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The question is simple.

h-bar, or $\hbar$, limits the precision of every measurement, books tell us. For example, length measurements are limited by the Compton wavelength.

What limit for the measurement of h-bar itself arises? Or is there no such limit?

Qmechanic
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  • The default uncertainty principle is not about measurements of precision of measurements, unless you have a strange definition of "precision". See e.g. https://physics.stackexchange.com/q/169730/50583 (in particular https://physics.stackexchange.com/a/169736/50583), https://physics.stackexchange.com/q/24068/50583, https://physics.stackexchange.com/q/114133/50583 – ACuriousMind Feb 05 '22 at 09:55

1 Answers1

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There is no uncertainty at all in the value of $\hbar$. In the 2019 revision of SI units, Planck's constant was defined to be exactly $6.62607015 \times 10^{-34}$ Joule seconds.

ProfRob
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  • This is interesting, and I'm confused. The video in the linked page cites measurement error. Does this mean that, in a real world, the unit of action measured in quantum systems might be very slightly off from the defined value of hbar? Or, there won't be discrepancy between the unit of action and hbar because other units will be adjusted? – norio Feb 05 '22 at 09:45
  • "Planck was able to calculate the value of h from experimental data" on black-body radiation https://en.wikipedia.org/wiki/Planck_constant#Origin_of_the_constant . So experimental errors should affect the value , The fact that the SI units define it as definite, must be within these, very small, errors, – anna v Feb 05 '22 at 09:48
  • @norio I think the video is unhelpful. The value of $h$ is fixed at an agreed measured value. The best measurements agree with this value to a few parts in a billion. If an action is measured to be $n\hbar$ then the only uncertainty in this product (in Joule seconds) is the uncertainty on $n$. – ProfRob Feb 05 '22 at 10:58