Could Planck's constant be changing? 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?
 A: 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.
A: 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.

A: 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

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.
