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The role of probability

  1. Dec 18, 2014 #1
    Is Probability the underlying law of nature, or does it only emerge from repeatedly recording observations of events that we cannot yet measure accurately enough?

    OR put another way

    If a new technology were to be discovered in the near future, which could allow us to observe without disturbing the "observables" we currently measure. Then Heisenberg's uncertainty principle ΔXΔρ > ħ/2 could be further refined?
  2. jcsd
  3. Dec 18, 2014 #2


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    In terms of physics, its an open question. In terms of philosophy, its a matter of taste! See here!
    According to Quantum Mechanics, the problem is not with technology limitations and uncertainty principles are intrinsic to quantum system. But this is sometimes a matter of debate between different interpretations of QM too.
  4. Dec 18, 2014 #3
    The way I see it , is that interpretations are formalized to better understand certain concepts which allow us better to
    understand nature.

    An apple may taste different for different people , but most of us still concede that we call it an apple, through collective observations.
    This does not mean that one day we might distinguish through "finer" observation that there is a subset of different kinds of apples.

    Have we not limited ourselves through probability , by saying it looks a little different so its there is 90% probability that it IS an apple.
    Are we not just smoothing the curve to connect the dots?
  5. Dec 18, 2014 #4


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    You can connect the dots a couple of different ways. Or not at all. There are several interpretations, and each leaves a different apple-like taste in your mouth. :)

    None of them really involve throwing out the Uncertainty relations, though.
  6. Dec 18, 2014 #5


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    It turns out that "OR put another way" is not correct. The answer to the first question is yes, it may be possible that nature is deterministic. But the answer to the second question is no, because the commutation relations underlying the uncertainty principle (plus a few other assumptions that are usually true in quantum mechanics) guarantee that the observables in the position-momentum uncertainty relation cannot be measured without disturbance, because they cannot even exist simultaneously.
  7. Dec 18, 2014 #6


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    Regarding the possibility of simultaneously accurate measurements of non-commuting canonically conjugate position and momentum, there isn't a "debate" between different interpretations, except maybe in special cases like 1D motion. The related theorems that hold in all interpretations are:
  8. Dec 18, 2014 #7


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    Probability is a modelling tool defined by the Kolmogorov axioms - just like classical mechanics, relativity etc etc. Physical theories are basically mathematical models.

    You misunderstand QM - it says that's impossible. If such occurred it would prove QM wrong and would be a major earth shattering discovery.

    Last edited: Dec 18, 2014
  9. Dec 18, 2014 #8


    Staff: Mentor

    If you want to revolutionise QM by ridding it of probability - feel free. Many have tried - they all failed. The best that has been achieved is to have the underlying probabilities depending on other things like lack of knowledge in initial conditions (Bohmian Mechanics) or things going on at the sub-quantum level (there are a number that take that route eg Nelson Stochastics and Primary State Diffusion).

    Although no one can prove we cant find a theory that does away with such things the fact so many have tried and failed, including really great figures like Einstein, strongly suggests its intrinsic. Of course no one can know what future progress will bring.

  10. Dec 19, 2014 #9
    Interesting , thanks

    Just a question. The third of the Kolmogorov axioms refers to "mutually exclusive events" .

    When we apply probability to experimental outcomes of entangled particles , is it fair to call these events mutually exclusive.
    Since they are " entangled" , and part of a single system as sometimes described?
  11. Dec 19, 2014 #10


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    Correct. The usual terminology though is correlated.

    This is an important point about locality in QM. 'Locality' is encapsulated in the so called cluster decomposition property:

    It does not apply to correlated systems like EPR.

    Whether such violates locality or not depends on your definition of locality.

  12. Dec 19, 2014 #11
    Ok I think I understand better .

    Is this where the famous Bell inequality is violated?
    1. In the entangled experiments the bell inequality is violated when the results show inconsistencies with predicted probability outcomes.
    2 Inferring that FTL/instantaneous correlations must then be possible.
  13. Dec 19, 2014 #12


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  14. Dec 19, 2014 #13
    I am not saying intrinsic uncertainty could eventually be overcome, but it may become negligible.

    See link below
  15. Dec 19, 2014 #14
    Yes I read most of his links previously , and I must say.
    I have not found a more comprehensive detailed description on the topic.
    Thanks Dr Chinese and to you Bill.
  16. Dec 19, 2014 #15


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  17. Dec 19, 2014 #16


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    Yes, the outcomes of measurements on any quantum system, including entangled systems, are mutually exclusive. It basically states that each measurement has a single definite outcome (except in the Many-Worlds approach). For example, if Alice and Bob measure whether their spins are up or down, they will get one of 4 definite results {up-up, up-down, down-up, down-down}. When the same measurement is repeated on another identically prepared system, the outcome will again be one of these 4 possible definite outcomes, but it may not be the same one as on the previous identically prepared system. The distribution of definite outcomes is given by the Born rule.
  18. Dec 19, 2014 #17
    Wow is this article getting attention in the physics community? If those experiments can be repeated by other laboratories with the same result we have a break-through in QM indeed. The conclusion of that article is the same one as the original paper, it's not misinformation like it happens in many cases.
  19. Dec 19, 2014 #18


    Staff: Mentor

    The article gives the wrong impression that they violating the uncertainty principle - they aren't. What they have done is fully explainable in QM - if it wasn't that would be BIG news - it isn't.

    What they are doing is work on so called weak measurements:

    Because it is weakly coupled to the system and does not disturb it there is a large uncertainty in the measurement result. To be specific what it is measuring is an average of if you took a large number of individual measurements.

    Last edited: Dec 19, 2014
  20. Dec 20, 2014 #19
    Which is the better approach , many measurements with large uncertainty or few measurements with less uncertainty.
    Which better describes nature?
    My view is we learn from experience , the more times we do it , the better we can understand the holistic picture.
    And that is what they are doing here.

    On a roulette table rolling the zero 3 times in a row is less informative , than getting the average of the last 10000 spins.
  21. Dec 20, 2014 #20
    The word "intrinsic" has been mentioned a lot without explanation of what it means. Using the example of position and momentum, here is a different look.

    Momentum is the product of relativistic mass times velocity. Velocity is the rate of change of position. To measure the momentum of a particle precisely, you have to at least measure it's velocity precisely. But you can not measure velocity at a single point. You need to measure position at least 2 points and divide by the time it took to travel between the two points. The further apart the two points are, the more accurately you can determine it's velocity but then which of the points do you attribute measured velocity to? Point A, B, or between both points (don't forget uncertainty due to potential acceleration and deceleration)? The further apart the points, the higher the uncertainty associated with the velocity (and thus also the momentum). The smallest distance between two points is the Planck length, so that is the highest accuracy (smallest uncertainty) you can have for a position to assign to the velocity measurement.

    Therefore "intrinsic" uncertainty between position and momentum is due simply to the fact that they are mathematically defined in a complementary manner, momentum being defined relative to the rate of change of position, ie momentum and position are not defined within the same basis. In short, the uncertainty between position and momentum comes from the fact that the definition of momentum involves the behaviour of a particle over more than one position. This is what "intrinsic" means.
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