Can the accuracy in Planck's constant ever be increased?
Solution 1
Following on from Jon's comment above, this is from the NIST Website (Dated June 21, 2016), discussing a more accurate measure of the kilogram, and the involvement of Planck's constant.
A hightech version of an oldfashioned balance scale at the National Institute of Standards and Technology (NIST) has just brought scientists a critical step closer toward a new and improved definition of the kilogram. The scale, called the NIST4 watt balance, has conducted its first measurement of a fundamental physical quantity called Planck’s constant to within 34 parts per billion – demonstrating the scale is accurate enough to assist the international community with the redefinition of the kilogram.
Planck’s constant lies at the heart of quantum mechanics, the theory that is used to describe physics at the scale of the atom and smaller. Quantum mechanics began in 1900 when Max Planck described how objects radiate energy in tiny packets known as “quanta.” The amount of energy is proportional to a very small quantity called h, known as Planck’s constant, which subsequently shows up in almost all equations in quantum mechanics. The value of h – according to NIST’s new measurement – is 6.62606983x10^{34} kg∙m^{2}/s, with an uncertainty of plus or minus 22 in the last two digits.
The NIST4 watt balance has measured Planck’s constant to within 34 parts per billion, demonstrating that the hightech scale is accurate enough to assist with 2018’s planned redefinition of the kilogram.
Solution 2
Planck's constant's accuracy can indeed be increased. As detailed by this website, there are five main different ways of calculating Planck's constant, each with varying levels of uncertainty.
Approximately every four years, a organization called CODATA (more specifically, its Task Group on Fundamental Constants) publishes the most uptodate values for fundamental constants, including Planck's constant. The most recent update came in 2014 (though it was technically published in the middle of 2015). The value for Planck's constant in this update was $6.62607004 \times 10^{−34}\,\mathrm{J}\cdot \mathrm{s}$, with a standard uncertainty of $0.000000081 \times 10^{−34}\,\mathrm{J}\cdot \mathrm{s}$.
This paper as well as the websites linked have more information.
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Bosoneando
Updated on August 01, 2022Comments

Bosoneando 5 months
I guess I am having some confusion about the history of calculating Planck's constant. I see the mass of the electron may come into the equation here but isn't the measurement of mass based mostly on how accurate instruments are? I assume it's not something that can be derived like the ratio of a circle to it's diameter? (flat space). There is measurement involved here and limitations of instrumentation? So can its accuracy ever change or am I just way off course here, may be the case.

Jon Custer over 6 yearsGroups around the world, such as NIST, spend lots of time trying to improve measurement technology and techniques so they can measure fundamental constants more accurately. So, yes, the accuracy will change.


Xerxes over 6 yearsHuh. Am I getting downvoted because people don't know that this is true? Or they hate my casual tone? Or they want more citations? Or what? I'm puzzled.

Schwern over 6 yearsAssigning an official value to the Planck constant doesn't suddenly remove the problems in measuring its actual value. Declaring a year to be 365 days still means the calendar will drift out of sync with the seasons.

Schwern over 6 yearsThe downvote button says "This answer is not useful". Sure, you can redefine anything you like to be 1, but you still need to measure it to be useful."What is the mass of the Sun?" "1." "1 what?" "1 Sun." It's a circular definition. You don't suddenly know how massive the Sun is just because you declared its mass to be 1. Any derived measurements can still only be as accurate as your measurement of the Sun's mass.

Jonas Heidelberg over 6 years@Schwern My understanding is that the uncertainty in measurement will still be there, but instead of uncertainty about the value of Planck's constant given the mass of "the" kilogram in Paris, it will then be the uncertainty of the mass of said kilogram given the thendefined value of Planck's constant...

Xerxes over 6 yearsI don't believe that's actually true. You certainly can't define something unitful to be 1 in a sensible way. Planck's constant is a ratio of units, so it defines the relationship between mass, length and time in a specific way. There's a deep and significant meaning to the fact that this, G and c can be set to 1.

Massimo Ortolano over 6 years@JonasHeidelberg Yes, it's exactly like that: the uncertainty will be transferred to the realization of the kilogram. I'm writing from the phone and I couldn't expand on that now.

Schwern over 6 yearsThis is, basically, what the SI units are doing. Except instead of setting it at 1 they're keeping their historical values. But you still have to measure them. And that still has inaccuracies. You'll still get slightly different measurements of what 1 is supposed to be.

Xerxes over 6 yearsThis is why I posted a new answer even though 2 people already offered these measurements of the value of the kilogram as answers. The value of the kilogram is interesting (to humans) and measurable and you can express Planck's constant as a ratio of the value of the kilogram to some other stuff. But fundamentally, the value of the kilogram it doesn't have anything to do with the universal constant.

Admin over 6 yearsXerxes...I think your approach is significant. I am researching this further and will get back latter.

peterh over 6 yearsI've found your style funny :) But some people thinks it is bad. Afaik, there is a problem with the Planck units: the gravitational constant can't be measured very well, compared to the mass of the good old platina brick.