A Boost For Quantum Reality

Eponymous Hero sends this excerpt from Nature: "The philosophical status of the wavefunction — the entity that determines the probability of different outcomes of measurements on quantum-mechanical particles — would seem to be an unlikely subject for emotional debate. Yet online discussion of a paper claiming to show mathematically that the wavefunction is real has ranged from ardently star-struck to downright vitriolic since the article was first released as a preprint in November 2011. ... [The authors] say that the mathematics leaves no doubt that the wavefunction is not just a statistical tool, but rather, a real, objective state of a quantum system."

Comments

Re:Heh

[locofungus]

It knows, but you don't. You don't because you haven't measured it yet.

No. Well, maybe for the cat, we're not able to do the experiment to tell.

But in the equivalent test using a photon in place of a cat and orthogonal polarization states in place of dead or alive, the photon most certainly does not "know" what state it is in.

This is the essence of Bell's inequality and the fact that there is no local hidden variable theorem compatible with the results of QM.

Tim.

Arxiv.org link

[sugarmotor]

http://arxiv.org/abs/1111.3328v2

http://arxiv.org/pdf/1111.3328v2.pdf

Summary

[FrootLoops]

The article confused me greatly so I read some of the arxiv preprint linked above. Here's the idea and context as I understand it. I've included some basic quantum background since most people here don't have it.

* Intro to wavefunctions via an example. Electrons have a property called "spin" which has two states, "up" or "down". These can be measured in, for instance, the Stern-Gerlach experiment where those electrons with spin up are deflected up by a magnetic field and those with spin down go down. The wavefunction corresponds to a list of the probability of each outcome occurring. The probabilities evolve through time via the Schrodinger equation which allows predictions to be made. One might prepare an electron where its spin wavefunction corresponds to the list [1/3, 2/3], so 1/3 of the particles go up and 2/3rds go down. [I've oversimplified; wavefunctions are actually elements of an abstract Hilbert space and complex-number amplitudes are used instead of real-number probabilities. I love Hilbert space but it's too much to explain here.]

* Spin is not a classical property. One can measure spin "left" and "right" in addition to "up" and "down" by rotating the Stern-Gerlach (SG) device mentioned above and measuring left/right deflection. Suppose you run a stream of electrons through an up/down SG device which gives 80% of them "up". You then run those "up" electrons through a left/right SG device--it will always come out with 50% "left" and 50% "right". Even more strangely, if you then run the "left" electrons through another up/down SG device, the probabilities will now be 50%/50%, even though you selected only spin up electrons at the first stage so you'd expect 100%/0%. The act of going through the left/right device altered the spin up/down state somehow.

* Hidden variables. Perhaps the electrons above have definite "spin vertical" and "spin horizontal" properties before the experiment starts. The act of going through a device must change the other property, though everything might be deterministic if there is some further hidden property controlling which electrons have their spin up/down states altered in which ways by passing through the "left" SG device. The alternative is that there are no definite properties which determine the wavefunction; the wavefunction is all there is, reality is somehow fundamentally probabilistic, and the wavefunction is "real" instead of a statistical construct.

* Bell's theorem. Suppose spin up/down and spin left/right are definite properties and some hidden variables explain the above results. Using entanglement (which I'll leave undefined) and the assumption that information cannot travel faster than light, one can measure both the spin left/right and spin up/down values of a particle before the hidden variables have a chance to act (note: they might act in a very bizarre, perhaps even non-deterministic, manner, but we get to measure things before they have that chance). This gives a testable prediction which differs from quantum mechanics. If the experiment is performed, the "definite property" theory does not predict reality while the use of wavefunctions does predict reality. This is strong evidence for the reality of wavefunctions, though it's not completely conclusive.

* The paper. It derives Bell's fundamental contradiction from fewer assumptions. In its own words,

The result is in the same spirit as Bell's theorem, which states that no local theory [i.e. one without faster-than-light communication] can reproduce the predictions of quantum theory. Both theorems need to assume that a system has a objective physical state L such that probabilities for measurement outcomes depend only on L. But our theorem only assumes this for systems prepared in isolation from the rest of the universe in a quantum pure state [e.g. a particle measured as spin "up" right after the SG experiment above]. This is unlike