I understand that the problem with fundamental particles is that they are $0$-dimensional and therefore infinitesimal in size. This seems unphysical and leads to infinities in calculations.

The advantage of strings is that as they are $1$-dimensional they do have a finite size.

Do strings obey the following version of the uncertainty principle?

Uncertainty in length $\times$ uncertainty in vibrational momentum $\sim$ $\hbar$


1 Answer 1



The uncertainty principle is a general relation between expectation values of quantum mechanical operators - the Robertson-Schrödinger uncertainty relation. The string length is not an operator in string theory, it's just a constant $\propto \sqrt{\alpha'}$, where $\alpha' = \frac1{2\pi T}$ for the tension $T$ that appears as the free multiplicative parameter in the Polyakov action $$ S_P[h,X] = -\frac{T}{2}\int_\Sigma\sqrt{h}h^{ab}\partial_aX^\mu\partial_bX_\mu.$$ Constants do not fulfill uncertainty relations.


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