(November 14, 2012 at 9:07 am)Daniel Wrote: Not really, QM simply replaces classical mechanics, it isn't an underlying structure ontop of which classical mechanics operates.
I bristled a bit when I first read this. I think it's your use of the word 'replaces'. CM has incredible predictive capability and is what's used for mass resulting in very small de Broglie wavelengths (objects with mass greater than an electron and certainly anything as massive as a molecule).
What I think you were trying to get at was that QM is considered fundamental; whereas, CM is simply a powerful approximation for predicting the location and velocity of relatively large objects (think molecule and above here). Conceivably, QM mathematical formalism could be used to 'replace' CM; however, we quickly run into the Heisenberg uncertainty principle. Not only would our data be imprecise, but the volume of data would be so unwieldy that it becomes impractical. This may come off as snarky, but CM was used to put rovers on Mars, not QM.
In addition, the entire effort to find a Grand Unified Theory (think String and M theories) is because QM has not 'replaced' CM (Stimbo recently created a thread regarding the continued elusiveness of experimental validation of String Theory).