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kith

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Initially, the spin state and the spatial wavefunction are independent. After the interaction, you have entanglement: if a particle is detected in the upper part of the detector, its spin state is up. If it is detected in the lower part, its spin state is down.

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naima

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A pure state is defined as a state, whose statistical operator is a projection operator

$$\hat{\rho}=|\psi \rangle \langle \psi|$$

with some normalized state vector. Unitary time evolution maps a projector into a projector, and thus a pure state stays a pure state.

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naima

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I was talking about the entanglment with the SG apparatus with its screen

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naima

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What you said is valid in classical physics. You can talk about static devices and of particles in an external field. In QM particles interact with the external field. and there is no static device.

When a subsystem evolves while interacting with another subsystem, there is a unitary time evolution but it acts on the global system.

Take the case of the "static" Young screen with two slits.

It can be decribed with two orthogonal vector; Its ground state |Y0> and its excited state |Ye> when a photon is captured.

The photon at the slit can be described with 3 orthogonal vectors |S1>, |S2> and |S3> (in front of slit 1 or 2 or somewhere else)

At the beginning we have the tensor product of Y0 and of a superpositon S1,S2 andS3.

A unitary interaction maps this to ##Y0> \otimes(aS1> +bS2>) + Ye>\otimes c S3>##

After interaction, the photon is in a mixed state of## |S_0>< S_0|## and ##(|S_1> + |S2>)(<S_1|+<S2|)##

We can also place the SG device behind the Heisenberg cut and have the same thing.

When a subsystem evolves while interacting with another subsystem, there is a unitary time evolution but it acts on the global system.

Take the case of the "static" Young screen with two slits.

It can be decribed with two orthogonal vector; Its ground state |Y0> and its excited state |Ye> when a photon is captured.

The photon at the slit can be described with 3 orthogonal vectors |S1>, |S2> and |S3> (in front of slit 1 or 2 or somewhere else)

At the beginning we have the tensor product of Y0 and of a superpositon S1,S2 andS3.

A unitary interaction maps this to ##Y0> \otimes(aS1> +bS2>) + Ye>\otimes c S3>##

After interaction, the photon is in a mixed state of## |S_0>< S_0|## and ##(|S_1> + |S2>)(<S_1|+<S2|)##

We can also place the SG device behind the Heisenberg cut and have the same thing.

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I agree with that. So if the application of the field alters the state (and I am supposing also the spin directions) why are we surprised that the correlations in the SG experiment are greater than we would expect if the angles of spin were fixed in a given direction?

Initially, the spin state and the spatial wavefunction are independent. After the interaction, you have entanglement: if a particle is detected in the upper part of the detector, its spin state is up. If it is detected in the lower part, its spin state is down.

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kith

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Ah, I didn't get that this is what you are interested in from your initial post.So if the application of the field alters the state (and I am supposing also the spin directions) [...]

Ok, let's suppose we send a particle in state ##| \! \uparrow \rangle_x## through an SG-apparatus oriented in ##z##-direction. The probability to observe ##| \! \uparrow \rangle_z## is 50%. So the interaction with the SG-magnet at least doesn't simply align the spin magnetic moment with the magnetic field gradient deterministically.

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kith

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How would you apply this logic to the state ##| \!\! \nearrow \rangle##?

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I would rotate the whole setup by 45 degrees.

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kith

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I think you are saying that it wouldn't work for 30 degrees or 60 degrees. Is that correct?

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kith

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On the other hand, it is a bit difficult for me to tell what exactly "it" is because you didn't elaborate much. I'm not interested in leading an endless discussion here. If you want to talk about why some classes of models don't work, please specify such a model in more detail so that there's something tangible to discuss.

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OK, thanks for your responses.

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