0
$\begingroup$

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 $\sim$ $\hbar$

$\endgroup$

1 Answer 1

4
$\begingroup$

No.

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.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.