- 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
Having reviewed more of the literature on this topic, I concede that I was incorrect, so I'm removing the discussion regarding electron clouds and acknowledging that the current description in the article is correct -- Matt Stoker
Perhaps some mention of the problem that inspired Planck to invent Quantum Mechanics is in order. IIRC, physicists were trying to figure out what electromagnetic waves were in an oven that had a certain amount of heat in it. They knew that an integer multiple of the wavelength of the light in the oven would have to equal one of the dimensions of the oven, but every time they tried to figure it out, they ended up concluding that the oven had infinite energy in it. Planck was able to find the answer by assume that the energy in an electromagnetic wave was quantised such that E ∝ f. This went directly counter to the classical mechanics assumtion that E ∝ Amplitude.
I would like to request that we start an article "Mathematical content of quantum mechanics" and move most of the math material that is right now in the main article there. Two reasons:
- This article was meant as a general introduction, accessible without a deep understanding of the math or specifically devised notations like bra-ket.
- The math treatment right now is incomplete (it doesn't mention that the operators don't have to be defined everywhere, it doesn't mention which operators belong to which observables, it doesn't mention the possibility that an operator may not have eigenvalues, it doesn't mention the importance of the spectral theorem in dealing with operators that don't have a point spectrum.
Correcting the problems in 2 would compound problem 1.
Good idea. How much of the current material do you think should be left in the article, and how much moved to the new page? The old section on "Mathematical Formulism" I found very difficult to read, which was why I expanded it. -- CYD
I can write a very simple version, basically saying that states are elements of Hilbert spaces, observables are operators, and the states evolve according to the Schrodinger equation, and then link to the math article. --AxelBoldt