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See the quote below from Dirac's 1975 "An historical Perspective on Spin".

Question:

You seem to feel very strongly about the necessity to have a description of one electron by itself in the framework of quantum mechanics. What about the description of one photon by itself.

Answer: P. A. M. Dirac

That is provided by the Maxwell theory. There is the difficulty that we cannot talk about the probability of a photon being at a given place. We can give a definite meaning to a particle being at a given place only in the case of a particle with a spin of 1/2. For any other kind of particle, we cannot talk accurately about its position. We can talk about its momentum and this is sufficient for most purposes. The spin 1/2 particles are unique in that we can discuss accurately the probability of their positions.

Is Dirac correct that only a spin 1/2 particle can have a position, and why is that?

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    $\begingroup$ Related physics.stackexchange.com/q/419969 $\endgroup$
    – nemui
    Commented Aug 25, 2022 at 22:21
  • $\begingroup$ Elaborated here (search for 'spin'): mat.univie.ac.at/~neum/physfaq/topics/localization Also "Chiral spin 1/2 particles" also do,not have a position according to: arnold-neumaier.at/physfaq/topics/position.html $\endgroup$
    – nemui
    Commented Aug 26, 2022 at 2:58
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    $\begingroup$ I think Dirac was being misleading. The real point is that it’s extra difficult to define position operators for fields with gauge redundancy, which occurs for massless fields of helicity 1 and higher. As for massive fields, there’s no real distinction between different spins. $\endgroup$
    – knzhou
    Commented Aug 31, 2022 at 19:32
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    $\begingroup$ When Dirac says spin 1 is hard, it’s because the only spin 1 particle he knew about was the massless photon. When he says “only 1/2” and omits 0, it’s because he didn’t know of any particles with spin 0. $\endgroup$
    – knzhou
    Commented Aug 31, 2022 at 19:33
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    $\begingroup$ @knzhou If you like you can type up a short answer. At the moment there is no longer answer and noone to award the bounty to. $\endgroup$
    – don't train ai on me
    Commented Sep 6, 2022 at 16:17

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