Does Quantum Contextuality only apply to spin?

[Jarrodmccarthy]

I have just recently started learning about quantum contextuality and can only seem to find examples where contextuality is need to explain measurements of spin.
So I am curious as to whether quantum contextuality only applies to measurements of spin?

Also, If someone could clarify where the quantum number for spin 'comes from' since I haven't been able to find a solution where it comes out of the Schroedinger equation?

Any responses would be fantastic and apologies if the questions aren't well formulated.

 

[bhobba]

Quantum contextuality applies to momentum and position as well as spin.

Quantum spin is what you get when you apply quantum rules to angular momentum:
http://ocw.mit.edu/courses/physics/...all-2013/lecture-notes/MIT8_05F13_Chap_09.pdf

Thanks
Bill

 

[Nugatory]

Also, If someone could clarify where the quantum number for spin 'comes from' since I haven't been able to find a solution where it comes out of the Schroedinger equation?

Spin was discovered by observation. During the 1920s it became clear that a bound electron had an additional degree of freedom beyond the n,l,m quantum numbers that appear when you solve Schrodinger's equation for a spinless charged particle around the nucleus.

As with any observable, to make spin show up in Schrodinger's equation, you have to include it in the Hamiltonian. If the physical system is such that spin-related effects are negligible or non-existent (for example, a free electron in the absence of a magnetic field) then there won't be any spin-related terms in the Hamiltonian.

 

[Nugatory]

I have just recently started learning about quantum contextuality and can only seem to find examples where contextuality is need to explain measurements of spin.
So I am curious as to whether quantum contextuality only applies to measurements of spin?

As far as the mathematical formalism of QM is concerned, everything is contextual. Spin and photon polarization are used as examples most often because it's relatively easy to design experiments using them to demonstrate contextually.

 

[Jarrodmccarthy]

As far as the mathematical formalism of QM is concerned, everything is contextual. Spin and photon polarization are used as examples most often because it's relatively easy to design experiments using them to demonstrate contextually.

Thank you very much.
All of what you said made sense so thank you.

 

[dextercioby]

Quantum spin angular momentum is a consequence of group theory (Galilei group for Newtonian spacetime, Poincare group for Minkowski spacetime), and Pauli's equation for the non specially relativistic case follows as the only option to have a 2nd order PDE which incorporates spin. This derivation was made by Levy-Leblond in the golden era of the 1960's.