I did some maths and I found that angular momentum operator does not commute with normal mometum:(adsbygoogle = window.adsbygoogle || []).push({});

[tex][ J_{\alpha \beta}, P_{\gamma}] = \eta_{\alpha \gamma} P_{\beta} - \eta_{\beta \gamma} P_{\alpha}[/tex]

Now, the "third" component of angular momentum:

[tex]J_{z} := J_{x y}[/tex]

[tex][J_{z}, P_{x}] = -P_{y}[/tex]

[tex][J_{z}, P_{y}] = P_{x}[/tex]

[tex][J_{z}, P_{z}] = 0[/tex]

It does not commute with two components od momentum!

So how it is possible to measure both momentum and spin? Why is spin the "third" component, in the direction of momentum, when the act of determining momentum should make measurement of spin impossible?

Am I wrong somewhere?

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# Do spin and momentum commute?

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