The well known Malus law predicts $\cos^2\theta$ for the probability of passing through a filter oriented with an angle $\theta$ w.r.t. the polarization direction of the incident photon. On the other hand the standard quantum treatment of spin $1/2$ particles gives for the same question the result $\cos^2\frac{\theta}{2}=\frac{1+\cos\theta}{2}$ (see for example http://www.lecture-notes.co.uk/susskind/quantum-entanglements/lecture-4/measurement/ ). Is this difference coming only fron the spin (1 vs. $1/2$) or am I comparing apples and oranges? My question is motivated by the fact that in many treatments of EPR experiments people speak of electron and photons while using always the simple Malus law.
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1$\begingroup$ The fact that the photon is massless turns out to be very important in this regard. $\endgroup$– dmckee --- ex-moderator kittenCommented Sep 19, 2017 at 17:54
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$\begingroup$ Coulld you elaborate on this? The fact that the photon is massless implies that only two states are available, so in principle this could be assimilated to spin $1/2$, but I am unsure about the details. $\endgroup$– Arnaldo MaccaroneCommented Sep 20, 2017 at 6:53
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$\begingroup$ I believe your question is answered here $\endgroup$– Yuval NissanCommented Mar 11, 2018 at 16:11
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Maybe you are comparing different flavors of apples. Think about it experimentally. A polarizer is just a metal grid, so if you rotate it 180 degrees you have the same thing. For 1/2 particle you have a Stern Gerlach experiment, and if you turn this 180 degrees you have up and down switched. So the angle in the formula has to be divided by 2.
Apart from the Faktor of 2, I do not think there is a conceptual difference.
