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A Key problems in classical and quantum measurement

  1. Jan 14, 2017 #1

    A. Neumaier

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    Quantum mechanical foundations are usually phrased in terms of measurement. I believe this is the main cause why these foundations remain shaky after almost 100 years of a good mathematical basis. Classical mechanics never had any reference to measurement in its foundations, and hence it was always clear what the terms meant on a theoretical level. It should be like that in any foundations that deserve this name.

    For measurement is an exceedingly complex process that cannot be taken as unexplained primitive, vague to the point of meaninglessness when used in foundational arguments. In the present foundations of quantum mechanics it looks as if there were a miraculous process that creates measurement results when an experimenter sets up a corresponding setting. No wonder that the traditional interpretations of quantum mechanics are similarly miraculous in one or more respect!

    In reality (i.e., in actual practice) measurement results are nothing miraculous at all but appear as the result of complex physical activities. Thus whatever can be said about measurement must be based on a description and analysis of these activities. This makes measurement an area of statistical mechanics that cannot be discussed without having already the whole theoretical set-up of a background theory that defines what the objects measured are and what the items mean that go into the description of a protocol for how valid measurements are created by those (people or automata) who take measurements.

    The proper theoretical description and analysis of these measurement activities is the real measurement problem, and it is an unsolved problem both in classical mechanics and in quantum mechanics, and for very similar reasons. Without progress in solving these problems there is little hope of clarifying even the meaning of the present foundational discussions.
     
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  3. Jan 14, 2017 #2

    A. Neumaier

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    From a pragmatic point of view, wikipedia describes the measurement setting quite well. One sees already that it is far more complex than what the traditional axioms of quantum mechanics suggest; indeed the description seems to be almost disjoint from that one finds in the discussion of the latter. This shows that the traditional foundational discussions on quantum measurement are extremely superficial.
     
  4. Jan 15, 2017 #3

    ftr

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    But isn't it that already in QM we assume that the object is in a superposition of the observable (some say AND , and some say OR). So before the measurement the object had an undefined value, that is already way weird and not straightforward. Then on top of that you have HUP and its interpretation, now you have a wild party:)
     
  5. Jan 16, 2017 #4

    A. Neumaier

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    No. Observables cannot be in superposition.
    Yes, if you put it like that, the foundations are completely crazy. But this is only the view taken in some of the many written foundations.

    The unwritten foundations - the actual practice of interpreting experimental arrangements and results - shows a quite different picture:
    Here the unmeasured particle is in an ion trap, or in a beam, and people perfectly know (or at least assume) that it is there! Otherwise they couldn't make experiments with it. Thus the particles have a well-defined position to within some uncertainty, and this is in full accord with Heisenberg's uncertainty relation.

    The particles have all the properties their state has, just as in classical physics!
    No less and no more!
     
    Last edited: Jan 16, 2017
  6. Jan 16, 2017 #5

    Mentz114

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    I could have written the bold sentences myself, but (naturally) I wouldn't dare.

    It makes nonsense of 'unmeasured' position has no value - which I never believed in any case. This is linked to the superstitious belief that only an act of measurement can allow us to make factual statements. Another casualty of the hallowed ( and incorrect) measurement theory.
     
  7. Jan 16, 2017 #6

    dextercioby

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    Classical mechanics in any of its formulations (Newton, Lagrange, Hamilton, Hamilton-Jacobi) makes no reference to measurements of observables. Why should the quantum mechanics do?
     
  8. Jan 17, 2017 #7

    A. Neumaier

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    They shouldn't. But the unfortunate fact is that the traditional foundations do make reference to it, and thus make the foundations fuzzy.
     
  9. Jan 17, 2017 #8

    zonde

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    Classical mechanics makes predictions about physical facts. These predictions can be compared to measurements to test the theories.
    I suppose that quantum mechanics do not have to refer to measurements as long as it talks about electron states in atoms. But to go further you have to have predictions about particle positions as physical facts that can be compared with measurements.
     
  10. Jan 17, 2017 #9

    A. Neumaier

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    One only needs to have predictions about things like black spots in a Stern-Gerlach experiment and photocurrents in a Bell-inequality test experiment. The latter are well-described by the expectations calculated in statistical mechanics.
    The measurement problem in classical mechanics consists of explaining how a multiparticle system called the observer can collect perfect information about the physical facts defining the few-particle system measured. In fact, perfect information cannot be obtained. Whatever is obtained experimentally needs a justification why it deserves being called a particle position or momentum and how uncertain it is.

    Giving this justification is also a problem in statistical mechanics. But it has attracted almost no attention by the philosophically minded (only pragmatically from a few people such as Suppes) since it doesn't get the huge weirdness publicity that the traditional foundations give to quantum mechanics.

    Thus the measurement problem is a difficult statistical mechanics problem in both the classical and the quantum situation.

    The so-called foundations of quantum mechanics (and the much slimmer Hamiltonian or Lagrangian foundations of classical mechanics) sidestep this problem by assuming that the measurement results appear miraculously upon performing an experiment. Those working in quantum foundations refer to the classical view by drastically simplifying the picture, assuming that, miraculously, the measurement result is identical to the exact particle position. But they treat the quantum view differently - they explain the miracles inherited by ignoring the true nature of measurement by equipping the quantum world with all sorts of miraculous things, such as wave function collapse, splitting of worlds, or the invention of a submicroscopic level of particles with highly nonlocal, in principle unobservable properties.

    Thus everyone invents miracles to explain miracles. Hardly anybody tries to explain the miracles by looking at their origin - the idealization that ignores the fact that measurement means that one subsystem of a big system ''has'' some information about another subsystem in the form of correlations, due to couplings for which we already know the laws.

    The only rational approach to the measurement problem is to study how these laws give rise to these correlations.
     
    Last edited: Jan 18, 2017
  11. May 29, 2017 #10

    A. Neumaier

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    For a discussion in the quantum case see this thread.
     
  12. May 29, 2017 #11
    The reason we don't have to talk about measurement in classical physics is the fact that we can always control and account for the influence of the measuring bodies on the objects under investigation. For example we can make the effect of the measuring bodies as small as we want, or if it is finite, we can control and take that finite effect into account in our description. This means that we can talk about the state of a system as something that exists independently of observation.

    This is not possible in quantum physics because the effect of the measuring bodies is uncontrollable. If a body is to serve as a clock, then there will be an uncontrollable exchange of energy with the clock, which cannot be separately taken into account in order to specify the state of the objects. Any experiment where we attempt to prove that "an amount of energy E went into the clock" will destroy the original phenomenon.
     
  13. May 29, 2017 #12

    A. Neumaier

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    Only under the idealized assumption that the bodies are macroscopic. If you try to measure a microscopic point particle with a classical ##N##-particle system you get very similar (and unsolved) statistical mechanics problems as in the quantum case.
     
  14. May 29, 2017 #13
    That is of course only because you are working with a situation where you voluntarily choose not to know the mechanical state of the N-particle system, and you voluntarily choose a thermodynamic or statistical mechanical description. Nothing prevents you in classical physics from knowing the exact mechanical state of something you might describe using thermodynamics.
     
  15. May 29, 2017 #14

    A. Neumaier

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    This is not true, independent of any thermodynamics. Knowing is a physical process, and the knowledge must somehow enter the knower. We are all born knowing nothing, and learn only through interaction with the environment.

    Moreover, even when there is exact knowledge of the initial condition and exact deterministic dynamics, the measurement device is a complex system that cannot be made to exactly represent the state of the particle solely through the physical interactions. God may know the state of every particle and the precise nature of all the interactions of a classical universe under his control. But if it is governed by classical mechanics without supernatural intervention, his knowledge will invariably tell him that there is no ##N##-particle system whose pointers would exactly reproduce the state of any given particle brought into interaction with it. Thus he knows the state information but he cannot measure it using the tools of his classical universe!
     
  16. May 29, 2017 #15
    I don't know why you say that, maybe you can give an example or calculation which shows this.

    But in quantum theory, for example, if you assume that the particle passes through one of the slits of a double-slit experiment, then there is a logical consequence, which is that there is no interference pattern. Since however you do observe an interference pattern in certain situations, this assumption is wrong. If you measure which slit it passes through, then you will destroy the interference. This is why you can't talk about the state of the particle as something independent of what you are experimentally doing. You simply cannot assume that the particle passes through one slit or another if you are not measuring it, because the conclusions from it will be wrong.

    This situation is clearly different from what you describe, where there is some exact state which you are unable to measure.
     
  17. May 29, 2017 #16
    I think your view here clearly exceeds the limits of science to enter the personal beliefs.
     
  18. May 29, 2017 #17

    A. Neumaier

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    In contrast, any claim that it can be done would have to be shown by an argument, as this would be a very miraculous thing!

    ??? Physicists routinely talk about states independent of experiments. States do not depend on experiments for their existence. The ##N##-particle system called the Earth has a well-defined state long before there were physicists who did experiments.

    Well, you had assumed that one can know the exact state!
     
  19. May 29, 2017 #18

    A. Neumaier

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    This has nothing to do with a personal belief. God is the conventional label attached to an all-knowing entity, assumed to exist for the sake of an argument. It is used as metaphorical as the demon in Laplace's argument.
     
  20. May 29, 2017 #19
    I'm not referring to the use of that word as a conventional label, I understood it as such. I' referring to the belief that there are certain complexities that are unkowable in principle, or that are a given. Precisely it is the role of physics to question this.

    Previously you referred to getting information through interaction with the environment, so you must concede that it is not necessary to invoke arguments about independence from experiments performed by humans here. Interaction with the environment are a much broader notion and it only depends on the existence of the universe.
     
  21. May 29, 2017 #20

    A. Neumaier

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    But experiments (i.e, what you had talked about and what I was referring to) require an educated experimenter.
     
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