the vector potential. "Particles", if it makes sense to call them that (but it's the nomenclature we're stuck with), can only be described as excitations of the field; as such they are dimensionless, but in no sense is it meaningful to say that they are points. That would be pointless.
Maybe I'm jumping the gun to say Hilbert space is "real", but one thing is for certain, space-time isn't fundamental, it's a basis set transform.
(I'm not just thinking of the Schrodinger wavefunction here, although it suffices for the explanation. The relativistic Dirac equation has a wavefunction - a Spinor wavefunction. Maxwell's Equations have a wavefunction in the form of the vector potential. "Particles", if it makes sense to call them that (but it's the nomenclature we're stuck with), can only be described as excitations of the field; as such they are dimensionless, but in no sense is it meaningful to say that they are points. That would be pointless.
Maybe I'm jumping the gun to say Hilbert space is "real", but one thing is for certain, space-time isn't fundamental, it's a basis set transform.
Moon Girl Technologies horrendous beanbag,
Mon 24 May 2010, 16:27,
archived)
but... but...i still think that without a theory that includes both, say, electrons and gravity we can't actually comment on anything gravitational on such scales. anything else is extending a current theory severely past its range of applicability. "it's not, because a schroedinger wavefunction has no position!" isn't really an answer, that's basically saying "it's not, because in a theory that only applies on much larger scales and at much lower energies an electron can -- in a given interpretation -- be described as a wavefunction, therefore when we push the energy up by about 100 orders of magnitude and explicitly include gravity it will *still* be described as a wavefunction!".
can you see my objection to that...?
basically i may well say "OK, gravity is probably emergent" because i feel that actually it is (and in a way which isn't yet popular -- i actually think that a "fundamental" theory is more likely to be found by *removing* symmetries and working in a system in which all the symmetries emerge when excited. volovik's shown that this occurs in superfluid helium iia; perturb it and you get basically the entire standard model + massless spin 2 quasiparticles. the dynamics are totally wrong but the kinematics of the entirity of modern science are all there. there are other models too, some of which pick up the dynamics as well.) but i can equally say "what makes you so sure that electrons aren't emergent? what makes you think that the wavefunction isn't emergent?"
similarly i could point to, say, bohmian qm. the wavefunction here is identical to the schroedinger wavefunction but it's emergent (closely related to the classical action) and the theory is totally deterministic. aesthetically ugly, but still...
we simply have no idea what form a theory applicable at the kind of energies and on those kind of scales will take. sure, spacetime may be emergent in some sense, but so may wavefunctions, whatever they would be. so might all the various spaces on which our "particles" are defined, and all the symmetry groups between them.
(can you see my objection to that...?
basically i may well say "OK, gravity is probably emergent" because i feel that actually it is (and in a way which isn't yet popular -- i actually think that a "fundamental" theory is more likely to be found by *removing* symmetries and working in a system in which all the symmetries emerge when excited. volovik's shown that this occurs in superfluid helium iia; perturb it and you get basically the entire standard model + massless spin 2 quasiparticles. the dynamics are totally wrong but the kinematics of the entirity of modern science are all there. there are other models too, some of which pick up the dynamics as well.) but i can equally say "what makes you so sure that electrons aren't emergent? what makes you think that the wavefunction isn't emergent?"
similarly i could point to, say, bohmian qm. the wavefunction here is identical to the schroedinger wavefunction but it's emergent (closely related to the classical action) and the theory is totally deterministic. aesthetically ugly, but still...
we simply have no idea what form a theory applicable at the kind of energies and on those kind of scales will take. sure, spacetime may be emergent in some sense, but so may wavefunctions, whatever they would be. so might all the various spaces on which our "particles" are defined, and all the symmetry groups between them.
boris the spider,
Mon 24 May 2010, 16:47,
archived)
I see your objection but I think you are missing the point,because I think you are thinking about it in a very general sense. My point is simply that the question of why electrons aren't black holes simply doesn't come up unless you assume to begin with that electrons are point particles, and there is no reason to assume that, and every reason not to. It's merely the last vestiges of our intuitive grasp of how "matter" behaves at human scales.
I think everything is emergent, fermions are "twisting space" somehow, EM is just a special case of gravity. I can't prove nothin' but I'm absolutely convinced that our sense perceptions don't directly tell us what's really going on. There is a reason that the Universe appears to exist in four dimensional space-time, and I reckon the Gamma matrices have something to do with it.
(I think everything is emergent, fermions are "twisting space" somehow, EM is just a special case of gravity. I can't prove nothin' but I'm absolutely convinced that our sense perceptions don't directly tell us what's really going on. There is a reason that the Universe appears to exist in four dimensional space-time, and I reckon the Gamma matrices have something to do with it.
Moon Girl Technologies horrendous beanbag,
Mon 24 May 2010, 16:57,
archived)
I probably am missing the pointI'm really tired for some reason. And I've just found that the reason my codes have been crashing for the last few days (causing me to work over the weekend and today, which is a bank holiday here) is that I didn't compile the libraries up with the Intel fortran compiler but used gfortran instead. Fuck's sake.... But it works now :)
I think my point ultimately might be that the question of why electrons aren't black holes doesn't come up unless you have a sound theory to work with in the first place -- which would be in some respects a theory of quantum gravity. Put that way, we seem to be arguing about exactly the same point, in totally different ways.
(Likewise that everything is emergent. But I'm not convinced about EM being a special case of gravity, attempts to do that pretty much always produce a dilaton and I don't like dilatons. But I believe the two of them are subsets of something else. There's a fair bit of focus on 3-forms at the minute, and a theory built on 3-forms automatically includes what are basically Maxwell tensors along with what are basically Ricci tensors, unless I've got totally the wrong end of the stick which I probably have. Something like that might be the way to unite the two without bogging ourselves down in string theory...)
(I think my point ultimately might be that the question of why electrons aren't black holes doesn't come up unless you have a sound theory to work with in the first place -- which would be in some respects a theory of quantum gravity. Put that way, we seem to be arguing about exactly the same point, in totally different ways.
(Likewise that everything is emergent. But I'm not convinced about EM being a special case of gravity, attempts to do that pretty much always produce a dilaton and I don't like dilatons. But I believe the two of them are subsets of something else. There's a fair bit of focus on 3-forms at the minute, and a theory built on 3-forms automatically includes what are basically Maxwell tensors along with what are basically Ricci tensors, unless I've got totally the wrong end of the stick which I probably have. Something like that might be the way to unite the two without bogging ourselves down in string theory...)
boris the spider,
Mon 24 May 2010, 17:04,
archived)
I think that just comes down to nomenclature,I'd call the superset "gravity", still, gravity is rank-2 tensor so there's definitely scope for some quite complex behaviour, and going up to rank 3 intuitively would cause more problems than it solves.
There was some guy I read about a while ago who was working on a gauge theory based on the exceptional group G2, don't know if anything ever came of that.
(There was some guy I read about a while ago who was working on a gauge theory based on the exceptional group G2, don't know if anything ever came of that.
Moon Girl Technologies horrendous beanbag,
Mon 24 May 2010, 17:11,
archived)
beats meunless that was the surfer dude who used straight e8 to get everything out. last i heard no-one was actually convinced in the end.
i keep meaning to read through mcelrath's papers, he's currently convinced he's got out the standard model + neutrino masses + gravitons + a small cosmological constant + the correct dynamics from a cloud of interacting neutrinoes and anti-neutrinoes. but i don't even understand the setup since he preassumes the existence of neutrinoes and then finds what i can only assume are neutrino-like quasiparticles. but he's absolutely convinced and he knows a lot more particle theory than i do.
(i keep meaning to read through mcelrath's papers, he's currently convinced he's got out the standard model + neutrino masses + gravitons + a small cosmological constant + the correct dynamics from a cloud of interacting neutrinoes and anti-neutrinoes. but i don't even understand the setup since he preassumes the existence of neutrinoes and then finds what i can only assume are neutrino-like quasiparticles. but he's absolutely convinced and he knows a lot more particle theory than i do.
boris the spider,
Mon 24 May 2010, 17:15,
archived)
Yeah that guy,Garrett Lisi, I think he still has a small minority following. I don't like superstring theory much though so I hope someone comes up with something better that works.
( Moon Girl Technologies horrendous beanbag,
Mon 24 May 2010, 17:32,
archived)
i'm hoping bob mcelrath's rightor at least along the right lines. but then i did do my masters in analogue gravity so i'm not quite unbiased on this... :)
i don't like string theory much either. it probably shows. but i'm not really sold on loop quantum either. i prefer their *intentions* -- they just want to quantise gravity, they're not shooting for the top right from the start -- but the theory itself is somehow unpersuasive.
(i don't like string theory much either. it probably shows. but i'm not really sold on loop quantum either. i prefer their *intentions* -- they just want to quantise gravity, they're not shooting for the top right from the start -- but the theory itself is somehow unpersuasive.
boris the spider,
Mon 24 May 2010, 17:37,
archived)