Miggy, hasn't QM failed to reconcile with SR, though?
Very much this. Electricity and magnetism are unified into the electromagnetic force. This has been unified with the strong and weak forces. However, there is NO real workable way to get gravitiational force into the same mathematical framework. Einstien went to his grave seeking this, and Hawking has been trying for years.
Stuff...
IMHO, you have a few things not quite right. Quantum mechanics doesnt become Newtonian dynamics which doesnt become relativity - basically at one scale one set of tools works better than another set, and at another scale both work with similar levels of accuracy. Neither one or other set of equations is more true than the other and neither one nor another represents the actual rules the universe runs on, just a model that we use to make predictions about the future state of the universe with varying degrees of success. All three clearly work for thier intended purpose, which is to explain particular behaviours. The fact that quanta and relativity dont reconcile is not really admissable for either being wrong on the grounds that they arent absolute truth.
One of the very, very first and strictest requirements of all of the wacko theories are always that they must reconcile with what we already know.
I shall assume you know of the Michelson-Morley Experiment. I apologise if I have spelt thier names wrong. Remember, everyone
KNEW there was an ether. Everyone. A "wacko" theory can stand alone if needs be. Chemists need not use string or M-theory. Nasa need not use MOND. Protons et al used to be indivisible. "Wacko" results are wonderful as they encourage new models to emerge which can be different to existing frameworks if needs be. If they can be incorporated into what we can already model, great. If not, then until "better" models emerge, then in a box of thier own they must remain.
Miggy, hasn't QM failed to reconcile with SR, though?
I... Don't think so? I'll admit that I'm a chemist and not a physicist, so I haven't delved so deep into quantum mechanics or special relativity that I know them in and out, but The Dirac Equation is, to my understanding, special relativity applied to quantum mechanics, which yielded explanations for unsolved matters, for instance the atomic spin.
I don't know if either theory directly predicts the other. I guess that if you assume the Dirac equation is true (which we do because of the consistency with observations), the only way to formulate it would be by using the relativistic models, which would then lead onto relativity.
For pretty much hydrogen, yes. We have that worked out. But thats not much more than a proton/electron isnt it. It cant really be applied to more complex atomic systems (in particular, things that arent spin 1/2... which is why it works so well with an electron or positron). One result in the form of a specific and specialized equation cant be said to be unification.