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dsaun777
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In the lab, how accurately can we measure momentum? What is the max value of the uncertainty in position as the uncertainty in momentum approaches zero? Or vice versa. What experiments do these types of measurements?
The Heisenberg Uncertainty Principle is not about the accuracy of measurements. It's a statistical law about the variance of measurements on an ensemble of identically prepared systems.dsaun777 said:In the lab, how accurately can we measure momentum? What is the max value of the uncertainty in position as the uncertainty in momentum approaches zero? Or vice versa. What experiments do these types of measurements?
But the hup puts a limit on measurements. Forget about mathematical derivation of hup, I am interested in how the hup influence measurements.PeroK said:The Heisenberg Uncertainty Principle is not about the accuracy of measurements. It's a statistical law about the variance of measurements on an ensemble of identically prepared systems.
It does not put any limit on the accuracy of individual measurements. It only puts limits on the statistics of ensembles of measurements of non-commuting observables.dsaun777 said:the hup puts a limit on measurements
That is a common misconception, one that made it into the popular consciousness almost a century ago and has persisted as sort of urban legend ever since.dsaun777 said:But the hup puts a limit on measurements.
The uncertainty in any particular measurement depends on the measurement process. Not on the HUP. The theoretical, minimum variance (to use the precise statistical term) over a number of measurements on identical systems is determined by the HUP.dsaun777 said:So the single measured momentum in a single experiment is the exact momentum for that measurement. It's only when you try and reproduce that measurement that the uncertainty raises?
How do you define a measured momentum in physics? What device is used? how is it we have such exact values of certain particle momenta like photons and electrons? For instance, we want to know the wavelength of light from the sun. how close is our measurement of such wavelengths to the actual wavelength?PeroK said:The uncertainty in any particular measurement depends on the measurement process. Not on the HUP. The theoretical, minimum variance (to use the precise statistical term) over a number of measurements on identical systems is determined by the HUP.
In particular the HUP specifies a lower bound for the product of the variance in momentum and position in any system.
$$\sigma_x \sigma_p \ge \frac \hbar 2$$
try this:dsaun777 said:How do you define a measured momentum in physics? What device is used? how is it we have such exact values of certain particle momenta like photons and electrons?
There is no "actual" wavelength. There is only the measured wavelength. That's quite fundamental to QM.dsaun777 said:For instance, we want to know the wavelength of light from the sun. how close is our measurement of such wavelengths to the actual wavelength?
Thank you for the paper. It appears that the time of flight method of slit experiments that utilize transverse momentum is the most common method for measuring momentum. And there is no discussed limit on how accurately you can measure the momentum from a "single shot." It is only when you introduce the second, third, etc do you get the generated statistical ensemble of measurement results that shows up in the HUP. The atom trap method was interesting I haven't heard of that yet, but a similar principle to the slit measurement.PeroK said:try this:
https://arxiv.org/abs/2302.12303
There is no "actual" wavelength. There is only the measured wavelength. That's quite fundamental to QM.
dsaun777 said:But the hup puts a limit on measurements. Forget about mathematical derivation of hup, I am interested in how the hup influence measurements.
Yes, assuming you have prepared the position exactly the same. That's what @PeroK was talking about when he saiddsaun777 said:So the single measured momentum in a single experiment is the exact momentum for that measurement. It's only when you try and reproduce that measurement that the uncertainty raises?
PeroK said:The Heisenberg Uncertainty Principle is not about the accuracy of measurements. It's a statistical law about the variance of measurements on an ensemble of identically prepared systems.
It might best to think of it as a limitation on state preparation, one that follows from the non-commutation of some pairs of observables.dsaun777 said:Ultimately, the HUP is just a mathematical result that is derived from the Fourier transform from wave analysis and should not have any meaning in a single measurement experiment.
The HUP is often misinterpreted, which has historical reasons. The funny point is that Heisenberg published his first paper on the HUP without discussing its contents with Bohr, and there he interpreted it as if it would mean that you couldn't measure accurately momentum without disturbing the system in such a way that momentum gets more uncertain and vice versa. This is, however, not what the HUP, derived from QM, is saying, and that was corrected by Bohr. Unfortunately the first interpretation somehow stuck within the literature.dsaun777 said:But the hup puts a limit on measurements. Forget about mathematical derivation of hup, I am interested in how the hup influence measurements.