Talk:EPR paradox

IF the electrons were opposite each other when they were together, of course they'd still be opposite once they were apart. The article doesn't demonstrate that there's any paradox.user:hackwrench

Have you actually read the article? -- CYD

Yes, and it doesn't actually establish the contradiction when "locality", "realism", and "completeness" is addeed that this experiment is designed to cure.

Not all local realist theories are local hidden variable theories

Mention needs to be made of the fact that there are local realist theories that are not local hidden variable theories and hence escape Bell. Remember that a hidden variable theory must have a space of hidden variables with a suitable structure that allows one to define integration on it and recover probabilities by integrating. There seems to be a lack of appreciation amongst non-mathematicians of the importance of this. One can define local realist theories in which there is no suitable way of integrating over variables and such theories escape Bell. Back in the early 80s I think, Arthur Fine characterized the local realist theories that satisfy Bell's inequality - the important point being that not all such theories do!

Two16 on lead para

It would be a good thing to put that thing on hold, until you consider what I have to say about the lead paragaph:

The EPR paradox is a thought experiment named after Einstein, Podolsky, and Rosen who devised it in 1935 to attack the theory of quantum mechanics by demonstrating a seemingly paradoxical consequence. It was the subtlest and most successful of the several objections Einstein raised against quantum mechanics, which he disliked for its use of probability.

Properly, it is an illustration of one philosophical objection to the Copagenhagn Consensus. Bohr, Einstein and their elite collegues struggled to deal with the implications of scientific discoveries after 1922. This community process, carried out in person, corrospondance, and journals, resulted in a meeting to developed a framework for further scientific research. Together they reached a concensus named after the city where they met.

Very crudely, Bohr won Einstein lost.

Bohr, who had his ideas refined through hundreds of hours of conversation and warm letters exchanged with Einstein, increased his stature in the scientific communmity. Einstein while respected, became increasingly irrelevant as time went by. The 1935 ERP paper was probably the high point of his later career.Relationship between the two men was strained and became more distant with time. Quantum Mechanics went on to become the most successful theory of all time.

Nils, is one of the best philosophers of the 20th centuary. The reason that ERP is subtle was because Bohr's position had to become subtle in response to several years of dialogues with elite minds, especially Einstein.

For what its worth Two16 and what moral you can find.

Is is appropriate to use a link to "Probability" in the second paragraph when "probabilistic" is really referring to the antonym of "deterministic"? The Probability link does not describe this model of the universe but rather basic probability in math. (Perhaps it is being used correctly, here and elsewhere, but it doesn't appear so in context of Einstein's objection). - Texture 22:01, 21 Nov 2003 (UTC)

spliting the page

I agree that the whole page got a bit too long. I suggest to leave the top of the page which gives conceptual overview, and which mentions as a link to other pages - more technical and/or mathematical topics such as

EPR setup
Bell Inequality (derivation, assumptions)
entanglement
Do some still try to 'escape Bell' ..
any other technical issue

So, we move the technical stuff of the current EPR page (the bottom half) to those linked pages- leaving just the conceptual overview here ..

But I notice that Bell already moved once, to a separate page, and came back.. so I would liketo ask if there are any objections?

I also do thank all those who corrected my clumsy markup - and spelling and grammar too.

I am stil learning how do this - how the markup works This was actually is my first contribution - so I am quite a newbie Petr 07:01, 2004 Jan 15 (UTC)

A minor point - is "potentia" singular, plural or invariant? It looks like a Latin plural (of a would-be "potentium", perhaps) but is used as both a plural and a singular in the text. This needs to be corrected if it is incorrect; maybe a brief note could be added (along the lines of "singular: 'potentium'" [or whatever]) if it is already correct. -- Paul G 14:35, 9 Feb 2004 (UTC)

Modern Perspectives

The article reads "Today most physicists agree that ... the principle of locality does not hold."

I am not sure what to make of this statement in view of the fact that all known quantum field theories are explicitly local. Does locality in QFT violate Bell's theorem?Lethe

I poked around a little on spr to see what people say about Bell's theorem and locality, and it seems like maybe locality in the sense of QFT (which i notice is missing from Principle of locality. I should add that) and local realism in QM are really different and perhaps unrelated issues. I suppose this doesn't matter so much for this article, but i think that last statement "most physicists agree..." should be qualified a bit more. Lethe 23:13, Jun 17, 2004 (UTC)

I found the following quotes particularly illuminating:

"The key thing to keep in mind is that different people mean different things by this word. There are also, I suspect, plenty of people who don't know what they mean. This is part of why people are able to argue forever about whether QM is `local.'

"One meaning is important in understanding Bell's inequality. This is the sense of locality that appears in the term `local realism,' and by this sense QM is not local. Roughly speaking it amounts to this. Say a physical system is in a pure state - i.e., we know everything about it that can be simultaneuously known. Suppose the system is spread out through space (like they always are). Then we say we have `local realism' if we can describe the state of the system by first saying everything that's going on in *this* little patch of space, then in *this* little patch of space, and so on. I.e., a pure state can be described by specifying pure state in each region of a partition of space. (Space is good old 3d space here!)

"This fails in QM. In the jargon of algebraic QM, there are pure states of the tensor product of several algebras of observables that are not just tensor products of pure states of each algebra.

"Another meaning is important in understanding quantum field theory. This is the sense in which quantum field theory IS local. It goes like this. The Hamiltonian of a quantum field theory is what describes how things evolve in time. The Hamiltonian is always an integral over space of a product of fields and their derivatives *at a single point*. That is, two things only interact when they're at the same place. Again, the "space" is good old 3d space here.

"Closely related to the locality of quantum field theory is its causality. This says that the state of a system within some region R at time T can be computed from knowing the state within any region R' at time T' as long as no paths moving at the speed of light or slower that don't pass through R' at time T' can pass through R at time T. In other words, signals propagate no faster than light.

"In a sense, traditional quantum field theory is what you get when you try to do quantum theory in a way that it is local and causal, as well as invariant under the symmetry group of special relativity." - John Baez spr google link (http://groups.google.com/groups?selm=35433%40galaxy.ucr.edu)

and

"Well, I wouldn't go so far as to say 'under ANY reasonable sense of the word'. There are lots of different meanings of 'locality' in physics, and getting them mixed up causes people lots of trouble.

"One is the idea of no information going faster than light. Another is the idea of spacelike separated observables commuting. Both these are incorporated in AQFT. Another is the idea that fields satisfy differential equations of finite order. This is not incorporated in AQFT because they don't want to rule out theories that are not described by differential equations - of which QCD might well be an example! Another is the idea that every pure state factorizes into pure states on subsystems: this is the sense used when people say Bell's theorem prohibits "local" hidden variable theories.

"Though I haven't investigated all 2^4 possibilities, my impression is that all 4 of these concepts of locality are logically independent." - John Baez spr google link (http://groups.google.com/groups?selm=9r5f82%24q82%40gap.cco.caltech.edu)

What I infer from these quotes is that there are two kinds of locality. I also list the type of locality that we describe here on wikipedia, both here in EPR aradox and over in Principle of locality.

where observables commute when they are spacelike seperated and the Lagrangian depends on only fields at a given point of spacetime
Pure states factorize into pure states.
distant objects cannot have direct influence on one another. this is the description found on wikipedia in this article

(btw: are 1 and 2 equivalent?)

Now, naïvely, it seems that both, either, or neither of 1 and 2 could be equivalent to the layman description 3. But clearly 1 holds for, say, the standard model, or any QFT, and 2 fails for any quantum theory, so they cannot both be equivalent to 3. The distinction should be made (although perhaps this is all more appropriate to the Principle of locality article) Lethe 23:59, Jun 17, 2004 (UTC)

Para from the intro...

(William M. Connolley 09:06, 22 Jun 2004 (UTC)) The intro finishes with:

Of the several objections to the then current interpretation of the quantum mechanics spearheaded by Einstein, the EPR paradox was the subtlest and most successful. The EPR paradox has not been resolved or explained, in a way which agrees with classical intuition, to this day. It brought a new clarity and permanent shift in thinking about 'what is reality' and what is a 'state of a physical system'. First, a review of the history:

This seems misleading to me, because although "successful" in the sense of stimulating debate it was a total failure in its primary goal - to shake QM. To say "The EPR paradox has not been resolved or explained, in a way which agrees with classical intuition" is similarly odd. Vast swathes of QM share this same feature of not being explicable in a classical sense. Better would be: resolution of the EPR "paradox" within the framework of QM has strengthened the mainstream "copenhagen interpreation" view of QM.

(William M. Connolley 09:22, 29 Jun 2004 (UTC)) I've edited this a lot now.

Bell test loopholes

(William M. Connolley 09:22, 29 Jun 2004 (UTC)) I seem to be in a revert war with Caroline Thompson over the text of this page. To take one example: CT doesn't like:

EPR is fully resolved within QM.

I'm not sure what she objects to, though. What aspects of EPR are unresolved?

I don't know of any way in which the EPR paradox can be resolved other than by studying the experimental evidence carefully and, if appropriate, rejecting the QM formalism as a viable model. This is what I've been doing for the past 10 years or so. I have not yet found one experiment that stands scrutiny -- that is not possible to explain by local realist methods. The experts know this to be true. This is why they continue to try and devise "loophole-free" experiments. The fact that the theory is wrong does not prevent a few useful applications being developed, since QM gives empirically correct predictions in the special cases that are used. As a matter of principle, though, it is illogical to imply that all experiments support quantum entanglement and that hidden variables and local realism are out. Do have a look at my papers on fair sampling. I've just updated the version in the quant-ph archive (http://arxiv.org/abs/quant-ph/0210150). I do hope next time I make changes you will leave them alone! Caroline Thompson 11:17, 29 Jun 2004 (UTC)

(William M. Connolley 13:13, 29 Jun 2004 (UTC)) You didn't answer the question. As far as I can tell, the standard explanation of EPR fits perfectly within QM and there are no contradictions. You don't like it, but thats not persuasive. You think the same experiments can be interpreted otherwise: that might be fine, but it *doesn't* affect whether EPR is resolved within QM. All your stuff about fair sampling is just trying to show that other explanations might be possible.

It is my understanding that experimental tests of Bell's inequality to date, while convincing for most physicists, have so far not been totally conclusive for the experts researching in that area. So on the one hand, I support Caroline's softening the language somewhat (e.g. "It was Bell who proposed a test that has the potential to close that escape route" over "It was Bell who closed that escape route". We could also add something like "the majority of physicists consider the issue closed in favor of quantum nonlocality"). If there is another article about the conclusiveness of experimental violation of Bell's inequality (Bell test loopholes), then I think most of the stuff supporting the fact that Aspect (or whatever experiment) hasn't been conclusive should go in that article, but the idea that it is not completely settled should be allowed in this article as well, along with links to Bell test loopholes

On the other hand, I do agree with William that, regardless of whether or not Bell's inequality is confirmed or violated conclusively, EPR is no longer a paradox. Quantum nonlocality is not a contradiction to special relativity. EPR is not a paradox. Therefore I am against statements like "the EPR paradox was the subtlest, though it is currently generally considered to be unsuccessful", and think instead that "the EPR paradox was the subtlest but ultimately unsuccessful" is more appropriate

-Lethe 13:45, Jun 29, 2004 (UTC)

Caroline Thompson 15:15, 29 Jun 2004 (UTC): William: you are right in that my opinion on how QM deals with EPR is not relevant, though, incidentally, I seem to have lost track of exactly what this means!

Lethe: I'm glad you agree that strong statements implying QM has been conclusively confirmed need to be softened. They are untrue. I'm glad you would allow links to my Bell test loopholes page. (Incidentally, is there any way of changing the name of a page? I mistakenly used the wrong convention, so everyone is going to get it wrong.)

Yes, Caroline, i changed the page name for you. the old page name is now a redirect to Bell test loopholes Lethe 11:07, Jun 30, 2004 (UTC)

The matter of whether or not the EPR paradox was "successful" or not depends on what you mean! EPR set out to challenge QM. The way their paper was worded (it was in fact written by Podolsky) was as a challenge to the completeness of QM. What I understand they actually proved was that QM could not be completed using deterministic hidden variables. Their paper was clearly unsuccessful -- Bohr pulled QM through. The paradox remains, though, unless you go along with the people who say "Shut up and don't ask awkward questions". As Einstein later said more clearly, and as Bell confirmed by devising his theorem, you can't have QM and local realism. Yet local realism is the universal assumption behind the whole of the scientific enterprise! Was Bell successful in his attempt to use the EPR paradox to re-establish local realism? Again, clearly not! So perhaps one could say the paradox was unsuccessful, but the way it is put in the page at present is confusing.

(William M. Connolley 16:55, 29 Jun 2004 (UTC)) I agree with a lot of this, but then it falls at the last (and most important) step: "Yet local realism is the universal assumption behind the whole of the scientific enterprise". This is simply not true. No transmission of information faster than light is certainly a basic (nowadays). Good old classic theories like newtonian graviation or heat transfer fail that test. But QM passes it.

On the contrary, William, even Newton's graviation is a local (in the sense of local reality) theory, and will therefore satisfy Bell's inequality. Just because a theory is not Lorentz invariant does not mean that the theory fails local reality. Local reality is what seperates quantum theory from classical theory (if we believe the results of Aspect's experiment). Newton's gravity is not local in the sense that its lagrangian contains terms that depend on more than one spacetime point. this leads to the violation of causality, but not to a violation of locality (local realism). Lethe 10:59, Jun 30, 2004 (UTC)

(William M. Connolley 15:54, 30 Jun 2004 (UTC)) I didn't say Newtons gravity was non-local. I said it leads to information transmission faster then light (instantaneously, in fact).

OK, then of course we agree. Newton's gravitation violates relativistic causality, because it allows information transfer faster than light. What I was responding to was your use of Newton as a counterexample of Local Realism. Newton does, in fact, respect local realism, and this has nothing to do with the question of whether or not it allows signals which travel faster than light. It is true that local realism is not at the foundation of all physics, not because Newton isn't a locally real theory (it is!), but because QM is not. When you respond to the question of Local Reality with a statement about faster than light travel, you are conflating local realism with causality. This is the idea that I want to excise. Lethe 21:44, Jul 6, 2004 (UTC)

(William M. Connolley 22:09, 6 Jul 2004 (UTC)) I'm being misunderstood here (the fate of all genius :-). I didn't use N as a counterexample to LR. I don't even really know what LR is. CT said that LR is the foundation of all science, or somesuch. I disagreed. I asserted that *no transmission of info faster than light* was a foundation of science, and that N (and classical thermo) fails this.

Yeah, in general, it is probably an extremely difficult position to hold to say something like "X is the foundation of all science". It's probably NPOV, and should be avoided I think. On the other hand, I would quickly admit that causality is the foundation of all modern physics. Or at least all modern high energy physics. Still, i don't know how useful such a statment is. And I don't know how thermodynamics fits in here. Does it respect LR? I don't know, I guess it might not. I only know that Newton does. And any nonrelativistic theory will not satisfy causality, I guess that is your point. Lethe 23:29, Jul 6, 2004 (UTC)

I go mainly by the way language was used in the old days, before QM was fully accepted. People such as Furry in 1936 (his article can be downloaded from [[1] (http://fangio.magnet.fsu.edu/~vlad/pr100/)]) took it for granted that local realism and causality were the same thing. Incidentally, the definition of entanglement given is not strictly correct. The article says that entanglement means that "measurements on spatially separated quantum systems can instantaneously influence one another." As I understand it, quantum entanglement means that the choice of what to measure on one particle can influence the result of measurement on the other. Caroline Thompson 08:40, 7 Jul 2004 (UTC)

Yeah, you can see me complaining about that very sentence below. That is very bad wording and we have to change it. Entanglement means the the results of two spatially separated measurements are correlated. this does not mean that one measurement somehow influences the other. Lethe 14:16, Jul 7, 2004 (UTC)

Caroline Thompson 08:14, 30 Jun 2004 (UTC) No space in this file for my response!

Unfortunately, the Fermat reply is not a replacement for consensus. there is no limit to how much you can type in this Wiki. therefore, before you revert the article, wait until a consensus is reached on the talk page. Just to reiterate, i don't think it is accurate to change "The EPR "paradox" is fully resolved" to "It is at present considered to have been unsuccessful, the existence of hidden variables having been refuted experimentally and the EPR "paradox" taken to be fully resolved". If you disagree, present your case here before you revert the article again. No one wants to get into an edit war, OK? Lethe 10:54, Jun 30, 2004 (UTC)

By the way, what's this bunk in the article about faster than light and action at a distance? whether or not the EPR inequality is violated, whether or not local realism describes our universe, neither of these situations imples or somehow allows for violation of causality (which is completely unrelated to local realism. there are acausal classical theories (Newton), causal classical theories (Einstein), acausal quantum (i.e. not locally real) theories (Schrödinger), and causal quantum theories (QED). Thus causality (allowing action at a distance, faster than light signals) is completely unrelated to local realism (correlated pure states which are not composed of component pure states)). In my opinion, it is irresponsible for this article to reinforce the (common, i admit) misconception that the failure of local realism allows action at a distance influence, or faster than light signaling. This is most certainly false, and should be deleted forthwith. Lethe 11:05, Jun 30, 2004 (UTC)

(William M. Connolley 15:54, 30 Jun 2004 (UTC)) I'm confused. My reading of the article is that is specifically, and correctly, deals with the issues you are complaining about. Which bits do you mean?

a few more complaints

mostly for my own reference, but also as an opportunity for more dialogue, get comments, etc. I am listing a few things that I think are problems with this article and should be changed. I would just change them myself right now, but I think we should encourage coming to a consensus instead of these endless edit wars.

"measurements on spatially separated quantum systems can instantaneously influence one another."
- This is very misleading. just because two measurements are correlated, does not mean that one "influences" the other (any more than Bertlmann's one sock "influences" the color of his other sock).
"quantum mechanics violates a principle formulated by Einstein, known as the principle of locality or local realism"
- Causality is a principle formulated by Einstein. Local realism is not. Local realism is sometimes called locality. Causality is sometimes called locality, but the two are NOT the same. Conflating the two ideas is the source of endless confusion. Furthermore, nonrelativistic quantum mechanics violates causality, AS WE MIGHT EXPECT BECAUSE IT IS NONRELATIVISTIC!! Relativistic quantum theory does not violate causality. So at best, this statement is very misleading, at worst, it is just wrong.

(William M. Connolley 15:54, 30 Jun 2004 (UTC)) I agree with you. #1 would be better as "measurement on one aspect of a spatially ?distributed? quantum system (singular) can...". #2 is about the history and I think some of the history implicit in this page is dodgy - see my comment far above - I don't think EPR was that important in people view of reality.

on #2, see my above reply. The issue with this quote is that it seems to think that locality as described by Einstein (which I call causality), is violated by QM. Of course it is not (for a relativistic QM). Either that, or the article implies that it violates loca realism, which it does, but local realism was not an idea invented by Einstein. If he had understood this distinction, he never would have formulated the EPR paradox in the first place. Lethe 21:44, Jul 6, 2004 (UTC)

(Caroline Thompson 18:02, 30 Jun 2004 (UTC)): Sorry, William and Lethe. When I said "No space in this file for my response" I was not trying to be clever: the system had told me the file already was more than 32k, which it said was the limit. I'm afraid I've gone ahead and edited the page. I hope you approve.

WMC: I'll reserve comment on that but I have archived some old talk.

Some questions for the experts

I've read almost every article linked off the EPR paradox and every article linked from those articles. Maybe somebody can answer either or both of these questions for me, in the most layman term possible:

Given the entanglements exist, why is it that information cannot be transmited faster than light? It seems to me that by observing an engangled particle far away, the fact that the other entangled particle changes is a form of information. For example, one could observe a certain number of particles as a code to the other observer on the other side of the universe.
What exactly is the spontaneous change the entangled particle experiences far away? If it is spin that is being measured for example, and the first observed particle is 1/2 spin, does that mean the other particle is now assured not to be -1/2 spin? Or does is mean it is now random? And how could anything except -1/2 spin not violate conservation of angular momentum?

Any input would be helpful! Wodan 21:31, Aug 28, 2004 (UTC)

Rather than answer your question directly why this is not possible (at least in any known way), may I suggest you try to think of a specific protocol for Alice to transfer 1 bit to Bob. (That is Alice tosses a coin and does some measurement of some observable on her "half" of the entangled system, which observable is based on the outcome of the coin toss and Bob performs a measurement and can determine Alice's coin toss).CSTAR 01:54, 29 Aug 2004 (UTC)

I'm afraid the answer, as far as I am concerned, is that since all the experiments can in fact be explained without assuming entanglement I chose to believe these alternative explanations to represent what really happens. The question of whether or not information can be transported FTL does not arise. My question to you, Wodan:

What makes you think entanglement really happens?

I've recently, as you may have noticed, created several new pages on the Bell tests. Among those that are all my own work (based on about 10 years of study) one that might interest you is Local hidden variable theory, but another, which I copied from Shimony's new "Bell's Theorem" article, is Quantum mechanical Bell test prediction. It struck me whilst battling with the formatting etc that the argument was simply not logical. It certainly comes over as very inflexible.

a: What is the justification for suddenly assuming Malus Law? For one thing, Malus Law applies to light of a given polarisation direction passing through one polariser. What is the justification for assuming it applies to coincidences between two separate beams of light passing through two separate polarisers?

b: What if we are dealing with imperfect polarisers or with detectors whose response is not quite proportional to the input intensity?

The local realist models have no problem, but it strikes me that QM is in deep trouble.

Caroline Thompson 10:41, 29 Aug 2004 (UTC)

Getting back to Wodan's questions, the answers are: (i) You can't transmit information faster than light because the results of a measurement are random. The result of Bob's measurement depends on the result of Alice's measurement, but Alice can't control what result she gets. Therefore Alice can't send information to Bob simply by performing a measurement. Now, there are clever ways to transmit information by entanglement, but it turns out that no one has ever thought of one that would allow faster than light transmission, even in principle. (ii) The change that the entangled particle experiences is that the result of a measurement becomes 100% certain. If Alice performs a measurement and gets (say) spin up, Bob will definitely get spin down. Whereas if Alice doesn't perform a measurement, Bob would get spin up and spin down with equal probability.

By the way, the EPR paradox article and related articles are getting more and more difficult to understand. It's too bad; they used to be quite readable. -- CYD

Problems with the EPR article

Could you be more specific? Would you be willing to suggest improvements? Or should we just all wallow in self-doubt?CSTAR 13:31, 20 Sep 2004 (UTC)

Re CYD's comment about the pages becoming less readable, I'm afraid it's more a matter of me having made changes so that the content is no longer so familiar. The previous versions stuck to the accepted story, simplified for the benefit of the general reader but also factually wrong in that, by glossing over the loopholes associated with the conduct of the real experimental tests, the impression was given that the experimental evidence for quantum entanglement was conclusive. The new story is not so very difficult once you get used to it! Caroline Thompson 17:51, 20 Sep 2004 (UTC)

Certainly I could suggest areas of improvement. Despite Caroline Thompson's insinuations (the "accepted story", by the way, is certainly what a wikipedia article must talk about; no original research and all that, you know) what I'm concerned about is that the article isn't doing a great job of explaining just what the EPR paradox is, as evidenced by Wodan's questions. I might add that a lot of the fault lies with me, since the earliest versions of the article were mostly written by me. As the article has grown, these faults have become more obvious, and it may need to be restructured. I don't have the time to work on it, but here are some quick observations if anyone is interested:

The opening sentence seems to be POV. The principle of locality is not necessarily "intuitive", nor non-locality "counter-intuitive." As has been pointed out elsewhere, Newtonian gravitation is perfectly non-local (as indeed is every other classical field theory.) It might be more accurate to say that the EPR effect runs counter to relativistic intuitions -- though it turns out not to violate relativity itself, just the intuitions! Also, there was a rather important statement in older versions of the article, to the effect that the EPR effect is not actually a paradox in the usual sense, which has somehow disappeared.
The article contains huge sections talking about "how entanglement affects our understanding of particles", etc., without describing what entanglement means. It's true that quantum entanglement has its own article, but we probably need a short section to at least sketch out how entanglement works. In particular, it must mention the role of measurements and probability, pre-empting questions like Wodan's.
It would be better to first describe a physical apparatus for the experiment (albeit an idealized one), before introducing the color analogy. One should not present an analogy before we know what it's an analogy of! Either the "correlated spins from an oven" picture or a more realistic picture based on photons should be fine for this purpose.
The "Mathematics of the EPR paradox" section is not so hot. It might be better to use the usual "up arrow" and "down arrow" labels for the spin states rather than e1, e2, etc. Also, the remark on the uniqueness of the spin singlet is interesting but irrelevant; it's sufficient to assert that the system is prepared in the (up/down - down/up) state. It's also worth considering moving the color analogy to this section, where it would serve a clearer purpose.

On a final note, Caroline Thompson has asked the question "What makes you think entanglement really happens?" It strikes me that one reason to think (or at least strongly suspect) that entanglement "really happens" is the existence of the laws of thermodynamics. As the Gibbs paradox demonstrates, the statistical mechanics of gases only gives rise to thermodynamics if the particles are indistinguishable, which implies that the states of different particles are somehow mixed together (irrespective of whether you believe in "quantum states" or not.) Statistical results of this sort, by the way, give rise to a whole array of "quantum mechanical" behavior that has nothing to do with manipulating individual photons or electrons. May be interesting for you to think about. Cheers ;-) -- CYD

Re the Gibbs paradox, the indistinguishability of particles is surely a separate issue? It is in any event untestable. The fact that the theory gives correct predictions does not prove this is the only way to explain the observations! The point about the Bell tests is that they cover a prediction of QM that 'is testable, and the results have been presented in a way that has, I fear, been strongly biased in favour of QM.

Caroline Thompson 10:02, 23 Sep 2004 (UTC)

Particle indistinguishability is not a separate issue; it means that the individual particle states are as strongly entangled as it is possible to be. And, of course, the indistinguishability of particles is testable, that's why I mentioned the Gibbs paradox. The test is that gases obey the laws of thermodynamics, which they obviously do. Now, this doesn't say whether this is quantum entanglement or a local variable theory's version (i.e. an infinite number of correlations between an infinite number of hidden variables.) But it does answer your question: it appears that entanglement "really happens". -- CYD

The question that is still open is whether entanglement happens in Bell test experiments. I don't think anyone ever claimed these were indistinguishable. They are necessarily distinguishable since they have to be measured separately. A result from the behaviour of gases cannot be used to argue for entanglement in actual Bell tests. Caroline Thompson 09:16, 24 Sep 2004 (UTC)

You think so? It must be strange indeed to accept the existence of entanglement in something as familiar as a gas, while raising doubts about it in a highly controlled and artificial system like a Bell test. -- CYD

There is no need to assume when modelling a gas that the molecules interact by means of instantaneous influences acting at a distance. In the Bell tests, if QM is correct then the influence is necessarily instantaneous. Indeed, isn't it claimed that it can even be backwards in time? The Bell test version of "entanglement" is contrary to what has always until now been assumed to be physically possible. Caroline Thompson 18:12, 27 Sep 2004 (UTC)

You're dancing around the issue. First of all, misleading language - entanglement isn't really an interaction between particles, and Gibb's paradox applies to ideal gases in which there are no forces between the particles. Next, how else would you model a gas other than using entangled particle states? Recall that the whole idea of entanglement is that you can prepare many-particle systems in such a way that it is impossible to think of an individual particle in isolation; you have to look at the state of the entire system. (This statement, by the way, is quite independent of whichever theory of measurement you are using, be it Copenhagen's "wavefunction collapse" (the one you seem to be hung up on), Everett's "many-worlds" interpretation, or something else totally different.) In this case, you can't look at one particle in the gas without looking about all the other particles, since they're all indistinguishable. That's precisely analogous to the Bell test spin singlet: you can't say that one particle has spin up or spin down, you have to talk about both particles instead. -- CYD

Whatever it is, the kind of entanglement involved in the QM prediction for the Bell test setup is incompatible with local realism. The outcome on the B side varies with the setting on the A side.

I'm not concerned with Gibb's paradox but with the Bell tests. Surely nobody is saying that the ideal gas model is anything more than a model? Since it does not give results that conflict with anything counterintuitive it is harmless. Everyone is quite free to imagine that in real gases there are real particles with definite identities, interacting to some extent but not instantaneously. In the Bell test case it's quite different. The model has unacceptable features and yet is being interpreted as if it is a true one. Moreover, in all real cases we can see our way to a physically plausible alternative. Have you looked at the local hidden variable theory page?

You can in fact talk about the separate "photons" in a real experiment. You have a real instrument that gives a real click when a certain electrical pulse exceeds a pre-set threshold and is taken as indicating the detection of a single photon. Admitedly you can't do your Bell test until you've looked at a whole ensemble of pairs of photons, but at any one stage there is no reason to suppose that individual ones don't have definite polarisation directions. How else would the outcome for the whole group be able to be sensitive to the polariser setting?

Caroline Thompson 09:33, 28 Sep 2004 (UTC)

You seem to have a real difficulty (no pun intended) thinking about anything except those little Bell tests, so let me spell it out for you: Bell tests aren't the only place you get entanglement. In particular, I haven't actually seen you raise any objection to the statement:

Entanglement occurs in gases.

Please stop making tangential comments like "the ideal gas model is just a model" - all physical theories are just models, but that is neither here nor there. You could of course wave your hands and say that for "real gases" there is some mechanism that gives rise to thermodynamics without requiring particle indistinguishability, but what is that mechanism? Go ahead and try to find one; you'll realize there's no way, because the argument behind Gibb's paradox is so simple and fundamental.

As for talking about "separate photons", of course you can do that after the measurement, since that breaks the entanglement. But can we describe the system before the measurement as a bunch of separate particles in well-defined states? Hidden variable theories say yes, and quantum mechanics says no. And statistical mechanics also says no. -- CYD

This discussion is about the EPR paradox, or so I thought. As I understand it, the only way so far proposed for testing whether or not entanglement actually occurs is to do a Bell test experiment. Therefore I'm concerned with the Bell tests, not with the behaviour of gases. The physics community has come to believe that the Bell tests support QM and entanglement. Not only this but it is often claimed that the results are not compatible with local realism, meaning that the quantum world really does behave incomprehensibly and we just have to accept this "fact". The interpretation using the QM model is being confused with the real world. But the experiments (as is known to those actually concerned with them) are not conclusive and do not force us to accept anything counterintuitive. Please believe me: statistical mechanics is a separate issue. The kind of entanglement involved there is not testable. Caroline Thompson 20:28, 28 Sep 2004 (UTC)

That may be the story that you like to keep telling yourself, but it's wrong. Granted, the Bell tests are important, because they provide a way to look at entanglement in a highly controlled manner. However, the effects of entanglement can be seen in a wide variety of situations that have nothing to do with them. I would encourage you to look into the subject. Any elementary statistical mechanics textbook should have a discussion of Gibb's paradox; see, for example, Fundamentals of Statistical and Thermal Physics by Frederick Reif. -- CYD

I strongly disagree with Caroline Thompson's assessment that entanglement does not happen. Unfortunately, I am not qualified (at least not currently) to look into the details of what she wrote down. I would hope that these remarks would be put into a form which would be less idiosyncratic and less "invasive" of the whole article. Caroline Thompson's view is certainly not the prevalent one.CSTAR 14:10, 21 Sep 2004 (UTC)

Yes, I wish these QM articles on wikipedia were not the object of Thompson's plan to change the general understanding about quantum mechanics. wikipedia is here to represent physics as understood by the mainstream, in my opinion, not as a platform to campaign against the mainstream. -Lethe | Talk

You are right that I think QM incorrect in some areas, but I have tried hard not to present a biased view. What I have attempted is to present the facts as known to the experts in the field as opposed to those in popular books. Is it right that wikipedia should publish misleading information? The experts are well aware (as the editors and referees of certain journals are fond of telling me!) that the evidence for quantum entanglement of separated particles is far from conclusive. They await the perfect, "loophole-free" experiment.

Yes, and until we have the perfect zero mass measurement of the photon, we should be teaching physics students all over the world that the measurement of the mass of the photon has loopholes, and to say that it is zero is factually incorrect. this is what i infer from your argument. -Lethe | Talk

Incidentally, I'm not sure I fully agree with the idea that any encyclopaedia should stick to accepted opinion. It should, though, stick to facts.

Caroline Thompson 10:02, 23 Sep 2004 (UTC)

Yes, and I don't think it is bad to say that the book isn't closed on EPR experiments. That it is not is a fact. However, you seem to be persuing an agenda not only to state the facts on the matter, but to overstate them. A novice reader might come to these articles and think that the question of local realism is wide open and contraversial, when in fact, the question is nearly closed and completely forgotten in the minds of 999 in 1000 physicists.

Hmmm ... but 999 out of 1000 physicists are not directly involved with Bell tests! Ask the editors and referees of Physical Review Letters or Physical Review A. They have repeatedly told me that the loopholes are well known. Other experts with whom I have corresponded have, almost to a man, told me that they accept entanglement provisionally, in view of the success of QM in other areas, but are waiting for a loophole-free Bell test to confirm it. Meantime, the reader has every reason to be confused, I'm afraid. The question is still wide open and controversial. Caroline Thompson 09:16, 24 Sep 2004 (UTC).

I'm not sure why you want to do this, but I think it will prove misleading to the reader who isn't familiar with the field, and is therefore undesirable. -Lethe | Talk

I do it partly simply because in some quarters belief in entanglement is harming the reputation of physics as a true science; partly because of the wider implications. If entanglement were to happen (the Bell test type, involving definitely separated particles) then it would follow that there were facts in this universe that even the experts don't understand. The implication is that nobody can hope to understand the world around them. This is defeatist. I think it influences decisions outside theoretical physics, ones that concern how we try and run the planet.

Incidentally, the other day I had a look at some of the wiki pages concerned with light. There is remarkably little reference there to the "photon". It is belief in the photon that makes it so difficult for theorists to accept local realist explanations for the Bell tests. Like it or not, the existence of the photon is also an open question!

Is it right that the reader should be screened from such sources of confusion? The editors of the American Journal of Physics recently rejected one of my papers on the grounds that it would confuse their readers. The latter are mainly physics teachers. Shoud they too be protected?

Caroline Thompson 09:16, 24 Sep 2004 (UTC)

Excuse me?

"because in some quarters belief in entanglement is harming the reputation of physics as a true science"

Allow me to quote from Newton on the subject of gravity:

" ... that one body may act upon another at a distance through a vacuum, without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity, that I believe no man who has in philosophical matters a competent faculty of thinking, can ever fall into it." [from letter (1693) to Richard Bentley]

Newton's quote is about nonlocal interactions, which are fortunately banished from physics ever since Einstein. Realism is a completely independent issue, which has been present in physics ever since Heisenberg. You are arguing against entanglement as if it were nonlocality, which it is not. -Lethe | Talk

How can a local theory avoid complying with Bell's inequality? QM infringes it, and this is the whole point of doing Bell tests. Infringement implies nonlocality. What are you trying to say? That there are "unreal" theories that are local and compatible with entanglement? That does not make sense! Caroline Thompson 22:09, 27 Sep 2004 (UTC)

To laymen and philosophers alike, the idea of entanglement of separated particles involving any instantaneous interaction, whether or not it can convey "information", is absurd. If there is an alternative that is compatible with the observations, this is to be preferred.Caroline Thompson 18:12, 27 Sep 2004 (UTC)

There is no instantaneous interaction. if you think there is information that is even eligible to be conveyed instantaneously, you have already assumed local realism. without realism, there is no "instantaneous interaction" in orthodox quantum mechanics. no one who knows the theory thinks there is anything absurd about it. quantum mechanics does not have to conform to what laymen and philosophers think is or is not absurd, but rather to what is logically consistent and measurable. -Lethe | Talk

What quarters are those? And are you sure you really meant to say the folowing?

"then it would follow that there were facts in this universe that even the experts don't understand"

No, I suppose not exactly. What I mean is that physics always used to be pursued on the assumption that there was nothing intrinsically incomprehensible in Nature. QM, and in particular the part concerning entanglement of separated particles, has long been accepted as a mystery that we cannot hope ever to understand. Caroline Thompson 18:12, 27 Sep 2004 (UTC)

Well yes, I think that is true. Why is this bad and why does this imply that entanglement should be abandoned?

"the existence of the photon is also an open question!"

Yes, indeed everything in science is open to scrutiny and challenge. That is the scientific method. But you simply don't shrug your shoulders and say We don't know nuttin' It is the responsibility of scientists to lay the facts as currently known.CSTAR 14:25, 24 Sep 2004 (UTC)

True. Which is why I should like people consulting wikipedia to be presented with the experimental facts, not only the opinions of people who believe QM to be correct. And the experimental facts don't mean much unless one also suggests rational interpretations of them, i.e. appropriate local hidden variable theories.Caroline Thompson 18:12, 27 Sep 2004 (UTC)

It sounds like you think that experts don't understand entanglement, and therefore, if entanglement is a real phenomenon, experts don't understand facts about our universe. well this is at best simply wrong, because many experts do understand entanglement, and I would wager even a great cross section of sufficiently educated nonexperts. It's counterintuitive to one's classical muscles, to be sure, but it's really not hard to understand. Or at worst complete nonsense, since physicists don't study "facts in this universe", but rather only models which predict results of experiments, of which (orthodox) quantum mechanics is an excellent example. -Lethe | Talk

Right. QM is satisfied with models that give correct predictions. If the local hidden variable model is correct, though, it can be predicted that this success story will not last for ever. Other theories, based on solid physical principles, should be able to give better predictions. I have my own ideas of the situations in which the advantages of realistic models would show up but there is nothing published on them. See my web site:

http://freespace.virgin.net/ch.thompson1/ . Caroline Thompson 18:12, 27 Sep 2004 (UTC)

Is uniqueness of spin singlet state relevant to EPR?

CYD I disagree that the uniqueness of the spin state is irrelevant. It is equivalent to the following remark in Box 2.7 on page 113 of Nielsen and Chuang:

It turns out that no matter what choice of <math>\vec{v}<math> we make, the results of the two measurements are always opposite to one another.

Notice the argument given in Nielsen and Chuang in the following lines is a disguised form of what the Wikipedia article currently says. CSTAR 14:10, 21 Sep 2004 (UTC)

This is just saying that the direction along which we measure the spins doesn't matter, as long as we choose a direction. This is of course true, but it's not relevant to the discussion, because the goal here is just to show how entanglement causes a correlation in measurement results. -- CYD

Well again I disgree -- the point of the EPR, I thought, was to show the difference between electrons and (Bertelman's) socks! (Of course I'm aware that Bertleman's socks story came after EPR) CSTAR 13:23, 22 Sep 2004 (UTC)

Read the section. It doesn't explain the difference between electrons and socks. -- CYD

OK it doesn't say literally electrons aren't socks, although adding that explanation should present little problem. But then again the section is called -- Mathematics of the EPR paradox. Moreover, it doesn't say that the only point of EPR is entanglement (as you seemed to be suggesting in your earlier comment). My point in this dialogue is that any accurate account of the EPR paradox has to use --- in some form or other--- the uniqueness of the spin singlet state. Your point originally, I believe was that this uniqueness was irrelevant to EPR. Now I agree this phrasing may not be appealing to everyone, but I think it is accurate and is mathematically correct. Mainly, however, the presence of a section Mathematics of the EPR paradox is not the cause of the article having the readability problems you mentioned.CSTAR 14:29, 22 Sep 2004 (UTC)

POV?

Despite my disagreement with CYD about the spin singlet state (which I think can be resolved by adding text or deleting text or marginally changing text), Lethe and CYD ---I think, myself and possibly others, seem to agree that the more serious problem with the article is dealing with or accomodating a minority viewpoint which is hostile to the commonly accepted view of entanglement. As I said, I don't consider myself qualified to act as a "reviewer" for her work. This puts the article into a state in which it is misleading to a reader unwilling to tackle the debate implicit in that article. Also why was the experimental setup for EPR moved somewhere else?CSTAR 16:30, 22 Sep 2004 (UTC)

Formalisms for QM: More comments

Comment on the following paragraph:

Which is why I should like people consulting wikipedia to be presented with the experimental facts, not only the opinions of people who believe QM to be correct. And the experimental facts don't mean much unless one also suggests rational interpretations of them, i.e. appropriate local hidden variable theories.Caroline Thompson 18:12, 27 Sep 2004 (UTC)

Now this is certainly NOT a statement of fact. There are lots of rational interpretations of QM formulated in terms of C*-algebras. Though these interpretations may be semantically more complex than rational interpretations of classical mechanics, that in and of itself is no reason to think they fail to be rational. And again though the "layman and philosopher" may not like them, so what?CSTAR 21:46, 27 Sep 2004 (UTC)

What I am talking about is physically plausible explanations of the actual results of Bell test experiments. I should not have said "rational". Caroline Thompson 22:13, 27 Sep 2004 (UTC)

I don't understand why you don't think that orthodox quantum mechanics gives a plausible explanation. -Lethe | Talk

QM does not even pretend to give an explanation. It merely presents a formula. Have you studied the derivation of the QM prediction for Bell tests? I copied the page from Shimony's paper, and in the course of so doing became much more aware of just how implausible the argument was. What is the justification for assuming Malus' Law to apply to the coincidences between the outputs from two separate analysers? Malus' Law applies to the output from two polarisers in series, not two in parallel. In contrast, every stage of the local realist model makes physical sense. The only slight hitch is that it does not quite give the right answer if the polarisers and detectors are perfect. Since in real experiments they are not, there is no real problem in adapting the model to fit the observations. Caroline Thompson 22:56, 27 Sep 2004 (UTC)

What is an explanation?

QM does not even pretend to give an explanation. It merely presents a formula.

Again that is a caricature of the mathematical formalisms of quantum mechanics. You have created for yourself and everybody else a notion of explanation which is excessively narrow -- it has to fit into a Rube Goldberg contraption concept of causality. If you can't explain why an event happens in terms of immediate local causes understandable by naive physics, then in what consistently appears to be your view, you haven't explained anything. In response, I'm sure to those that believed the earth was supported by a tortoise, the whole concept of stability of the solar system balanced by gravitional forces seemed bizarre and untenable.

You seem to be demanding that quantum mechanics fit a particular mold of physical theory; To draw an analogy which is actually quite accurate, you want to force quantum mechanical observables to be a commutative algebra of observables when the evidence suggest they are not. Trying to find hidden variables to explain the statistical structure of correlation experiments is tantamount to trying to show that there is a commutative C*-algebra of observables with the given correlation structure. The evidence is that there isn't. None of this is odd, mysterious or spooky.CSTAR 01:43, 29 Sep 2004 (UTC)

I am well aware of the fact that no hidden variable theory can have exactly the same structure as quantum theory — this is what Bell's theorem showed. However, what we are trying to model is not quantum theory but the real world, and, as indicated in the Local hidden variable theory page, the experimental evidence does not preclude a local realist model. Such a model is fully causal, as well as being able to give the same predictions as quantum theory, to within the experimental error limits. Surely, since it is intuitive, it is to be preferred? A model that one can understand at this level will be easier to use than one that is merely a formalism. Wikipedia readers deserve to be told the experimental facts, including the existence of loopholes, so that they can make up their own minds on this crucial question.

To your mind, the quantum theory formalism may not involve anything mysterious or spooky, but this is certainly not the impression of the rest of the world. Moreover, I suspect that, when you get down to it, the actual prediction for "quantum correlations" amounts to the assumption that Malus' Law applies to the coincidences! Have a look at the Quantum mechanical Bell test prediction page that I copied from Shimony. Can you explain why Malus' Law should be assumed here? Caroline Thompson 11:05, 29 Sep 2004 (UTC)

Resolving an impasse

There are several issues in play

The current predominant view of QM and entanglement. Though Lethe, CYD and myself may disagree on the details of the mathematical formalism, I think we are in substantive agreement about its general form. Within this formulation entanglement is a completely intelligible concept and a mathematically consistent (at least as consistent as ZF) model of quantum mechanics, accounting for (1) system preparation, (2) measurement and observation and (3) statistical and correlation behavior can be constructed.

Bell's inequalities CHSH forms of them etc. Again I don;t think there is any dispute about what these are and what the predominant view is about these.

The current status of experimental test of Bell's inequalities. I certainly don't object to people trying to poke holes into existing theories and to the extent that CT can point to the literature in which people are trying to find these gaps, I thik it is fair to put them in as just that. But unfortunately, CT seems to have taken it upon herself to express her viewpoint in prominent places throughout the articles. At best I can say this is unscientific.

My suggestion is that the article be rewritten entirely. A first step is that the experimental setup of EPR be returned as part of the main article. The mathematics of EPR can be simplified as per CYD's suggestions (although I am unhappy about removal of the uniqueness of the spin singlet state for the reasons I mentioned). COncepts such as realism and local realism should be defined at some point. The discussion in Omnes book on Quantum Mechanics is useful.CSTAR 15:18, 30 Sep 2004 (UTC)

It is only right and proper that the EPR paradox page itself should present mainly the accepted view, i.e. should be written on the assumption that quantum mechanics is correct even when modelling apparently nonphysical phenomena such as entanglement of separated particles. I have, you may notice, hardly altered this page, only correcting a statement here and there where the original implied that the experimental confirmation was unambiguous. When it comes to the other pages, though, it seems to me more correct that they should be written with a local realist bias. Bell's theorem and the other related tests were all devised from a local realist point of view. Clauser, one of the authors of both the CHSH and the CH74 test and involved with Freedman in the first proper Bell test experiment in 1972, wrote an important paper discussing the fact that almost all phenomena covered by quantum theory could alternatively be modelled using "semi-classical" theory. [See Clauser, J E, “Experimental limitations to the validity of semiclassical radiation theories”, Physical Review A 6, 49 (1972).]

Incidentally, if anyone is going to re-write the EPR paradox page, I should like to recommend that the analogy using colours be replaced by one that has a geometry that is relevant to the Bell test experiments. The colour analogy does not lend itself to modelling using the kinds of hidden variables that are needed in real situations. If you want a better one, my Chaotic Ball model (http://arXiv.org/abs/quant-ph/9611037) might be suitable. It is not ideal, since it models a spin-1/2 experiment that has never been done, but it does involve angles in an appropriate way. Caroline Thompson 20:24, 30 Sep 2004 (UTC)

Probability amplitudes

Feynman was perfectly happy to consider probability amplitudes. Probability amplitudes aren't probabilities. Whta's the problem? Why is Caroline Thompson so determined to use one formalism -- classical mechanics and probabilities to explain QM? This is surely not an instance of Occam's razor. This is more like Occam's fingernail which perpetuates an itch.CSTAR 01:22, 3 Nov 2004 (UTC)

What is it?

After reading this article, I still have no idea what the EPX paradox even is. Maybe I missed something, but it doesn't appear to be defined anywhere. It talks at great length about its ramifications and objections and all, but what is the experiment, and why is it paradoxical? Derrick Coetzee 18:45, 1 Nov 2004 (UTC)

For the experiment, see the wikipedia article with that specific title. You're right, this article doesn't say what it is. As you can glean from the dialogue above, the article is currently involved in an ideological dispute about whether entanglement is real or not. Entanglment is real, at least according to almost every physicist that has written something on Quantum Mechanics, but unfortunately not according to at least one writer of this article. For now, look at the Roland Omnes reference in the Quantum logic article.

As to why it's paradoxical, well it really isn't. A phenomenon is paradoxical only relative to some way of looking at things. This may have been paradoxical at one time, but it certainly isn't now. CSTAR 19:00, 1 Nov 2004 (UTC)

Hmmm ... well, the fact is that Quantum Mechanics predicts something that is not possible if things obey the ordinary laws of probability, and this is paradoxical. I advise looking at the Bell's Theorem page and links therefrom. The experimental tests that are supposed to support the prediction have known loopholes, so that whether you believe quantum entanglement really happens or not is at present a matter of personal preference. The phenomenon is believed by many to be involved in real applications in quantum cryptography and elsewhere, but if you look closely you find that it is possible (and in my view likely) that they are merely exploiting the fact that there are very interesting ordinary correlations present. If you would like to know a bit more about these correlations, see an unpublished article of mine that explains what I think is the main mechanism behind experiments such as that of Gregor Weihs et al.. Quantum cryptography is in practice based on the same kind of light source.

My article:

Thompson, C H, “Rotational invariance, phase relationships and the quantum entanglement illusion”, http://arxiv.org/abs/quant-ph/9912082

Weihs' experiment:

Weihs, Gregor et al., “Violation of Bell’s inequality under strict Einstein locality conditions”, Physical Review Letters 81, 5039 (1998) and http://arXiv.org/abs/quant-ph/9810080

Caroline Thompson 22:39, 1 Nov 2004 (UTC)

What you mean to say is: "Quantum mechanics predicts something that is not possible if things obey the ordinary laws of classical mechanics." Probability is a mathematical framework, not a physical theory, so the "ordinary laws of probability" place no constraints on physical measurements. -Lethe | Talk

Actually I meant either or both. QM does not allow the multiplication of two probabilities that classical mechanics tells us are independent. In point of fact, one way of describing the paradox is to say, as Feynman did[*], that QM requires negative probabilities. Something is wrong, whether the physics or the maths.

[*] Feynman, R P, Simulating Physics with Computers, International Journal of Theoretical Physics 21, 467-488 (1982)

Caroline Thompson 22:49, 2 Nov 2004 (UTC)

Quantum mechanics allows the multiplcation of probabilities of events that quantum mechanics tells us are independent. Measurements that classical mechanics tells us are independent are not really relevant in a discussion of quantum mechanics, now are they? They are simply different theories. -Lethe | Talk

Fair enough! So it boils down to which theory is "better". At present the quantum theorists hold all the cards. They have done experiments using parameters of their own choosing. I could suggest different choices that would show that the actual logic was that of local realism, not QM. See Local hidden variable theory, some suggestions on my web site, http://freespace.virgin.net/ch.thompson1/, and C H Thompson and H Holstein , “The ‘Chaotic Ball’ model, local realism and the Bell test loopholes”, http://arxiv.org/abs/quant-ph/0210150. Caroline Thompson 17:53, 3 Nov 2004 (UTC)

OK! So you concede that quantum mechanics is not inherently paradoxical, it is simply contradictory with local realism. That's good, so you can stick to making claims that are simply unlikely, rather than making claims that are wrong. Please don't go around telling people that our fundamental theories are paradoxical. -Lethe | Talk 21:31, Nov 3, 2004 (UTC)

Sorry, but I belong to the real world and the real world is local and real, as far as any of us can prove. So a theory that says otherwise is necessarily "paradoxical"! There is no "simply" contradictory when you come to talk about something that is so fundamental. Without the universal assumption of local realism, the interpretation of scientific experiments is impossible.

If the universe obeys local realism, then quantum mechanics is wrong, but that still doesn't make it paradoxical. Please stop asserting that it is paradoxical. Do you understand what paradoxical means? Also, your claim that without local realism, there is no possible interpretation of scientific experiments is ridiculous. Tens of thousands of physicists all over the world interpret scientific experiments all the time without the benefit of local realism. -Lethe | Talk

This assumption is not in practice restrictive. It can allow for all sorts of influences from the environment, but they cannot travel infinitely fast. Faster than light is not in principle excluded. The kind of interaction supposed to be demonstrated in Bell test experiments, though, is such that if it is there it is instantaneous, or can even go backwards in time if there is relative motion.Caroline Thompson 09:35, 4 Nov 2004 (UTC)

Parenthetically, a similar argument might be made against special relativity with the barn and pole paradox (http://math.ucr.edu/home/baez/physics/Relativity/SR/barn_pole.html): I belong to the real world and in the real world simultaneous events do exist, as far as any of us can prove. So a theory that says otherwise is necessarily "paradoxical"! Without a universal definition of time, the interpretation of scientific experiments is impossible. The point is that everyday intuitions are not a good guide for judging theories in totally different realms of experience. And, despite what C.T. has insinuated, there is a vast bulk of experimental evidence that quantum mechanics is basically correct. -- CYD

You'd better not get me started on SR! I'm afraid in my model of the universe, Phi-Wave Aether theory (http://freespace.virgin.net/ch.thompson1/Essays/PWA.Apeiron.htm), SR is redundant and merely another unnecessary source of confusion. All radiation travels at the same speed with respect to the aether (with some minor qualifications). We don't always know what speed the aether is going at, but that doesn't mean to say it hasn't got one. Effects such as change of mass with velocity have alternative explanations. Caroline Thompson 12:49, 4 Nov 2004 (UTC)

Heheheheh. Would someone like to compute C.T.'s Crackpot Index (http://math.ucr.edu/home/baez/crackpot.html)? The last paragraph just bumped it up by 10. -- CYD

The whole issue of whether or not we have a "paradox" and what I believe about the aether is totally irrelevant to my contributions to the discussion on EPR. My area here is the actual Bell test experiments and the fact that, owing to the presence of serious loopholes, not a single one has in fact disproved local realism.

[incidentally, the word "crackpot" means, effectively "original thinker".] Caroline Thompson 09:27, 5 Nov 2004 (UTC)

Special relativity and Occam

I confess that I couldn't resist the urge to check who made recent edits to Special relativity. My god, C.T. why are you bringing up aether?

Have a look at the Michelson-Morley experiment page. You will find that the experiment was not as null as the books say. Dayton Miller later repeated it, with interesting results that have yet to be fully interpreted. The Special relativity page does not [yet!] mention this. Nor, I suspect, does it mention the fact that in effect GR brings back the aether, though not under that name. As I said above, though, my beliefs here are not relevant to the issue of the validity of the Bell tests the the existence of local hidden variable theories that can equally well match the experiments.Caroline Thompson 09:27, 5 Nov 2004 (UTC)

Talking about poor Occam and his beard --- now you're plunking the man in a vat of jelly! He'll need more than a razor to get out of there! Why don't you look at Asher Peres' book on Quantum Mechanics published around 1993. It's really expensive, but it's available in most University libraries and is possibly the first textbook to take an information-theoretic view of QM. This whole issue of local realism is a red-herring. What is more to the point is flow of information between principals.CSTAR 04:00, 5 Nov 2004 (UTC)

I am surprised by your statement that "local realism is a red-herring". It is my understanding that a proper understanding of local realism is exactly the right approach to understanding the EPR paradox. I don't know what "flow of information between principles" means, but I have checked out from the library the book you recommended. Can you say a bit more about it, and maybe suggest some passages from the text? -Lethe | Talk

Local realism is usually formulated in terms of a naive view of causality. This is a red herring because if we adopt the causal interpretation of locality, it raises a problem: That of providing an intermediate causal chain to explain action at a distance, or to avoid "spooky" interactions. This I think is the trap that C. T. has fallen into. A more neutral formulation involves information. Now again this presents a minor expository problem because I don't want to use the conventional language physicists use : observers.

I fear we are suffering from a semantic barrier. When I say "local realism", in no way do I mean that this concept should be confused with causality or any other form of locality. When I say that quantum mechanics violates "local realism", I mean that quantum mechanics has compound pure states which cannot be built from two pure states from different regions. In other words, there are elements in H_A⊗H_B which are neither in H_A nor in H_B, where A and B are two spacelike separated regions. I call this property local realism, following Baez, but it's very important that it not be confused or conflated with any of various other things which are called "locality". Having read chapter 6 of the book you suggest, I feel that I am in agreement with the author, and hopefully with you. Peres calls these states nonfactorable, and doesn't use the phrase "local realism" anywhere in the book, so I guess it's not a universally accepted usage. Most people would call these "entangled states". But understanding that entangled states do not lead to violations of causality is the everything. Once you have done that, you see that the EPR paradox is no paradox. Are you in agreement? -Lethe | Talk

A principal is just some receptacle for classical information. This is terminology used by researchers in communication protocols (see for instance the part of Nielsen and Chuang which talks about cryptographic key exchange).

However I am by no means suggesting realism is undesirable I am a realist in that sense. I'm just troubled by the most frequent interpretation of local in local realism. That is, as a form of what I referred to in a previous note as "Rube Goldberg Causality". See my comments below.CSTAR 23:40, 5 Nov 2004 (UTC)

Hi CSTAR: You say "if we adopt the causal interpretation of locality, it raises a problem: That of providing an intermediate causal chain to explain action at a distance, or to avoid "spooky" interactions." This is no problem in my Phi-Wave Aether (http://freespace.virgin.net/ch.thompson1/Essays/PWA.Apeiron.htm) (PWA) theory. Both forces and information are carried by phi-waves at the speed of light (relative to the aether). Everything depends on the pattern imposed on the phi-waves, which are in themselves very high frequency longitudinal waves. They can carry transverse patterns, or, indeed, any pattern, created as a result of motion of their source. For an example, see the animation at Gabriel LaFreniere's site: http://www.glafreniere.com/light.htm.Caroline Thompson 09:57, 6 Nov 2004 (UTC)

Of course, it's easy to come up with a "solution" -- Angels can do the trick of conveying the interaction at a distance, as I suggested below. Such theories aren't likely to be realist theories, though, or at least theories whose realism is consistent with the realism of other theories. CSTAR 15:41, 6 Nov 2004 (UTC)

Realism and local realism

One of the main points of the EPR experiment was to draw attention to a notion of realism of a model of a system S (I prefer to use the word model instead of the more grandious term theory, which I think of as being made up of lots of models and experimental techniques). The best account of this I have seen seems to be in the Roland Omnes reference given at the bottom of the quantum logic page. Following is my interpretation:

For purposes of argument I will think of the model as being a mathematical model, that is in purely formal terms this is a mathematical theory, e.g. a formal language with a mathematical semantics.

Realism is a property of a model. It means that any property that is unambiguously determined by the model (such as the value of some variable) actually corresponds to a real property of the modelled system S. Models can be useful even if they don't satisfy the property of realism. I suppose it is possible to have two models of the same physical system and such that both can't be realist. (Interesting research topic for a philosopher of physics!)

For instance, one could have a model with "angels" as an explanatory element; It is possible to build elaborate physical models with angels doing all the work. I suspect this cannot be a realist model if more conventional models of physics are realist models.

Completeness is also a property of models. This means that any property of S corresponds to some (definable) property in the model.

Locality is somewhat more complicated, and unfortunately is usually phrased in terms of causality. Information flow is a less loaded concept and phrasing locality in terms of it makes it empirically testable.CSTAR 22:01, 5 Nov 2004 (UTC)

As I said above, I never meant to conflate "local realism" with "locality". Let me expand a bit on that here. Here is a list of principles which you might want a physical theory to follow:

information cannot travel faster than light, or more precisely, the state of a system is determined solely by initial data within its past lightcone. I call this causality. Newtonian mechanics and NRQM violate this, classical EM and RQFT respect it.
the commutators of all quantum observables vanish at spacelike separated insertion points. I call this microcausality. NRQM violates this and RQFT respects it.
The Lagrangian of the theory is written only in terms of fields at a single insertion point, in other words, no terms in the Lagrangian like ∫A(x-y)B(y)dy. I call this locality. I think that theories that violate locality tend to violate causality as well. Newtonian gravity violates this.
pure states that are spread out in space can be realized as the products of pure states in each local region. I call this local realism. Newtonian gravity and classical EM respect this, NRQM and RQFT violate it.
I have also occasionally heard the requirements that the fields satisfy diff eqs of finite order (which QCD may violate) or that there be only a finite number of fields (which string theory violates) called locality. It is not clear to me how this notion of locality is related to the above notion.

So these are the things that float around in my head when i talk about locality or local realism. I have to admit that I am not really what you're talking about with "completeness". A property of the system corresponds to a property of the model? what does that mean? what does that have to do with EPR? -Lethe | Talk 12:33, Nov 9, 2004 (UTC)

I agree with everything you said about 1) - 4). This is just what every physicist believes. However, 5) I'm not sure about.

In regard to EPR: It was never really clear whether the EPR paper was intended as a reflexion on realism, on completeness, or on both. Lots of confusion was added by people who commented on the paper afterwards. However, I think if you actually look at what EPR wrote, they wanted to say that Quantum mechanics was not a complete theory; e.g., there were functions of the state of the system S, which were not accounted for by Quantum mechanics or at least could not be accounted for in a way which preserved local realism. An example of such a function would be the predicted spin of Bob's photon in the EPR - Bohm experiment.

I don;t think a theory being incomplete is in of itself a bad thing. The comments in the 1982 Preface Karl Popper's Quantum Theory and the Schism in Physics may be relevant here: (Routledge 1995). But in fact I have a somewhat more radical view which is similar to Omnes view. The whole idea that Bob can actualy predict anything is wrong!. I'll return to this later, using the machinery of density states and quantum operations. This is by the way, one of the main tools of Peres in his approach to Quantum Mechanics. That's why I brought up his book. CSTAR 15:17, 9 Nov 2004 (UTC)

Quantum operations and EPR

I am advocating what is sometimes called the "ignorance interpretation of mixed states". This means that mixtures with the same density states are indistinguishable. (see for instance D. Terno (http://arxiv.org/ps/quant-ph/9912002)).

Suppose Alice and Bob are presented with a system

<math> H = H_A \otimes H_B <math>

by an independent observer. The state of the composite system is given by a density operator on H (I'll assume everything is finite dimensional to avoid convergence issues in this discussion). The density operator σ is a sum of separable density states:

<math> \sigma = \sum_i T_i \otimes S_i <math>

A is allowed to perform operations on the system (i.e. make measurements) which are given by a quantum operation on the system state of the following kind

<math> P(\sigma) = \sum_k (V_k \otimes I_B)^* \ \sigma \ V_k \otimes I_B <math>

where

<math> \sum_k V_k^* V_k = I_{H_A \otimes H_B} <math>

B observes the state σ at some point. Let us assume for purposes of argument a non-relativistic situation, if B looks at the state after A performs her measurement, he will see the relative state given by the partial trace:

<math> \operatorname{tr}_{H_B}(P(\sigma)) = \operatorname{tr}_{H_B} \left(\sum_k (V_k \otimes I_B)^* \sigma V_k \otimes I_{H_B} )\right) <math>

<math> = \operatorname{tr}_{H_B} \left(\sum_k \sum_i V_k T_i V_k^* \otimes S_i \right)<math>

<math> = \sum_k \sum_i \operatorname{tr}(V_k T_i V_k^*) S_i <math>

<math> = \sum_i \sum_k \operatorname{tr}(V_k T_i V_k^*) S_i <math>

<math> = \sum_i \sum_k \operatorname{tr}(T_i V_k V_k^*) S_i <math>

<math> = \sum_i \operatorname{tr}(T_i (\sum_k V_k V_k^*)) S_i <math>

<math> = \sum_i \operatorname{tr}(T_i) S_i <math>

<math> = \operatorname{tr}_{H_B}(\sigma) <math>

In the above sequence

<math> \operatorname{tr}_{H_B} = \mbox{relative trace mapping} <math>

That is statistically, B can't tell the difference whether A did anything! Now I'm willing to admit there are a lot of things suspicious in the above argument. But anyway, it does say that the naive interpretations of incompleteness of QM suggested by some commentaries on EPR may themselves missing the point.CSTAR 17:20, 9 Nov 2004 (UTC)

I don't think what EPR may have intended back in 1935 is as important as what is happening today, with so many people quoting the supposed fact that local realism has been refuted. What matters to me is that real "photons" (quite apart from what any model of them may say) cannot influence each other instantaneously at a distance, and if a valid Bell test really had been infringed this would mean something impossible had happened. The whole modern attitude in which this is so calmly accepted seems wrong to me!

The belief that entanglement really happens has led to other curious attempts at explanations of phenomena such as "Mandel dips". Arguments are put forward in terms of two photons being "indistinguishable", when a perfectly straightforward explanation in terms of ordinary interference would be available if only it were not for other quantum-mechanical beliefs. The "ordinary interference" is not quite ordinary, of course, since it depends on features of beamsplitters, detectors and filters that have not reached the text books. Why is this so, you may ask? In my view it is because it is inconvenient to deal with these things within the quantum formalism. Genuine scientific explanation has been sacrificed in the cause of elegant mathematics.

I am not alone in thinking this way -- or, at least, I had company until E T Jaynes' death. See for example http://bayes.wustl.edu/etj/articles/scattering.by.free.pdf. Caroline Thompson 17:40, 9 Nov 2004 (UTC)

Quantum key exchange

I'm surprised C. T. didn't pick up on an obvious "incompleteness" of the statistical interpretation of EPR-Bohm given in the previous section. Namely, that it would seem that a minor modification of this scheme (involving three individuals: A-Alice, B-Bob and E-Eve the eavesdropper) could also prove that there is no protocol which would with high probability indicate whether an eavesdropper was present. This would directly contradict the schemes now being proposed (even comercially developed) for quantum key exchange. Unfortunately, I haven't thought about this enough to give an adequate answer, although I do (now at least) believe in quantum key exchange or at least "key size amplification". CSTAR 18:37, 9 Nov 2004 (UTC)

Reframing the article

The EPR paradox refers to some aspects of a thought experiment published in a 1935 paper by Einstein, Podolsky, and Rosen. The paper was meant to draw attention to how quantum mechanics might be less satisfactory than classical physics, or even incomplete, in the way it accounts for some elements of physical reality. The aspects highlighted by EPR have often been described by people commenting on EPR as paradoxical or counter-intuitive, but most physicists today consider them puzzling only insofar as we regard them from the viewpoint of purely classical physics.CSTAR 23:52, 9 Nov 2004 (UTC)

The discussion of EPR given here follows a later version due to Bohm: A pair of electrons of opposite spin is sent from a source to a pair of destinations A-Alice and B-Bob. Alice measures spin along the x-axis and obtains one of two possible outcomes: spin up or spin down. For purposes of argument, say Alice measures spin up. By the fact the particles have opposite spin, when Bob subsequently measures spin along the x-axis, Bob will obtain spin down, the exact opposite value Alice obtained.

So far this involves nothing unusual. However, notice that we can predict the value that Bob will obtain in his measurement. Based on this observation, EPR argue this value is an element of reality. As Roland Omnes points out, this is a truly remarkable statement, since EPR are attempting to define what constitutes at least part of reality! Moreover, EPR argue: a theory that is complete should be able to account for this value, for instance as the value of a function defined on some state space. A somewhat fanciful way of phrasing this is as follows: if a physical system has committed itself to producing a certain value upon measurement, then that value is an element of reality and should be accounted for by a complete theory.

However, if one tries to do this for the EPR-Bohm experiment, with Quantum Mechanics we appear run into a problem: If Bob measures the spin (in any direction) before Alice does, Bob will obtain with equal likelihood the measurement spin up or spin down. Using the commmitment metaphor, "the electron spin is not committed" to a particular value. Prior to Alice's measurement, there is no possible "realism obeying" account of his measurement. On the other hand, that "realism obeying" non-commitment must instantly change to a committed value once Alice carries out her measurement. By what was said in the previous paragraph, that value is now an element of reality. However, this instantaneous commitment of the value violates seemingly another principle, that of locality.CSTAR 05:34, 10 Nov 2004 (UTC)

The above seems an improvement on the present page. The next thing the page needs, I think, is to remove the "Color metaphor" section. Colour does not have the right geometrical properties as a model for a Bohm-type EPR experiment. We need something that rotates. The best model I know of that fits the bill is my own Chaotic Ball one (http://arXiv.org/abs/quant-ph/9611037). I ought to produce a short wikipedia page on it. Perhaps the EPR Paradox page could include the basic diagram and a few words then a link to the main page. Caroline Thompson 10:59, 10 Nov 2004 (UTC)

Please stop pimping that paper. Quite apart from Wikipedia's "no original research" policy, it's incredibly tactless. I don't see any mention of your "chaotic ball" in the standard references on the EPR paradox, and, whatever its merits may be, attempting to promote it through Wikipedia is extremely inappropriate. Also, to forestall a predictable objection, just because it got published in a peer-reviewed journal doesn't mean it deserves an encyclopaedia article. This would be true even if Foundations of Physics Letters were an A-list journal, which it is not. -- CYD

I'm sorry, but just about all who have taken the trouble to read it -- including many experts in the field -- have agreed that it is the best model around. The main reason that journals such as Physical Review A have refused to publish it is that they consider that its message is already well known. Incidentally, one prominent figure has recently referred to it publicly, namely Abner Shimony. See his encyclopaedia article (http://plato.stanford.edu/entries/bell-theorem/). Caroline Thompson 08:48, 11 Nov 2004 (UTC)

I'm sorry, but you simply shouldn't be adding your own work to the wikipedia. There's no way you can have an unbiased view about it, and that's just not what wikipedia is for. I don't care how relevant the model is, if it's your own work, you cannot add it. -Lethe | Talk

Modern perspectives?

The section with that name sounds really fishy. The book is not closed? On what exactly is the book not closed? Of course the book in science is never closed. The scientific method should always allow criticism and reexamination, but who are we kidding? If somebody wants to do this research as a hobby that's fine. But certainly we shouldn't pretend that finding these loopholes is mainstream physics and even more irresponsibly suggest to some kid reading this article and wanting to do science that this is a great area for future research.CSTAR 03:50, 11 Nov 2004 (UTC)

The Modern perspectives section makes the claim that

Today, most physicists believe ... that the principle of locality does not hold. Therefore, the EPR paradox would only be a paradox because our physical intuition does not correspond to physical reality. However, the book is not closed yet on this issue.

Oh Really? The purpose of the argument I gave abive in this page (in the section quantum operations and locality) was to show that in fact, locality is preserved at least statistically. Moreover, I would argue that for quantum states, the statistical interpretation (formalized by density matrices) is the only operationally meaningful one.CSTAR 04:29, 11 Nov 2004 (UTC)

Unintuitive etc

Could we please remove unqualified references to counterintuitive, unintuitive etc? I think this perpetuates the idea that quantum mechanics is unnatural or unsatisfactory. It's unintuitive within some mental framework, but so is everything else.CSTAR 16:16, 11 Nov 2004 (UTC)

But then we'd have no incentive to continue to search for a better theory! Perhaps you think that all is perfect as it is? Many do not, though, and where have you seen any article that referred to entanglement that has not referred to it as counterintuitive, weird or the like? It is common knowledge that we are talking about a counterintuitive phenomenon, and, for once, "common knowledge" is right. Caroline Thompson 16:40, 11 Nov 2004 (UTC)

CSTAR is right. It's only counterintuitive based on certain kinds of intuition. The goal of this wikipedia article is not to incite people to search for a better theory, especially not by misrepresenting quantum mechanics. -Lethe | Talk

Response to C. T.. Notice that I didn't say get rid of uses of uninintuitive, I specifically said unqualified references. It's fine if you say something is unintuitive if you say what particular expectation is dashed. Your remark

we'd have no incentive to continue to search for a better theory!

is a non-sequitur. You don't have to swallow Thomas Kuhn's thesis in its entirety to agree that new theories are created because experimental results no longer fit existing paradigms. It has nothing to do with the lack of intuition or weirdness of the existing paradigms. In fact, it's usually quite the opposite that occurs. That is, the new paradigms seem weird at first, until intuitions sharpen and evolve and accept them as normal.CSTAR 22:33, 11 Nov 2004 (UTC)

It's the EPR paradox we're talking about here, and surely the motivation behind the 1935 paper was that they found QM counterintuitive? I don't see the need to qualify it. But then, of course, I'm a realist! Have it your own way on this page, just so long as you don't eliminate all references to loopholes! Caroline Thompson 22:48, 11 Nov 2004 (UTC)

Showing property 1) in Mathematical formulation section

There are two possible ways of showing 1), that is, the fact that Bob's value is not determined until Alice performs a measurement on spin.

The probabilistic one I gave,
What in fact seemed to by CYD's intent, that Alice could non-deterministically decide to measure spin along any axis.

Are they equally valid ways to establish 1), or a there some subtle differences which I haven't thought about? Are they equally clear?

In the first case, the value is probabilistic. In the second case it is definitely non-deterministic since it depends on Alice's choice at the ballot box of coordinate axes. However, though our models of physical processes can assign probabilities to physical events in consistent ways, our models of psychological processes -- such as those that might be going on in Alice's head as she chooses between coordinate axes -- cannot assign probabilities with as much assurance. CSTAR 22:58, 11 Nov 2004 (UTC)

Actually, it is not necessary to show that Bob's value is not determined until Alice's measurement. The only important thing is that it is determined after the measurement. Therefore, it is an "element of reality" by the EPR definition. Because Alice can choose to measure spin along any axis, then if the principle of local reality holds, then the spin components along every possible direction should be elements of reality too. This conflicts with the completeness of quantum mechanics, because the components along the other directions are not determined. This is the line of argument used in the original EPR paper. -- CYD

OK, but then you need to put that explanation in.CSTAR 03:02, 12 Nov 2004 (UTC)

Done. By the way, your argument that it might not be possible for Alice to generate classical non-deterministic results is, of course, the entire idea of the Everett many-worlds interpretation. -- CYD

Modern perspectives again

We're still left with the "modern perspectives" section. I'm in favor of chucking it entirely, but note this would delete the references to loopholes.CSTAR 04:50, 12 Nov 2004 (UTC)

Wholesale deletion is probably not the way to go. As a first step to debogification, I have reshuffled these parts into a "resolution of the paradox" section. Some of the subsections still need correction or elaboration. -- CYD

Other comments

Should something more be said about causality, or a link to a page on causality? By causality I mean something about information flow.
Should the attention banner be removed?

Heisenberg uncertainty relations and non-commutativity

Isn't it a lot easier to argue that a pair of self-adjoint 2 × 2 matrices S_x, S_z which have one common (non-zero) eigenvector actually are simultaneously diagonalizable and therefore commute?

Proof: if e is a common eignvector for S_x, S_z then the orthogonal complement of e (a 1-dimensional space by the 2 × 2 assumption) is also invariant and hence is an eigenspace. QED CSTAR 02:08, 14 Nov 2004 (UTC)

The Heisenberg relation argument has the virtue of being true for all non-commuting observables. -- CYD

The interest of the more general fact, is (I suppose), that the original EPR paper used P, Q instead of S_x, and S_y together with the fact that

commutator of P, Q = self-adjoint unitary × some scalar

then the same argument applies. This certainly prevents feelings of guilt for not having put it in, but does this help the non-cognoscenti reader if something isn't explicitly pointed out?CSTAR 03:45, 15 Nov 2004 (UTC)

I've changed the article to speak of x and z spin being "incompatible observables" rather than "non-commuting". The concepts are not identical. Commuting implies compatible, but it is not true that non-commuting implies incompatible yet people always make this fallacious argument. (Think of the situation where the commutator while never being zero can nevertheless be made arbitrarily small.) Kuratowski's Ghost 14:14, 24 Dec 2004 (UTC)

Definition of incompatibe?

What exactly is your definition of incompatible? If you mean the spectral projections of A, B don't commute (or contrapositively A, B compatible iff all spectral projections of A, B commute) then

Theorem, A, B are compatible iff A, B commute.

Proof. Reformulation of spectral theorem.

If by incompatible you mean the Heisenberg uncertainty relation holds for some pure states? Again A, B incompatibe iff A, B don't commute. Apply mathematical formualtion of the Heisenberg uncertainty relations and spectral theorem.

If by incompatible you mean Heisenberg uncertainty relation holds for all pure states then incompatible means commutator is either strictly positive or strictly negative (and some other more technical domain assumptions).

CSTAR 15:01, 24 Dec 2004 (UTC)

The way I was always taught it, compatible means that the product of the uncertainties can be made arbitrarily small. This occurs when A and B commute (in which case the Heisenberg relation imposes no constraint it just says ≥ 0) but also occurs when there is a constraint but where we can still always find a state making the product of the uncertainties less than any chosen amount. What I remember is that to be incompatible, A and B have to be non-commuting, unbounded and not have point spectrum eigenstates in each others domain. Kuratowski's Ghost 17:07, 24 Dec 2004 (UTC)

OK then your definition of incompatible I guess means the commutator i [A, B] has 0 in its spectrum. (which could be an isolated spectral value of finite or infinite multiplicity or an element of the essential spectrum). I don't object to your using this term; I was just curious as to what you meant.

Thanks. CSTAR 17:22, 24 Dec 2004 (UTC)

Please don't you edit past remarks in a way that makes subsequent responses strange or incomprehensible. My response above was to your previous comment before you edited it. Again, in many cases there's nothing objectionable about changing the past — if you can get away with it. It does become objectionable, however, if it makes the present meaningless.CSTAR 17:50, 24 Dec 2004 (UTC)

Sorry never intentionally did it, I hit submit, then realized I wanted to say more and hit Back, then got a conflict when I submitted again because you had replied in the time I was editing and ended up just merging before even reading what you had said. Kuratowski's Ghost 23:07, 24 Dec 2004 (UTC)

The no-communication theorem

The result stated and shown above concerning no information transfer between Bob and Alice (formulated using quantum operations) is essentially the No-communication Theorem as formulated in the Peres and Terno paper referenced below. I don't know whose result this is originally, although the authors Peres and Terno credit Florig and Summers (I haven't seen their 1997 paper).

BTW I think the proof presented above is a little more detailed mathematically than the one in Peres Terno.

Maybe we should start an article on the no-communication theorem as a relevant support for information theoretic aspects of causality. CSTAR 21:31, 18 Nov 2004 (UTC)

Some references

D. Bruss, Characterizng Entanglement, arXiv:quant-ph0110078 v1 12 Oct 2001 (The relevance of protocols)

D. Deutsch, The Structure of the Multiverse, April 2001 (I don't remember where I got this from).

M. Florig and S. J. Summers, J. Math Phys 38, 1997.

A. Peres and D. R. Terno, Quantum Information and relativity Theory, arXiv:quant-ph/0212023, v1 4 Dec 2002

CSTAR 16:22, 6 Nov 2004 (UTC)

EPI

In the section on resolving the paradox I'd like to see some comments on how realist theories based on loopholes relate to EPI and Fisher information. Anyone? Kuratowski's Ghost 16:04, 6 Apr 2005 (UTC)

Recent changes

Though some appear to be minor wordsmithing changes, some of these seem to be very strange and highly idiosyncratic. In particular, the use of the expression quantum mechanic theory is very unusual. These should be reverted to CYD's last version. --CSTAR 20:23, 21 Apr 2005 (UTC)

EPR paradox hidden variables if polarisation is interpreted in an other way

I have a Question. Couldn't the entanglement of particles be interpreted if the theory of polarized light would be reinterpreted as shown here:

If the theory of polarised light is reinterpreted on the following shown way, then this would allow to create particles that seem to be entangled but in reality arent:

       1. Assumed light can be polarised in any angle from 0 to 180°. 
          (Exactly 0 to 360°, but from 181 to 360° it can be interpreted 
          as the same as 0 to 180°)

       2. Every particle emiteded has a pre-defined polarisation randomly 
          chosen from between 0 and 180°.

       3. Once a particle hits a polarisation filter then the particle 
          passes if and only if: 
               (a) The particle passes the polarisation filter with a 
                   angle +/- 45° of the defined angle of the polarisation 
                   filter.

       4. Once a particle has passed a Pol.-Filter the angle of the 
          particle is rearranged randomly in a angle +/- 45° of the angle 
          of the polarisation filter.

       5. The exact angle of a particle can=3Ft be determined.

So if two entangled particles are generated then just two particles with a random angle are generated, but the angle of particle a exactly + 90° of the angle of particle b.

This type of discussion really doesn't belong here. This area is for discussion of the article presentation itself - not the science of the article. I would recommend that you take your questions to www.PhysicsForums.com and its Quantum section so you can get a better understanding of the issues involved.-DrChinese 20:34, 26 May 2005 (UTC)

I am not, it appears, an acceptable contributor to Physics Forums (my membership has now twice been arbitrarily terminated) so I'll answer here, and the answer is simply "No". This is on two counts:

There is simply no evidence that this is what light does. For a macroscopic beam it behaves as a wave and, roughly speaking, obeys Malus' law, the energy being reduced in proportion to the square of the cosine of the relevant angle. For a "single photon" beam (if such exists!) the picture is not so clear, but I have never seen any theory to back the suggestion that photons behave quite as randomly as suggested.
If the behaviour were random on each side, what would cause the two detected photons to be at 90 deg? Whatever the theory there would be no correlation between the two sides so no version of Bell inequality would be violated.

Caroline Thompson 08:32, 27 May 2005 (UTC)

physicist?

I thought that one of EPR was not a physicist, but a logician, who helped Einstein with the reasoning, but didn't know much about physics. Am I mistaken? --MarSch 14:21, 13 Jun 2005 (UTC)

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