Spin & the Stern-Gerlach Experiment: Real Answer?

[alfredblase]

The Stern-Gerlach experiment tells us that when we ascertain the spin of an elementary particle in a particular direction, this can only take 2s + 1values. If I ask "why does this phenomenom occur?", is there a real answer, or is the only answer we can give, "it just does"?

 

[marlon]

The Stern-Gerlach experiment tells us that when we ascertain the spin of an elementary particle in a particular direction, this can only take 2s + 1values. If I ask "why does this phenomenom occur?", is there a real answer, or is the only answer we can give, "it just does"?

You should answer that this property is inherent to nature just like the sun rises and sets each day Or, just answer that it is a manifestation of rotational symmetry of our physical laws and equations.

On a more mathematical level, spin arises due to the fact that QM (and physics in general) is invariant under rotations. For example, suppose you know the expectation value of some QM observable that depends on the x, y and z coordinates. If you perform a rotation onto these coordinates, the expectation value cannot change. It must have the same value before and after the rotation has been performed. Hence, you have invariance under rotations.

If this property is respected (and it is ofcourse) the wavefunctions must behave in a "certain way" under rotations. "Certain way" means that if you rotate them over 360 degrees, you get the opposite value. Do this again and you get the same initial value. Objects that behave this way under rotations are called spinors and the spin quantumnumber is a number that labels such spinors.

Keep in mind that spin has nothing to do with atoms rotating along some axis. The link with rotations is that of "invariance under rotations" so it is not the object that is rotating but the coordinates !

regards
marlon

 

[Rade]

...The link with rotations is that of "invariance under rotations" so it is not the object that is rotating but the coordinates !regards marlon

I have a few questions--(1) exactly how many "coordinates" are predicted by QM theory to be rotating in relation to an "object" ? (2) If we assume the "object" has mass and a wavefunction, would not the wavefunction exist with both external motion (within configuration space) and internal motion (within spin space)--and thus would not the "object" also rotate within spin space, not just the coordinates ?

 

[abszero]

Objects with spin rotate in different ways. Fermions and bosons pick up different phases with rotations, so it depends on what your real space wave function is producted with in terms of spinors. To get a full rotation, you have to have the rotation operator in both real space and spin space, and they are different.

 

[marlon]

The spin part of the wavefunction is ofcourse defined in spin space. When performing the rotation of the spin coordinates, this wavefunction acquires the shift in phase which determines the spinor behaviour i talked about.

marlon