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A change of magnetic field caouses an electric field and an associated potential which is as high as the time derivative of the magnetic field.So is it possible that the change of the spin should be a finite derivative regarding time?

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  • $\begingroup$ The question is not very clear: why electric field should affect spin? What change of magnetic field are we talking about? - instantaneous? electromagnetic wave? $\endgroup$ – Vadim Oct 2 at 13:15
  • $\begingroup$ @Vadim in simple cases the spin couples to the B field, but the E field can affect the spin if the particle is moving. For example, the spin of an electron in an atom is coupled to the electric field of the nucleus via the Dirac equation. $\endgroup$ – Quillo Oct 2 at 13:36
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The spin evolution is continuous and deterministic (i.e. you have to evolve the state of the particle, or atom, containing information about its spin with the Schrodinger equation). In fact, Schrodinger equation is deterministic and the evolution will depend on the externally changing fields that couple to the spin (and possibly other degrees of freedom of the atom/particle).

It can be a messy evolution, especially in an atom where there are electron-electron interactions. For a single particle it's simpler (i.e. you have to consider the Schrodinger equation for a single electron in an external electro-magnetic field that can change in time).

However, as long as the external fields change continuously, the state of the particle (and its spin) will evolve continuously. Only if you "measure" the spin, then the state will collapse into a definite spin eigenstate (immediately, according to standard QM), but this has nothing to do with the changing magnetic field (it is simply the fact that the measurement procedure is not governed by the Schrodinger equation).

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  • $\begingroup$ I agree with this answer mostly; however, I don't like how it equates the changing quantum state with the spin of the particle actually changing. If the state is a superposition of spin states then you can't really talk about the spin of the particle. $\endgroup$ – BioPhysicist Oct 2 at 13:23
  • $\begingroup$ Not sure what you mean. I was just saying that you have to write down the Sch evolution for all your dof that are relevant to the spin evolution. The quantum state contains everything in principle as it depends on the physical setting you want to consider. You can also consider just a single spin in a B field, that's easy. In an atom it's not, and you are forced to consider a many-electron wave function. $\endgroup$ – Quillo Oct 2 at 13:30
  • $\begingroup$ I just find it odd to talk about spin evolving continuously when it is quantized $\endgroup$ – BioPhysicist Oct 2 at 13:36
  • $\begingroup$ The $S_z$ eigenvalue is quantized, this does not mean that the state (i.e. the wave function) cannot evolve continuously. Simplest example: think about the eigenstates of the harmonic oscillator. They are quantized, but the state of a particle in the harmonic trap evolves continuously. The same for the spin: in the simplest single-particle scenario you will have a non trivial mixture of UP and DOWN with relative phase that evolves in time.. but the evolution is continuous. $\endgroup$ – Quillo Oct 2 at 13:56
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    $\begingroup$ Right, so you should qualify your answer by saying you are talking about the average spin changing continuously, not the spin itself. $\endgroup$ – BioPhysicist Oct 2 at 14:08
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Answering the title:

When a particle changes its spin orientation is it instantaneous?

An elementary particle is a quantum mechanical entity which is described by the numbers in the table, including a fixed spin. The spin of a charged particle will be changing orientation when interacting with electric and magnetic fields. Even though the changes in direction obey classical electromagnetism, there is still the quantum mechanical energy-time uncertainty

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that imposes a non instantaneous interaction, given the energies involved. The uncertainty principles are the envelopes of the possible exact solutions of a particular quantum mechanical interaction.

The same is true in all problems where there exists and intrinsic quantum mechanical total spin, as with composites like protons , or even atoms and molecules, i.e. where the quantum mechanical frame is necessary.

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