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As I understand there is a problem in physics where point-like massive (or charged, etc.) particles would have infinite mass/energy (or charge, etc.) density.

I'm curious how in the context of String Theory how we address the same problem?

I have come to understand Strings as 1-dimenstional objects from which I conclude they have no volume.

Do they have infinite energy density because they have no volume?

(This question comes from a discussion which you can follow here for further context. https://www.facebook.com/notes/gm-jackson/is-string-theory-really-mathematically-consistent-with-classical-physics/1006863599387308)

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  • $\begingroup$ There are no point particles. That leaves only one question: why should there be strings? $\endgroup$
    – FlatterMann
    Commented Apr 23, 2023 at 1:17
  • $\begingroup$ @FlatterMann Are you saying the classical limit does not exist? $\endgroup$
    – Simp
    Commented Aug 30 at 16:45
  • $\begingroup$ @Simp I have yet to see either a point particle or a sting in the classical limit, either. The classical limit of "point particles" (which is a mirage, by the way) would be particle tracks, but I don't see how we can ever hope to resolve a similar emergent phenomenon for strings. $\endgroup$
    – FlatterMann
    Commented Sep 23 at 18:06

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"Do they have infinite energy density because they have no volume?"

Energy density is E/V. If V = 0, then the energy density is infinite.

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  • $\begingroup$ Sure. Why not? The whole point of string theory is to create a theory of everything. $\endgroup$
    – William Pinn
    Commented Mar 4, 2016 at 16:32
  • $\begingroup$ What does creating a ToE have to do with the validity of the assumption that a 1D object must have infinite energy density? There are an infinite number of points along a line segment. Can't the energy be split up into infinitely many finite but tiny pieces and stored along the string's length? Might the total energy be a converging sum and the density at each point along the string's length approach zero? $\endgroup$
    – James William
    Commented Mar 4, 2016 at 18:34
  • $\begingroup$ en.wikipedia.org/wiki/Density $\endgroup$
    – William Pinn
    Commented Mar 5, 2016 at 3:14
  • $\begingroup$ "Might the total energy be a converging sum and the density at each point along the string's length approach zero?" Good question. Quantum physics measures energy in discrete integer units. So I don't know that it can approach zero like a calculus limit. $\endgroup$
    – William Pinn
    Commented Mar 5, 2016 at 5:03
  • $\begingroup$ But we're talking about String Theory, not Quantum physics. How is energy actually "stored" in strings? Don't the properties of fundamental particles (charge, color, mass, etc.) arise from vibration modes of strings? So maybe my question would have been better put as, "Do strings themselves contain gravitational singularities as would point-like particles?" $\endgroup$
    – James William
    Commented Mar 5, 2016 at 21:33

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