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Background

So I am reading the following here (Blog: Not Even Wrong, Blog post: Not So Spooky Action at a Distance, Commenter: vmarko)

"The collapse postulate is also present in QFT, only hidden inside the LSZ formula. But if you are against using the collapse postulate to describe measurements, then your main problem is neither non-locality nor Bell’s theorem, but rather the measurement problem of QM."

Question

I'm still confused how: "The collapse postulate is also present in QFT, only hidden inside the LSZ formula"? Infact, I wasn't even aware the LSZ has anything to do with the measurement.

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  • $\begingroup$ Minor comment to the post (v2): Please consider to mention explicitly author, title, etc. of link, so it is possible to reconstruct link in case of link rot. $\endgroup$ – Qmechanic Sep 12 '19 at 10:06
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    $\begingroup$ QFT is a special case of quantum theory, but with a more systematic way of constructing observables. The same postulates governing measurement in quantum theory are also present in QFT, and they're not "hidden" at all. Not even sure what "hidden" would mean. Maybe the author is thinking of QFT in terms of scattering (as though that were its only application) or even perturbation theory. That view of QFT has been the source of all kinds of strange statements, and it does indeed "hide" some things that would otherwise be pretty obvious. $\endgroup$ – Chiral Anomaly Sep 12 '19 at 12:33
  • $\begingroup$ @ChiralAnomaly I'm pretty sure the author feels like LSZ has the measurment hidden in it somewhere. Atleast that much is clear to me from the context. Did you read the blogpost? $\endgroup$ – More Anonymous Sep 12 '19 at 12:36
  • $\begingroup$ @MoreAnonymous I skimmed it, focusing on the paragraph with the statement you cited. I think that the author's reference to "LSZ" is actually beside the author's point. I think the author's point is simply that the same measurement postulates that quantum theory uses are also used in QFT, which is trivially true because QFT is a special case of quantum theory. I don't know why the author singled out LSZ, unless the author was really thinking about scattering probabilities. $\endgroup$ – Chiral Anomaly Sep 12 '19 at 12:42
  • $\begingroup$ @ChiralAnomaly I'm under the impression he really was. No one even asks him to clarify which gives me the impression at that level it's fairly common knowledge. $\endgroup$ – More Anonymous Sep 12 '19 at 12:53
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The LSZ formula is just a prescription to compute a particular probability amplitude (the probability to observe a given scattering result for a given scattering in state). If there is collapse "hidden" inside it, then it is hidden inside every single probability amplitude.

If you believe that measurement induces collapse then of course all probability amplitudes (which you use to compute the outcome probabilities of measurements, after all) are somehow related to it - but it is strange in any case to single out the LSZ amplitudes. QFT is not different from QM when it comes to its foundations - the difference is in the amount of degrees of freedom necessitating a different formalism to compute useful results, but not in the basics.

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