uncertainty principle of spin in (super)string theory

Question

In quantum mechanics, uncertainty principle states that we can only measure the quantity of spin in one axis but not others.

Then what about in superstring theory? As quantum mechanics is basically three-dimensional world, this does make sense, but superstring theory adopts more than three-dimensional space...

Answer 1

The properties of spin in higher dimensions mean that you can measure d/2 spin directions simultaneously, corresponding to a set of maximally commuting rotation planes. For example, in 4d, you can measure the spin in the x-y rotation plane and the z-w rotation plane, simultaneously, but not the spin in the x-y and x-w planes.

The angular momentum of objects in string theory obeys the same commutation relations as in any other quantum theory, so in string theory, the spins are restricted as above--- you can measure as many of these simultaneously as there are independent rotation planes.