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String mass - what do we know?

  1. Sep 8, 2004 #1
    As I understand the situation, string theory really has made no connection to reality yet. We don't seem to be able to calculate anything from string theory and confirm those calculations with observation. Or have I misunderstood? For example, we cannot even calculate the mass of a particle yet. Hatfield's book, QFT for points particles and strings, page 485, writes, "We know that all observable particles are not massless, and that the world at ordinary energies is not supersymmetric. Therefore, it is impossible to do true phenomenology from perturbation theory alone. (When we mentioned that some candidate vacuum states gave reasonable phenomenology, the supersymmetry breaking effects had to be added by hand.)"

    However, we find equations for the mass squared operator on page 513 of Hatfield eq 20.52 and also in Zwiebach's, First Course in String Theory, page 163 eq 9.82 for classical relativistic strings, page 232 eq 12.173 for quantum relativistic open strings, page 255 eq 13.48 for quantum relativistic closed strings, and page 265 eq 13.99 for supersymmetric strings. These are put in terms of the number operator defined in Zwiebach, page 233 eq 12.174.

    Are these in the general, non-perturbative form that Hatfield speaks of? Is there anything we can learn about the dependence of the mass on, say, frequency and mode number from these equations?
    Last edited: Sep 8, 2004
  2. jcsd
  3. Sep 12, 2004 #2


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    The massive particles determined by the expressions you quote are TOO massive to be observed in our low energy world; their energy equivalent is orders of magnitude above any energy we could hope to create. So the phenomenology, like Zweibach's chapter 15, works with massless particles, and assumes they get mass form some broken symmetry, like the Higgs mechanism.
  4. Sep 13, 2004 #3
    So is anything salvagable from the formulas I reference? Or do we simply not know at this point anything about the behavior of the final formula for the mass of massive strings?

    For example, wouldn't it be true that the apparent mass of a fast approaching string would not depend on the angle at which it approaches? Must it also not depend on the frequency of vibration so that time dilation does not reduce it to zero at "c"? Even if the mass were to depend only on the number of nodes, the mode number, which happens to be Lorentz invariant, even then, is it possible that time dilations slow the frequency so much that it becomes impossible to distinguish the number of nodes? Questions, questions... Are there any answers? Thanks.
  5. Sep 15, 2004 #4
    I thought that finding the mass spectrum of particles was the whole inspiration that started string theory. Could it be that one of our starting assumptions about how strings operate is in error? If not, then why does this incongruence not prove string theory wrong?
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