Talk:Quantum mechanics

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

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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

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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.

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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:

1. This article was meant as a general introduction, accessible without a deep understanding of the math or specifically devised notations like bra-ket.
2. 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.

--AxelBoldt

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

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I've correct some mistakes here,

1. ``three things that QM explains was misleading. Quantum mechanics explains (literally) thousands of things classical theory cannot. I changed the wording to reflect this.

2. There are classical systems where vairables can only take on discrete values (vibrational modes for example) so I took that part out

I put it back in, since arguably the explanation of energy quanta is the major achievement of QM and gave it its name. The fact that classical theory can explain some quantizations doesn't take away from the fact that most quantizations are explained only by QM. --AxelBoldt

It's not a matter of ``most. The point is that quantum theory explains the right quantizations (energy levels in atoms for example). But the wording seems better now. --Matthew Nobes

3. The idea that quantum mechanics ``omits quantum field theory is a bit strong. I changed the wording of that paragraph to more accurately reflect things.

4. The history of quantum field theory was off. I corrected the QCD part and added about about the electroweak force.

5. To the primary author, why such an emphasis on the many-worlds interpretation? It's really not widely accepted...

I hear that Hawkings and with him all cosmologists believe in it (since you can't really talk about a measurement apparatus separate from the system if your system is the whole universe) and Feynman also seems to have been a many-worlder. --AxelBoldt

Just because he wrote a pop-sci book does not mean that Hawking speaks for most physicists (or cosmologists). My main point is that there is no particular reason to emphasize many-worlds over (say) Bohmian mechanics. -- Matthew

6. Also, the quotes section seems really silly to me. It gives the impression that QM is somehow wrong, misguided and/or incompherensible. It is none of these things. I would strongly encourge dropping it.

Well, if you are not worried by QM, maybe you don't really understand it... :-) Isn't it remarkable that almost all the major researchers in the field expressed their unease in some way? Why should we suppress these sentiments? Instead, maybe we should add some positive quotes. --AxelBoldt

Umm did you add the new quote? If so you made my point about ``big names versus people who nobody has ever heard of. --Matthew

Rest assured I understand QM just fine :) If read in context the writings of the founders of QM often appear less negative, further by including quotes from before the 1980's you throw out all of the interpretive work that has been done since. Things have been improved by leaps and bounds. Of course problems still remain. A quotes section cannot do justice this vast amount of work. As for positive quotes that doesn't really work becuase the average reader would assume that the Einstein quote is somehow ``better then the (say) Mermin quote on the basis of name recognition, despite the fact the the latter physicist understands *modern* quantum physics. In the end do what you wish, I'm only giving my perspective as a practicing physicist. --Matthew

Could you add some information to the Philosophy part of the article (or maybe create a new Philosophy of quantum mechanics[?]) about the newest improvements in interpretating the theory? Is Copenhagen not the state of the art anymore?

Umm the philosophy/interpretation of QM is really not my field, so I'd be extremely reluctent to write anything about it. Ideas like dechoerence play a large role. It would also be importent to stress the crucial role experiments are now playing in resolving some of the mysteries. --Matthew

Also, what I never understood and maybe you could clear up on mathematical formulation of quantum mechanics: does the theory give a general (hopefully axiomatic) rule about which operator belongs to which observable and which unit vector belongs to which state of the system? In other words, if you encounter a completely new "black box" system with a couple of observables, which Hilbert space and which operators do you use? --AxelBoldt

This seems like two (or more) separate questions. The first is asking how one assigns the various operators to the observable. This is typically done with symmetry areguements a la Wigner. There is a different (practical) problem of mesurments on an unknown state. This is done by applying known measurement tools to the unknown state (i.e. a Stern Gerlach device) --Matthew

I guess the Wigner arguments are the ones I'm looking for. What would be a good reference? --AxelBoldt

Try a graduate level QM textbook. They all treat this stuff, with more or less detail. I learned it from the very clear presentation in L. Ballentine's ``Quantum Mechnics: A Modern Development. Sakurai or Merzbacher might also be good places to look. There's a new book out by Schwinger (posthumously published, entitled Quantum Mechanics) which looks like it treats things very clearly, but I've not had a chance to go through it. Also, the first volume of Wienberg's QFT textbook has a very clear and concise discussion, except he uses the Poincare group instead of the Gallian group. If you can understand his discussion then the application to non relativistic systems will be clear. --Matthew

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I'm not the primary author, but I don't see any special emphasis on the many-worlds interpretation in the article. Could you elaborate?

Also, I believe the many-worlds interpretation has become more widely accepted amongst physicists than the Copenhagen interpretation, especially given the work in the past couple of decades on decoherence. Correct me if I'm wrong, though.

The quotes section is silly, I agree.

The philosophy section is currently rather poor. I ripped out a long description of the Cophenagen interpretation and the many-world interpretation, because those points are duplicated in the respective dedicated articles, and don't explain the philosophical issues. It needs to explain why Einstein felt that a probabilistic theory sucks, the philosophical problems with Copenhagen, etc.

-- CYD

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I took out the following passage:

Quantum mechanics consists of 3 basic principles:

1. 1. All matter and energy is quantized. In other words, everthing comes in packets, or bundles. Therefore, one cannot have any amount of material. Instead, one must have a multiple of the smallest unit.
   2. All matter and energy exhibit has wave-particle duality. Matter and energy exhibit the properties of waves in some instances, and the properties of particles in others, depending on the experiment set up to observe it.
   3. Measurements of physical quantities are probabilistic. This is Heisenberg's Uncertainty Principle, which states that the position and velocity of a particle is not absolutely fixed at any given instant and can only be described in a range of probablities. Furthermore, any object does not have a definite position or velocity until it is measured.

I believe these are very misleading comments, and do not add anything to the article, but I'm willing to discuss it.

In (1), it is unclear what it means for "matter" or "material" to be quantized; less sloppy language is required. Furthermore, many quantum mechanical observables have continuous, not discrete spectra.

(2) had been mentioned earlier in the article, and Wave-Particle duality had already been linked to.

(3) had already been mentioned in the preceding paragraphs, and is much less clear than the prior explanations. Furthermore, it is momentum that is the conjugate observable to position, not velocity. Furthermore, the Heisenberg uncertainty principle works for observable pairs other than position and momentum.

I have not seen these three "principles" in any quantum mechanics textbooks. The postulates of quantum mechanics are described in the article mathematical formulation of quantum mechanics, which admittedly still needs work.

-- CYD

I agree, the first one is simply wrong, and the other two are already covered. And I also agree that we have to start getting serious about the math. forumulation :-) --AxelBoldt

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Can AxelBoldt please justify his recent removal of the statement that QM explains and quantifies the particle nature of light? It seems to me that the particle nature of light is inherent in the definition of the wavefunction - one could dismiss it as a mere "postulate", but the same argument could be applied to the wave nature of matter. AFAIK the relationship between photon energy and frequency is derivable - say from the quantisation of angular momentum.

Actually, in my opinion that whole first section could be replaced by a description of the empirical observations leading to QM (currently relegated to the first paragraph of the "history" section). It seems strange to me to introduce QM with a randomly selected handful of theoretical results. -- Tim Starling

Quantum mechanics doesn't talk about light; Quantum electrodynamics does that. Quantum mechanics is strictly about masses moving around. A photon is a quantum of the electromagnetic field, so you need quantum field theory. AxelBoldt 01:59 Nov 11, 2002 (UTC)

That's all very well, but it leaves us with nowhere to discuss the historical development of QM in a balanced way. Planck's and Einstein's work involving light came well before QED was developed. Perhaps this page should be moved to Quantum physics (which I note is just a redirect to this page at the moment) - that way we can talk about the early development of quantum theory without guilt or confusion. We would also have a place to talk about popular thought experiments such as the single photon double slit interference pattern. -- Tim

Planck's and Einstein's work is mentioned in the History section without guilt or confusion: it preceded and lead to QM, so it belongs there. It is not part of QM however. The particle wave duality page discusses the double slit experiment. AxelBoldt

Okay, I give up. I guess I'm just used to the historical development being used as an intro.

Afterthought: you say QM doesn't talk about light, but what would you call the theory of atomic radiation based on time-dependent perturbation theory and classical electrodynamics?

I don't know what that is. AxelBoldt 04:14 Nov 11, 2002 (UTC)

Easily fixed - [1] (http://electron6.phys.utk.edu/qm2/modules/m10/time.htm) -- Tim Starling

The particle nature of light goes back to Einstein's explanation of the photoelectric effect, which is one of the foundations of quantum mechanics and obviously predates quantum field theory. Quantum mechanics doesn't necessarily deal with masses; you're thinking about the Schrodinger equation for a massive particle. For example, the quantum mechanics of spins doesn't talk about masses. -- CYD

Yes, I think Axel would argue that "quantum mechanics" is different to "quantum physics" - "mechanics" referring only nuts and bolts and the like. After four years of studying the subject, this distinction is new to me, and it sounds like it's new to you too. Obviously mathematicians are better at nitpicking than mere physicists. Nitpicking aside, there's a certainly common usage of the term QM which encompasses QED and the other "extensions". We have to ask ourselves - do we want to use Axel's definition, or everyone else's definition, in this encyclopedia? -- Tim Starling

Well, if you guys agree that QED is a part of QM rather than an extension of QM, then this article definitely needs to be changed. What is the proper name for the theory "observables are self-adjoint operators"? AxelBoldt

I wasn't sure, so I emailled God. Okay, maybe it wasn't God, just a professor of theoretical physics from my university. Anyway, here's what he said:

Yes, I would say that by common usage "quantum mechanics" usually

refers to the (nonrelativistic) quantum mechanics described by the

Schroedinger equation, while the full relativistic theory involving

"second quantization[?]" is referred to as "quantum field theory". But then

an alternative usage of "quantum mechanics" would be to refer to the whole

field of quantum phenomena. As you say, "quantum physics" would be a

better term here; but the second usage certainly does exist.

So what do you think, guys, do we

1. Move the page to quantum physics
2. Change to the popular science definition
3. Stick with the technical definition

I'm going for (1) - it's obviously a less ambiguous term. We can redirect from QM to QP, and put a note in QP about usage of the term QM. -- Tim Starling

In your characterization of the Prof's answer, why did you relabel his "common usage" as "technical definition" and his "alternative usage" as "popular science definition"? This seems to be a distortion to me. AxelBoldt 00:32 Nov 15, 2002 (UTC)

If it's a distortion then I apologise - I only meant to summarise, with labels based on my own experience of the usage of those terms. I take it by your tone that you're voting for number 3? Tim Starling