One finds action in photon emission and particle paths. What is it when its magnitude is expressed by a Planck Constant for emission versus when it may be expressed as a stationary integral value (least – saddle – greatest) along a path? The units match. Action is recognized as a valuable concept and I would like to appreciate its nature in Nature. (Struggling against the “energy is quantized” error has distracted me from the character of the above inquiry in the past.)
Brief aside: Max Planck and Albert Einstein emphasized energy as discrete amounts for their blackbody radiation and photoelectric studies, but they always added at a specific frequency! Energy without that secondary condition is not quantized! I emphasize this because it has been frustrating for decades and it interferes with the awareness that it is action that is quantized! Now, granted that it is irrelevant to “grind out useful results” activity, which also is valuable, it is relevant to comprehending the nature of Nature, thus this post.
The existence of The Planck Constant has been a mystery since Max Planck found it necessary to make emissions discrete in order to formulate blackbody radiation mathematically. He assumed discrete emission energy values for each frequency that made the action of radiated energy at each frequency equal to the Planck Constant value. (This can be said better – please, feel free to fix it.) Action had been being used to find the equations of motion for almost two centuries by then. Is a stationary integral of action along a path equal to an integral number of Planck Constants? Is the underlying nature in these several instances of mathematical physics the same? What is that nature; how can this be? If the natures are different, how is each?
Happy Trails, Len
P.S. My English gets weird and succinct sometimes trying to escape standard ruts in meanings: how is each? is a question that directs one to explain, i.e., to describe the processes as they occur – causes, interactions, events, etc., I hope.