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Wigners Friend where is the paradox?

  1. Mar 21, 2010 #1
    So i try and try to understand why physics should suggest a quantum entanglement of wigner friend and the observed system, because instantaneous measurement makes a collapse in the system, there should be no question when the wave function is determined.

    Suppose we consider two equations:

    [itex]\zeta_{\delta^{\alpha=i}_{\beta=i}} |\psi (t)>=\sum_n |\psi_n (\alpha_{\delta}, \beta_{\delta*} (t))|^2[/itex]

    and

    [itex]\zeta_{\delta^{\alpha=j}_{\beta=j}} |\psi (t)> \ne \sum_n |\psi_n (\alpha_{\delta}, \beta_{\delta*} (t))|^2[/itex]

    It's destinctive immediately that eq. 1 has a squared modulus value solution, whereas the equation with the subscripts containing [itex]j[/itex] in eq. 2 shown here as [itex]\delta^{\alpha=j}_{\beta=j}[/itex] do not lead to a real positive value of 1. The Dirac Delta is used trivially to express when both equations can be valid. In these equations, [itex]\alpha[/itex] is the observer and [itex]\beta[/itex] is the observed. Reference of the states of [itex]\alpha[/itex] and [itex]\beta[/itex] is given by the association of the collapse when both [itex]\alpha[/itex] and [itex]\beta[/itex] converge in a collapse.

    If the observer and the observed have not collapsed, then the remain in a superpositioning in a joint state with the observed system:

    [itex]|\psi \alpha_{\delta_{t_1}} ... ... \psi \alpha_{\delta_(t_2)}> + |\psi \beta_{\delta_{t_1}}... ... \psi \beta_{\delta_{t_2}}>[/itex]

    The joint state can be seen as evolving linearly, and being in a superpositining state then by:

    [itex]\zeta_{\delta^{\alpha=i}_{\beta=j}} |\psi (t)>=|\psi \alpha(t)> + |\psi \beta(t)>[/itex]

    Remember that iff [itex]\alpha[/itex] and [itex]\beta[/itex] have values of [itex]i[/itex] can they collapse -interaction between the scientist and the state happens - no question of when the wave function truely has collapsed as the scientist holds it as an absolute fact of the exeriment.

    Let's take [itex]\alpha*[/itex] as the second observer. If [itex]|\psi \alpha_{\delta_{t_1}} ... ... \psi \alpha_{\delta_(t_2)}> + |\psi \beta_{\delta_{t_1}}... ... \psi \beta_{\delta_{t_2}}>[/itex] converges into a collapse (the collapsed states as the observer and the observed) in an earlier time than which the second observer measures the experiment, then [itex]\alpha*(t)<\alpha (t)[/itex]. Information on the state of [itex]\beta[/itex] is then assertained in an early period. The description of:

    \zeta_{\delta^{\alpha=i}_{\beta=i}} |\psi (t_1)>=\sum_n |\psi (\alpha, \beta(t_1)|^2

    states that the wave function of the observed system has collapsed, and time has been expressed in a past time sense [itex]t_1[/itex]. Since one of the questions of Wigners Friend is if the first observer and the system are themselves in a state of quantum superpositioning?

    How could it be though, if not vanishingly small, since we can state that the observers wave function and the observed wavefunction coheres, and the observed system has observable attributes; it seems valid to state the wave function collapsed when the meaurement was first taken, not whether or not a second observer is required.
     
    Last edited: Mar 21, 2010
  2. jcsd
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