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When an electron goes thru a Stern-Gerlach appliance it changes its spin projection. Then there must be a change of energy content of the electron due to this event. But it is also known that magnetic field carries no energy. So I wonder where the energy (if any) can come from?

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    $\begingroup$ "But it is also known that magnetic field carries no energy" this is wrong: the magnetic field does carry energy (see, e.g., Magnetic energy). Maybe you mean that the magnetic field doesn't do work, which is a common misconception. Magnetic fields do do work! Your question is a bit unclear I'm afraid... $\endgroup$ – AccidentalFourierTransform May 1 '16 at 22:14
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    $\begingroup$ "When an electron goes thru a Stern-Gerlach appliance it changes its spin projection" - no, not at all, or at the very least only in an interpretation-dependent way. It is equally as accurate (i.e. not much) to say that the electron 'already had' that projection; other interpretations will insist that it is meaningless to talk about the electron's spin projection before the measurement, so the 'change' is also meaningless. $\endgroup$ – Emilio Pisanty May 1 '16 at 22:19
  • $\begingroup$ @AccidentalFourierTransform well I mean work. But is it not the same. If doesn't do work it can not change the energy of electrons. Hence it doesn't carry E. Ok I will look at your link. Do you think an electron passing SG will take energy from a magnet? $\endgroup$ – Mercury May 1 '16 at 22:39
  • $\begingroup$ @Emilio Pisanty The spin projection of an electron can quite well be prepared before going into SG. (b.e. 45* to B). So it is save to say it had spin projection not the same as had after it went out of SG. On the exit it will B up or down, measured by the tracks. I never encountered in any textbook such a statement as you imply. Take Feynman lectures for example. $\endgroup$ – Mercury May 1 '16 at 22:51
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    $\begingroup$ Not really - on exit, it will be an entangled state with equal amplitudes on spin up on the up track plus spin down on the down track. Only then do you perform the projective measurement on position, which thereby also collapses the spin state as well. There's additional subtleties at play (particularly the fact that the 'energy' of the system includes the interaction Hamiltonian used to perform the measurement) but that's enough to be getting on with. $\endgroup$ – Emilio Pisanty May 1 '16 at 23:15
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After realizing that the electron energy does not depend on the projection of the spin it seems obvious that the energy of the electron doesn't change when it passes a magnetic field (or SG). But then something very peculiar immerges: 1.the state of something changes without any energy exchange 2.the magnet induces a change in the electron but it doesn't change a bit

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