Tuesday, October 18, 2011

Brief Note on Tachyons

It appears I have neglected to state the obvious, but AP must note it.

Bosonic strings, in particular in dimension $26$, have tachyons. When dimensions are emergent for information spaces, one does not stop at dimension $26$. The tetractys brane labels the $27$ dimensions of three (real) qutrits. Dimension $27$ is the first dimension with internal nodes on the toric diagram. Fourier supersymmetry does not limit the dimension.


  1. Reminds me of a day back in '94. We had just sat through another lecture on Strings by David Gross, at a Canberra summer school. I was discussing the whole business with another bright student, and I simply could not get my mind off those damned tachyons. Funny how events trigger long forgotten memories.

  2. Actually, the tachyon in the bosonic string spectrum just means that there is a state with a negative mass-squared, not that there is a state which travels faster than the speed of light. The presence of the tachyon signals that the vacuum of the bosonic string is unstable. This state is removed when supersymmetry is incorporated.

  3. So that would be the form of supersymmetry that does not work well phenomenologically, then? And I suppose all the mathematical M theorists that think about tachyons are just idiots, hm?

  4. I had this discussion with David Berenstein recently. The link I provide there gives the standard argument as to why even tachyons (in the form of scalar particles with imaginary mass) are to be thought of as slower than light, as well as the one loophole in that argument - the possibility of faster-than-light wavepackets if you start with states that are totally delocalized.

    There's a paper which tries to explain black hole infall in matrix models in terms of tachyonic strings. Very roughly, I think of a matrix model like this as consisting of n branes, with the matrix element A_ij being the string between brane i and brane j, and so I believe the idea is that the strings connecting branes that are part of the black hole, and branes that are outside the black hole but falling in, are the ones in which the tachyonic modes come to life.

    When I ran across that paper, it certainly reminded me of your "neutrino gravity", in which mass is due to mirror neutrinos created at the cosmological horizon. It sounds very similar, except the tachyonic modes extend to a cosmological horizon rather than to an event horizon.

  5. Sounds good, Mitchell. And since I mix up cosmological and 'event' horizons through emergence, there isn't actually much difference.

  6. Oh look, Evil String Theorist, now there is a BBC documentary with leading String Theorists saying that String Theory might explain FLT neutrinos. Shouldn't you be following the leaders, now, like a good boy?

  7. But the leaders would all be thinking in terms of shortcuts through extra dimensions (hello, "number 26"). Regarding the tachyons of string theory, they would all say what Berenstein said to me and what E.S.T. said to you - such a tachyon indicates a vacuum instability, not an opportunity for FTL motion; the spacelike commutators of a tachyon field are still zero. They won't believe that OPERA's neutrinos could be that sort of tachyon, unless someone demonstrates that you *can* get an appearance of spacelike motion from a tachyon condensate. Pointing out that there are basis functions which do exhibit superluminal motion (the delocalized states I mentioned previously) is a start, but it would still need to be shown that some trace of this motion can show up - that it doesn't just cancel out somehow.

    I think the best argument for superluminality within the framework of Lorentz invariance yet presented is still that VUW paper from a few weeks back (Ahluwalia et al, arXiv:1110.1162). There was a longer follow-up this week by Tim Morris of CERN (arXiv:1110.3266), which argues that the effect is real but inherently too weak to show up at 17 GeV. However, it's still early days for this idea and I expect that there are loopholes in Morris's argument, just as the idea that the right-handed neutrino is a singlet for the standard model gauge group is a loophole in the Coleman-Glashow argument.

    I even think it's conceivable that the Ahluwalia/Morris effect (also called "superluminal spreading") could show up in a conventional tachyonic theory. What if you had a neutrino-antineutrino condensate that was a tachyonic scalar, which was the cause of the spacelike scattering behind superluminal spreading? Superluminal spreading might actually be one way for "genuinely" tachyonic properties to show up.

  8. It's a Canterbury (Christchurch) paper, not a VUW paper, Mitchell. And I very much doubt they are the first to discuss such a thing, given how many people worked on tachyonic neutrinos BEFORE the OPERA result.

    And if you want to ramble on about condensates independently of emergent geometry, that's nice but please do so elsewhere. So far your opinions on this topic, although interesting, sound to me suspiciously like a condensed matter theorist's. Many of them seem to think that quantum mechanics and GR together are good enough to understand gravity. That is why there is a fluidity in discussions of condensates in the literature, but I do not accept these concepts just as they stand (especially now that so many of my prejudices have proven correct, even if nobody else notices).

    The braids, however, are fundamental, giving us a definite set of neutrino 'states'. And as we discussed some years ago, there are good basic reasons for considering two or three canonical speeds, in the sense of ordinary SR, without overspecifying the states of matter using old physics.


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