Wikipedia: Quantum Mechanics/Talk

: Quantum mechanics has provoked a strong philosophical debate. The fundamental problem is that causality and determinism is lost: while the probability distributions evolve according to a well established deterministic law, the values of the observables themselves do not. Because of this, Albert Einstein held that quantum mechanics must be incomplete.

It would be helpful to try to give some basic explanation of why Einstein's view is widely held to be incorrect--his view seems like common sense, but common sense is often wrong, as theoretical physicists enjoy pointing out. So, why is it wrong, in this case? By the way, please don't answer this question on the /Talk page--please put the answer on the QM page. Thanks in advance! --LMS

It's not entirely clear that Einstein was wrong on all counts, just wrong on at least one of them. :-) The Bell's-inequality experiments of Aspect prove beyond any doubt that either (1) Observable effects exist that cannot be deterministic results of inherent properties of matter; or (2) The universe is non-local; i.e., physical effects can propogate faster than light. Nobody knows which. --LDC

It proves neither, since neither is the case in the multi-universe interpretation. --JG

I'll put a discussion of these issues on the Copenhagen interpretation page. --AxelBoldt

In the "Description of the theory" section, it states that the view of the electron circling a protron was replaced by the view of a static "probability cloud". However, this gives the misleading interpretation of the electron as being "smeared" in some distribution around the proton, which isn't really case. The electron does in fact move around the proton, we are just unable to predict the nature of this movement and can only predict the probability of finding the electron in any given location.

That the electron is not "smeared" throughout the distribution, but occupies unique points in space is evidenced by the relative inaccuracy of the Hartree-Fock approximation compared to Density Functional Theory or other methods that attempt to account for the "correlation energy" that arises due to the interactions between moving electrons. --Matt Stoker

Current understanding is that the electron is smeared. If a wave function was just a probability distribution for a particle that actually had a given position, the double-slit experiment wouldn't work, since the electron would have to travel through one slit or the other. I'll admit to not knowing precisely how correlation energy works, but absolutely none of the fundamental quantum mechanics I have seen treats orbitals as anything other than stationary states. --Josh Grosse

The electron cannot be smeared over the orbitial, since if it were then the electric field would also be smeared. This smeared view of the electric field is the limiting assumption in the Hartree-Fock approximation and is the reason for it's limited applicability to multi-electron systems. The electric field cannot be treated in an average or smeared fashion because electrons repulse each other, this repulsion results in an instantaneous distortion of the probability distribution for a given electron that depends on the instantaneous position of the other electrons at any given point in time. The difference between the exact energy and the Hartree-Fock energy due to these instantaneous electron interactions is called the "correlation energy".

My understanding is that modifications of the double-slit experiment were performed in which the researchers attempted to detect which slit the electron passed through. In these experiments, they were able to determine which slit each electron passed through, but the measurements perturbed the system, such that the typical diffraction patern did not occur. In other words, when the electron was detected as a particle with a definite position, the system behaved as if the electron were a particle. The wave function collapsed, because the electron position was detected. I would imagine that the interactions between electrons are similar. Instantaneous interactions between electrons cause the wave functions to collapse, so at any given time the electrons "see" the other electrons with a unique position and the electric field corresponds to specific electron positions. --Matt Stoker

But electrons are always interacting with other electrons, so if this was enough to collapse the wave function, you could never have an electron in two places at once. What happens when two electrons interact is that their wave functions become entangled, and that's where the correlation comes from, although I don't know the mathematical details. In the copenhagen interpretation, you need a real observer to cause collapse, while in the many-worlds interpretation, collapse does not occur at all (only entanglement between the system and observer). --JG

When I wrote the sentence about static electron probability clouds, I did not have "smeared out electrons" in mind; rather, I thought about a probability distribution that tells you how likely it is to find the electron at a given point, the electron being a particle, not a cloud. Maybe I should clarify that somehow? Any suggestions?

Also, we have some treatment of the double-slit experiment in Wave-Particle duality. Let me know if that is inaccurate. --AxelBoldt

Request to leave the sentence alone. In copenhagen electrons are clouds until observed - that's what wave-particle duality is all about - and in other interpretations they are clouds period.

Actually there's no conflict between having an electron "smeared out" and it having a velocity (~momentum). Since the electron is described by a wave(function) it can (and will) do both at the same time. The prime example here is a free electron. If a free electron has an exactly determined momentum its wavefunction will be spread out evenly over whole space (maybe a rather theoretical example..). Actually the electrons around a nucleus also both have a momentum and are delocalized (and you can solve the Shrödinger equation for Hydrogen exactly). Even if you go from Hartree-Fock to Full CI (Which is a method to solve the Schrödinger equation exactly within a finite basis-set) you still get delocalized electrons. -- Ulf Ekström