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This is a technical question not one of interpretation or philosophy.

On page 267, end of section 70 existence of spin, of Dirac - Principles of Quantum Mechanics, 4th edition revised (1968), it having been proved from QM and SR that all particles have 1/2 spin, Dirac notes that some particles are observed with integer spin. The resolution given is that the proof had the hidden assumption that the position is an observable. Given that Fermions all have 1/2 integer spin and Bosons integer spin - that appears to mean that no Boson has an observable position; at least not in any relativistic QM.

This conclusion seems technically and philosophically compatible with my understanding of QM, but I have not managed to find a clear statement that confirms or denies this as a known required conclusion in the literature or on forums. Just, statements such as that the photon position is not observable in GR or that massless particles ditto. Can one measure the position of a W-Boson, for example? Can this question be meaningfully tackled using Schrödinger QM? Or do we need QFT?

Actually measuring the position of a W-Boson seems difficult, due to its short lifetime. This clarifying sub-question is about the principle of measuring it.

What about Helium atoms?

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    $\begingroup$ There is a very great difference in saying that there exists a position operator (describing the statistics of position measurements) and that a particle has a position. The latter is not a very meaningful statement unless you use a formulation of quantum mechanics in which positions really figure, i.e. de Broglie-Bohm-theory. $\endgroup$
    – Luke
    Commented Jul 30, 2018 at 10:41
  • $\begingroup$ The question is intended to be about position as an observable, that is an appropriate operator. I am not asking anything philosophical or interpretational. But, thatnks - maybe you have pointed out why I got crickets on this one. $\endgroup$
    – Ponder Stibbons
    Commented Jul 30, 2018 at 23:06
  • $\begingroup$ Also - in purely pragmatic sense, you can never measure anything exactly. We say that physical quantities exist in practice due to the ability to measure to greater and greater accuracy without limit. In QM, you can measure the position of an electron to indefinite accuracy - the uncertainty principle just says that you cannot also measure the momentum at the same time. Having no operator for position would seem to mean that one cannot even measure its position approximately. Like trying to measure the position of Maxwell's equation. $\endgroup$
    – Ponder Stibbons
    Commented Jul 30, 2018 at 23:18

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