Realism vs Locality in Quantum Entanglement

[Markus Hanke]

I have a question with regards to quantum entanglement, and how it relates to the concepts of realism and locality. I am just an interested amateur who has self-studied QM in my free time, so perhaps I should first run my understanding by you first, to make sure it is accurate : the basic idea is that quantum entanglement creates a statistical correlation between the measurement outcomes taken from the individual components of the entangled system. While an isolated measurement taken from an isolated component of such systems will have an essentially random outcome, the comparison between separate measurements taken from separate components will show a correlation that is stronger than would be expected classically. More technically, an entangled state is one that cannot be separated into pure states, so its state vector cannot be written as a simple tensor product of simpler vectors. This is merely a statistical correlation, not any kind of causation, action or FTL transmission. In other words, we are dealing with a system the individual components of which are described by a single wave function, irrespective of their spatial separations. I hope this overall understanding is largely correct.

Now my question : how does this relate to the concepts of realism and locality ? I was always under the impression that, because entanglement does not depend in any way on the spatial separation between particles, this phenomenon is an example of quantum non-locality. However, the other day I came across this :

http://physics.stackexchange.com/qu...nglement-and-spooky-action-at-a-distance?lq=1

specifically the first answer by ACuriousMind. This seems to imply ( or maybe I am just not understanding it correctly ) that entanglement is best understood not as a manifestation of non-locality, but rather of abandoning realism.

So what is the answer ? What are the real meanings of realism and locality in the context of quantum mechanics, and how does this relate to entanglement in particular ?

I just wish to understand this a little bit better. Thank you in advance !

 

[zonde]

I have a question with regards to quantum entanglement, and how it relates to the concepts of realism and locality. I am just an interested amateur who has self-studied QM in my free time, so perhaps I should first run my understanding by you first, to make sure it is accurate : the basic idea is that quantum entanglement creates a statistical correlation between the measurement outcomes taken from the individual components of the entangled system. While an isolated measurement taken from an isolated component of such systems will have an essentially random outcome, the comparison between separate measurements taken from separate components will show a correlation that is stronger than would be expected classically. More technically, an entangled state is one that cannot be separated into pure states, so its state vector cannot be written as a simple tensor product of simpler vectors.

Yes

This is merely a statistical correlation, not any kind of causation, action or FTL transmission.

Statistical correlation is what we observe, causation or FTL transmission on the other hand are explanations of statistical correlations.

specifically the first answer by ACuriousMind. This seems to imply ( or maybe I am just not understanding it correctly ) that entanglement is best understood not as a manifestation of non-locality, but rather of abandoning realism.

So what is the answer ? What are the real meanings of realism and locality in the context of quantum mechanics, and how does this relate to entanglement in particular ?

ACuriousMind describes what is understood as realism in the context of quantum mechanics right at the start:
"The assumption (if you cry it or not) "but the particle does have a definite spin, we just don't KNOW what it is, until it is measured! Duh!" is called realism, or in mathier speak, a theory of hidden variables."
This is basically right. Only we can extend hidden variables idea (I wouldn't call it a theory) so that spin measurement is determined by hidden variables (hidden variables don't have to be associated exclusively with particles).

This statement however is quite misleading:
"Most people choose [to give up] realism, since giving up locality would totally destroy our conceptions of causality."
It is right that there are people that chose to give up "realism" (as understood in QM contexts).
But it is misleading in implying that giving up "realism" opens the door for some other local explanation.

Additional point is that experiments can (and do) rule out all possible local hidden variable explanations that obey relativistic locality (no FTL transmission). But they in no way rule out "superluminal locality" and preferred simultaneity based causality. So if we talk about giving up relativistic locality then causality is not totally destroyed contrary to what ACuriousMind stated.

 

[Markus Hanke]

This is basically right. Only we can extend hidden variables idea (I wouldn't call it a theory) so that spin measurement is determined by hidden variables (hidden variables don't have to be associated exclusively with particles).

Ok, I think I get the idea.

But they in no way rule out "superluminal locality" and preferred simultaneity based causality.

I am not familiar with these two concepts. Would you be able to jot down the basic ideas behind these ( or link to an external resource that does this ) ?

 

[ddd123]

But it is misleading in implying that giving up "realism" opens the door for some other local explanation.

This is something I still haven't understood, what exactly are, if they exist, local non-realistic theories?

The other day I was reading this hilarious/delirious article by Lubos Motl http://motls.blogspot.it/2013/10/superdeterminism-ultimate-conspiracy.html mostly for laughs, but what struck me was this part:

"So no non-locality is needed; what's needed is the proposition-based, probability-laden framework that quantum mechanics indisputably demands. Locality is guaranteed to hold due to the rules of special relativity."

I really don't understand what he means (apart from the "indisputably" which is Motl's usual attitude), but it seems to be something akin to what you're talking about here.

 

[zonde]

I am not familiar with these two concepts. Would you be able to jot down the basic ideas behind these ( or link to an external resource that does this ) ?

With these two concepts I basically refer to LET interpretation of special relativity. Basic idea behind LET is that preferred frame is compatible with special relativity. You can read something about it in wikipedia https://en.wikipedia.org/wiki/Lorentz_ether_theory

 

[Demystifier]

I just wish to understand this a little bit better. Thank you in advance !

Try
http://arxiv.org/abs/quant-ph/0609163
Secs. 5 and 6.

 

[A. Neumaier]

an entangled state is one that cannot be separated into pure states

This is nonsense. An entangled state is itself a pure state, and can be written in infinitely many ways as superposition of other pure states. Separation is a meaningless concept unless you specify what it should mean. (The second half of your sentence is sensible.)
To avoid being confused and confusing others you need to learn to be precise in your language (as far as possible).

 

[DrChinese]

... This seems to imply ( or maybe I am just not understanding it correctly ) that entanglement is best understood not as a manifestation of non-locality, but rather of abandoning realism.

So what is the answer ? What are the real meanings of realism and locality in the context of quantum mechanics, and how does this relate to entanglement in particular ?

These questions are a source of much ongoing debate. You will find many different (and good!) answers that are completely contradictory. So be patient!

Do you accept the Heisenberg Uncertainty Principle (with its limits) as being a complete description of a quantum system? This question was famously raised in the EPR paper of 1935. The HUP essentially gives an indeterminate/undefined value to an observable when its non-commuting partner is known with great accuracy. You could call that non-realistic! A particle with a well-defined momentum therefore has no localized position.

Do you believe that the nature of an observation on entangled particle here shapes reality of its entangled partner there? If you do, that is non-realism. I.e. we live in an observer dependent universe.

I'm not trying to convince you of anything, just showing you what a non-realistic interpretation might look like. Obviously, in a non-local interpretation, there is no distance limit for interactions that relate to a single quantum system. At the end of the day, there is no known method to test one interpretation over another.

 

[zonde]

This is something I still haven't understood, what exactly are, if they exist, local non-realistic theories?

If you are asking me, I think there is no scientific local non-realistic explanation for entanglement correlations.

 

[DrChinese]

This is something I still haven't understood, what exactly are, if they exist, local non-realistic theories?

They exist. MWI is local non-realistic.

Retrocausal and time symmetric interpretations are also non-realistic because they make the future a contributor to outcomes of measurements now, neatly solving one quantum riddle. One of the most fleshed out technically is Relational Blockworld (no relation to the usual blockworld ideas - and please note that the authors consider RBW acausal rather than retrocausal):

http://arxiv.org/abs/0903.2642

We propose a discrete path integral formalism over graphs fundamental to quantum mechanics (QM) based on our interpretation of QM called Relational Blockworld (RBW). In our approach, the transition amplitude is not viewed as a sum over all field configurations, but is a mathematical machine for measuring the symmetry of the discrete differential operator and source vector of the discrete action. Therefore, we restrict the path integral to the row space of the discrete differential operator, which also contains the discrete source vector, in order to avoid singularities. In this fashion we obtain the two-source transition amplitude over a "ladder" graph with N vertices. We interpret this solution in the context of the twin-slit experiment.

 

[RUTA]

Here are a couple Insights that are relevant:
https://www.physicsforums.com/insig...elayed-choice-no-counterfactual-definiteness/ https://www.physicsforums.com/insights/retrocausality/

 

[RUTA]

Here is a recently published explanation of Relational Blockworld which satisfies realism and locality http://www.ijqf.org/wps/wp-content/uploads/2015/06/IJQF2015v1n3p2.pdf

 

[DrChinese]

Here is a recently published explanation of Relational Blockworld which satisfies realism and locality http://www.ijqf.org/wps/wp-content/uploads/2015/06/IJQF2015v1n3p2.pdf

Nice RUTA!

 

[bremsstrahlung]

Now my question : how does this relate to the concepts of realism and locality ? I was always under the impression that, because entanglement does not depend in any way on the spatial separation between particles, this phenomenon is an example of quantum non-locality. However, the other day I came across this :

So what is the answer ? What are the real meanings of realism and locality in the context of quantum mechanics, and how does this relate to entanglement in particular ?

I just wish to understand this a little bit better. Thank you in advance !

You're right Non-locality is here to stay. Read What Bell did by Tim Maudlin. The EPR argument ruled out local indeterministic theories and Bell's theorem ruled out local deterministic theories. We have to abandon locality. Bell's theorem does not rule out non-local deterministic theories like Bohmian Mechanics which is a non-local deterministic theory which fully reproduces the behaviour of quantum mechanics. As long as some theorem comes up with an inequality ruling out Bohmian mechanics realism is here to stay.

Thanks to Tim Maudlin for clearing the confusions surrounding the Bell's theorem.

 

[DrChinese]

The EPR argument ruled out local indeterministic theories...

I disagree. EPR demonstrated that if QM is complete, then the reality of an observable "here" must be dependent on the nature of a measurement "there". There is nothing about the EPR conclusion that actually ruled out any type of indeterministic theories.

It is true that they ended their paper with the opinion that QM must be incomplete. They thought the final QM would necessarily be deterministic. But that idea was absolutely not a conclusion of the paper. That was in fact an ad hoc assumption thrown in at the very last. Specifically, they said that any other view was not reasonable. Hardly the basis of a scientific conclusion. Although at the time they made it, they had in fact identified a critical point of contention.

There are in fact local indeterministic interpretations today, and they comply with EPR and Bell. Those are the non-realistic types such as MWI, and the ones I mentioned that are acausal/retrocausal.

 

[Jilang]

Hi Markus, you have a choice that comes down to interpretation. If realism is your thing you have to abandon locality and vice-versa. QM says you cannot have both at the same time. I don't think one is less worrisome than the other!

 

[RUTA]

You're right Non-locality is here to stay. Read What Bell did by Tim Maudlin. The EPR argument ruled out local indeterministic theories and Bell's theorem ruled out local deterministic theories. We have to abandon locality. Bell's theorem does not rule out non-local deterministic theories like Bohmian Mechanics which is a non-local deterministic theory which fully reproduces the behaviour of quantum mechanics. As long as some theorem comes up with an inequality ruling out Bohmian mechanics realism is here to stay.

Thanks to Tim Maudlin for clearing the confusions surrounding the Bell's theorem.

I have two points of disagreement with Maudlin. First, I disagree that locality is the only assumption that can be questioned in Bell's proof. He relates determinism and counterfactual definiteness in his footnote 1 then states in his explanation of Bell's argument on p 24, "each particle in a singlet state must have definite spin values in all directions." This counterfactual definiteness is precisely the "realism" aspect of Bell's argument he later seeks to deny when he says, "But such claims never manage to make clear at the same time just what 'realism' is supposed to be and how Bell's derivation presupposes it." Second, all of Maudlin's arguments implicitly assume the time-evolved perspective Wharton calls the Newtonian Schema. He hasn't said anything about the global 4D perspective of retrocausality, so I must assume he erroneously relegates retrocausal accounts to superdeterminism, which he (rightly) dismisses on p 26. In making this erroneous conflation, he denies the possibility that fundamental explanation is not to be found in time-evolved stories, but rather in the distribution of 4D configurations (processes) in spacetime. Again, see my Insight "Understanding Retrocausality" https://www.physicsforums.com/insights/retrocausality/

 

[RUTA]

Hi Markus, you have a choice that comes down to interpretation. If realism is your thing you have to abandon locality and vice-versa. QM says you cannot have both at the same time. I don't think one is less worrisome than the other!

Again, you can have both locality and realism in retrocausal accounts.

 

[zonde]

I have two points of disagreement with Maudlin. First, I disagree that locality is the only assumption that can be questioned in Bell's proof. He relates determinism and counterfactual definiteness in his footnote 1 then states in his explanation of Bell's argument on p 24, "each particle in a singlet state must have definite spin values in all directions." This counterfactual definiteness is precisely the "realism" aspect of Bell's argument he later seeks to deny when he says, "But such claims never manage to make clear at the same time just what 'realism' is supposed to be and how Bell's derivation presupposes it."

Let me quote Maudlin:
"Recall the dilemma posed by the EPR argument: if a theory predicts perfect correlations for the outcomes of distant experiments, then either the theory must treat these outcomes as deterministically produced from the prior states of the individual systems or the theory must violate EPR-locality. The argument is extremely simple and straightforward. The perfect correlations mean that one can come to make predictions with certainty about how system S1 will behave on the basis of observing how the other, distant, system S2 behaves. Either those observations of S2 disturbed the physical state of S1 or they did not. If they did, then that violates EPR-locality. If they did not, then S1 must have been physically determined in how it would behave all along. That’s the argument, from beginning to end."
This counterfactual definiteness is part of EPR-locality. Without it EPR-locality is vacuous concept.

Second, all of Maudlin's arguments implicitly assume the time-evolved perspective Wharton calls the Newtonian Schema. He hasn't said anything about the global 4D perspective of retrocausality, so I must assume he erroneously relegates retrocausal accounts to superdeterminism, which he (rightly) dismisses on p 26. In making this erroneous conflation, he denies the possibility that fundamental explanation is not to be found in time-evolved stories, but rather in the distribution of 4D configurations (processes) in spacetime.

He does not deny possibility of superdeterminism. He just says it's non-scientific. And if retrocausality in time-evolved perspective looks identical to superdeterminism then the same arguments apply to retrocausality.

 

[bremsstrahlung]

I disagree. EPR demonstrated that if QM is complete, then the reality of an observable "here" must be dependent on the nature of a measurement "there". There is nothing about the EPR conclusion that actually ruled out any type of indeterministic theories.

There are in fact local indeterministic interpretations today, and they comply with EPR and Bell. Those are the non-realistic types such as MWI, and the ones I mentioned that are acausal/retrocausal.

I don't see how giving up counterfactual definiteness alone explains the quantum correlations in entanglement. A measurement "there" still disturbs the system "here" irrespective of whether the system possesses predefined properties or not, otherwise how does the system "here" know what happened to the system "there".

"Already at the time Bell wrote this, there was a tendency for critics to miss the crucial role of the EPR argument here. The conclusion is not just that some special class of local theories (namely, those which explain the measurement outcomes in terms of pre-existing values) are incompatible with the predictions of quantum theory (which is what follows from Bell's inequality theorem alone), but that local theories as such (whether deterministic or not, whether positing hidden variables or not, etc.) are incompatible with the predictions of quantum theory. This confusion has persisted in more recent decades, so perhaps it is worth emphasizing the point by (again) quoting from Bell's pointed footnote from the same 1980 paper quoted just above: "My own first paper on this subject ... starts with a summary of the EPR argument from locality to deterministic hidden variables. But the commentators have almost universally reported that it begins with deterministic hidden variables."

- Bell's[/PLAIN] theorem, Sheldon Goldstein et al. (2011), Scholarpedia, 6(10):8378.

 

[DrChinese]

1. I don't see how giving up counterfactual definiteness alone explains the quantum correlations in entanglement.

2. ...

- Bell's[/PLAIN] theorem, Sheldon Goldstein et al. (2011), Scholarpedia, 6(10):8378.

1. This is a fair opinion, and I can certainly see why you would believe it, but has nothing to do with EPR's argument and what they proved.

2. This is a terrible reference and is, unfortunately, circular. The authors of the articles are all Bohmians, and this entire article is written as a sort of revisionist view of Bell (and EPR). Although I respect the authors, this article should be labeled at the top: "From the Bohmian Mechanics viewpoint". I say it is circular because if you accept it, you simply believe that the existence of entanglement is proof of action at a distance. That is certainly far from generally accepted. Bohmians are a minority of physicists, not the norm.

So I can tell you that I reject Goldstein et al's reasoning and historical analysis on EPR and Bell as biased. I have told Norsen (one of the authors) as much myself, as we have had numerous discussions about this (that changed no one's mind).

BTW Scholarpedia is not a typical peer reviewed journal for original research. I loosely would equate it with Wikipedia (which is up and down) as a suitable source here.

 

[Markus Hanke]

Try
http://arxiv.org/abs/quant-ph/0609163
Secs. 5 and 6.

Thank you, that document was very helpful; I was looking for something like this !

 

[Markus Hanke]

These questions are a source of much ongoing debate. You will find many different (and good!) answers that are completely contradictory. So be patient!

Yes, I noticed that, and it is something that has really confused me; if even the experts disagree so much, what chance does an amateur like myself have

At the end of the day, there is no known method to test one interpretation over another.

Do the results of Alain Aspect's and John Clauser's ( among others ) experiments not place very stringent limits on the existence of "hidden variables" ? To my understanding, the results would indicate that in all likelihood QM is a complete description of reality, thereby preferring explanation #1 in your post. Or am I wrong ? I feel like I am really missing something here, and that bothers me.

 

[DrChinese]

Do the results of Alain Aspect's and John Clauser's ( among others ) experiments not place very stringent limits on the existence of "hidden variables" ? To my understanding, the results would indicate that in all likelihood QM is a complete description of reality, thereby preferring explanation #1 in your post. Or am I wrong ? I feel like I am really missing something here, and that bothers me.

Yes, definitely they place constraints on hidden variables. They cannot be local (if they exist).

I consider QM to be "complete" in the sense it is used by EPR. I don't think you are missing too much, it is a quandary.

 

[RUTA]

Let me quote Maudlin:
"Recall the dilemma posed by the EPR argument: if a theory predicts perfect correlations for the outcomes of distant experiments, then either the theory must treat these outcomes as deterministically produced from the prior states of the individual systems or the theory must violate EPR-locality. The argument is extremely simple and straightforward. The perfect correlations mean that one can come to make predictions with certainty about how system S1 will behave on the basis of observing how the other, distant, system S2 behaves. Either those observations of S2 disturbed the physical state of S1 or they did not. If they did, then that violates EPR-locality. If they did not, then S1 must have been physically determined in how it would behave all along. That’s the argument, from beginning to end."
This counterfactual definiteness is part of EPR-locality. Without it EPR-locality is vacuous concept.

He does not deny possibility of superdeterminism. He just says it's non-scientific. And if retrocausality in time-evolved perspective looks identical to superdeterminism then the same arguments apply to retrocausality.

I think you’re right, zonde. If I demand that fundamental explanation be couched in the spatially localized, forward-time-evolved causal perspective of the Newtonian Schema (NS), then Maudlin’s claims are correct. For the first point, given the NS demand, the two outcomes must be due to two spatially separated entities (as described by their states, as he explains). Since the outcomes are spacelike separated, you have non-locality if you have counterfactual definiteness with Bell-inequality-violating outcomes, exactly as he states. Second, the spatiotemporally holistic nature of explanation via a 4D global constraint would have to be explained by superdeterminism when the spacelike separated, correlated outcomes violate Bell’s inequality, since explanation must be based in the forward-time-evolved causal perspective per the NS demand. In other words, I have to provide some forward-time-evolved causal mechanism per the NS demand and since the spacelike separated outcomes are related per a block universe constraint, that causal mechanism defines the superdeterministic conspiracy. So, in order to make his arguments logically complete, all he has to do is articulate his demand for NS explanation at the outset.

This NS bias is precisely what Price & Wharton are trying to get people to understand and acknowledge. In that respect, in order to cover all possible explanations of Bell-inequality-violating, spacelike separated correlations, one should acknowledge the possibility that explanation per the Lagrangian Schema (LS) is fundamental to that of the NS. Accordingly, it’s possible that some phenomena explained by the LS simply defy reasonable explanation by the NS, thus giving rise to the conundrums of quantum mechanics. Price & Wharton aren’t asking people to subscribe to the fundamentality of the LS explanation, they are only asking people to acknowledge that it is one possible resolution of quantum mysteries.

 

[Markus Hanke]

This is nonsense. An entangled state is itself a pure state, and can be written in infinitely many ways as superposition of other pure states. Separation is a meaningless concept unless you specify what it should mean. (The second half of your sentence is sensible.)
To avoid being confused and confusing others you need to learn to be precise in your language (as far as possible).

My apologies. You are of course right. As an interested amateur who is only starting to self-study QM in any serious detail, I am still missing the exact meaning and definition of a number of important concepts, such as for example "pure state". It will take me more time and effort, but I will get there in the end, because I want to understand it.

I have thus far been through Griffiths' Introduction to Quantum Mechanics, and I am attempting to extract the main ideas from Sakurai's Advanced Quantum Mechanics, but to be honest, I find the latter to be quite challenging in terms of the mathematics. Do you have a recommendation for a text that could be placed "in between" ( if you know what I mean ) these two ? Ideally I am looking for a text that goes beyond Griffith and discusses things like entanglement and relativistic QM, but doesn't quite go all the way into QFT yet ( I don't feel I am ready for that at all ). I am comfortable with Dirac notation, and found Griffiths easy enough to follow and understand.

Any recommendation would be appreciated ! I am not afraid to put in the time and effort to go through an undergrad textbook in detail.

 

[Markus Hanke]

Yes, definitely they place constraints on hidden variables. They cannot be local (if they exist).
I consider QM to be "complete" in the sense it is used by EPR. I don't think you are missing too much, it is a quandary.

Thank you, and from my ( very limited ) point of view I would intuitively tend to agree - I think QM actually is a complete description, in the sense that there aren't any unobservable, hidden variables. From that point of view, I think Einstein and others did the world a great disservice by coining the term "spooky action at a distance"; certainly for me as an amateur, it caused a lot of confusion when I first encountered the concept of quantum entanglement.

By the way, something just occurred to me here - is entanglement an observer-dependent concept in any way, shape or form ? How does this tie in with relativity of simultaneity, and is entanglement affected by the background geometry ( i.e. does the metric play a role if you create a situation where you have an entangled system across a larger region of curved space-time ) ? Just curious here now

 

[A. Neumaier]

recommendation for a text that could be placed "in between" ( if you know what I mean ) these two ? Ideally I am looking for a text that goes beyond Griffith and discusses things like entanglement and relativistic QM

I'd like to suggest the http://www.fisica.net/quantica/Peres%20-%20Quantum%20Theory%20Concepts%20and%20Methods.pdf (to be read first) together with one of his articles (to be read afterwards), concerning the relativistic case. Peres is one of the most down-to-earth writers on the subject among those who keep the technical part reasonably limited. (On the other hand, you'd polish your math background if you want to understand quantum mechanics in a little more depth.)

 

[Nugatory]

By the way, something just occurred to me here - is entanglement an observer-dependent concept in any way, shape or form ? How does this tie in with relativity of simultaneity

As all observers will agree about the recorded macroscopic results of the interactions taking place at the two detectors, entanglement is not an observer-dependent phenomenon. What is observer-dependent is which measurement happened first.

Alice measures her particle and gets spin-up; we then know that when and if Bob makes a measurement on the same axis it will come out spin-down. Bob later makes his measurement; sure enough it comes out spin-down so the naive will swiftly conclude that Alice's measurement caused Bob's wave function to collapse. However, thanks to the relativity of simultaneity we could just as easily say that Bob's measurement happened first and in fact it was his measurement that caused Alice's wave function to collapse. If you find this situation paradoxical (as most people would) you have an easy way out: Abandon the assumption that one measurement must cause the other measurement to come out the way it does, and settle for the one thing that we can always take to the bank: When Alice and Bob get together to compare notes after the fact, they will find that the two measurements are opposite.

 

[Markus Hanke]

I'd like to suggest the http://www.fisica.net/quantica/Peres%20-%20Quantum%20Theory%20Concepts%20and%20Methods.pdf (to be read first) together with one of his articles (to be read afterwards), concerning the relativistic case. Peres is one of the most down-to-earth writers on the subject among those who keep the technical part reasonably limited. (On the other hand, you'd polish your math background if you want to understand quantum mechanics in a little more depth.)

That is brilliant, thank you so much !

 

[Markus Hanke]

As all observers will agree about the recorded macroscopic results of the interactions taking place at the two detectors, entanglement is not an observer-dependent phenomenon. What is observer-dependent is which measurement happened first.

Noted, with thanks. This makes sense to me.

If you find this situation paradoxical (as most people would)

I don't actually find it paradoxical, in fact, unless I am missing something crucial, I don't even see how it could possibly be considered a paradox at all. In my mind, I do not think of entanglement as involving any type of "action" over and above the initial interaction required to create the entangled state; to me it is just simply a statistical correlation between measurement outcomes thereafter. In many ways it is really just a trivial observation - like encountering someone whom you know is married on the street. If you meet the man, you know automatically that the other spouse ( who is potentially far away ) must be female, and vice versa, simply on account of your knowledge of them being in a heterosexual marriage. Your meeting that person does not in any sense of the word cause the gender of the absent spouse. At the same time, which of the two you meet is a random occurrence - it could be the man or the woman, with equal probability. The very same for the spin states in your example - whether, for a single measurement, you get spin-up or spin-down is essentially random, but you always know that, if the particles are entangled, the same measurement performed on the other particle must yield the opposite result, since they can't both be in the same spin state. There is no cause and effect here, just a correlation, and as we know correlation does not necessarily imply causation.

Correct me please if I am wrong on any of this.

 

[Nugatory]

I do not think of entanglement as involving any type of "action" over and above the initial interaction required to create the entangled state; to me it is just simply a statistical correlation between measurement outcomes thereafter.

That's right - there is no paradox as long as you're just thinking in terms of the statistical correlation. However, in your married couple example, you are going way beyond that; to be stay within the spirit of "just a correlation" you would have to say that the other spouse will be of the opposite sex if you look, but if you don't look you can make no statement.

To see the distinction you need more than one measurable attribute. Suppose every couple consists of a man and a woman, one blue-eyed and one brown-eyed, one tall and one short. If you and I each encounter one member of the couple, you meet a man and I meet a blue-eyed person... It does not mean that you met a brown-eyed man and I met a blue-eyed woman.

 

[zonde]

In many ways it is really just a trivial observation - like encountering someone whom you know is married on the street. If you meet the man, you know automatically that the other spouse ( who is potentially far away ) must be female, and vice versa, simply on account of your knowledge of them being in a heterosexual marriage. Your meeting that person does not in any sense of the word cause the gender of the absent spouse. At the same time, which of the two you meet is a random occurrence - it could be the man or the woman, with equal probability.

Exactly this type of model is proved incompatible with quantum mechanics predictions by Bell. If you are not familiar with Bell's theorem you can try DrChinese website
Even more it is ruled out by recent loophole free Bell inequality experiments.

 

[ddd123]

Correct me please if I am wrong on any of this.

The correct meaning of "paradox" is an impossible or contradictory result, so of course there's no paradox here, since nonlocal correlations are a logical possibility. But your marriage example isn't applicable because you cannot assign definite properties to each particle of the pair throughout their travel towards the measurement instruments, so that they can be compatible with the experimental results (i.e. local hidden variables).

 

[Markus Hanke]

Thank you Nugatory, zonde, and ddd123. So basically, what I missed in my classical analogy was that quantum objects do not actually have definite properties, until a measurement is performed, so the "entanglement information" isn't somehow carried along with them in the form of some hidden attribute or variable - it couldn't be, because no definite state has been "selected" yet. So for example, for two entangled electrons, they would exist in a superposition of all possible spin states for that particular setup, from the moment of entanglement until such time when a measurement of the spin is performed - only then is it meaningful to actually consider them as having a specific, definite spin state, and only then does entanglement become apparent when one compares the outcomes of measurements. In that case, it seems wrong to even consider the pair as separate, independent entities - the pair of electrons is really just one system described by one wave function, so if you perform a measurement on any part of the system, you collapse the wave function as a whole for both particles - which naturally reveals the correlation between the outcomes. Does that sound about right ?

Apologies if this stuff seems really basic to all of you, but as an amateur I am really trying to understand it correctly, as opposed to all the imprecise pop-sci babble that's out there. It's one thing to see it written down as a mathematical statement, but it's quite another to actually get an intuitive feel for how entanglement manifests. So thank you for your time in explaining it.