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I was watching Susskind lectures in string theory. There he explains that open strings can both, split at any point, and also join at the ends when the ends touch at a single point. I have one question about each of these two processes.

  1. Is not the likelihood that the two ends of a string end up at the same spatial position of measure zero? Or the two ends do not need to really meet at the same point, but only be close and then they will be attracted to each other to make it closed?

  2. If and open string breaks at an arbitrary point, would not this create particles of arbitrary mass? as the rest mass is proportional to the length? but we know particle masses do not form a continuum.

What am I thinking wrong?

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    $\begingroup$ The problem of "infinitesimal objects meeting at the same point" also applies to e.g. an electron absorbing a photon, if you think of those as point particles. But they are actually described by wavefunctions over all the possible positions, and wavefunctions easily overlap. The same applies to strings, although the configuration space for a string is more complicated (it becomes tractable by considering the center of mass, and the Fourier modes, as the classical string's degrees of freedom, on top of which the string wavefunction is defined) $\endgroup$
    – Mitchell Porter
    Commented Oct 13, 2023 at 2:16
  • $\begingroup$ @MitchellPorter Thanks, any comments on the second question? $\endgroup$
    – Pato Galmarini
    Commented Oct 13, 2023 at 2:18
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    $\begingroup$ Again the answer would be to think in terms of string wavefunctions. One is not considering line segments of arbitrary length, with mass proportional to their length, but rather string wavefunctions which are mass eigenstates, and in which mass depends on the excitation of modes of the string as quantum harmonic oscillators... But also, the basic facts are more complicated. Open strings have to be attached to branes and can only break at a point touching the brane; and an open string that isn't spinning contracts to zero length, i.e. just a point.. physics.stackexchange.com/a/5302/1486 $\endgroup$
    – Mitchell Porter
    Commented Oct 13, 2023 at 2:29
  • $\begingroup$ @MitchellPorter Thanks a lot $\endgroup$
    – Pato Galmarini
    Commented Oct 13, 2023 at 2:31
  • $\begingroup$ Those should be answers. $\endgroup$
    – mmesser314
    Commented Oct 13, 2023 at 2:45

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