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In quantum mechanics, the spin of a particle corresponds to a magnetic moment - and so a particle in a magnetic field gradient, e.g. a Stern-Gerlach experiment will have its spin measured by the magnetic field.

Furthermore, measurements in quantum mechanics collapse of the quantum state of the system, irrespective of whether a sentient being is there to watch it happen. So, if you have a box opaque to all EM radiation (so we cannot "see" inside) which contains a Young's Double slit experiment and a fully robotic sensor on one of the slits, you will not see an interference pattern when you check the results of the experiment after it is complete.

My question is the following:

Take a spin $\frac{1}{2}$ particle. We know from quantum mechanics, the possible values of its spin along any axis are $\hbar/2$ or $-\hbar/2$.

Can the spin of this particle be measured, and will the wavefunction collapse, due to an arbitrarily small $B$-field gradient? If so, then shouldn't the spin of every particle being measured always be due to the fact that $B$-fields extent to infinity, so the nearest bar magnet, MRI machine, star, etc. will always have an effect on a quantum system?

So often textbooks say something like "prepare a spin $\frac{1}{2}$ particle in a state $|\uparrow\rangle$ and shoot it through a Stern-Gerlach experiment" - but as soon as this state is prepared, its spin will be measured by countless external $B$-fields giving $\hbar/2$s or $-\hbar/2$s in a bunch of random directions and so your state is ruined.

My guess is that the examples given in an introductory QM course are, like a lot of things, a simplification. Any explanation would be appreciated though.

Brendan Darrer
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Poo2uhaha
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  • What is $\hbar/2$s or $-\hbar/2$s? Do you mean the plural, i.e. lots of $\hbar/2$ or $-\hbar/2$ spin states? – Brendan Darrer Mar 06 '22 at 12:49
  • Also, in your second paragraph, do you mean to say this: "Furthermore, measurements in quantum mechanics collapse of the quantum state of the system, are irrespective of whether a sentient being is there to watch it happen."? – Brendan Darrer Mar 06 '22 at 12:53
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    "We know from quantum mechanics, its possible values of its spin along any axis " ' I think you are using the word "any"as if it means "all". The "any" means "any choice of axis to measure the spin on". For a given set up, the magnetic field adds up to one direction in the location of the particle whose spin is to be measured. – anna v Mar 06 '22 at 13:23
  • I am not an experimental physicist (rather, just a mathematician) to provide a definite answer to your question, but from what I understand it will not be the case that there will be the spin measurement (as a "strong measurement") if the magnetic field (gradient) is weak; it has to be very strong, actually. Otherwise, there is just a (one of the possible infinity of) interaction of the "particle" with the environment or apparatus (resulting in an entanglement). In fact, this can just as well be used to "unitarily control" the "particle". – Mahir Lokvancic Mar 06 '22 at 14:32
  • @BrendanDarrer In response to your comments (in descending order): I mean the plural; I don't think your correction is grammatically correct, c.f. Rainclouds make my clothes wet, are grey - I may be wrong though, apologies if so. – Poo2uhaha Mar 06 '22 at 17:48
  • Also, very closely related: https://physics.stackexchange.com/questions/460855/why-arent-particles-constantly-measured-by-the-whole-universe. In particular, this answer answers OP's question perfectly IMO. –  Mar 06 '22 at 22:39

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