# In QFT scattering, why is the summing over spins done after squaring the amplitude?

Is it possible that the incoming particles, in a scattering experiment, have a superposition state of up and down spin? In this case, aren't we supposed, after we calculate the matrix elements for the different spin states, to add these amplitudes rather than their squares?

In other words, why do we always do this $\sum_{ss'}\left|\mathcal{M}\right|^2$ rather than $\left|\sum_{ss'}\mathcal{M}\right|^2$?

• – AccidentalFourierTransform Nov 18 '17 at 17:07
• @AccidentalFourierTransform I saw both of these links before I asked the question. Neither of them answers my question. – MOKO Nov 18 '17 at 17:25
• That's just a statistical sum, frankly. You are just calculating the average over an ensemble of experiments, each one with random spins involved. No superpositions here. – Prof. Legolasov Nov 18 '17 at 19:53