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Thread: Probability theory: The Quantum Measurement Problem

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    Probability theory: The Quantum Measurement Problem




    There is a famous double-slit experiment in Quantum Mechanics that attempted to measure whether electrons and photons are comprised of particles or waves. The counter-intuitive result is that when no observation takes place of which “slit” electrons or photons pass through, then they act like waves (for which their location can be identified only as a function of probability). The "wave-like" case was evidenced by an interference pattern that results from waves travelling through, and meeting on the other side of, the two slits.

    On the other hand, when measurement and observation is added to the experiment, that enables the observer to identify which slit an electron or photon passes through, then they act like particles, with no interference pattern.

    The debate on the significance of this result in determining the nature of matter on the quantum (micro) scale has raged for decades, and has even delved into the role of human consciousness in influencing the outcome. What seems absent from the debate, as far as I know, is the significance of the result in shedding light on the nature of probability itself, rather than on the nature of matter.

    So here are my questions. Have there been any statistical studies outside of the realm of quantum mechanics that would attempt to mimic the double slit experiment? If so, what have been the results? I could envision a test structured with two sets of trials, as follows:
    1. Perform a large number of trials in which a single, ordinarily marked die is rolled 600 times, and calculate a distribution of outcomes for each trial that reflects:
    a) The number of times “1” comes up in each trial (the first "slit");
    b) The number of times “6” comes up in each trial (the second "slit");
    2. Then perform an equal number of trials, except using a die on which there are no numbers, and on which two sides are painted red, and the other four sides are painted blue, and calculate a distribution of all outcomes that reflects the number of times that “red” comes up (equivalent to knowing that outcomes came through one of two slits, but without knowing which one).

    Would there be any statistical basis on which to expect that the distribution of outcomes on the second trial would be anything other than the sum of the distributions for “1” and “6” on the first trial? If so, what would the difference look like? Would trial results on the second ("blind") set of trials correspond in any way with wave-like interference? Is the structure of this test sound? Does it properly mimic the double-slit experiment?
    Following is a slight modification, intended to be equivalent to “narrowing” of the slits, which I understand to be important in the double-slit experiment.

    1. Perform a large number of trials in which a single, ordinarily marked die is rolled 600 times, and calculate the number of trials for which “1” comes up between 99 and 101 times, as well as the number of trials for which “6” comes up between 99 and 101 times:
    2. Then perform an equal number of trials, except using a die on which there are no numbers, and on which two sides are painted red, and the other four sides are painted blue, and calculate the number of trials for which “red” comes up between 198 and 202 times.
    Would there be any statistical basis on which to anticipate that the number of trials for which “red” comes up between 198 and 202 times, would be any different than the sum of the number of trials for which “1” and “6” come up between 99 and 101 times? Have any tests like this been performed? What would be the relevance of these tests to the double-slit experiment? All comments welcome. Thanks!

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    Re: Probability theory: The Quantum Measurement Problem

    Quote Originally Posted by Michaelamcshane View Post
    The debate on the significance of this result in determining the nature of matter on the quantum (micro) scale has raged for decades, and has even delved into the role of human consciousness in influencing the outcome.

    Have there been any statistical studies outside of the realm of quantum mechanics that would attempt to mimic the double slit experiment? If so, what have been the results?
    Well Princeton University's School of Engineering published some results from their experiments on the human mind affecting "random" event generation. Not sure how interesting this is to you?

    Look at all these papers!

    PEAR program -- watch video on right to see what they were doing "...to enable better understanding of the role of consciousness in the establishment of physical reality."

    Researchers at The Princeton University have found that a simple REG (eg coin flipper), when operated by someone who wanted to see more heads, resulted in more heads. This statistical anomaly would only appear 1-in-a-trillion by chance. But yet it appears across a variety of physical systems.
    All things are known because we want to believe in them.

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    Re: Probability theory: The Quantum Measurement Problem


    Thanks for the reply. Those papers are interesting -- and talk about counterintuitive! While my question overlapped the research in those articles, the question I was raising is a bit more fundamental, arguably simplistic. Is there any evidence that probability itself has wave-like characteristics, for which there would be the equivalence of interference patterns in trial outcomes if a test was structured in a manner analogous to the double-slit experiment? I am not sure if the test structure I proposed is quite on the money. However, the basic question is whether there is any statistical basis on which to expect the number of positive outcomes on an "either event A or event B" test, (with A & B having equal probability, but without the tester having knowledge of which of the two possibilities generated positive outcomes) would ever be different that the sum of positive outcomes for event A and event B tested separately. Thanks.

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