Is Planck's Constant Irrational?

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SUMMARY

The discussion centers on the rationality of Planck's constant, with participants debating its classification as rational or irrational. It is established that Planck's constant, defined in SI units, is subject to experimental uncertainty, making its exact value indeterminate. In atomic units, Planck's constant can be defined as 1, leading to the conclusion that its rationality depends on the chosen units. Ultimately, only constants with precisely known values can be categorized as rational or irrational.

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  • Understanding of irrational and rational numbers
  • Familiarity with Planck's constant and its significance in physics
  • Knowledge of measurement uncertainty in scientific constants
  • Basic concepts of unit systems, particularly SI and atomic units
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  • #31
LeonhardEuler said:
If you add atoms one by one, you will probably come to a point where you have slightly less than 12g, and if you add one more atom you will have slightly more.

That's exactly what I was thinking. Atoms' masses are so small so we have no practical way of measuring so precisely, but I don't see a reason to believe that a whole number of 12C happens to weigh exactly 12 g. It could be that the closest one can get is barely under or barely over exactly 12 grams by half the mass of a neutron or any other small, positive number. And since it's nigh impossible to get two 12-gram samples of 12C with exactly the same percentage of isotopes, Avogadro's number will vary from sample to sample, which I hadn't thought of before...
 
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  • #32
If one defines units of measure on phyisical observations (as the speed of light), then yes it is possible to exactly know what the constant equals (since one is using the constant as the new "yard stick")

And I can see Avogardo's number being defined some day to be so many atoms of standard C12 atoms (or some other standardizable atom) - and define the kilogram to be so many of those. This completely changes the conversation though.

Of course, there is always the issue as to whether all neutrons weigh the same etc.

But we digress. Some constants are rational, some aren't.

--Elucidus
 

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