Talk:Interpretation of quantum mechanics/Archive1

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< Talk:Interpretation of quantum mechanics

This is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page.

1 Old, untitled discussion
2 Why is a Yes or No desirable?
3 Bell's theorem, hidden variables and loopholes in the tests
- 3.1 Doubt over the Copenhagen interpretation and wave-particle duality
4 POV on quantum mechanics as a weird or unsatisfactory theory
5 Proposed POV tag
6 Proposed first paragraph
7 Philosophical problems
8 Interpretation in classical physics
9 In a nontechnical sense
10 very high status as a scientific theory
11 Comparison table
12 Shut up and calculate
13 Disputed claim
14 Another edit
15 On the aboutness of Quantum Theory
16 Capitalization
17 Why no discussion of these alternatives
18 Quantum philosophy
19 Probabilities
20 von Neumann measurement
21 Fix for instrumentalist view
22 Organization and the place of this artcle
23 Edit of intro
24 no wavefunction collapse in transactional interpretation
25 Proposition for a modern decoherence interpretation

Old, untitled discussion

The text below was in the main article. It appears to be notes on topics that should eventually be covered.

Once you eliminate the impossible, whatever remains, no matter how improbable, must be the truth. - Sherlock Holmes (by Sir Arthur Conan Doyle)

(I'd like to take a hound of the baskerville approach here. Start with the obvious interpretations of quantum mechanics, show why then don't work.)

Much of the non-intuitive nature of the their deals with its probablistic nature.

It's not just that it's probabilistic. If that's all, there probably wouldn't be that much fuss. It's that it's not described by classical probability in the measure theoretic sense, but is some sort of noncommutative probability. Phys 20:01, 27 Nov 2003 (UTC)

(The nature of light)

(Why light is a wave won't work)

(Quantum mechanics contains probablistic descriptions of particles.)

(The double slit experiment and why that doesn't work.)

(QM is due to local hidden variables)

(The aspect experiment and why that doesn't work.)

Why is a Yes or No desirable?

It seems to me that it does not make sense to presuppose that all "yes"es in the table is desirable. Nature is the way she is.

I think the last 2 paragraphs should be removed (or significantly changed)

Oz 04:00, 13 Sep 2003 (UTC)

What about this interpretation: Transactional Interpretation of John G. Cramer and Online version of old Analog magazine article by Cramer? --Cardiffman 21:55, 29 May 2004 (UTC)

Bell's theorem, hidden variables and loopholes in the tests

The article said that a theory should have no hidden variables. Surely this is the opposite of what EPR and Bell wanted? They wanted hidden variables to convert the theory from a probabilistic to a deterministic one. The variables would be like the exact position and momentum of every molecule in a gas: not knowable in practice but assumed to exist and, under the kinetic theory, to in fact determine its properties.

I've corrected the statement about the experiments that are interpreted as supporting quantum mechanics and ruling out local hidden variable theories. Look carefully at any experimental report and you will find that the interpretation is being made subject to the assumption of "fair sampling" or something to that effect. But it has been known since about 1969 that this assumption is not in fact reasonable for Bell test experiments. If it is false (which is all to likely) then alternative hidden variable explanations can be found for the observations. The fair sampling assumption represents the main loophole in this kind of experiment. There are others. Caroline Thompson 21:08, 19 Jul 2004 (UTC)

William Connelly seems to think that a fundamental theory should have no "hidden variables", whereas I've always tended to think of them as a "good" thing! I suppose the truth is that when explaining the Bell test results I've got used to referring to intrinsic properties of light pulses (alias "photons") such as polarisation direction as being "hidden variables", but this is only because everyone else does. It is conventional for the basic local realist model (see local hidden variable theory) to term any intrinsic property a hidden variable and proceed to integrate over the hidden variable space. However, if QM had never been invented one would not talk this way. They are just plain "variables", and William is really quite right: a fundamental theory should ideally include all relevant variables. I've compromised on this page by deleting the link to the local hidden variable theory page. The reader should get the picture from following the other links.

Caroline Thompson 17:15, 21 Aug 2004 (UTC)

Doubt over the Copenhagen interpretation and wave-particle duality

There is currently (August 2004) some doubt over the validity of wave-particle duality and the Copenhagen interpretation due to Shahriar Afshar's 2004 contradictory result using a variation on the double-slit experiment. The results have yet to be peer-reviewed.

Actually...... no....

http://axion.physics.ubc.ca/rebel.html

Roadrunner 06:37, 22 Aug 2004 (UTC)

I think there was some doubt but the establishment had now reassured everyone that nothing has changed. And indeed nothing has: there have always been doubts. But I'm waiting till I see Afshar's full report before trying to give my own explanation. I get the impression that New Scientist and your link (Unruh, which has nice diagrams but I've not yet read) have oversimplified things.

So far as the wiki page is concerned, though, I agree. Afshar is probably just a flash in the pan.

Caroline Thompson 08:46, 22 Aug 2004 (UTC)

See my article about it at [1].--Lumidek 04:09, 27 Nov 2004 (UTC)

POV on quantum mechanics as a weird or unsatisfactory theory

There is a description of quantum mechanics given by this article as expressed in sentences such as

However it becomes philosophically troublesome once it is mathematically demonstrated that it cannot have all of the properties that one would intuitively expect for it to have.

or even worse

The possibility that quantum mechanics is simply wrong has still not been completely ruled out by the Bell test experiments.

Of course, nothing rules out any theory being ruled out by experimental evidence, whether it's Bell's inequality or the unexpected discovery of the agency of angels. The phrase "simply wrong" is tendentious. Quite simply, if it's wrong, it's simply wrong.

I have added some comments on interpretation on the Bell's inequalities talk page.CSTAR 20:43, 10 Jan 2005 (UTC)

Apart from the point you mentioned, I want to express my doubts about:

that is deterministic: given one set of circumstances, there is only one possible outcome;

being an undesirable aspect of any theory. I'm fine with it, and there are even voices which feel better this way around, hoping that it also implies a free will.

Pjacobi 21:42, 2005 Jan 10 (UTC)

In fact, this whole business of coming up with desiderata of this kind seems ludicrous. The only desideratum of any merit is whether the theory conforms to the facts or not. If it doesn't, we chuck it and find something else.

And I fully agree that determinism is not (and arguably hardly ever was) a desirable ingredient in theories. Although I would not say anything about the relation of determinism to free will; that's a red herring. CSTAR 22:59, 10 Jan 2005 (UTC)

Proposed POV tag

This article expresses as a predominant view, what in fact is a fringe view of the nature of quantum mechanics. Fringe views may be presented on WP, and sometimes there is benefit in doing so, but provided such views are labelled as having little or no support in the scientific community. The determination of the level of support is determined by articles in the peer-reviewed literature. In this case there is no doubt that the view of QM as weird or unsatisfactory has is a fringe view.

I therefore propose putting a POV tag on the article and will do so unless there is some compelling reason not to. CSTAR 03:55, 14 Jan 2005 (UTC)

What are you trying to say? That a page devoted to the interpretation of quantum mechanics has to imply that there are no conceptual difficulties? Surely the whole world agrees that it would be desirable to have a local realist theory instead? It should be deterministic at the lowest level, though it is bound to have effectively random interactions with the environment, giving it an effective measure of indeterminism. This is what Einstein wanted and, indeed, surely what everyone would like to see, if only they had not been persuaded by the Bell test experiments that it was impossible. As you know, the tests were not by any means conclusive and my personal view is that if they were to be repeated with a range of parameter settings it could be shown that the "obvious" local hidden variable theory was perfectly viable.

When gou say that wikipedia should present the majority point of view, what subset of the world's population are you considering? Just quantum theorists?Caroline Thompson 09:23, 14 Jan 2005 (UTC)

It's somewhat religious to judge, what everyone would like to see. And yes, the Wikipedia, as every encyclopedia, should present the majority scholarly POV as such. In contrast to other encyclopedias, the Wikipedia will present also other POVs, to some extent, if relevant enough.

An encyclopedia is rather dull, conservative project. There no original research here and it is not the place to decide any POV clashes, only to report them.

Pjacobi 11:54, 2005 Jan 14 (UTC)

I don't think this article needs a {{NPOV}} tag; there is no throughly peer-reviewed experiement with currently favors any particular QM interpretation right now. Samboy 11:58, 14 Jan 2005 (UTC)

Huh? I'm not talking about favoring one interpretation over another! The article needs to explain what an interpretation is and why some physicists regarded it as necessary for QM and why it wasn't deemed necessary say for statistical mechanics (although in retrospect probability requires intepretation as well). As to the failure of {{NPOV}}, I'm referring to:

The list of desiderata.
The view that the reason QM needs interpretation is because it's troubling or bizarre in some way
The view of causality as expressed in a very limited idea of local realism.

CSTAR 14:32, 14 Jan 2005 (UTC)

(William M. Connolley 13:38, 14 Jan 2005 (UTC)) CT said: Surely the whole world agrees that it would be desirable to have a local realist theory instead? - this is near meaningless. The world would like truth, justice and harmony but that doesn't mean we're going to get it. The article should spend most of its time on the dominant POV and mention speculative stuff as such. Don't put on a POV tag - edit the article to remove it and hopefully people will support you. I will. CT is welcome to express her personal POV on the talk page but not in the article.

The reason is that this is an ambitious task that will very likely take several months of edit, counteredit and discussion. CSTAR 14:32, 14 Jan 2005 (UTC)

(William M. Connolley 15:17, 14 Jan 2005 (UTC)) Maybe. But it would be better to have a good start at getting rid of the worst bits and seeing if that works. If you try that and it fails, then try the tag. In fact, looking at the page, it says One might intuitively like a physical theory... *not* it is desirable for a theory... and the phrase on the page seems fairly reasonable. I've done a bit of an edit which may help.

One might intuitively like a physical theory... does seem like desideratat to me

You did remove some of the more egregious offending phrases (such as simply wrong). However the article never says what an interpretation is; a good WP should say this in the first few sentences and why it is necessary. Interpretation in general may have two parts:

A formal reduction of a set of linguistic structures (such as a language or the terms of a theory) to another formal structure. This can be accomplished by many worlds, consistent histories etc.

A statement of what there actually is: the elements of these other formal structures are actually elements of the real world (principle of reality)

Issues of completeness, locality and so on are irrelevant for sayinh what an interpretation is, I think. CSTAR 18:18, 14 Jan 2005 (UTC)

Proposed first paragraph

In a nontechnical sense, an interpretation of quantum of mechanics is an attempt to answer the question what exactly is quantum mechanics talking about. That such a question is even asked is a reflection of a number of facts:

The mathematical structure of the theory based on fairly abstract mathematics such as Hilbert spaces and operators on Hilbert spaces.

The historical development of the theory which went through through various stages of understanding of what particular formalisms meant. This includes various attempts by leading scientists such as Einstein to come to terms with the theory.

Why single out Einstein here? He was a local realist who never really came to terms quantum mechanics in anything approaching its modern form. As far as important contributions to interpreting QM, probably the single most important was Bohr's interpretation (or was it Born's?) of Schrödinger's wavefunction as a probability density. Right? I dunno. Just a thought. Lethe | Talk

You're right about Einstein. I don't think he ever came to terms with it which has been the source of endless hassles. Yeah Bohr, Born one of those two should be mentioned.CSTAR 22:06, 14 Jan 2005 (UTC)

The apparently peculiar nature of the measurement process in quantum mechanics which is tied in with the statistics of certain ensembles.

CSTAR 21:18, 14 Jan 2005 (UTC)

(William M. Connolley 21:28, 14 Jan 2005 (UTC)) Could be.

Now that's non-commital. CSTAR 22:06, 14 Jan 2005 (UTC)

I'm in danger of getting out of my depth here, but... I dislike the first point, or at least your formulation of it. Perhaps something like "In classical mechanics "commonsense" proterties of an object - location, or velocity - are described by a single number and there does not seem to be any need to "interpret" the theory to see the association of number with physical structure. In QM, the objects of the theory are more abstract and the connection to observed reality - via measurement - is <insert your favourite phrase here>.

Is this really true? If so why did Mach, Bridgeman and others go to such great lengths to provide operational meanings to the physical concepts of classical mechanics? CSTAR 00:15, 15 Jan 2005 (UTC)

More significantly, however, is that interpretation is now a common theme in any explanatory system: so quantum mechanics is less of an outlier in that respect as it once was.CSTAR 22:06, 14 Jan 2005 (UTC)

(William M. Connolley 10:44, 15 Jan 2005 (UTC)) Yes, I'd agree with that last. You've added "measurement destroys the state". I don't think thats defensible in that form.

What Im trying to say in an introductory way is that measurement (generically) carries a pure state to a density state. One should also say something about the double slit experiment. But anyway, if you find a better formulation, please put it in.CSTAR 14:08, 15 Jan 2005 (UTC)

(William M. Connolley 19:10, 15 Jan 2005 (UTC)) I'm not going to try to correct it, because you've lost me already (I thought measurement took a possibly-mixed state to a pure state; I don't know what a density state is).

Have a look at quantum operation.CSTAR 22:32, 15 Jan 2005 (UTC)

Philosophical problems

One has to define for any interpretation (whether it is understood as a formal equivalence or an ontological one) what it means for that interpretation to have the properties of "reality", "completeness" etc. I am treading on dangerous waters here.

I also agree that the Feynman dictum should be put back in. I only meant to remove the phrase "neutral interpretation". CSTAR 16:47, 16 Jan 2005 (UTC)

Interpretation in classical physics

I suggest changing the sentence

are described by real numbers nd there does not seem to be any need to provide a special interpretation for these values. A similar comment can made in regard to the understanding of electromagnetism.

are described by real numbers and functions defined on sets which have direct spatial meaning. In this case, there does not seem to be any need to provide a special interpretation for these objects . A similar comment can made in regard to the understanding of electromagnetism.

CSTAR 20:26, 9 Feb 2005 (UTC)

In a nontechnical sense

Could we remove that adverbial phrase at the beginning? Yes I put it in, but at the time it seemed a like a plausible step to set up a transition from the previous content of the page. CSTAR 23:13, 10 Feb 2005 (UTC)

very high status as a scientific theory

Could we delete this sentence or somehow integrate it into another one? CSTAR 17:44, 19 Feb 2005 (UTC)

Comparison table

I'm not sure the comparison table is accurate. Comments? CSTAR 16:47, 20 Feb 2005 (UTC)

In particular I'm a little puzzled by the use of "locality" in that table; locality can mean

local realism (very narowly defined in this article, which suffices for its purposes)
local of transfer of information (e.g. no communication theorem)
some other kind of locality (but in reference to some specific property)

In what sense is MWI local? It is not local realist, but it is local information theoretic. To the maker of this table, what exactly did you mean?CSTAR 06:14, 23 Feb 2005 (UTC)

Puzzled me too. ---- Charles Stewart 01:38, 24 Feb 2005 (UTC)

Shut up and calculate

"later expressed in Richard Feynman's famous dictum: "Shut up and calculate"." Attribution to Feynman, althought widespread, may be bogus. see http://www.physicstoday.org/vol-57/iss-5/p10.html Mermin is not able to find a reference with a source to Feynman ever saying this, although Mermin said it in 1989 64.165.202.199 22:10, 2 May 2005 (UTC)

Thanks for the tip. I included your reference into the article.--CSTAR 05:15, 3 May 2005 (UTC)

Disputed claim

A recent edit claims that the assertion is disputed. How is this dispute to be "interpreted". (This BTW is a fairly standard view, e.g., from Omnes).--CSTAR 22:27, 17 September 2005 (UTC)

Another edit

Another recent edit asserts that measurement and non-determinism are not within the theory"? Wht not? One of von Neumann's big contributions in his book was the theory of measurement. He made a big deasl out of this. More over every article amnd book I've seen on interpretation of quantum mechanics makes this into a big deal. If not, why are quantum operations important? Is the editor who made the above claim also claiming that these are not part of the theory?--CSTAR 20:59, 18 September 2005 (UTC)

Maybe I am being too picky, but my point is that the probabilities are not in the purely quantum picture. They come from the relationship between quantum mechanics and its classical approximation. I have tried to explain this in Philosophical interpretation of classical physics, as well as why I prefer that point of view. So they are in no way an obstacle to "direct interpretation". The trouble is that, except possibly if one had a quantum computer, experimental results always have to be classical. --David R. Ingham 19:56, 19 September 2005 (UTC)

That is, they are not an obstical to philosophicaly calling quantum mechanics "reality".--David R. Ingham 20:11, 19 September 2005 (UTC)

I looked at quantum operation and density operator. They have to do with quantum statistical mechanics, and with measurement. These are important, but they have to do with knowledge, rather than with reality. The real world is in a single pure quantum state that changes deterministically according to its Hamiltonian. It obeys the uncertainty principle. Statistical mechanics is used for incompletely know systems (too complicated to calculate in detail). Measurement, I think necessarily, involves using the classical approximation, which for a single system, means inserting dummy information to make it possible to use a description that violates the uncertainty principle. The time dependent Schrödinger equation is explicitly deterministic. That determinism doesn't go away when one adds more particles, includes relativity, etc. So the lack of determinism is not an obstacle to calling quantum mechanics reality. It is an obstacle to calling classical mechanics reality. --David R. Ingham 16:27, 20 September 2005 (UTC)

On the aboutness of Quantum Theory

"In particular, the bare instrumentalist view of quantum mechanics outlined in the previous section is not an interpretation at all since it makes no claims about elements of physical reality." (see section "properties of interpretations")

The statement above is incorrect. A genuine instrumentalist view would state the following:

"A particular experimental pattern run in a precise configuration (e.g. a Stern & Gerlach experiment with a specific relative orientation between the "green" apparatus and the "red" one) generates a flux of discrete informations whose distribution function over a fixed (potentially infinite) set of values is stable, reproducible at will, valid for any experimentator".

The distribution function is a property of the experimental pattern (this is a tautology and thereby a true statement). Running the experimental pattern results in a measurement of the distribution function. It creates knowledge about a property of the experimental pattern. It adds value if considered within the framework of a theory about experience, about "what it means to be the Actor of an experiment in the world", within the framework of a "phenomenology". This is precisely what "Quantum Theory" is about.

Of its own, the distribution function does not bring any knowledge nor information about "what happens inside the experimental device". It does not add any value if considered within the framework of a physics theory, until it is converted ("interpreted")into a property of our "model" or "simulation" of "how the world is, how it works, what happens there inside the experimental device".

"In the case of quantum mechanics, the most common instrumentalist description is an assertion of statistical regularity between state preparation processes and measurement processes. This is usually glossed over into an assertion regarding the statistical regularity of a measurement performed on a system with a given state φ." (see section "instrumentalist interpretation")

Stating that the information gathered through participating into an experiment is "about a system", meaning "about something in the world" is already the result of an interpretation for which conversion rules have not been defined. This statement is neither true nor false: it simply cannot be falsified or verified by an experiment. SUGDUB (07 Sept 2005)

Your formulation seems like an extremely radical form of instrumentalism. A more traditional function of instrumentalism is to reconcile divergent models of observations: for example, an earth-centrist might consider a copernican model of the universe as a useful theoretical tool (or instrument) to make calculations and predictions. Am I mistaken? --CSTAR 19:24, 8 October 2005 (UTC)

What I'm suggesting is actually to come back to facts, instead of building up theories based on uncontrolled interpretations of facts. The article on interpretation of quantum mechanics is fine insofar it presents the views of physicists, but I feel important to mention that even "bare instrumentalist" presentations of quantum experiments remain amazingly far from genuine facts. The description of a Stern & Gerlach experiment used above as an example can be pushed one step further (and this is not the last step):

"for a different orientation of the green apparatus wrt the red one, the distribution function measured is different, but stable and reproducible as well. And the same is true for any intermediade value of the relative orientation. The distribution function evolves continuously in response to a continuous change of the relative orientation of both apparatuses, it evolves when swapping from one experimental context to another one." This is a fact.

It is quite interesting to compare the above factual statement with the "instrumentalist view" which states that the distribution function describes the property of "something" in the world, property which takes a certain value at a precise location inside the experimental device, and evolves from one place to another, e.g. left or right to an apparatus. This instrumentalist view does not report facts. It is a metaphoric statement resulting from the unspecified transcription of experimental facts into a simulation of the world.

Interpreting facts is not forbidden, it is the duty of a physics theory, but beware that this particular interpretation eventually leads to the famous "measurement problem": comparisons between various experimental patterns impose that discontinuous changes of the distribution function may happen inside the experimental device, and any attempt to precisely localise where the gap takes place leads to contradictions or paradoxes. Experimentation will never bring a factual evidence of any property changing value inside the experimental device. Changes of the distribution function can only be evidenced by comparing the outcome of different experiments.

Conversely, the factual description of quantum experiments is immune from the "measurement problem" since the issue of where the change takes place is meaningless: dis-continuous changes of the distribution function reflect dis-continuous changes of the experimental pattern, e.g. when swapping from an S&G device without shutter to the same one with a shutter. Installing the shutter translates into a dis-continuous change of the distribution function, and this will never raise an issue.

The "measurement problem" originates into the uncontrolled transcription process from bare experimental facts to an interpreted view of facts, and I think this justifies the interest for coming back to facts. May I suggest that a sub-section of this article be devoted to non-interpretative descriptions of quantum experiments (this is far from being a trivial exercise) and subsequent analysis ?

SUGDUB (12 Oct 2005)

You can certainly add such a section. --CSTAR 02:27, 13 October 2005 (UTC)

I suggest a distinct article on the instrumentalist interpretation. linas 18:12, 23 October 2005 (UTC)

Done. I started with a "factual" description of the S&G experiment, alongside the above. Larmor's experiment should follow. However the section title is misleading, since the aim is to avoid any interpretation, trying to stick to facts. (SUGDUB - 01/11/2005)

To quote from Einstein, "I don't undrstand it.". David R. Ingham 03:21, 15 October 2005 (UTC)

You'll have to me more specific: You don't understand what? --CSTAR 03:26, 15 October 2005 (UTC)

I suppose the main thing I don't understand is how anyone can think about quantum mechanics from a classical point of view. Anyway, I do get lost very quickly when reading things here. That all went on in the first few years after quantum mechanics was discovered. It was shown that quantum mechanics gave a consistent and much more accurate description of nature, so why are people still thinking classically a century later? I think a lot of why I don't understand it is that my father read me physics books before I could read much myself, so I did not grow up thinking classically. When I have studied classical physics, I have always thought of it as an approximation and not based my world view on it. David R. Ingham 05:17, 24 October 2005 (UTC)

Well you are pointing to the fact that much of what is regarded as interpretation is an artifact of history, a transitional intellectual activity. I prefer Axiomatic quantum mechanics myself.--CSTAR 05:27, 24 October 2005 (UTC)

The question is what to say, if anything, in ordinary language. It is nice to be agreed with, for a change. David R. Ingham 07:28, 2 November 2005 (UTC)

Capitalization

I don't think "quantum theory" is capitalized, even though Messiah does capitalize "Quantum Mechanics" and "Classical Theory" in the first section.

Why no discussion of these alternatives

Why has there been no discussion of quantum logic? Doesn't this count as an interpretation of QM? I just inserted a very brief discussion of the topic. However, I don't like where it is, and am not fully happy with how the article is structured. Suggestions are welcomed. RK 21:28, 21 October 2005 (UTC)

Also, there was no discussion of consciousness causes collapse, even if only to note that most physicists consider it silly, new-agey, and bordering on wish-fulfillment.

Also, I note that the article doesn't even attempt to briefly mention neorealism, even if it has been discredited. Nick Herbert writes:

Quantum Reality #6. Neorealism (The world is made of ordinary objects.) An ordinary object is an entity which possesses attributes of its own whether observed or not... The clarity and ubiquity of ordinary reality has seduced a few physicists - I call them neorealists - into imagining that this familiar kind of reality can be extended into the atomic realm and beyond.

Neorealists...accuse the orthodox majority of wallowing in empty formalism and obscuring the world's simplicity with needless mystification. Instead they preach return to a pure and more primitive faith. Chief among neorealist rebels was Einstein...

Quantum logic is not so much an attempt to interpret quantum mechanics as it is to axomatize it. However, I think you make a valid point. In fact, I had though about adding a section called Axomatic quantum mechanics which would include approaches such as the C*-algebraic approach. --CSTAR 21:42, 21 October 2005 (UTC)

Consciousness causes collapse is mentioned to the extent that other interpretations are mentioned at all (in the comparative table). Now that table is of questionable accuracy so we might want to replace it by listing the various interpretations. Now consciousness causes collapse seems to have a special role with its own section --CSTAR 22:19, 21 October 2005 (UTC)

I agree. Either all interpretations have their own sections, or none and we update the table. I prefer the second option, becuase the first will make a big hunk of additional text; also, all of them already have their own pages, so there's no point in duplicating content, and the focus should be on those pages concerning particular interpretations. Karol 16:13, 22 October 2005 (UTC)

I lean towards Karol's view here. linas 18:22, 23 October 2005 (UTC)

In line with what Wikipedia does in many other articles, I would argue that this article should summarize each of these interpretations in a paragraph; this gives the reader a general idea of what each interpretation is about. Then we should like to the proper article, where it is discussed in depth. I don't like the idea of discussing each interpretation in depth here; that would clutter up this article and be redundant as well. Not only redundant, but also unnecessary, since it is redundant. :) However, I shudder when I see an article appear as a list of links, so some brief discussion would seem to be called for. RK 23:36, 23 October 2005 (UTC)

Quantum philosophy

H0riz0n: How about "Quantum philosphy" why was it deleted and redirected WITHOUT DEBATE? I had put up the page put the "Wiki Control Group" against alternative views. Deleted it and redirected it here. Quantum Philosophy isnt "interpretation" its applying philosphical and theoogical interpretation into the realm of QM and Quantum Cosmology. Quantum Philosoper are making far reaching interpretations of QP into the realm of theology and philosophy. That is why such discussion is not merrited to this page because Interpretation ISNT philosphy.

This act of redirection is being discussed at Wikipedia_talk:WikiProject_Physics#New_.26_interesting and whether to merge with Quantum mysticism. Please move discussion there. GangofOne 05:46, 6 April 2006 (UTC)

Probabilities

Ahem, the following

$\operatorname{P}_{\operatorname{up}} =\langle \varphi_{\operatorname{up}} \mid \varphi \rangle$

$\operatorname{P}_{\operatorname{down}} =\langle \varphi_{\operatorname{down}} \mid \varphi \rangle$

in conjuction with the subsequent statements is incorrect:

the proportion of values with outcome "down" is P_down and the proportion of values with outcome "up" is P_up. Note that P_up, P_down are both non-negative numbers and

so that P_up, P_down can indeed be considered as probabilities.

I am rather amused that exactly the same mistake was made in the early days of QM; the realization that this was incorrect came in 1933, I believe, and was made as a correction to a printer's proof in a paper about to be published; unfortunately I don't remember by whom. Maybe Wigner or Bohm. (Name is on the tip of my tongue, they're the xxx relations).

Suggest change:

$\operatorname{P}_{\operatorname{up}} =\vert \langle \varphi_{\operatorname{up}} \mid \varphi \rangle \vert^2$

$\operatorname{P}_{\operatorname{down}} =\vert \langle \varphi_{\operatorname{down}} \mid \varphi \rangle \vert^2$

and

$\operatorname{P}_{\operatorname{up}} + \operatorname{P}_{\operatorname{down}} = \vert \langle \varphi_{\operatorname{up}} \mid \varphi \rangle\vert^2 + \vert \langle \varphi_{\operatorname{down}} \mid \varphi \rangle\vert^2 = 1$

The full derivation requires the explanation that projection operators are nilpotent:

$\operatorname{E}_{\operatorname{up}}^2 = \operatorname{E}_{\operatorname{up}}$

and that they're orthogonal:

$\operatorname{E}_{\operatorname{up}} \operatorname{E}_{\operatorname{down}} = 0$

but that would clutter the article, no? I could be bold and just fix this, but thought I'd mention it here first. linas 17:36, 23 October 2005 (UTC)

Never mind, I just fixed the article. linas 17:56, 23 October 2005 (UTC)

Reply to Linas: Huh? Indeed

$\operatorname{E}_{\operatorname{up}} + \operatorname{E}_{\operatorname{down}} = 1$

so that if φ has norm 1, by linearity and the definitions,

$\operatorname{P}_{\operatorname{up}} + \operatorname{P}_{\operatorname{down}} =\langle \varphi_{\operatorname{up}} \mid \varphi \rangle + \langle \varphi_{\operatorname{down}} \mid \varphi \rangle = \langle \operatorname{E}_{\operatorname{up}} \varphi \mid \varphi\rangle + \langle \operatorname{E}_{\operatorname{down}} \varphi \mid \varphi\rangle =\langle (\operatorname{E}_{\operatorname{up}} + \operatorname{E}_{\operatorname{down}}) \varphi \mid \varphi\rangle = 1$

as claimed. Isn't this obvious?

If you agree this is true, then the numbers you claim are probabilies, cannot actually be be probabilities. Proof: For if a+b=1 where a, b are non-negative reals, then a²+b²<1 unless one of a,b are 0.--CSTAR 17:57, 23 October 2005 (UTC)

Huh, indeed. CSTAR, did you have coffee this morning? I am simply changing the notation to correspond to the standard usage and language of QM: the probabilities are the square of the probability amplitudes. Here, the inner products $\langle \cdot \vert \cdot \rangle$ are complex-valued (possibly negative) probability amplitudes. Its their square-norm that is a probability. linas 18:19, 23 October 2005 (UTC)

Linas, any self-projection is a non-negative self-adjoint operator. Therefore the numbers are non-negative reals. QED. --CSTAR 18:22, 23 October 2005 (UTC)

For sure one of us is confused, and I still believe, that in this case, it is you.--CSTAR 18:24, 23 October 2005 (UTC)

This is the standard von Neumann interpretation of measurement. The meaning of probability amplitudes is something else entirely.--CSTAR 18:28, 23 October 2005 (UTC)

Oh, good lord. Per standard QM, a two-state system has basis vectors

$\vert u \rangle$ and $\vert d \rangle$

A general state of the system is a linear combination

$\vert \psi \rangle = a \vert u \rangle + b \vert d \rangle$

where a and b are complex numbers satisfying $| a | 2 + | b | 2 = 1$ The dual basis is given by

$\langle u \vert$ and $\langle d \vert$

which satisfy

$\langle u \vert u \rangle = 1$ ,

$\langle d \vert d \rangle = 1$

$\langle u \vert d \rangle = 0$

$\langle d \vert u \rangle = 0$

The projection operators are given by

$\Pi_u = \vert u \rangle \langle u \vert$

and

$\Pi_d = \vert d \rangle \langle d \vert$

The nilpotency and orthogonality follow immediately. The interpeation is that $E u p = Π u$ and $E d o w n = Π d$

The probability amplitude of a measurement on a system in state ψ is

$\langle u \vert \psi \rangle = a$ and

$\langle d \vert \psi \rangle = b$

so that

$\vert \langle u \vert \psi \rangle \vert^2 + \vert \langle d \vert \psi \rangle \vert^2 = \vert a\vert^2 + \vert b \vert^2 = 1$ .

The interpretation to the article is

$\langle \phi_{down} \vert = \langle d \vert$

and $\vert \psi \rangle = \vert \phi \rangle$

I know you know this. I'm not sure why you're confused. linas 18:45, 23 October 2005 (UTC)

There is an intervening measurement which changes the expression for probability amplitude. See below. --CSTAR 19:02, 23 October 2005 (UTC)

von Neumann measurement

Suppose A is an observable with two eigenvalues +1, -1 with eigenprojections E, F. If φ is a pure state (i.e., vector of norm 1) the probability that a measurement of A will be +1

$\langle E \phi \mid \phi \rangle$

and -1 wil be

$\langle F \phi \mid \phi \rangle$

These are non-negative reals which add up to 1. It's as simple as that. If you square 'em as you are suggesting, you cannot get two numbers which add up to 1. Period. --CSTAR 18:36, 23 October 2005 (UTC)

In QM, the hilbert spaces are complex, not real. linas 18:50, 23 October 2005 (UTC)

Reply. Of course. But if A is self-adjoint operator, the number

$\langle A \phi \mid \phi \rangle$

is always real. Note that the relevant probability amplitude is

$\langle \phi_\mathrm{up} \mid E_\mathrm{up} \mid \phi \rangle$

This is different from

$\langle \phi_\mathrm{up} \mid\phi \rangle$

There has been an intervening measurement which has to be taken into account in computing the probability amplitudes.--CSTAR 19:00, 23 October 2005 (UTC)

OK, I think I see the source of the notational confusion. Per my notation above, we had for a general state ψ

$\vert \psi \rangle = a\vert u\rangle + b \vert d \rangle$

so that the expectation value for the projection operator is

$\langle \psi \vert \Pi_u \vert \psi \rangle = [a^*\langle u\vert + b^* \langle d \vert ] \;\; \Pi_u \;\; [\; a \vert u\rangle + b \vert d \rangle ] = a^* a$

so that for any vector &psi, the expectation value of the projection operator is real and positive. The problem is notational. For standard text-book QM, $\langle \cdot \vert \cdot \rangle$ is a complex-valued inner product. The correct way of writing the expectation value of an operator using standard QM notation is

$\langle \psi \vert A \vert \psi \rangle$

and never

$\langle A \psi \vert \psi \rangle$

The last expression is notationaly avoided precisely because it leads to the confusion here: a wave-function is always written as $\langle \cdot \vert \cdot \rangle$ and a wave-function is always a probability amplitude, and the square of a wave-function is the probability. I'd prefer to stick to the standard notation. linas 19:36, 23 October 2005 (UTC)

What you wrote in the article is still wrong.--CSTAR 19:42, 23 October 2005 (UTC)

OK, we maye be talking about different φ ups and downs. Take what I wrote, normalize the φs by dividing by the norms, and that might make both of us happy. But what's there now is wrong. --CSTAR

Gack. OK, I see the error now.

The article calls φ a state. The word state has a distinct meaning, in particular, states are always normalized. Per notation, I identify φ with $\vert \psi \rangle$ , as would any reader who knows QM. The projection of a state is

$\Pi_u \vert \psi \rangle = a \vert u \rangle$

By calling $φ u p$ a state, the reader is invited to identify $φ u p$ with $\vert u \rangle$ (which is normalized, and is a legit basis state) and not with $a \vert u \rangle$ (which is not normalized, and has no special status in the theory). I see now that the article is making the latter identification not the former. This is misleading, and has certainly mislead me. This is the peril of mixing two different types of notation.

I propose replacing

φ u p = E u p (φ)

with

$a \vert \phi_{up} \rangle = E_{up} \vert \phi \rangle$

although this now requires explaining what a is. Sigh. I have to run an errand. Do you have a better idea?

I have to argue against a revert: it's deeply engrained in the educational system that the probability is the square of the amplitudes, so the notation has to respect that. The old article appeared to be adding amplitudes and calling them probabilities, and just about any classically trained physicist would object to that. The answer might be to have fewer formulas, and not more. linas 20:22, 23 October 2005 (UTC)

φ u p = E u p (φ)

is certainly not right. How about

$\phi_{\operatorname{up}} = \frac{1}{\|\operatorname{E}_{\operatorname{up}} (\phi)\|} \operatorname{E}_{\operatorname{up}} (\phi)$

(a small quibble: the denominator may be 0), or just simply write down the formulas the probabilities which is what matters anyway.--CSTAR 20:47, 23 October 2005 (UTC)

Fix for instrumentalist view

Might it be better to change the instrumentalist view to talk more about expectation values instead of wave functions? This is because the former are "real" in that they're measureable, whereas the latter are the subject of interpretation. Thus, I propose that the text would be something like the below, prettied up. It has a side benefit of cleaning up the math and making the math less akward (in my opinion):

An arbitrary (pure) state of the system may be represented by a wave function ψ. When an experimenter chooses to measure some observable A, then the outcome of the experiment is given by the expectation value of A with repsect to ψ. To compute this expectation value, the theory states that ψ is an element of a vector space, and that it must be written in a vector space basis

$\vert \phi_1 \rangle, \vert \phi_2 \rangle, \cdots$

of eigenstates of A, where an eigenstate is a vector satisfying

$A\vert \phi_n \rangle = \lambda_n \vert \phi_n \rangle$

for some real number $λ n$ . To compute the outcome of the experiment, the state of the system ψ must be decomposed as

$\vert \psi \rangle = c_1 \vert \phi_1 \rangle + c_2 \vert \phi_2 \rangle + \cdots$

with some certain specific complex numbers $c n$ resulting from that decomposition. The outcome of the experiment is then nothing more than the expectation value of A, which is given by the expression

$\langle \psi \vert A \vert \psi \rangle = c_1^* c_1 \lambda_1 + c_2^* c_2 \lambda_2 + \cdots$

This experimentalist view gives a simple, direct way to compute the outcome of an experiment. To compute the outcome, there is no need to inquire into the meaning of the numbers $c n$ or $λ n$ ; they are merely components of a formula where only the final value matters.

Optionally, have also the following paragraph (which I think is superfluous) but:

The probability of finding the system in a given state $\vert\phi_n\rangle$ is given by computing the expectation value of the projection operator

$\Pi_n = \vert\phi_n\rangle \langle \phi_n \vert$

The probability is then the non-negative real number given by

$P_n = \langle \psi \vert \Pi_n \vert \psi \rangle = c_n^* c_n = \vert c_n\vert^2$

The sum total of probabilities of finding the system in a state $φ n$ must add up to a total of one:

$P_1 + P_2 + \cdots = 1$

I think that this might bring the math closer to actual practice/education, as well as minimizing discussion of the wave function (which, I believe, is what the instrumentalists do). Also, I believe the math above is no harder than what the article currently contains, right? And its more edifying, as it reminds the reader that QM plays out entirely on vector spaces. linas 14:40, 24 October 2005 (UTC)

I have no objection. --CSTAR 15:09, 24 October 2005 (UTC)

OK, I'll try to clean this up and add it later today or maybe tommorrow. Another possibility is to omit the formulas entirely, and state something along the lines of (hack job):

In the instrumentalist point of view, QM is understood to be a set of calculations to be performed on a complex-valued vector space, of finite or possibly infinite dimension. The state of a system to be measured corresponds to a vector in this vector space. Experiments perform measurements on observables, where observables correspond to Hermitian matrices. The result of a measurement is given by the expectation value $\langle \psi \vert A \vert \psi \rangle$ where ψ was the vector, and A was the observable.

This is much briefer, maybe more appropriate? Or do you prefer the long version? linas 14:22, 25 October 2005 (UTC)

I liked your longer version.--CSTAR 14:59, 25 October 2005 (UTC)

OK, I've merged it in. Somehow, it got slightly more verbose. Fix/critique as needed.linas 22:21, 27 October 2005 (UTC)

It is longer, but that's the nature of the beast. And it's more in line with the educational system as you point out.--CSTAR 03:11, 28 October 2005 (UTC)

Organization and the place of this artcle

A change [[2]] has been suggested that would re-name and re-classify this article.

The suggested change is a bad idea, in my opinion. That article has problems of its own, documented there.--CSTAR 13:09, 26 October 2005 (UTC)

Agree with CSTAR. That other article is highly unusual, bordering on original research; it needs to be fixed first. Its also not at all about classical physics. linas 14:30, 26 October 2005 (UTC)

From a physics point of view, the probabilities are due to the classical approximation. As the originator, I agree that "Philosophical interpretation of classical physics" has problems, but I argue that that approach is more valid than "Interpretation of quantum mechanics ". Physics is mathematical more than linguistic. Readers should not be lead to believe that they can gain a global understanding of mathematical physics theories, by talking bout them.

Messiah, Albert, Quantum Mechanics, volume I, p. 150.David R. Ingham 07:55, 2 November 2005 (UTC)

Edit of intro

Re: Edit summary:I'm not sure what that sentence was trying to say, but hopefully now it's clearer

What it was trying to say, was I though pretty clear:

Quantum mechanics is succesful
Some people (Philosophers of science, -- some people) argue over what it means (whether this is in fact what they're arguing about is itself subject to argument).
This requires some explanation

Now you may argue that's a non-sequitur, but then you should fix the non-sequitur. --CSTAR 19:52, 26 October 2005 (UTC)

Actually you (User:Laurascudder) may want to rewrite the whole intro. Although I suggest that the Jankiw and Kleppner quote be kept. --CSTAR 20:10, 26 October 2005 (UTC)

no wavefunction collapse in transactional interpretation

"In fact, the notion that the state vector collapses to a particular value of a variable "at a given instant" is inconsistent with the transactional description." quote from [3] Cramer's own description of his interpretation. Wouldn't this mean that there is no wavefunction collapse in transactional interpretation in contradiction with what the diagram claims? --MarSch 14:00, 2 November 2005 (UTC)

That diagram is highly suspect. --CSTAR 14:16, 2 November 2005 (UTC)

It appears so. Transactional interpretation is also not deterministic.--MarSch 16:08, 2 November 2005 (UTC)

Blow it away, if you want.--CSTAR 16:11, 2 November 2005 (UTC)

Changed to non-deterministic --Michael C Price 13:42, 13 June 2006 (UTC)

Proposition for a modern decoherence interpretation

I propose that a modern decoherence be added to the table. Here is Joos' webpage in decoherence. http://www.decoherence.de/ His Springer book THE book.

Deterministic = Yes

Waveform real = Yes

One Universe = Yes

Avoids Hidden Variables = Yes

Avoids Collapsing Wavefunction = Yes

Key ideas include

There is one universal wavefunction. And that wavefunction evolves via regular quantum mechanics
The classical world emerges from regular quantum mechanics via decoherence
collapse is caused by interaction with an environment. The measurement causes the collapse
probability is stochasic. You are averaging over the environment variables.

There is some other good stuff on Joos' website.

Interpretations varry slightly even within the Decoherence community. But I think Joos' statements are pretty concrete and grounded.

The good thing Decoherence has going for it is that it is completely consistent and it is basic QM with no new theory. It has Occam's razor firmly on it's side. On the other hand there are still many experiments and calculations left to confirm. However decoherence has been confirmed in certain theoretical models. I plan on adding a full page on Quantum Brownian Motion at some point in the future.

The last thing I have in mind is that this really isn't an interpretation as it's basic QM with no new theory. Only one assumes QM actually works by itself and requires no interpretation. But it really should be compared to these interpretations. So it does belong on the page. (Unsigned comment by User:C h fleming circa 9 December 2005)

I won't argue against this, however, the statements appear to be contradictory:

Deterministic = Yes

probability is stochasic. You are averaging over the environment variables

Uhh, either its not stochastic, or it is stochastic, you can't have it both ways. So I don't get it. QM always evolves unitarily, so its "deterministic" until such time as a measurement is made. At the time of the measurement, its stochasitc. By this definition, I don't see how decoherence is "determnistic".

It is stochastic in the limit of the degrees of freedom in the environment are infinite. This is similar to the thermodynamic limit. It is called stochastic in the same sense that the brownian motion of a particle is stochastic, even though the fundamental theory is deterministic mechanics.

Avoids Collapsing Wavefunction = Yes

collapse is caused by interaction with an environment. The measurement causes the collapse

This sounds like a contradiction as well. But maybe what is meant is that the decoherence theory provides a specific hypothetical mechanism to actually describe the process of collapse, and tht's an improvement over "collapse by handwaving". linas 22:46, 9 December 2005 (UTC)

I use collapse here losely. The wavefunction is localized in some space by the process of decoherence, superselection rules, ...

I will try to see if I can clarify these things. They only make sense to me because I already know it. I need to make it make sense for everyone else.(CHF 23:35, 9 December 2005 (UTC))

Just to add clarification there is no absolute randomness or absolute collapse of the wavefunction. There is effective randomness due to the many degrees of freedom in the environment and there is something close to collapse in the strong diagonalization of the density matrix as caused by environment (And this is something that we quantify in QBM). In decoherence, the equations of motion are taken to be the absolute truth, while the Born interpretation: collapse and probabilistic projection are taken to be very good approximations for a very large environment.

In analogy to old stuff, the Shroedinger Equation is to Classical Mechanics and the Born interpretation is to Thermodynamics.(CHF 07:15, 11 December 2005 (UTC))

I always thought decoherence was an effect rather than an interpretation? I mean, isn't it a consequence of the Schrödinger equation? I'd suggest taking it out of the chart, or making a new column that says which *role* decoherence plays in each of the interpretations. BTW: A new column "needs to adjust Schrödinger equation" in the comparison chart might be helpful, too.

Correct. As I said, Decoherence isn't really an interpretation, but it should be compared to these interpretations and the reason is as follows. If decoherence is true, then you do not need any interpretation at all. With decoherence you can throw all of these interpretations out of the window. You have your equations of motion, your observables, and that's all you need. That is why I listed the "interpretation" as Decoherence (Schroedinger equation with no additional theory)" It is true that some physicist maintain both decoherence and some interpretation, but with decoherence and the emergence of classical from quantum, interpretation is no longer necessary for understaning or explaination. Decoherence is at odds with all of these interpretations is the same manner that the Schroedinger equation is at odds with these interpretations.

Now OTOH to play Devil's Advocate, it is not rigorously proven that we can get the classical picture from ordinary quantum mechanics. Work is being done in this field. I do related work. But it is not ABSOLUTELY known that decoherence will explain and make right everything. But decoherence is definitely something that is proven to happen to a large degree.(CHF 22:08, 11 December 2005 (UTC))

Decoherence really shouldn't be listed. Insofar as it really does do away with the collapse of the wavefunction, it is really a different theory from standard QM and it will generate different predictions. This is because there even with decoherence one cannot do away with all superpositions of observable states. So either decoherence is not in fact deterministic (because on a small scale there are still collapses) or it disagrees with standard QM.

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