I may be completely wrong but I'm slightly confued about this - is it true that we can apply quantum mechanics to a macromolecular scale, but can't apply classical to an atomic level? If so, why don't we use quantum mechanics to solve everything and abolish classical theory which is apparently "outdated"? Thanks in advance.
The reason that the mathematics of quantum mechanics isn't applied at the macroscopic level, is because the mathematics of it is extrodinarily complex. That mathematics is so complex, that quantum mechanics can't even be used (perfectly) for atoms above hydrogen. In other words, if you want to get to the moon, you aren't going to solve schrodinger's equation to do so, you are going to use Newton's laws. But, in principle, if quantum mechanics were the theory of everything, then in principle it could be used to get you to the moon, except for the fact that someone using Newtons laws would have a far shorter computer program, for onboard computers. All this having been said, quantum mechanics is not the last word on physics, because there are serious problems with the interpretation of the mathematics being used. Consider the quantum measurement problem, consider Schrodinger's cat, etc.
Also, quantum theory (as currently formulated) doesn't apply at every level. There currently is no complete and experimentally established quantum theory of gravity. Also, as far as I know there is no quantum theoretic treatment of nonconservative forces. So we could not even solve a problem as humble as the inclined plane with dry friction. And even if we could, it would be impossibly complicated.
But surely, despite being more complecated, this way would be more "correct"? That is to say that if quantum is more "accurate" than classical theory, ie - applies to more situations (classical cant be for quantum), then it is a more correct aproach to deal with a question?
In the case of gravitation, the answer at present is a defiinitive no. The classical field theory of General Relativity is far more correct in this domain than any existing quantum theory.
When you do physics, you always use approximations when you can. Instead of using Pi, you use 3.14, instead of calculating every term in an infinite series, you calculate the first few. Similarly for quantum vs classical theories. Classical theory is a perfectly acceptable approximation to quantum theory when the problem allows it.
A lot of people say that classical theory is wrong - would you say this is the case? ie - let us take F=ma or F=dP/t; is our reasoning for why these should work wrong and are in fact just results of experiments appearing to work? Should we in fact be approaching these problems from a different angle? (eg - quantum theory) And in turn, i take it this would give us a different as to why eg 1N force accelerates and 1kg mass by 1 m/s2?
1.You've posted the same arguments on another thread. 2.Those people who say that classical (newtonian) dynamics is wrong wre wrong themselves.A theory which gives results/makes predictions that are not falsified by physically possible experiments,but in turn cannot account for experimental facts within its domain of applicability is called "incomplete".Classical mechanics accounts for all experimental results within its domain of applicability and therefore is "complete" (i'd like to call it "closed wrt to itself").It is so,as it is a limit case for a more general theory called "classical/general relativity"and we've exhausted all possible experiments to test it(did we??). Daniel. PS.I'm not 100% sure my last phrase is correct.Brighter fellows are invited to contest it.
If you have access to the magazine "Physics Today" you can read Frank Wilczek's enlightening essays on the subtleties of F = ma, which appeared in last month's and this month's issues, in the column "Reference Frame". There's another installment to come in next month's issue.
This aspect is treated within the decoherence program (study of the quantum damped oscillator, decoherence of an oscillator coupled to a bath of oscillators, etc ...). Seratend.