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Varon
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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)."
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)."