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"Physical system" in quantum mechanics ?

  1. Aug 18, 2014 #1

    In the usual Hibert-space formulation of quantum mechanics, to each physical system is attached a separable Hilbert Space (generally infine-dimentionnal) over complex field.

    A crucial ingrediant in the description of a physical system is the notion of state and evolution of state, however what is a physical system ? Moreover, cutting physical system in "physical quantum object + environment" is arbitrary ?

    Behind is the question about Quantum decoherence between physical quantum object and environment. This division into physical sub-system is it always trivial to do ?

  2. jcsd
  3. Aug 18, 2014 #2


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    Science Advisor

    This is a very good question!

    In practice, I would say, one can say "what is a physical system" when one has the Hamiltonian. The Hamiltonian is a function of the form H(Q,P), and the system is essentially Q, that is, the set of all dynamical configuration variables.

    The object/environment cut is arbitrary, but decoherence depends on this cut.
    Last edited: Aug 18, 2014
  4. Aug 18, 2014 #3


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    Here is one case where the subsystem seems difficult to define because the Hilbert space is not a tensor product of the Hilbert space of the subsystems: http://arxiv.org/abs/1406.7304. Donnelly is discussing the entanglement entropy which does depend on the reduced density matrix, just like decoherence.

    Another place where it seems more natural to talk about the operators associated with subsystems is in strict quantum field theory, where one talks about operators at spacelike separation. When the Hilbert space is infinite dimensional, it seems that the full extent to which quantum mechanics violates the Bell inequalities is still unknown: http://arxiv.org/abs/1008.1142.
    Last edited: Aug 18, 2014
  5. Aug 18, 2014 #4


    Staff: Mentor

    This is the so called factoring problem.

    It has led to a bit of debate on this forum.

    A search will bring up the gory detail.

  6. Aug 18, 2014 #5
    To find the debates on this interrogation, I use the filter "factoring problem" in my search on this forum ?

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