By Alisa Bokulich
Classical mechanics and quantum mechanics are of the main profitable medical theories ever came across, and but how they could describe a similar international is much from transparent: one thought is deterministic, the opposite indeterministic; one thought describes a global during which chaos is pervasive, the opposite an international within which chaos is absent. concentrating on the interesting box of 'quantum chaos', this booklet finds that there's a sophisticated and intricate relation among classical and quantum mechanics. It demanding situations the obtained view that classical and quantum mechanics are incommensurable, and revives one other, mostly forgotten culture because of Niels Bohr and Paul Dirac. via artfully weaving jointly issues from the historical past of technology, philosophy of technology, and modern physics, this booklet bargains a brand new frame of mind approximately intertheory relatives and clinical clarification. it will likely be of specific curiosity to historians and philosophers of technological know-how, philosophically-inclined physicists, and non-specialists.
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Additional info for Reexamining the Quantum-Classical Relation
That is, you cannot change one word without ruining the whole thing. Everything is bound up. (Heisenberg 1963, February 27th, p. 24) Heisenberg’s claim here is that, in an axiomatized theory, the meanings of the scientific terms are no longer definable in isolation, but rather are inextricably tied to the meanings of other scientific terms within that theory. So, for example, one cannot define the classical notion of force, without also invoking the concepts of mass and acceleration (or equivalently, the time rate of change of momentum).
Correction terms above will be negligible when W(x, p) is a reasonably smooth function of p, that is when the higher derivatives of W with respect to momentum are small. However, the Poisson bracket alone predicts that, in the chaotic system, they will increase exponentially quickly as a result of the “squeezing” of W in momentum … Hence after [the break time]tħ quantum “corrections” will become comparable to the first classical term on the right hand side. (Zurek 1998, pp. 187–8) It is these no-longer negligible Moyal terms that lead to the divergence between classical and quantum predictions.
13). More recently, however, Wiebe and Ballentine’s conclusion has been challenged as inadequate by Schlosshauer (2006). 6 Conclusion Those who claim that classical mechanics simply reduces to quantum mechanics in the ħ → 0 limit are, at best, engaged in a drastic oversimplification. In discussing the relation between classical and quantum mechanics, the physicist Asher Peres recommends the following warning label: “Warning: The so-called principle of correspondence, which relates classical and quantum dynamics, is tricky and elusive” (Peres 1995, p.
Reexamining the Quantum-Classical Relation by Alisa Bokulich