Has the true value of Planck's constant always been a constant? As we progress we can get a more accurate measurement of the constant, but I would like to know if anyone has ever thought about the actual value of Planck's constant in the sense that it could change or evolve?


3 Answers 3


There have been distant measurements of the fine structure constant - that involves Planck's constant https://en.wikipedia.org/wiki/Fine-structure_constant#Definition

$$\alpha = \frac{ke^2}{hc}$$

where $k$ is a constant

and these measurements put stringent limits on any change of $h$ with time, for example

"New limits on variation of the fine-structure constant" https://arxiv.org/abs/1304.6940

this paper quotes a limit on the variation of $\alpha$ of $\dot{\alpha}/\alpha = (-5.8\pm6.9)\times10^{-17}$ per year. So unless other constants are changing too, that is a limit for the changing of Planck's constant.

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    $\begingroup$ @Al Brown seems to work out as about 2 parts per million, maximum since the Big Bang. Although there is the possibility that more than one constant is changing, quite non-mainstream but physics.stackexchange.com/q/620794 discusses this possibility $\endgroup$ Jul 28, 2021 at 14:05
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    $\begingroup$ I got 1.7 in 10^6. And called that a millionth. I’ll check that out thanks. $\endgroup$
    – Al Brown
    Jul 28, 2021 at 14:10
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    $\begingroup$ @John Hunter. It's obvious I am a novice, with that in mind, your answer says to me since all other constants are constants, and because all other constants are indeed constant, Planck's constant will be constant. Planck's constant is other constant dependent. True? $\endgroup$
    – therr
    Jul 28, 2021 at 14:11
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    $\begingroup$ @ therr Yes, the evidence seems to show that Planck's constant is constant. It could be that Planck's constant depends on other things, but that goes into non-mainstream territory, so probably best to say, that it's constant. Here was a speculative question connecting Planck's constant to cosmological numbers physics.stackexchange.com/q/622686, but if all that is going over the top for you, just take away from this that it's constant. $\endgroup$ Jul 28, 2021 at 14:21
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    $\begingroup$ @therr Only for dimensionless constants can we meaningfully speak of them "changing". If you want to ask whether Planck's constant is changing, you have to put it in terms of a dimensionless constant. $\endgroup$ Jul 29, 2021 at 17:01

Planck's constant is now actually a "constant" along with several other fundamental constants including Boltzmann's and the speed of light. SI revised the International System of Units so that units are now defined in terms of fundamental constants (seven of them) whose value does not change. See here for an announcement.

Planck's constant is used to define the kilogram. From the source above:

Now, after today’s vote, those seven constants will be set at exact values—their presumed uncertainties will be zero.

  • $\begingroup$ The seven seem to also include the speed of light , 'e' and isn't relative permeability of free space defined as $4\pi \times 10^{-7}$, this seems to fix the fine structure constant, although aren't there still experiments checking for possible changes of it in the past? $\endgroup$ Jul 28, 2021 at 14:40
  • $\begingroup$ @JohnHunter Great question! In the old SI unit definitions, the permittivity of free space was an exact value. In the new definitions, it now has an uncertainty of 0.32 parts per billion. I don't know if you can access Physics Today articles? There is one "A More Fundamental International System of Units", and table 3 in that article gives changes in uncertainty values for physical constants in the old system versus the new system. $\endgroup$
    – CGS
    Jul 28, 2021 at 15:11
  • $\begingroup$ Interesting, but wouldn't the permittivity of free space also be fixed if $c$ and $\mu_0$ were fixed, by $c=\frac{1}{\sqrt{\epsilon_0\mu_0}}$? (cool avatar 'photo' of atoms btw) $\endgroup$ Jul 28, 2021 at 15:20
  • $\begingroup$ @JohnHunter thanks! That photo is from my grad school days. As I say, your question is a good one and I don't think I am able to give you a proper answer. I can tell you that the vacuum magnetic permeability also, in the new convention, has an uncertainty. According to the CODATA website, both $\mu_0$ and $\epsilon_0$ have uncertainties of 1.5E-10. See this page: physics.nist.gov/cgi-bin/cuu/… $\endgroup$
    – CGS
    Jul 28, 2021 at 16:32
  • $\begingroup$ @ CGS, Ok, that answers it, I didn't realise that the $4\pi$ had been changed, thankyou $\endgroup$ Jul 28, 2021 at 16:40

I don't think this is quite what you want but the accepted value of the Planck constant has varied since it was first measured.

This figure

enter image description here

taken from

Steiner R. History and progress on accurate measurements of the Planck constant. Reports on Progress in Physics. 2012 Dec 18;76(1):016101.

shows the evolution of the accepted value as the measurement techniques improved over time. Note that the current accepted value is outside the error bars of an entire cluster of values from measurements done between ~1915 to ~1930. I have not had time to re-read the paper by Steiner but I remember reading at some point (possibly elsewhere) that this cluster was explained in terms of confirmation bias, i.e. nobody dared to publish a result that would disagree too much with the previous results. The current value is now defined to be $6.626 070 15 \times 10^{-34}$ J Hz$^{-1}$ but is not the subject of consensus (section 7 of Steiner).

There is no theory that I'm aware of, similar to other hypotheses, to suggest that the Planck constant would change in time or not have a uniform value.

  • $\begingroup$ The question specifically said that he wasn't talking about more accurate measurement of it, but its actual value changing. $\endgroup$
    – Barmar
    Jul 29, 2021 at 14:27
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    $\begingroup$ @Barmar I’m aware of that, and in fact indicate so in my answer. It is clear from the graph that the accepted value has changed over time by amounts outside the experimental errors. $\endgroup$ Jul 29, 2021 at 16:27
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    $\begingroup$ It's still not what they asked, they specifically said "the actual value of Planck's constant in the sense that it could change or evolve.". I.e. what if it's not actually a constant? $\endgroup$
    – Barmar
    Jul 29, 2021 at 16:28

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