Quantum mechanics for big things?

[jarekd]

Sure the deeper theories might not lead to better direct observations, because of the fact that e.g. photons we can use are relatively bulky in the microscopic world - measurements are sophisticated and usually destructive complex processes.
The purpose of deeper theories is different - like understanding, intuitions ... and thanks of it also better models of what we cannot directly measure - which could not only explain, but also derive quantitative properties of more effective models, like parameters of the standard model ...

 

[Maui]

And why should this be a sensible definition? After all, it includes classical electrodynamics. Why do you reject the obvious definition that quantum effects are effects which are only predicted by quantum mechanics but not by classical mechanics / electrodynamics?

Because there is just quantumness and the wave-particle duality is just a crippled representation of its manifestations into 'particles'. Clasical mechanics is a special case of quantum mechanics as there exists no classical stuff to speak of. With regards to the definition of 'quantum behavior', the Nature article seems to use the same definition - everything behaves according to quantum rules, except in the classical limit where quantum effects and behavior is mostly 'washed out'.

PP. Quantum effects and quantum behavior are not the same thing, there is a subtle difference - and you seem to be discussing quantum effects which I never denied existed at all scales, what I was interested in was seeing the arguments on the existence of directly observed quantum behavior.

 

[kith]

The purpose of deeper theories is different - like understanding, intuitions ... and thanks of it also better models of what we cannot directly measure - which could not only explain, but also derive quantitative properties of more effective models, like parameters of the standard model ...

I agree. Different points of view regarding the interpretation of QM may lead to different paths for physics beyond the Standard Model.

@Maui: I don't like to discuss semantics more than I already have.

 

[bhobba]

It has the essence of wave-corpuscle duality: it is going from thermodynamics of a point particle (after some small correction it can be seen as stochastic modeling) to seeing them only through their wave nature.

But the problem with all of them is that the thing which is supposed to explain the random results, can not be observed in measurements even in principle. And QM suggests why this is so: any interaction leads to entanglement and in order to perform a measurement on a system, you have to interact with the system.

Yes - we are getting a bit off topic - so mods - if you feel this post should be removed I fully understand.

That said. WOW. I often get into discussions about the exact meaning of QM but only rarely do I think they get to the real issues. The above do.

Imaginary numbers are indeed right at the foundations of QM and, its a strange but true fact, you can actually derive Schrödinger's equation from the Hamilton-Jacobi equation by simply going over to complex numbers:
http://arxiv.org/pdf/1204.0653v1.pdf

And its a very deep fact, very deep indeed that has only been recently understood, that QM is basically the most reasonable generalized probability model that allows entanglement. There is just one other that satisfies these reasonableness criteria, and that is bog standard probability theory - but that does not allow entanglement. Entanglement is really what makes QM, well QM:
http://arxiv.org/pdf/0911.0695v1.pdf

'A remarkable result following from our reconstruction is that no probability theory other than quantum theory can exhibit entanglement without contradicting one or more axioms.'

Thanks
Bill

 

[jarekd]

Bill, Schrödinger's original derivation was practically based on Hamilton-Jacobi these nine decades ago: http://gallica.bnf.fr/ark:/12148/bpt6k153811/f373.image.langFR
Entanglement, like in EPR paradox is just causal connection/correlation - Noether law says that angular momentum has to be conserved, so the whole field guards that created together photons have opposite spins.
Sure there are "squares" relating amplitudes and probabilities and leading to violation of Bell inequalities required by our "evolving 3D" intuition, but the fundamental physics is time/CPT symmetric Lagrangian mechanics: "full 4D" instead, saying that the present moment is action optimizing equilibrium symmetrically between past and future (asymmetry has to be a property of the concrete solution we live in: discussion).
In 4D thermodynamics is e.g. assuming Boltzmann distribution among possible infinite paths, like in euclidean path integral formulation or maximal entropy random walk. In ensembles among paths, amplitude corresponds to probability at the end of past or future half-spacetime. To "accidentally" get given value in given moment, we have to get it simultaneously from the past and the future half-paths: probability is proportional to square of amplitudes:
https://dl.dropboxusercontent.com/u/12405967/fqm-1.jpg
But maybe let us take this discussion somewhere else, like to maximal entropy random walk thread which is practically euclidean path integrals, but corrected to be a stochastic model and seen not as "Wick rotation of QM", but just as corrected thermodynamics of point particles ... and started with discrete version, which is mathematically simpler.

 

[bhobba]

Bill, Schrödinger's original derivation was practically based on Hamilton-Jacobi these nine decades ago: http://gallica.bnf.fr/ark:/12148/bpt6k153811/f373.image.langFR

Not quite. As the link I gave carefully explains it was based on an unjustified ad-hoc assumption to get around the fact he did not take the necessary step of using complex numbers - if you don't you get the wrong sign in the Schrödinger's equation. This was an obvious mistake Schrödinger made because its well known Schrödinger's equation has complex solutions and if he spotted that he could have easily gone back and figured out the correct derivation.

That's not to be too hard on Schrödinger - as some historian of science put it during times of paradigm changes in physics the main players are often what he calls sleepwalkers - they have a sort of intuitive idea of where they are heading - but what they do to go there is a bit dubious.

Thanks
Bill

 

[jarekd]

Anyway we should have in mind that quantum mechanics was founded on the classical one ... which still is deeply there as approximation:
- in semiclassical approximation as the zeroth order,
- in path integral formulation as the path around which we make variations for the van Vleck formula.
Quantum mechanics is the classical one with h-order corrections because of the wave nature - caused by some intrinsic periodic process of particles.
Thanks,
Jarek

 

[A. Neumaier]

Why can't QM be applied to bigger objects?

Quantum mechanics is universal; it applies to all objects, including big objects. But most of quantum mechanics is simply not spectacular enough to make headlines. Only the quantum effects that sound weird in everyday language, and hence are the focus of most of the popular talk about QM, get weaker and weaker as the object mass grows, and hence are spectacular enough for public attention only for very small quantum systems of a kind with which one can readily make experiments with.

But our everyday life is full of quantum effects; they just go under unspectacular labels. Some examples:

• Whenever you sit on a chair you experience a quantum effect. You sit mostly on empty space - that the chair is a quantum object is the reason that you (who also consist mostly of empty space) don't glide through. Classical physics cannot explain this. (In elasticity theory, which is the classical theory of solid bodies, you have to assume solidity without knowing its reason.)
• Whenever you see something you experience a quantum effect. Electromagnetic radiation excites - a quantum effect - many electrons in the retina of your eyes, which in turn create electric impulses in your nerves, which are processed in your brain, ultimately resulting (in a not really understood process) in your sensation of moving colored objects (or whatever you happen to see).
• Whenever you burn a candle you experience a quantum effect. The wax and the air undergo chemical reactions - processes that were completely mysterious before the advent of quantum mechanics.
• When you go for a walk on a sunny day you experience a quantum effect. The sun gets all its energy (and you the sunshine) from quantum mechanical processes in its interior.

Thus quantum mechanics is everywhere in Nature. But once you make a few assumptions (about solidity, seeing, chemical reactions, superconductivity, etc.) that come from the quantum nature of big objects you can treat the remainder with classical physics. This is the reason why classical physics was discovered long before quantum physics.