...and the limit if Planck's constant were to go to zero.... Doc, is that "if" or "of" Planck's constant? (Are there two "if" statements here, or just one?)
Just trying to follow you here. I'd thought that Planck's constant was a defined value; yet maybe it's something one can "fiddle with" (i.e., trying different values in one's equations) to see what happens? I gather if different values are assigned for the cosmological constant, extraordinarily, drastically different results would obtain, theoretically speaking.
These connections between the micro and macroworlds truly are fascinating. I have a lot to learn!
Thank you for writing, Doc.
Planck's original idea was that black-body radiation was emitted in discrete chunks. The scale parameter for these chunks in Planck's constant. (You may wish to check the Net for a description.) The classical limit is that black-body radiation is emitted continuously. The classical computation does not agree with experiment.
Other things use Planck's constant. Angular of an electron in an atom is in units of h/(2 pi) as is the intrinsic spin of the electron.
While Planck's constant is really a fundamental constant of the universe, we can ask the question of what would be the physics if it were changed. If Planck's constant were to be much smaller (zero in the limit) then classical mechanics is recovered.