Thought Experiment: Force on magnets in a Stern Gerlach Experiment

Question

Background:

In the SG experiment, an inhomogenous magnetic field affects a force on particles passing between two magnets.

"Measurement" takes place when a screen is placed on one end, blocking one of the states. The final measurement we perform (spin state of particles exiting) is heavily dependent on whether we perform a measurement or not, whether by blocking particles exiting the device or by blocking particles by setting up a screen within a modified SG device

Modified SG device

The interaction between the particles and magnets should also exert a force on the magnets, causing them to move slightly.

The motion of these magnets seems to not affect the outcome of the experiment significantly, yet that would imply that the motion of the magnets could be measured without affecting the outcome of the experiment.

This seems at odds with Heisenberg's uncertainty principle, that we are getting information for free.

My Professor tells me that the force exerted on the magnets by the particles is so minuscule that it cannot be measured (I assume it is similar to how we can't measure particles' momentum and position simultaneously, because any photons we shoot at the particle will end up imparting change?)

What's going on here? I wanted to double check here and see where I went wrong with my assumptions.

A relevant Physics.SE answer about measurement: What constitutes an observation/measurement in QM? — BMS, Sep 10 '14 at 14:53
I would say that measurement is the magnet. Besides, the magnets are anchored. — Ignacio Vergara Kausel, Sep 10 '14 at 15:11
Help me to understand: what added information are you getting from your experiment? — CuriousOne, Sep 11 '14 at 00:38
My initial thought was that measuring the force on the magnets would tell you about how many particles are splitting up and down inside the chamber, respectively. — ejang, Sep 11 '14 at 13:28
The "photon imparting momentum" argument is bogus. So is most everything you hear about QM that invokes "measurement". There is no special measurement process, there is only time evolution according to the Schrödinger equation. — Robin Ekman, Mar 16 '16 at 09:35

score 2 · Accepted Answer · answered Sep 10 '14 at 15:20

2

The interaction is not a measurement because the probability that it will produce a measurable change in the momentum of the reflecting object is extremely small. The magnet is in a mixed state in which its momentum has a range of values that is large compared to the change in momentum produced by the force exerted by the electron. So the shift in the magnet's momentum as a result of the electron passing will be so small that it will not be detectable with very high probability. I don't know the exact numbers but let's say it's -1,000,000 to +1,000,000 in units of the momentum the electron will impart. The electron changes the magnet's momentum by +1 so that the range is now -999,999 to +1,000,001. So the probability is large that if you measure its state you won't detect any difference.

answered Sep 10 '14 at 15:20

alanf

7,424

Is this argument based on the limits of technology? – BMS Sep 10 '14 at 16:58
No. The probability of detecting a difference is small because the probability of such a difference is small. – alanf Sep 11 '14 at 08:40
This is the correct answer, I don't understand the downvote. The magnet's state after the interaction is indistinguishable from the state before, hence there is no additional information gained by measuring it. In particular there is no "which-way" information that would destroy interference (the OP's picture is essentially a Mach-Zehnder interferometer but with SG apparatus). – Mark Mitchison Feb 10 '16 at 21:17

Thought Experiment: Force on magnets in a Stern Gerlach Experiment

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