Wavefunction collapse postulate

[Zareon]

Hi, I have a question that's been bugging me for a while now. According to QM a measurement collapses the wavefunction into an eigenstate of the measured eigenvalue (projection upon measured eigenspace).

 

If I take the Stern-Gerlach apparatus. WHEN does the wavefunction collapse? (When is the measurement made?)

Is it when the electron leaves the magnetic field?

Or when the electron hits the plate?

Or when I look at the plate?

Or otherwise?

 

I thought (actually, just assumed) that it happened when the electron hits the plate, but I`m not sure anymore. Is there any detectable way in which we can distinguish these cases (in particular case 1 and 2).

[timo]

I am not really sure if the collapse of the wave function is actually understood at all. For technical purposes, you can simply assume that it happens at the point at which you don´t expect anything which requires a QM-description to happen anymore. Example: If you approximate your photo plate as a binary system which either marks a dot when it's hit by an electron or doesn´t when there is no electron coming in, then that seems like a very suitable point to collapse the wave function.

Making it dependent on whether you look at the plate seems a bit too esoteric to me. What if I look at it and tell you the result, for example?

[swansont]

As soon as they interact with the magnetic field — that's the relevant interaction. Spin up atoms go one way, and spin down atoms go the other way, and you no longer have a superposition of states.

[Zareon]

Thanks for the replies.

 

swansont, I believe to have read (I think in Cohen-Tannoudji's Quantum Mechanics) that in this case the wavefunction is spread in space in two parts. It's in a superposition of two wave-packets, one which goes up and one which goes down according to spin and it collapses when it hits the plate. It's fine with me either way. The relevant question is whether there is a measurable difference between the two.

I guess two measurements are involved. One of the z-component of spin, the other of the position, but they commute so you measure both at once and it doesn't matter.

But there's this new QM book "Quantum Physics" on the market by M. LeBellac which introduces something like an ideal measurement which does not disturb the state when you measure it (and says the measurement postulate is redundant). There have also been so-called 'quantum nondemolition' experiments which do this. It goes straight against what I learned: that you can't measure a quantum state without disturbing it.

 

Any enlightenment on this is greatly appreciated.

[swansont]

I guess two measurements are involved. One of the z-component of spin, the other of the position, but they commute so you measure both at once and it doesn't matter.

 

I think that's the salient point. They are two separate measurement, and don't have to occur at the same time.

[MattC]

As soon as they interact with the magnetic field — that's the relevant interaction. Spin up atoms go one way, and spin down atoms go the other way, and you no longer have a superposition of states.

 

Do any magnetic fields in the universe, regardless of how weak they are, ever completely fade to nothing? I have always imagined that the gravity and magnetic field of my body has some effect, however imperceptibly small, on every other piece of mass (by gravity) and every magnetic field in the universe. While it may never be possible to measure such a tiny effect, it should have some effect - perhaps because of me an entire star will move (during my lifetime) by 10^-1,000,000,000,000 meters.

[swansont]

The field from one source never drops to zero, but you have multiple sources and they fluctuate; you have fields from EM radiation continually present. What will matter is the field averaged over the size of the atoms, and over some period of time.