Hi Steven;
Thanks for your post.
Yes, I agree … its all very interesting, and the differences between the two approaches is more often than not, portrayed in terms of how QM evolved in history, as primarily a challenge to classical physics.
As far as the historical significance is concerned, perhaps the development of QM serves more as a kind of reminder that the phenomenological approach can, and does, leave gaps in the explanations and those gaps are likely to be filled by someone ... given an 'alternate name', and forever after will be seen as representing something fundamentally different in nature ?
Whilst I think following the historical development of QM might help in learning about QM, I’m not so sure this approach necessarily aids in re-inforcing the accuracy of QM, in so far as it more closely representing reality (whatever ‘reality’ is, eh ... might leave that one aside for the moment
). Sometimes the QM arguments are used in this sense over classically based arguments. I suppose at the end of the day, QMs evidence based, empirical track record speaks more directly to this point.
However, I wonder what might have happened if incomplete classical physics, simply proceeded on its normal course .. would it have eventually encompassed everything QM does, but in its own descriptive language and the ‘gaps’ we now see wouldn’t appear, and lead us to the conclusion that there seems to be a fundamental discontinuity in nature (along the lines suggested by the mathematical approach .. as in Bert’s post) ?
Steven mentioned the Balmer Series for hydrogen. Is it now possible to generate a discrete spectrum using classical wave principles (I wonder) ?
Cheers