Talk:Quantum entanglement

Standard error of sign regarding information and entropy.

Short before the sentences:

″The reversibility of a process is associated with the resulting entropy change, i.e., a process is reversible if, and only if, it leaves the entropy of the system invariant. Therefore, the march of the arrow of time towards thermodynamic equilibrium is simply the growing spread of quantum entanglement.[83] This provides a connection between quantum information theory and thermodynamics.″

... all entropy formulas, whether Shannon's or 'von Neumann' tell about possibilities and/or bandwidth. Real data transferred via classic or quantum methods show always the reverse sign, because a single of the many possibilities has been chosen for transfer. In the same way growing quantum entanglement does not increase but reduces entropy. For sure the internal order by entanglement is even the reverse of disorder maximization by thermodynamic equilibrium. If [83] is indirectly cited, it tells simply non-sense. Please drop the sentences above and the reference from the article. Many thanks!

Proposal to replace the History section

I propose to replace the History section with the content of User:Johnjbarton/sandbox/quantum_entanglement_concept#History. The significant changes are

1. FROM

• Their concept had two systems interact, then separate, and they showed that afterwards quantum mechanics cannot describe the two systems individually.

TO

• Their concept had two systems interact, then separate, and they showed that quantum mechanics predicts the measurements on those systems are related but provides no mechanism for the relation.<ref name="MerminMoon-1985"/>{{rp|38}}

BECAUSE: The end of the existing sentence is ambiguous; the new sentence is extracted from Mermin ref and relates to EPR incompleteness.

2. DROPPED FROM

• Like Einstein, Schrödinger was dissatisfied with the concept of entanglement, because it seemed to violate the speed limit on the transmission of information implicit in the theory of relativity.

TO

• Like Einstein, Schrödinger was dissatisfied with status of quantum mechanics, reasoning that "we do not have a quantum mechanics that takes into account relativity theory".

BECAUSE: Schrödinger says "caught the dogmatic quantum mechanics by the collar" and "we do not have a quantum mechanics that takes into account relativity theory, that is among other things, that respects the finite speed of propagation of all effects". The speed limit is just one issue and both men are taking aim at QM because of the prediction of entanglement rather than at entanglement itself.

3. DONE FROM

• Einstein later referred to this as "spukhafte Fernwirkung" or "spooky action at a distance".

TO

• Einstein described the effects of entanglement as "spukhafte Fernwirkung" or "spooky action at a distance", meaning the acquisition of a value of a property at one location resulting from a measurement at a distant location.

BECAUSE: "this" is ambiguous. In the current article "this" seems to refer to 'limit on transmission of information', but how can it then be "action"?

4. FROM

• In 1964 John S. Bell demonstrated an upper limit, seen in Bell's inequality, regarding the strength of correlations that can be produced in any theory obeying local realism, and showed that quantum theory predicts violations of this limit for certain entangled systems.

TO

• In 1964 John S. Bell showed that quantum entanglement predicted a different kind of correlation, one not discussed in the EPR paper, and this correlation cannot be reproduced by any local hidden variable theory alternative to quantum mechanics.

BECAUSE: As noted in the Mermin ref cited, the key was Bell's focus on other correlations. The correlations in EPR were not quantitative so strength is a distraction for the purpose of history.

5. Revised A section on Kocher concerning early EPR experiments. I moved this from a different part of the article. I checked the Clauser ref and they say "The experimental arrangement was similar to that of Kocher and Commins". There are probably more refs on Kocher. Sentence in the paragraph on early experiments demonstrating entanglement, with ref to Clauser's paper where the abstract says "A proposed extension of the experiment of Kocher and Commins, on the polarization correlation of a pair of optical photons,"

ADDITION:

• In his 1967 PhD work, Carl Kocher[15][16] presented results from apparatus in which two visible light photons successively emitted from a calcium atom were shown to be correlated.

6. FROM

• a student named Artur Ekert suggested that these super-strong correlations could be used as a resource for communication

TO

• a student named Artur Ekert suggested that these entanglement correlations could be used as a resource for communication

BECAUSE: the word "super-strong" is extraneous, ambiguous, and not used in Ekert paper.

I would normally put this 6 edits in separately to so the edit summary can help track the reasoning.

References

Johnjbarton (talk) 01:30, 27 November 2024 (UTC)

@ReyHahn Is this what you had in mind? Johnjbarton (talk) 01:31, 27 November 2024 (UTC)

1. Oppose. This is a terrible attempt to explain the EPR paradox. The sentence should be just erased instead.

2. Oppose. The proposed change removes the simple, clear explanation and inserts instead an unexplained reference to relativity. The original should be retained.

3. Support. This is correct and a helpful clarification.

4. Oppose. The EPR paper doesn't discuss correlations, but rather post-measurement states. Instead of trying to explain EPR badly, the original one is a simple summary of Bell's results and should be retained.

5. Oppose. WP:UNDUE. We're not here to WP:RIGHTGREATWRONGS. For better or worse Freedman and Clauser's work is the notable one, not Kocher's. Moreover the subject here is nonlocality, mentioning Kocher requires a break in the flow to talk about entanglement only.

6. Oppose. The proposed change is not even grammatical. "Entanglement" is a noun, not an adjective. In any case, Ekert was not proposing to use any correlation produced by entangled states, but specifically one that violated a Bell inequality. We are free to paraphrase our sources, we don't have to copy-paste what they say. Tercer (talk) 11:13, 27 November 2024 (UTC)

Regarding #5, I tried to find a source for "the first case of entangled visible light" from older versions of the article. The only one I could find was written by Kocher. On the other hand Clauser et al prominently mentions Kocher's work in their short abstract so they clearly considered the work vital to theirs. I scaled down the Kocher sentence and moved it up to the paragraph where the first entanglement experiments are discussed. Johnjbarton (talk) 17:49, 27 November 2024 (UTC)

1. The proposed change makes the text longer but not more clear. I do not like the existing sentence either. "Their concept had" reads as non-idiomatic.

2. This change makes the text less specific, for no apparent reason. If Schrödinger was dissatisfied with QM because of entanglement, he was dissatisfied with entanglement.

3. I like this change. It's a good clarification.

4. I prefer the original text to the proposed modification, but I'm not entirely happy with the original either. The focus on "the strength of correlations" ignores/obscures the essential point that Bell's theorem requires considering multiple different experiments and comparing the correlations obtained in different configurations. This is what Bell himself emphasized with the Bertlmann's socks story. Perfect correlation, or perfect anti-correlation, in a single experiment is just not interesting.

5. This sounds WP:UNDUE.

6. I don't like "super-strong". Not only is it vague, but also, trying to make it more precise doesn't help. Perfect correlations in a classical theory (Bertlmann's socks) are "super-strong", aren't they? What's special about entanglement here? XOR'easter (talk) 18:50, 27 November 2024 (UTC)

I think it's natural to say that a correlation that achieves a higher probability of victory in a nonlocal game is stronger than one that achieves a lower probability of victory. But I think you have a point, the reader is more likely to understand strength in terms of perfect correlation/anti-correlation.

Nevertheless, I don't like saying that Ekert proposed using entanglement; his idea was to use nonlocality. Tercer (talk) 19:05, 27 November 2024 (UTC)

My text was based on Horodecki Rev.Mod.Physics

• The first discovery within quantum information theory, which involves entanglement, is due to Ekert (1991).

Do you have a different reference? Johnjbarton (talk) 19:16, 27 November 2024 (UTC)

I see what you mean. My feeling right now is that it's OK, since we have two sentences that go from the more general to the more specific. I'm not passionately attached to the current phrasing, though. XOR'easter (talk) 20:39, 27 November 2024 (UTC)

I changed it then. While not wrong, I think it was misleading the way it was. Tercer (talk) 08:38, 28 November 2024 (UTC)

Looks like a good change. XOR'easter (talk) 21:47, 29 November 2024 (UTC)

Thanks. Regarding #2, "If Schrödinger was dissatisfied with QM because of entanglement," is not the case as far as I can tell. That is my point. He indicts QM for not being relativistic. Maybe we need to get rid of this bit.

Regarding #4 I agree with your point of view so maybe we can come up with a better way to say it. Johnjbarton (talk) 19:08, 27 November 2024 (UTC)

But it was the tension he perceived between entanglement and relativity that he found problematic: The imagined act of combining two or more systems into a single one leads to great problems as soon as one tries to introduce the special principle of relativity into Q.M. XOR'easter (talk) 20:28, 27 November 2024 (UTC)

Ok, the bit I don't like in the current text is "...it seemed to violate the speed limit on the transmission of information..." because this does not sound like anything I've read from that era. How about

• Like Einstein, Schrödinger was dissatisfied with the concept of entanglement because it seemed to violate the theory of relativity.

or

• Like Einstein, Schrödinger was dissatisfied with the concept of entanglement because it seemed to violate the finite speed of propagation required by relativity.

Johnjbarton (talk) 23:05, 27 November 2024 (UTC)

Sorry, but I don't understand the difference in substance between the current text that you don't like and your suggestion. Could you elaborate on what exactly you find unsatisfying? XOR'easter (talk) 00:17, 28 November 2024 (UTC)

Oh, just the focus on "information". Einstein, also mentioned in the paragraph, was still talking about 'particles'; the debates about the nature of QM were in early stages and would fill books over time. I think the focus on 'information' is a modern one. I think the sentence imagines what they would say today. Johnjbarton (talk) 00:24, 28 November 2024 (UTC)

Ah, I understand now. I'm not too concerned about that; the joke about the Physical Review expanding faster than light "but this is consistent with relativity because no information is transmitted" is decades old. Mermin says he heard it from Peierls in 1961. I suspect that older sources might be more likely to talk about signals rather than information, like Kennard did in 1934 and Eddington did in 1922. But it's the same idea. XOR'easter (talk) 01:11, 28 November 2024 (UTC)

Reprise We are making some progress and I've learned some thing about the outlook of other editors. I will make one more pitch for revised versions of remaining items (numbered as above) then give up.

1. The current text has no reference and it says "...afterwards quantum mechanics cannot describe the two systems individually." To me this is puzzling: in QM if I measure an singlet state (which will be "afterwards") I get two individual answers. Thus I want to read a reference that backs the text claim or to change the text.

4. How about:

• In 1964 John S. Bell published Bell's inequality, showing that certain entangled systems have a different kind of correlation, a correlation stronger in quantum theory than any correlation predicted by a theory obeying local realism.

5. I agree that the old text was over the top, but Kocher's 1967 work was a historic advance in experimental entanglement per Clauser's abstract; the technique as also used by Aspect. How about this sentence right after the Wu/Shaknov sentence:

• In his 1967 PhD work, Carl Kocher presented results from apparatus in which two visible light photons successively emitted from a calcium atom were shown to be correlated.

6. The current text says

• Artur Ekert suggested that the violation of a Bell inequality could be used as a resource for communication.

and it cites Gilder, Louisa "The age of entanglement: when quantum physics was reborn." Pages 314-315 discusses Ekert meeting Bll but it says nothing violation of Bell inequality. The closest is :

• "If the Clauser-Horne-Shimony-Holt inequalities are violated" (meaning that Alice and Bob's photons remain entangled),

The section says 'entangled' multiple times and for the history section I think we should say "effects of entanglement" and leave the details for direct discussion of Ekert's work.

References

Johnjbarton (talk) 19:27, 28 November 2024 (UTC)

As an example of entanglement

The paragraph beginning "As an example of entanglement..." discusses decay of a subatomic particle but I have not been able to find a reference that discusses this example in this way.

On pg 32 of

• Aharonov, Y., & Rohrlich, D. (2008). Quantum paradoxes: quantum theory for the perplexed. John Wiley & Sons.

they talk about photons from pion or positronium decay and about photons from atomic cascade. Peres on 155 in his QM book uses photons from atomic cascade. Both books are using this example is roughly the same way as the article, as an intro example to discuss quantum correlations. Peres' book also has the classical example of a bomb fragmenting into two parts with angular momentum. Clauser and Aspect use atomic cascade and their short experimental descriptions are easy to read.

So unless some knows of a reference for the current content I suggest we switch to atomic radiative cascade / photon polarization for the example. Any example we pick will necessarily require some background the reader may not have. Abner Shimony's Scientific American article uses "a sheet of polarizing film" which I think is about as good as we can do.

Other suggestions? Johnjbarton (talk) 01:37, 1 December 2024 (UTC)

Incorrect content in "Non-locality and entanglement" section

The article contains these two incorrect sentences: In the literature "non-locality" is sometimes used to characterize concepts that differ from the non-existence of a local hidden variable model, e.g., whether states can be distinguished by local measurements and which can occur also for non-entangled states; see, e.g., This non-standard use of the term is not discussed here. The sentences have multiple problems.

• The Bennett paper cited here is referenced in major reviews. For example: Every LOCC operation can be written in the above form, but not vice versa, as proved by (Bennett, DiVincenzo, Fuch, et al. 1999). as well as other places. Another example: It was shown by Bennett et al. (1999) that not all such superoperators can be implemented by local transformations and classical communication (LOCC). The Bennett paper has over 1300 citations in Google Scholar. The claim that Bennett's paper uses non-locality in a way that is not standard is incorrect. The neutral way to describe nonlocality concepts that differ from Bell's concept is simply to note that they differ.
• The Bennett paper is about LOCC as the refs make clear. Our article discusses LOCC in the section "Entanglement as a resource" so the claim that "this non-standard use of the term is not discussed here" is false.
• The claims of the first sentence are not sourced but merely asserted. No literature survey is cited to support the claim that "In the literature...". The first sentence implies that there are two forms of nonlocality, but the Bennett source discusses a variety of forms. They say In this paper we report a form of nonlocality qualitatively stronger than either of these antecedents. before they even discuss nonlocality and hidden variables.

I think the simple fix is to just delete these two sentences, but @Tercer reverted my fix. As a compromise we can replace these two sentences with content that adopts a neutral point of view. For example,

• The term "non-locality" is sometimes used to characterize quantum concepts that differ from the non-existence of a local hidden variable model. See, for example, the discussion of the Local Operations and Classical Communications paradigm.

This avoids claiming that LOCC is non-standard and points its discussion rather than claiming it does not exist.

References

Johnjbarton (talk) 17:28, 11 December 2024 (UTC)

LOCC is completely standard. The article is not claiming that LOCC is non-standard. What is non-standard is using the word "nonlocality" to mean "indistinguishability under local measurements". Tercer (talk) 18:31, 11 December 2024 (UTC)

Do you agree with my proposed compromise? By using "differ" we avoid the ambiguous "standard" and we correct the error. Johnjbarton (talk) 18:42, 11 December 2024 (UTC)

No, because there is no error, and LOCC has nothing to do with it. Tercer (talk) 19:01, 11 December 2024 (UTC)

As I have demonstrated above, two reliable major reviews cite the Bennett paper as LOCC. Perhaps you have another reference makes the claim that

• the word "nonlocality" to mean "indistinguishability under local measurements"?

Johnjbarton (talk) 19:08, 11 December 2024 (UTC)

The Bennett paper does talk about LOCC. And also about indistinguishability under local measurements. No, I'm not going to waste my time finding a source about the blinding obvious. Tercer (talk) 19:25, 11 December 2024 (UTC)

If we cannot agree on a compromise, then the sentences should be deleted. You are claiming that these sentences have some kind of delicate opaque meaning associate with one part of one primary reference, a part not discussed in secondary references. In that case, the content is not notable. In addition alternative meanings of nonlocality that are not directly related to entanglement belong in quantum nonlocality, not here. Johnjbarton (talk) 19:56, 11 December 2024 (UTC)

Not how Wikipedia works. You need consensus to make a change. Tercer (talk) 20:23, 11 December 2024 (UTC)

That is also incorrect. See for example Wikipedia:Editing policy. I only need consensus to undo your revert. Johnjbarton (talk) 03:01, 12 December 2024 (UTC)

I think that many people who work on constructions like those of Bennett et al. say they are studying "unextendible product bases", to avoid confusion with Bell's theorem and the failure of LHV models. But at least some of them do still talk about "nonlocality without entanglement". Here are a couple such papers from the past year: [1][2]. I am unaware of published sources that explicitly say one should avoid the term "nonlocality" in this sense. I would drop the sentence This non-standard use of the term... partly because finding a source that explicitly calls it a non-standard use would be a pain, but more importantly because we don't need to talk about what we're not talking about. We can just end the section. XOR'easter (talk) 04:11, 12 December 2024 (UTC)

That approach makes a lot of sense. MichaelMaggs (talk) 09:58, 12 December 2024 (UTC)

This would be a disservice to the reader. It explains why we're claiming in Wikivoice that entanglement is necessary for nonlocality. If calling UPBs "nonlocal" was a standard use of the term we wouldn't be able to do that. Tercer (talk) 11:31, 12 December 2024 (UTC)

Could you say specifically what you would like, including details of any necessary citation for your preferred wording? There might then be some alternative text to discuss. So far you've been objecting to almost every proposal, often with ad hominem comments about other editors. You may well be an expert in this area, I don't know because you so seldom do more than object to others' suggestions, but a majority of your comments here are not constructive contributions to creating an encyclopaedia. Wikipedia works on consensus building, and comments that merely appeal to authority don't carry much weight when consensus is determined. MichaelMaggs (talk) 13:17, 12 December 2024 (UTC)

Look, this has been going on for years. My patience with Johnjbarton is completely exhausted. He has repeatedly shown not only to be completely ignorant of the subject matter, but also incapable of learning or admitting he made a mistake. Now, for example, he failed to understand the point the article was making. The article says that "indistinguishability under local measurements" is a non-standard notion of nonlocality. He took that to mean that somehow LOCCs are non-standard. Which is complete nonsense. I told him so, as simply as I could. Instead of realizing that he made a mistake, he ignores everything I wrote and keeps insisting that the article is wrong and that we should "compromise" with his misunderstanding. So yes, it's yet another confirmation that talking to him is a waste of time.

XOR'easter, on the other hand, knows what they're talking about, and made a sensible suggestion, that I happen to disagree with. I'm free to do that. I politely told them why. Tercer (talk) 18:16, 12 December 2024 (UTC)

Your claim that "He took that to mean that somehow LOCCs are non-standard." is false. On the contrary if you read what I wrote, I provided reliable sources that LOCCs are standard. Johnjbarton (talk) 22:51, 12 December 2024 (UTC)

And you still haven't understood anything! Please read what I wrote. LOCCs are standard. Nobody is claiming otherwise. Not the article nor me. For some mysterious reason you think the article is claiming that LOCCs are non-standard: This avoids claiming that LOCC is non-standard. It is not the case. You found sources to support a point that nobody disputes. Tercer (talk) 08:15, 13 December 2024 (UTC)

You are correct that I did not understand this content. Your aggressive replies are mostly content free, simply echoing what is written in the article, so I mostly ignore them. XOR'easter comments helped clarify the issues.

Nevertheless I stand by my delete of these two sentences. They are not telling readers about entanglement. The Bennett paper is related to LOCC and the article discusses LOCC so the final sentence is confusing.

I encourage you to think of my edits in terms of how we can make the article better. That's why I am here. Johnjbarton (talk) 19:07, 13 December 2024 (UTC)

Since you mostly ignore my replies I won't waste my time writing them any longer. Tercer (talk) 20:10, 13 December 2024 (UTC)

Let me take this a bit further and apologize for missing your point in your replies here. I will try to pay closer attention in future. I also hope you will consider adjusting your approach. By toning down your language this could be a more cooperative and productive venture. I think this article is important and needs work. No one else is likely to take it up. Johnjbarton (talk) 22:37, 13 December 2024 (UTC)

Fair enough, apology accepted. Tercer (talk) 21:21, 14 December 2024 (UTC)

Tercer, Your reply makes it ever more clear that your editing behaviour is unacceptable. You've not only ignored the request to state specifically what your proposal is, but have simply repeated the very behavour complained of: an ad hominen attack plus an unsourced appeal to your own personal authority. I am not the only editor to have noted this editing pattern, most recently at Wikipedia:Administrators'_noticeboard/IncidentArchive1172#Request_TBAN_for_CIR_editor. MichaelMaggs (talk) 22:58, 12 December 2024 (UTC)

Have you considered the possibility that I'm saying the truth, though? I wonder how you would behave in my place.

Nothing needs to be changed. Johnjbarton's edit stems from a basic misunderstanding. My proposal is to leave the text as it is. Tercer (talk) 08:25, 13 December 2024 (UTC)

I think there is some confusion here; if I had to guess, perhaps Johnjbarton had not heard of "LOCC" in any other context before this and took it to be synonymous with the phenomenon Bennett et al. wrote about, rather than a prerequisite for it. The question of what one can do with local operations and classical communication was studied by Peres and Wootters (1991), for example, though they didn't have the acronym yet. XOR'easter (talk) 19:18, 12 December 2024 (UTC)

It is true I had not heard of LOCC before reading the Horodecki review. However the Bennett paper is clearly "about LOCC" in some sense. You say it is prerequisite for their work. The only notable commentary that the Horodecki review makes about the Bennett paper relates to LOCC. (I didn't claim the Bennett paper defined LOCC; BTW the Horodecki review has some historical content on LOCC).

I assume that a reader of Wikipedia should be understand what is written based solely on the content of the article and the references cited. I should not have to be named "Tercer" to understand the article. So what does this sentence in the article tell us about entanglement: In the literature "non-locality" is sometimes used to characterize concepts that differ from the non-existence of a local hidden variable model, e.g., whether states can be distinguished by local measurements and which can occur also for non-entangled states? I say "nothing". This sentence is about nonlocality definitions other than those related to local hidden variables. By itself this sentence has almost nothing to do with the article topic.

If this sentence is about LOCC then we should say so. If it is not it should be deleted as off-topic. Johnjbarton (talk) 22:41, 12 December 2024 (UTC)

I think you are making this much more complicated than it needs to be. The paper by Bennett et al., which is titled "Quantum nonlocality without entanglement", is about introducing something they call a form of nonlocality which does not require entanglement. This presumes the notion of local operations and classical communication, a class of operations that had already been discussed in the literature. They're not synonymous. The sentence is not "about LOCC"; it's about unextendible product bases, one of the many things that can be defined starting with the idea of LOCC.

Nor do I understand what is confusing about the sentences in question here. They say that the term "nonlocality" is sometimes used to mean other things (true), that one such thing does not require entanglement (also true), and that this article does not cover that meaning. Maybe that's off-topic. But there's nothing in principle wrong with a note that explains that a term is ambiguous. XOR'easter (talk) 15:00, 13 December 2024 (UTC)

Thanks, I appreciate you discussing the article and the source.

Ok, the sentence is not about LOCC, but about a form of nonlocality based on LOCC which does not require entanglement. So it's not related to the article and should be deleted.

The sentence is confusing because it is the "final-straw". The section reads like a series of technical waffles about the relationship between nonlinearity and entanglement, then tells us that the term itself is ambiguous in some unspecified way. I'm sure these many special cases are fun for experts but it is exhausting and confusing for readers. I think the section should start by specifying that is is about Bell nonlocality. Then if we really need this thing not related to entanglement we could replace the last two sentences with

• In addition to Bell nonlocality, there are other nonlocality concepts which do not required entanglement.(ref Bennett).

Johnjbarton (talk) 18:38, 13 December 2024 (UTC)

Well, some quantity of "waffles" are inevitable if we describe the subject correctly. All of the following are true:

• Entanglement is necessary to produce a violation of a Bell inequality.
• Entanglement is not sufficient to produce a violation of a Bell inequality.
• The violation of Bell inequalities is often called "nonlocality".
• Not everyone agrees that the violation of Bell inequalities should be called "nonlocality"; i.e., not everyone wants to call the failure of LHV models a nonlocality of nature itself.
• The term "nonlocality" is also applied in other ways, like the "nonlocality without entanglement" introduced by Bennett and coauthors.

One could argue that the last point is off-topic here, since the article is supposed to be about quantum entanglement. On the other hand, the concept of "nonlocality without entanglement" is still pertinent to the topic of entanglement, as evidenced by its appearing in a review article about entanglement. It's part of the study of what entanglement does and does not mean. XOR'easter (talk) 18:04, 14 December 2024 (UTC)

Well that is an awesome summary! This content would be a great improvement in my opinion. @Tercer If I added sources to this content would you agree to try it in place of the current content? Of course further adjustments might be needed. Johnjbarton (talk) 18:13, 14 December 2024 (UTC)

Since XOR'easter already added it I'm afraid the question is moot. One thing I dislike about it is that it removed the information that for pure states entanglement and nonlocality are in fact equivalent. Tercer (talk) 21:25, 14 December 2024 (UTC)

Multipartite tracing

The following sentence does not, in my opinion, have enough background for readers:

• Tracing out any one of the three qubits turns the GHZ state into a separable state, whereas the marginal produced by tracing over any of the three qubits in the W state is entangled.

Johnjbarton (talk) 02:37, 31 December 2024 (UTC)

What did Einstein actually say?

Did he say "spooky action at a distance" or "spooky actions (plural) at a distance"? 2600:8801:BE1C:1D00:FA07:6031:AB4E:440C (talk) 16:34, 12 January 2025 (UTC)

It's plural in the original letter: "Ich kann aber deshalb nicht ernsthaft daran glauben, weil die Theorie mit dem Grundsatz unvereinbar ist, daß die Physik eine Wirklichkeit in Zeit und Raum darstellen soll, ohne spukhafte Fernwirkungen." It should be on p155 of The Born-Einstein Letters, but the book is no longer accessible vie archive.org; I've found a pdf in German here (p 162 of the German edition). --Qcomp (talk) 11:11, 13 January 2025 (UTC)