The nature of wavefunctions collapse

[Jilang]

This post is a result of reading RKaster's links and I am wondering if there is some evidence that supports measurement being a two stage process. In the Stern Gerlach experiment the particles are in superposition until measured. But is the superposition ended once they enter the magnetic field?

If we have a particle prepared in a spin up direction and then seek to determine its direction in a left right direction what is occurring? Is the left/right distinction made when the magnetic field is applied or when it it finally measured? Is there an experiment that can distinguish between the two situations?

 

[mikeyork]

If we have a particle prepared in a spin up direction and then seek to determine its direction in a left right direction what is occurring?

When you select a new orientation to measure the spin projection you are changing the frame of reference (the choice of z-axis, for instance). This rotation is a unitary transformation in Hilbert space that effectively converts an eigenstate in one basis (choice of z-axis) to a superposition in another (a different choice of z-axis)

Is the left/right distinction made when the magnetic field is applied or when it it finally measured?

I think that is an unanswerable question without further assumptions concerning your interpretation of QM. IMO the best way to think of this is that the transition takes place the moment the magnetic field is applied, but which state results is not known (or knowable) until observed.
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[Jilang]

I think that is an unanswerable question without further assumptions concerning your interpretation of QM. IMO the best way to think of this is that the transition takes place the moment the magnetic field is applied, but which state results is not known (or knowable) until observed.
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I came to this conclusion too, but why would it be dependent on interpretation?

 

[mikeyork]

I came to this conclusion too, but why would it be dependent on interpretation?

Because some people think the state becomes determinate at the moment of observation ("collapse of the wave function").

 

[Jilang]

I suppose that hangs on what is defined by the "state". Namely the one that is truly indeterminate and the the one that describes what we just don't know. Seems to me that we need two separate definitions (is this the pure and mixed states? ) Without both of them the theory is somewhat cloudy.

 

[mikeyork]

By "determinate" I intended an eigenstate of the observable spin projection operator.

 

[Nugatory]

I suppose that hangs on what is defined by the "state". Namely the one that is truly indeterminate and the the one that describes what we just don't know. Seems to me that we need two separate definitions (is this the pure and mixed states? ) Without both of them the theory is somewhat cloudy.

There's only definition needed - the density matrix formalism covers both pure and mixed states. And in this context "somewhat cloudy" sounds like another way of saying "depends on your interpretation".

The only thing you have observed is the position where the particle landed on the screen, and the theory did a fine job of predicting the possible outcomes and their respective probabilities. Everything beyond that (Did the wave function collapse when the particle passed through the magnetic field? When the particle reached the screen? Did it collapse at all? Where was the particle between the the moment before it reached the screen?...) is interpretation.

 

[Jilang]

That's an interesting viewpoint. So when the magnetic field splits the beams would you regard the particles as still in superposition?
Afterthought. Does the density matrix formulation distinguish between the pure and mixed states or not?

 

[mikeyork]

As far as a future observer is concerned, yes. But, IMO, the underlying reality is that the particle is in an eigenstate from the moment of application of the splitting field. But we are getting into an area where some moderator will soon intervene and start deleting posts.

 

[Jilang]

That is interesting that you have such a concern, but I don't think it's a matter of interpretion. I was more wondering if there was a way to distinguish it either way,

 

[mikeyork]

That is interesting that you have such a concern

It's because I am inclined to the view that normal co-ordinate space-time is emergent and not fundamental. (Spin projection is a spatial property. But spin itself is intrinsic.) Apparently that is considered too speculative here.

but I don't think it's a matter of interpretion. I was more wondering if there was a way to distinguish it either way,

I don't know of any way.