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Thought experiment / paradox question

  1. Oct 20, 2005 #1

    NateTG

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    Let's say I start out with a (spin) neutral electron beam. Now, I can place an up/down Stein-Gerlach spin filter/detector in the beam so that I have a running tally of the "up" electrons, and a spin-down exit beam.
    Since the measuring device is accumulating spin-up electrons, it should also be accumulating net spin-up.
    Now, let's say I have a terminal for the beam, which splits the beam into left and right spin electrons using a Stein-Gerlach device, and takes counts of both. Now, the terminal is interacting with (what I expect to be) a roughly equal number of spin-up and spin-down electrons, so there should be no net accumulation of spin in the terminal.
    This seems problematic because the filter is accumulating net spin without conservation of spin. What am I missing?
     
  2. jcsd
  3. Oct 21, 2005 #2

    vanesch

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    The angular momentum in the magnetic field of the second apparatus.
    For each individual |z+> -> |x+> transition, there is a transfer of Lz from the electron to the magnetic field ; and for each |z+> -> |x-> transition, there is an EQUAL transfer of Lz from the electron to the magnetic field.
    Of course, for the |z+> -> |x+> transition, there was a positive contribution of Lx from the field to the electron, and for the |z+> -> |x-> transition, there was a negative contribution of Lx, so the Lx contribution averages out to 0, but not the Lz contribution.
    There's a net flow of Lz momentum from the electron beam to the B-field (and hence to the magnet).
    cheers,
    Patrick.
     
  4. Oct 21, 2005 #3

    NateTG

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    Sure, that makes sense, but doesn't that lead to a problem because you could know the spin state in two dimensions for a bunch of electrons?
    Let's say we have an EPR-like set up with an entangled electron source, and an up-down split count target on one side, and a left-right split target on the other. And, using timing we manage to restrict our runs to getting 5 electrons at a time. Then there's a 1 in 1024 chane that all the hits on the up/down detector will be up, and all the hits on the left-right detector will be right. Thus we would 'know' that all of the electrons that hit the up/down detector would have to have been up/left electrons, but those measurements don't commute, and thus be able to measure (and predict) the net spin of the targets?
     
    Last edited: Oct 21, 2005
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