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QM as defects in a solid media.

  1. Jan 8, 2006 #1


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    Cool paper:

    Aharonov-Bohm Effect and Disclinations in an Elastic Medium
    Claudio Furtado, A. M. de M. Carvalho, C. A. de Lima Ribeiro
    In this work we investigate quasiparticles in the background of defects in solids using the geometric theory of defects. We use the parallel transport matrix to study the Aharonov-Bohm effect in this background. For quasiparticles moving in this effective medium we demonstrate an effect similar to the gravitational Aharonov- Bohm effect. We analyze this effect in an elastic medium with one and N defects.

    Any comments? I'll read the paper tomorrow or the next day, but I had to start the thread first because I love the abstract.

  2. jcsd
  3. Jan 10, 2006 #2
    I wanted to reply to this message from Carl but I haven't come up with much of interest to say, other than that this work looks really cool, but I'm not sure how it could be used for 4D gravity and 4-geons.

    My main question after cursorily browsing the paper would be "how can this type of analysis be ported to the field of 4D geometrodynamics?" For instance, they talk of line singularities or singular torsion along line defects, but these are in 3D. Now if these are quasi-stable things in their elastic solid model then can one port such an argument over to spacetime models and say that analogous stable deformations of spacetime could propagate around? If so, then this would be worth some serious research because it could lead to some basic 4-geon models. It bears a similarity to work by Dzhunushaliev on minimal black holes and minimal wormhole structures in 5D, that is, topological structure on spacetime as models for elementary particles. My cursory comments would be that the Furtado paper is working with 1D too small for our geon theory interests and Dzhunushaliev works in 1D too high!

    My first thought upon reading the abstract was "Wow! Maybe such defects can directly be related to 4-geons?" because they seemed to be structures that are very similar to things I've been day dreaming about whenever I allow myself to think about geon theory (which these days is very rare). I suspected it would not be a huge stretch to sightly reword that paper by Furtado et al., and give it a title, "Topological Defects in Spacetime as Quasi-Particles". The solid medium gets replaced by flat spacetime.

    But then my hopes seemed ruined because this paper can only be ported to 3D spacetime, with Cartan structure, ie., it'd only be applicable to Newtonian gravity with curved spacetime, not Lorentzian. So any stability results would not port automatically to 4D gravity sadly. And it would take an expert to take anything from this paper of application to 4D geons.

    There seems however one faint connection between 3D and 4D implied by the Furtado paper, namely the Aharonov-Bohm efect. They cite a classical "gravitational Aharonov-Bohm effect" whereby particles moving in curvature-free regions of spacetime can exhibit effects due to non-zero curvature in regions from which the particels are forbidden. I had never heard of this effect before, and it struck me as quite amazing, since classical particles have no phase with which field effects can be imparted upon them as in the quantum Aharonov-Bohm effect, and so I had to take the cited article on this effect on faith for the moment. But supposing it is valid, then the Furtado paper provides a 3D version in an elastic medum where the particles are once again represented by quantum wavefunction of phonons.

    In other words, the papers of interest to 4-geon theorists would appear to be not only Furtado's paper but also the one they cite on gravitational Aharonov-Bohm effects,

    L. H. Ford and A. Vilenkin. J. Phys. A: Math. Gen. 14, 2353 (1981).

    Cosmic strings are things that cosmologists seem to take seriously, and I've always wondered "if cosmic strings, why not tiny Planck scale strings?" These would not be superstrings, they would be real topological defects in spacetime with associated Einstein-Ricci curvature. Do you really need vast quantities of matter to form cosmic strings? What if one could shatter a cosmic string into quadrillions of tiny pieces? Would you get smaller strings, and would they still be stable? I.e., is it the mass-energy density that counts when forming a stable defect or is it the shear raw amount of mass-energy that is important? If it is the density that is important then supposing we can talk about smashing cosmic strings up into Planck scale pieces, then is there a limiting size to such things below which they would vanish, above which they might be quasi-stable?

    Has anyone read that paper? Comments?
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