# Sequential stern-gerlach experiment

## Main Question or Discussion Point

I'm just getting the basics of quantum mechanics and I had a question regarding a modification of the stern-gerlach experiment that I think might help me understand the superimposed eigen-states better. Could someone please clarify what one would expect in the following situation?

Suppose we take a *single particle* and pass it sequentially through the following set of filters SGz, SGx, SGz, SGx, SGz, SGx, .... so on what will the measured values of the particle's spin be?
Say the result of the first two filters is +, - then will the following filters also record +,-,+,- so on or will the sequence be completely random?

Will the result predicted by QM depend on what sort of interpretation one subscribes to, for example copenhagen vs statistical or deterministic vs non-deterministc?

## Answers and Replies

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Do the + and the - outputs of the first SGz filter lead to the same SGx filter, or does each output lead to a different SGx filter, so the system is set up like a tree?

If there is just one linear sequence of filters, then they don't "record" anything - there is no way to tell whether they went + or - if you merge the output stream. Indeed, according to quantum theory it doesn't really make sense to say that there was a definite outcome.

If there is a tree of filters, so by looking at the detector at the very end, you can tell what the result of each spin measurement had to be, then the sequence will be random. A known output of an SGz filter, say +, will cause the next SGx measurement to be random all over again, and so on.

zonde
Gold Member
If I can propose answer from deterministic viewpoint then the answer is still this:
If there is a tree of filters, so by looking at the detector at the very end, you can tell what the result of each spin measurement had to be, then the sequence will be random. A known output of an SGz filter, say +, will cause the next SGx measurement to be random all over again, and so on.
And deterministic part in this answer is that after last SG filter only thing you can know from supposed hidden variable is whether particular particle will be included in measurement sample or not.

thanks guys ... that seems to clear up some of my doubts