2016 International Workshop on Quantum Observers

How to solve the structured tails problem of dynamical collapse theories?

This topic contains 2 replies, has 3 voices, and was last updated by Shan Gao Shan Gao 1 year, 2 months ago.

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  • #3194
    editor
    editor
    Keymaster

    Note: The following text aims to elicit more discussions about the question of whether and how dynamical collapse theories can solve the structured tails problem when considering the status of quantum observers in the theory.

    If a quantum observer being in a post-measurement superposition indeed is consciously aware of a definite result, which is not one of the possible results of the measurement (see the above analysis), then the final state of the observer after the measurement cannot be such a superposition. This means that the linear quantum dynamics will be violated during the measurement. Thus it seems that dynamical collapse theories are in the right direction to solve the measurement problem.

    However, it has been known that dynamical collapse theories are plagued by the tails problem (Albert and Loewer, 1996). In particular, the structured tails problem has not been solved in a satisfactory way (see McQueen, 2015 and references therein). The problem is essentially that dynamical collapse theories such as the GRW theory predicts that the post-measurement state is still a superposition of different outcome branches with similar structure (although the modulus squared of the coefficient of one branch is close to one), and they need to explain why high modulus-squared values are macro-existence determiners (McQueen, 2015).

    In our view, the key to solving the structured tails problem is not to analyze the connection between high modulus-squared values and macro-existence, but to analyze the connection between these values and our experience of the macroscopic world. This brings us again to the question of what it feels like to be in a quantum superposition.

    The above analysis of the mental content of a quantum observer may help solve the structured tails problem of dynamical collapse theories. In particular, if assuming the modulus squared of the amplitude of each branch indeed determines the vividness of the mental content corresponding to the branch, then the structured tails problem can be readily solved.
    Under this assumption, when the modulus squared of the amplitude of a branch is close to zero, the mental content corresponding to the branch will be the least vivid. It is conceivable that below a certain threshold of vividness an ordinary observer or even an ideal observer will not be consciously aware of the corresponding mental content. Then even though in dynamical collapse theories the post-measurement state of an observer is still a superposition of different outcome branches with similar structure, the observer can only be consciously aware of the mental content corresponding to the branch with very high amplitude, and the branches with very low amplitude will have no corresponding mental content appearing in the whole mental content of the observer. This will solve the structured tails problem of dynamical collapse theories.

    • This topic was modified 1 year, 3 months ago by editor editor.
    #3275
    Avatar of Kelvin McQueen
    Kelvin McQueen
    Participant

    This is an interesting solution. A version of it is discussed in section 4.4. of “Four Tails Problems for Dynamical Collapse Theories”. There it is discussed in the context of the matter-density interpretation of GRW (sometimes called “GRWm”). The “denser” brains are the ones with the experiences of measurement outcomes. Since high density is determined by high amplitude, it’s pretty much the same solution, it’s just expressed in GRWm (whereas you’re expressing it in GRW0). The problem raised for this solution, in 4.4., is that it leaves behind “zombie tails”. It’s quite a similar problem to the so-called “mindless hulk problem”, that is faced by one of David Albert’s Many Minds theories. See p130 of Albert’s QM and Experience.

    #3276
    Shan Gao
    Shan Gao
    Participant

    Thanks for your comments, Kelvin. It seems that you did not really understand my solution, which is different from the solution discussed in your paper. In my solution, there are no “zombie tails”. The observer being in the superposition has only one mind with the unique mental content. The key point is that according to my assumption about vividness, below a certain threshold of amplitude the observer may not be consciously aware of the mental content corresponding to the low-amplitude branch.

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