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Proof of validity of QM on the macro scale

  1. Apr 6, 2010 #1
    I claim that an experimental demonstration of interference using single particles like photons is also an experimental demonstration of the validity of QM on the macro scale.

    The idea is that any which path information will destroy the interference pattern. Formally, the visibility of the fringes is dermined by the overlap <psi1|psi2>, where the states |psi1> and |psi2> correspond to the state vectors of the universe in which the particle moves through slit 1 or 2, respectively.

    One can now think of experiments in which the which path information is accessible at the macrosopic level and would always be exactly determined in classical physics. The simplest examplre I can think of is to consider an interference experiment involving freely floating mirrors of which the particle reflects off. Here the which path information is present in the total momentum of the mirrors, which is unquestionably a macroscopic observable.

    Note that in an exact quantum mechanical treatment, we can factor out the center of mass part of the wavefunction. This is a direct consequence of translational invariance. We do need to assume that the mirror is exactly freely floating here so that the many particle Hamiltonian that exactly describes the mirror is indeed exactly translationally invariant.

    The fact that we do observe an interference pattern in experiments using freely floating mirrors (no one doubts that we would also observe interference if in such experiments the mirrors were exacly freely floating instead of only approximately freely floating), implies that the overlap between the two counterfactual states of the mirror where it reflects the particle or it doesn't is close to 1, which in turn means that the macroscopic center of mass motion of the mirror is described by a wavefunction with a width in momentum space that is larger than the momentum change due to the reflecting particle.

    Now, none of this is shocking news, as you can easily derive from decoherence theory what the typical width of the center of mass wavefunction in momentum space of a macroscopic object should be. But i.m.o. this is also an example of macroscopic quantum behavior that is directly probed every time we do an interfeence experiment.

    Arguably, even if the interference experiment does not involve floating mirrors, you still have which path information that should in principle be detectable if classical physics were valid on the macro scale. The fact that we do see interference can only be explained if classical physics also fails on the macro level.
     
  2. jcsd
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