Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Schrödinger's cat, pure or mixed state?

  1. Mar 15, 2012 #1


    User Avatar
    Science Advisor

    The usual description of Schrödinger's cat is that after being placed in the box, Schrödinger's cat in a superposition state of being alive and dead. Sometimes, I see this written as:
    [itex]\mid \Psi \rangle=\frac{1}{\sqrt{2}}(\mid alive \rangle+\mid dead \rangle)[/itex]
    This is representing a particular pure state which is distinctly different from
    [itex]\mid \Psi' \rangle=\frac{1}{\sqrt{2}}(\mid alive \rangle-\mid dead \rangle)[/itex]
    In some sense, these are different rotations of the alive-dead spinor.
    But, should this be more properly treated as a density matrix?
    [itex]\begin{bmatrix} 1/2 & 0 \\ 0 & 1/2 \end{bmatrix}[/itex]
    That is, we have incomplete information about the Schrödinger's cat's exact state, which is significantly less mysterious than claiming the cat is alive+dead.

    We could, for example, construct a Schrödinger box by loading an ampoule with poison, and triggering the poison with a photon detector which is behind a polarizer and a photon source. The photon source emits randomly polarized light. The photon polarization is in a mixed state, so the cat should be, too. Can we actually construct a pure state of cat actually be in a pure state of alive+dead?
  2. jcsd
  3. Mar 15, 2012 #2


    User Avatar
    Science Advisor

    You are right, Schrodinger cat is in the mixed state. The photon is also in the mixed state. But the cat, photon, photon-detector, and their environment TOGETHER are in a pure state.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook