Talk:EPR paradox/archive 1
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I think the whole argument now rests on the shape of the rotation operator. Why is the rotation operator an exponential of a Pauli matrix? --AxelBoldt
- That comes out of the relationship between rotation and quantum angular momentum, and Pauli's theory for spin 1/2. We need articles on these, but I'm not yet sure what the article titles ought to be. I'll definitely get round to this. -- CYD
I don't understand
- In reality, one can only measure the particles once without collapsing the wave function, and yet Bell's inequality involves talking about alternative measurements that cannot performed and assuming that these would result in well defined outcomes.
I think Bell's inequality only talks about measurements that can be performed, and have been performed, and obviously resulted in well-defined outcomes. What is meant with "alternative measurements that cannot be performed"? AxelBoldt, Sunday, June 9, 2002
- I would like to know the answer to that as well! Roadrunner, was it you who added that? Could you explain more clearly what the paragraph means? -- CYD
(BTW: I think the bra-ket notation was confusing the heck out of Wiki - this whole page was in italics. I inserted a space between "<" and "b", and that seemed to fix it - something to keep in mind...)
I think this a great article, that suffers from the problem of many technical articles at Wikipedia - it assumes that the reader already knows a lot about the topic.
For example, nowhere do I see a lucid example of a paradox here. If the title is "EPR Paradox", shouldn't we see a paradox somewhere? What was the formulation of EPR that made any body think there was a problem to start with?
I know, I know - why complain when you can boldly edit... :) Chas zzz brown 21:57 Oct 20, 2002 (UTC)
- The introductory paragraphs tries to explain why the "EPR paradox" leads to fishy results. Yes, it is somewhat hand-wavy, but I think Einstein's objections to quantum mechanics were rather hand-wavy in the first place. It's a "paradox" in the sense that quantum mechanics and the principle of locality cannot both be true.
- I clarified the introductory paragraphs. Does this help? -- CYD
- I like it better. I think what is needed now is an article on the principle of locality; which would describe why (among other things) calling Federation Headquarters via subspace communications is a bit problematic ;). Thanks for the effort. Chas zzz brown 19:37 Nov 4, 2002 (UTC)
What menas EPR ? Can this acronym be explained ?
As for explaining the meaning of the acronym:
- The acronym EPR is constructed from the last-name initials of Albert Einstein, Boris Podolsky, and Nathan Rosen who (in that order) appear as authors of the article
- Can quantum mechanical description of reality be considered complete?
- Physical Review 47, 777 (1935).
- Best regards, Frank W ~@) R, Jan. 5, 14:31 PST.
The following section of text (including viable links) has been found removed in its entirety by a Wikipedian from the article to be Talked about:
>>>Begin Section:
However, Alice and Bob may not have actually performed the experiment exactly as described above. Given
- their result values over a sufficient sequence of trials,
- their use of Etienne-Louis Malus's celebrated definition of how to obtain values of angle of two directions to each other from certain sets of observational results, and consequently
- their explicit determination that the three angles, pairwise between the three directions, a, b, and c, had all been equal, with value θ/2 = π/8,
they may choose to deny that the three directions, a, b, and c, had lain on one and the same plane in the trials from which Alice and Bob obtained their result values, and they may choose to let Bell's inequality become
- 1/2 sin2 θ ≤ 1/2 sin2 θ + 1/2 sin2 θ, i.e.
- 0 ≤ 1/2 sin2 θ.
This inequality holds true for all real number values of θ/2 which can be obtained; therefore in particular also for the three equal values which Alice and Bob obtained in their sequence of trials.
Consequently, the assertion that Alice and Bob actually performed the experiment exactly as described above using three directions that are separated by angles of π/8 does not necessarily have the Truth-value true. (In default of an exact description how to measure planeness of three directions to each other to begin with, the indicated assertion need not even necessarily have the Truth-value false either, but it may not constitute any logical proposition at all.)
Accordingly, the following instance of Non sequitur can be expressed and considered:
>>>End Section.
This referenced section was complementary to the text which followed:
- Therefore, if Alice and Bob actually perform the experiment exactly as described above [...]
and served as an introduction to the alternative point of view expressed in the presently remaining text of the article.
I'm going to reinsert the section in question in order to reinitiate a NPOV representation of both; editing somewhat in order to indicate the direction in which a NPOV may be approached.
Please edit boldly to represent the points of view expressed therein, even and especially if they may appear irreconcilable; but do not remove facts (incl. facts about opinions) from an encyclopedia.
Regards, Frank W ~@) R 22:57 Jan 13, 2003 (UTC).
Frank -
First: Add your talk at the end of the page, instead of the top - this makes it easier for all of us to follow the thread of an argument.
Second: I removed the above paragraph, since it obscures rather than illuminates the issues regarding the EPR experiment. The exact choice of angle is not critical here; it is sufficient for the argument to show that measurements arbitraily close to the given angle gives results which refute the "hidden variable" approach. There is no need to appeal to multivalued truth systems, or other side topics, for this point to be made. Cheers - Chas zzz brown 23:47 Jan 13, 2003 (UTC)
As for: Add your talk at the end of the page, instead of the top - this makes it easier for all of us to follow the thread of an argument.
- Thanks for expressing Your preference, which I'll adopt in this instance; otherwise I consider adding to Talk pages near the top, since this makes it easier for (some of) Us to edit a reply while reading the section of the page to which one replies.
As for: the above paragraph [...] obscures rather than illuminates the issues regarding the EPR experiment.
- I appreciate that You're referencing some of the issues to be illuminated here explicitly. I'd prefer they were expressed more explicitly in the article to be Talked about itself, to admit a more direct response.
As for: [...] The exact choice of angle is not critical here
- As far as the present article expresses this view exclusively, I'd like Us to observe and represent a preference to the contrary as well, namely: that the exact choice of how to measure values of angle is critical here, too.
As for: [...] it is sufficient for the argument to show that measurements arbitrarily close to the given angle [give] results which refute the "hidden variable" approach.
- Agreed. Therefore:
- it seems worth mentioning that with a choice of measurement procedure which obtains the values of the three angles under consideration as all equal, namely as θ, θ, and θ, these angle values are not arbitrarily close to the values θ, θ, and 2 θ which the article presently seems to presume "given". (That's unless
2 θ =arbitrarily_close_to= θ =arbitrarily_close_to= 0, of course, which however does not apply to the present example value of θ = π/8.)
As for: There is no need to appeal to multivalued truth systems
- Agreed. (Even the need to identify presumptions of "choices" or "gifts" of values in absence of measurements as not even wrong may be satisfied elsewhere.)
As for: or other side topics, for this point to be made.
- Surely this article ought not to make the point of demonstrating how to obtain results which refute the "hidden variable" approach to the exclusion of demonstrations of how to obtain results which don't refute the "hidden variable" approach. The paragraph in question attempted to respresent the latter, in terms of the existing example, and complementing the view presently represented exclusively. Taking the views and issues We expressed here into account, I'll modify and insert a statement about the point not yet represented for further discussion and modification.
- Best regards, Frank W ~@) R 04:32 Jan 14, 2003 (UTC).
- orientation angle of A{↑↓} and B{↑↓} to each other, over a set K of trials { k }, is to be determined as
- 1/2 arccos(
- Sum_{ k = first, second, ..., last }_( nk(A↑,B↑) + nk(A↓,B↓) - nk(A↑,B↓) - nk(A↓,B↑) ) /
- Sum_{ k = first, second, ..., last }_( nk(A↑,B↑) + nk(A↓,B↓) + nk(A↑,B↓) + nk(A↓,B↑) ) ),
- where the nk() are counts in any one trial, numbers equal to 0 or 1, i.e.
- cos2K( orientation angle( A{↑↓}, B{↑↓} ) ) = NK(A↑,B↑) + NK(A↓,B↓)
- where the NK() ≥ 0 are relative frequencies over the set of trials K,
- and if the example in the present article prescribes to consider three sets of trials,
- J = { j }, K = { k }, and M = { m }, resulting in the three determinations of values α, β, and γ for the orientation angles of A{↑↓} and B{↑↓} to each other, respectively over any one of these three sets of trials , such that
- α = β, and
- α + β = γ = 2 α, i.e.
- NJ( A↑, B↑ ) + NJ( A↓, B↓ ) = NK( A↑, B↑ ) + NK( A↓, B↓ ), and
- (cos( γ ))2 = (2 cos2( α ) - 1)2,
- NM(A↑,B↑) + NM(A↓,B↓) = (2 NJ(A↑,B↑) + 2 NJ(A↓,B↓) - 1)2
- then a Wigner - d'Espagnat inequality as in the article example, i.e. here specificly the presumption that
- (NM(A↑,B↑) + NM(A↓,B↓)) ≤
- (NJ(A↑,B↑) + NJ(A↓,B↓)) + (NK(A↑,B↑) + NK(A↓,B↓)) =
- 2 NJ(A↑,B↑) + 2 NJ(A↓,B↓),
- (NM(A↑,B↑) + NM(A↓,B↓)) ≤
- cannot be expected to hold in general at all, but is satisfied only if
- (2 NJ(A↑,B↑) + 2 NJ(A↓,B↓) - 1)2 ≤ 2 NJ(A↑,B↑) + 2 NJ(A↓,B↓), i.e. only if
- NJ(A↑,B↑) + NJ(A↓,B↓) ≥ (3 - √ 5) / 4.
- Frank W ~@) R 18:47 Jan 14, 2003 (UTC).
I removed it again. Frank, can you point to a reference (not written by you) where the above criticisms have been expressed in a coherent manner? If this is your original research, then it doesn't belong into Wikipedia. If not, then it needs to be explained better. AxelBoldt 19:10 Jan 14, 2003 (UTC)
I second Axel's complaints. Furthermore, the Fwappler-added sentence
- Alice and Bob would consequently find that the three angles, pairwise between the three directions, a, b, and c, had all been equal.
is certainly wrong. The three pairwise angles are not equal, since c bisects a and b. Two of the pairwise angles are equal, whereas the third should be twice as large.
In any case, a description of what an angle is and how to measure it does not belong in an article on the EPR paradox. It detracts from the article's focus, which is explaining what the EPR paradox is. -- CYD
As for: Two of the pairwise angles are equal, whereas the third should be twice as large.
- This is an unambiguous requirement only as far as it is specified how to determined the values of "angle" which are to be compared; and otherwise not.
- But of course your point is undeniable: If one does specify how values of "angle" ought to be measured (as I did in considering Malus's definition), then one cannot ignore the experimental prescription given in terms of these values. I tried to illustrate this with the p.s. above.
As for: a description of what an angle is and how to measure it does not belong in an article on the EPR paradox. It detracts from the article's focus, which is explaining what the EPR paradox is.
- Considering how to measure angle values, and the implications for whether the thereby obtained result values can satisfiy certain inequalities is at least a response to the situation which the present article expresses (albeit a curiously unpopular response). Or rather: it is a consideration which (experimental) physicists usually review before having such situations arise and (popularly) treated afterwards.
Regards, Frank W ~@) R 05:29 Jan 16, 2003 (UTC).
As for: I removed it again.
- Thank You for leaving a record of that action to which We can respond.
As for: Frank, can you point to a reference (not written by you) where the above criticisms have been expressed in a coherent manner?
- No -- can You please? As far as popular responses have been given to claims about violation of Bell's inequality, they appear only incoherent and therefore amount at best only to indirect criticisms to begin with; and as far as I know of coherent criticisms of claims about violation of Bell's inequality, I appear to be their author.
As for: If this is your original research,
- ... much of the instructive content of an encyclopedia appears to be the product of someone's original research ...
As for: then it doesn't belong into Wikipedia.
- Since this preference doesn't seem to have been expressed anywhere else in Wikipedia, let me emphasize the NPOV which seems to suggest that topical and factual research and knowledge ought to be represented; together, if applicable, with factual statements about corresponding opinions, say one having been characterized as original research, and the other as having invited criticism and further research.
- Note that the NPOV thereby aids Wikipedia as a durable reprository of growing knowledge.
As for: If not, then it needs to be explained better.
- Quite conceivably so. In order to allow some time, and to provide more references, for pointing out what can be, or ought to be, explained better, please let me start preparing an article about CHSH; perhaps addressing the Wigner - d'Espagnat inequality as well.
Best regards, Frank W ~@) R 20:32 Jan 14, 2003 (UTC).
I don't know why you insist on using such a convoluted language. Anyway, Wikipedia is an encyclopedia and as such reports on accepted human knowledge. Once your above ideas have been published by you or by someone else, we will certainly report about them. It is not the purpose of Wikipedia to serve as a publication vehicle for original research; no encyclopedia does that. Number 9 of Wikipedia:What Wikipedia is not probably comes closest. AxelBoldt 21:37 Jan 14, 2003 (UTC)
As for: Wikipedia is an encyclopedia and as such reports on accepted human knowledge. Once your above ideas have been published [...]
- Like any other language, mathematics (especially as basic as high-school algebra) is an essential element of the canon of knowledge even without or prior to dedicated publication. Encyclopedists who don't have confidence in their command of some particular forms of language, or in some particular fields of discourse, may surely request them to be made better accessable by encyclopedists who do.
As for: It is not the purpose of Wikipedia to serve as a publication vehicle for original research; no encyclopedia does that. Number 9 of Wikipedia:What Wikipedia is not probably comes closest.
- Since Wikipedia:Copyrights is concerned with original text submitted to Wikipedia, the submission of original text to Wikipedia is apparently admissible (under the stated copyright regulations).
- Also, per Wikipedia:1911_Encyclopaedia_Britannica, contributors are encouraged to restructure and rewrite material which appears old, outdated, and problematic in a modern encyclopedia.
As for: I don't know why you insist on using such a convoluted language.
- Where applicable, I appreciate advice on how to express myself even more effectively than I try and manage to do already.
Thanks, Frank W ~@) R 05:29 Jan 16, 2003 (UTC).
Roadrunner, I'm not sure that moving the bulk of the article to Bell inequality is correct. Bell's inequality and the EPR paradox are really quite closely related topics, so I'm not sure it makes sense to split the discussion into two pieces. Note that there is a lot of duplicated material, primarily due to the need to re-establish context in Bell inequality.
I would prefer redirecting Bell inequality to EPR paradox, and introducing both the EPR paradox and Bell's inequality in the topic paragraph. What do you think? -- CYD
Fine with me..... I don't like the current division myself.
User:Roadrunner _______________