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What really is a Weak Measurement?

  1. Jun 14, 2011 #1
    Does it explain what occur during strong measurement or "approximately" solve the measurement problem? I'm asking because below it is mentioned that "it is this uncertainty that creates the uncontrollable, irreversible disturbance associated with measurement". Does it mean that measurement problem is related to uncertainty inverse relationship between position and momentum? Can you give other example beside position, momentum where weak measurement is valid.. maybe energy-time uncertainty? Also isn't weak measurement like being a little "pregnant"?

    Here's about weak measurement from Kocsis, et al paper "Observing the Average Trajectories of Single Photons in a Two-Slit Interferometer" (What is the mainstream consensus about Weak Measurement? Is it still controversial. How do you understand it? Can you give other more obvious example about it as the language used below (like "pointer shift", "single shot", etc.) is somewhat hazy to me. Thanks.):

    "Weak measurements, first proposed 2 decades ago (7, 11), have recently attracted widespread attention as a powerful tool for investigating fundamental questions in quantum mechanics (12–15) and have generated excitement for their potential applications to enhancing precision measurement (16, 17). In a typical von Neumann measurement, an observable of a system is coupled to a measurement apparatus or “pointer” via its momentum. This coupling leads to an average shift in the pointer position that is proportional to the expectation value of the system observable. In a “strong” measurement, this shift is large relative to the initial uncertainty in pointer position, so that significant information is acquired in a single shot. However, this implies that the pointer momentum must be very uncertain, and it is this uncertainty that creates the uncontrollable, irreversible disturbance associated with measurement. In a “weak” measurement, the pointer shift is small and little information can be gained on a single shot; but, on the other hand, there may be arbitrarily little disturbance imparted to the system. It is possible to subsequently postselect the system on a desired final state. Postselecting on a final state allows a particular subensemble to be studied, and the mean value obtained from repeating the weak measurement many times is known as the weak value. Unlike the results of strong measurements, weak values are not constrained to lie within the eigenvalue spectrum of
    the observable being measured (7). This has led to controversy over the meaning and role of weak values, but continuing research has made strides in clarifying their interpretation and demonstrating a variety of situations in which they are clearly useful (16–21)."
  2. jcsd
  3. Jun 15, 2011 #2
    I wonder how this is related to decoherence. Here when a system is weakly coupled to environment, interference pattern still exist and intensity proportional to the coupling. So maybe Weak Measurement work because everything is quantum? But decoherence is not equal to collapse. It just looks like collapse. So collapse is still a mystery in addition to Decoherence and Weak Measurements.

    Also I wonder if the concept of weak measurement is used only in analyzing system based merely on HUP.. like momentum, position. This means the double slit can be analyzed soley on HUP and wave is just an 'extra' factor?
  4. Jun 15, 2011 #3


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    You can find an explanation of weak measurements "for children" in my blog
    https://www.physicsforums.com/blog.php?b=3077 [Broken]
    (second comment)
    Last edited by a moderator: May 5, 2017
  5. Jun 15, 2011 #4
    Lol... anyway you wrote the following in the blog. I was asking above if weak measurement was connected with momentum. Why is the example always about momentum. Is there weak measurement that doesn't involve momentum, how? Anyone else knows?

    Last edited by a moderator: May 5, 2017
  6. Jun 15, 2011 #5


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    Weak measurement may be about any observable, not only momentum.
  7. Jun 15, 2011 #6
    It works only on HUP partners like momentum-position, energy-time right? Because by changing one of them. The other is affected inversely. Or can weak measurement work on non HUP entities like between momentum and time?
  8. Jun 15, 2011 #7


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    When we talk about position and momentum in "general terms" in QM it is usually implied that we are talking about generalized position and momentum. "Generalized" here refers to the way they are used in the Lagrangian. Hence, any variable that for example takes the place of momentum in a Lagrangian can be thought of as being a "generalized" momentum.

    My favourite example is charge and phase, which are the generalized momentum and position for electrical circuits. A lot of the work on weak measurements (both theoretical and experimental) have been done on electrical circuits (such as superconducting qubits), so I'd say if is actually quite common for the weak measurements to be done on systems where we are not dealing with momentum in the usual meaning of the word.
  9. Jun 15, 2011 #8


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    Yes (provided that you know how to define the time operator).
  10. Jun 15, 2011 #9
    Does the existence of weak measurement also suggest that FTL transmission of "weak/partial/semi-reliable" information is possible?

    I have a feeling that:

    weak measurement, de Broglie-Bohm, DCQE, Coincidence counter --- are closely linked and there is an answer/understanding hidden there that explains why FLT is not possible.

    That understanding will also answer if randomness is inherent or not.
  11. Jun 15, 2011 #10
    Ok. But Weak Measurement seems to have its esoteric terms. Even in wiki entry on it says thus:

    "After the measurement the measuring device pointer is shifted by what is called the "weak value". So that a pointer initially pointing at zero before the measurement would point at the weak value after the measurement. The system is not disturbed by the measurement"

    Now let's say I want to apply this by putting a calcite in a tiny portion of say the right slit. Now I want to perform weak measurement such that if the photon passes thru the right slit, I can only detect 0.0001% of its passage. Would this constitute a weak measurement? You may say not because there mere detection of 0.0001% determines which slit the photon passes. But it's still weak measurement, isn't it?
  12. Sep 14, 2012 #11
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