- #1
MichPod
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- TL;DR Summary
- Can an atom coming out of Stern-Gerlach apparatus be considered to be in a superposition state?
Considering SG experiment, it is usually described as if an atom in the end of its path (but before being detected on the screen) is in the superposition state, say, ##|\textsf{spin up}, \textsf{upper path}\rangle+|\textsf{spin down}, \textsf{lower path}\rangle##. Some books (Feynman lectures, 3rd volume) go further and claim that this superposition state may be "merged" back by another SG apparatus, restoring the original spin of the atom, particularly, if the atom entering the first apparatus (oriented in Z-direction "up") had the state |spin-left> (oriented in X direction), then the same state could be restored after the second apparatus (oriented in Z-direction "down").
The problem I see in the above description is that IMO the states of the atom leaving the SG apparatus must be entangled with the vertical shift of the magnets of the apparatus which they acquire when deflecting the atom. Therefore, the actual state of the system (a case with one apparatus) should actually be
$$|\textsf{spin up}, \textsf{upper path}\rangle\otimes|\textsf{apparatus shifted down}\rangle+$$
$$+|\textsf{spin down}, \textsf{lower path}\rangle\otimes|\textsf{apparatus shifted up}\rangle$$
and very soon, probably, this state should decohere into the mixed state of the above two addends (due to the interaction of the apparatus with the environment).
But whether there is such a decoherence, or whether we have just an entangled state of the atom and the apparatus as a result of the first SG apparatus action on the atom, there is no possibility that the second apparatus acting on the same atom alone (and not on the first apparatus) may restore its original spin. Specifically, the second apparatus could, in theory, restore the original atom state if it got the atom in the superposition state, but the atom actually is not in such a superposition as it is entangled with the first apparatus.
I vaguely remember I could have read somewhere this sort of argument (I could not google it now). That is, I am not claiming there is something new here, I'd rather ask the participants to please review this and tell whether this argument is right or whether I am missing something.
The problem I see in the above description is that IMO the states of the atom leaving the SG apparatus must be entangled with the vertical shift of the magnets of the apparatus which they acquire when deflecting the atom. Therefore, the actual state of the system (a case with one apparatus) should actually be
$$|\textsf{spin up}, \textsf{upper path}\rangle\otimes|\textsf{apparatus shifted down}\rangle+$$
$$+|\textsf{spin down}, \textsf{lower path}\rangle\otimes|\textsf{apparatus shifted up}\rangle$$
and very soon, probably, this state should decohere into the mixed state of the above two addends (due to the interaction of the apparatus with the environment).
But whether there is such a decoherence, or whether we have just an entangled state of the atom and the apparatus as a result of the first SG apparatus action on the atom, there is no possibility that the second apparatus acting on the same atom alone (and not on the first apparatus) may restore its original spin. Specifically, the second apparatus could, in theory, restore the original atom state if it got the atom in the superposition state, but the atom actually is not in such a superposition as it is entangled with the first apparatus.
I vaguely remember I could have read somewhere this sort of argument (I could not google it now). That is, I am not claiming there is something new here, I'd rather ask the participants to please review this and tell whether this argument is right or whether I am missing something.
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