Imagine a z-basis spin Stern Gerlach experiment where a single particle is put through the apparatus. The output is a spin state vector consisting of the sum of the two z-spin states.
Each spin state is multiplied by a square root of the probability of being in that state. Each spin state is al...
@CuriousOne, the wave function's disjoint (but superposed) packets have a trajectory, but the position of the particle is still uncertain and governed by quantum probabilities.
The separation in a real Stern-Gerlach is so large that the uncertainty is of no importance. You should also estimate how many photons are involved and what that does to the particle in terms of an almost continuous weak position measurement.
@CuriousOne You mean photons from the environment? Let's keep it simple and say there are none. The Stern Gerlach part was just to set up the questions, so they can be visualized. Stern Gerlach is not essential to the questions.
In any case, I am wondering if a wave function can be created such that it has two non-zero Gaussians, separated in space, and Gaussian 1 can entangle with one thing and Gaussian 2 can entangle with something else.
Then, somehow, a measurement selects Gaussian 1. Does the effect that Gaussian 2 had on the "something else" get nullified at that time?
Well, in the double slit experiment, if you put a parallel polarizing filter over one slit and a perpendicularly polarizing filter over the other slit, the two emerging waves (which are part of the same wave function; superimposed) each entangle with a different polarization eigenstate. The result is they no longer interfere. So, different superimposed parts of the same wave functions can interact differently with their environment.
You are still not entangling different parts of the wavefunction, you are simply modulating the strength of entanglement. None of this has anything to do with what's really happening in Stern-Gerlach.
I don't now what dotted lines mean... maybe that I am writing?
Whatever we call it, the two superimposed parts of the same wave function each become linked to a different part of the environment. I find that interesting and am trying to follow that idea through.
I do think, by the way, that you got a valid point. If you were to perform the experiment in a really weak magnetic field, so that the separation is very small, there should be some sort of interference.
Aharonov is Mr. Weak Measurement, isn't he? I am only familiar with ordinary QM, not QFT or QED. Just a B.S. in physics and an enduring interest in the nature of wave functions. SQUIDs are beyond what I know. weak measurement with SG I have read about.
Anyway, if the wave function of X consists of W1 and W2 waves, superimposed, and W1 can interacts with system A while W2 does not, but instead interacts with system B, and then there is a measurement of X, wiping out W2, what happens to how B evolved since interaction with W2?
Aharanov-Bohm is when you pass the beam around a solenoid or a magnetized ring and you see an interference term even though the beam doesn't actually go trough the active magnetic region. It proves a phase shift effect by the vector-potential, if I remember correctly.
I see. Again, beyond me at the moment. I do find weak measurements interesting though. It seems like a bit of an attempt to introduce a kind of determinism.
Weak measurement can, for instance, explain why there are classical trajectories. Not sure you need that for your example. I only brought it up because as soon as you have macroscopic separations in Stern-Gerlach, you would be in a regime where quantum interference doesn't play any role any longer. You are clearly not analyzing in that regime.
Agreed. Anyway, it is 3:45 AM where I am. Have to go, now. Thank you for your interest and your insights! I welcome any further thoughts that you have.
Discussion between David and CuriousOne
Discussion between David and CuriousOne