String Theory & HUP: Exploring Planck's Constant

[alpha_wolf]

How does the Heisenberg uncertainty principle work within string theory, considering that the strings's size is on the order of Planck's constant?

 

[selfAdjoint]

It is important to note that what is actually quantized is the vibrations of the string (via the world sheet). In this case the "normal modes" of the vibrations appear as quantum simple harmonic oscillators, well known from basic quantum theory. And these obey the uncertainty principle.

 

[sol2]

How could we ever concieve of the differences in orbitals and their shape?

 

[alpha_wolf]

It is important to note that what is actually quantized is the vibrations of the string (via the world sheet). In this case the "normal modes" of the vibrations appear as quantum simple harmonic oscillators, well known from basic quantum theory. And these obey the uncertainty principle.

Hmm.. let me see if I got this right..
The position and velocity of the string are not the position and velocity of the particle. Instead, as the string sweeps across space, the worldhseet it forms looks like the familiar QM wavefunction of the particle, which then defined the position and momentum of the particle in accordance with QM and the HUP. Is this right or am I completely off here?

 

[selfAdjoint]

Hmm.. let me see if I got this right..
The position and velocity of the string are not the position and velocity of the particle.

Absolutely right.

Instead, as the string sweeps across space, the worldhseet it forms looks like the familiar QM wavefunction of the particle, which then defined the position and momentum of the particle in accordance with QM and the HUP. Is this right or am I completely off here?

Still some misunderstanding. The particles we have in our low energy world ARE the vibrations. They are not the string, nor yet its geometrical positions. You use the worldsheet (and lots of math on the worldsheet) to get details on the vibrations. But it's a vibration of such and such a momentum and wave number that makes a particle. Or maybe a combination; in bosonic string theory the graviton is a combination of left moving and right moving vibrations around a closed string .