I Is this popular description of entanglement correct?

[entropy1]

In some popularized discussions of entanglement, you often hear that:

IF particle A is found to be spin-up, "we know that" particle B "has" spin-down.

This seems to me not necessarily the case. In this formulation, particle A is viewed through measurement outcome and particle B through ontology. If the measurement basisses of Alice and Bob are parallel, Alice's outcome practically matches (the opposite of) Bob's. If the measurement basisses of Alice and Bob have a difference of 90 degrees, Alice's outcome is uncorrelated to Bob's. In the latter case if Alice measures spin-up, Bob will measure spin-up or spin-down with 50/50 probability (ie spin-right/spin-left).

Now, if we assume like in the quote that particle B "has" spin-down, this agrees with observation. But it is still an assumption it seems to me, because what Bob measures in the second example is 50/50 spin-up and spin-down.

I am wondering if we should not confuse measurement with ontology in this case.

So I wonder if the formulation in the quote accurately reflects entanglement as a phenomenon. If not, entanglement may be more subtle to interpret.

EDIT: Likely we can describe entanglement more accurately with the wavefunction.

 

[phinds]

IF particle A is found to be spin-up, "we know that" particle B "has" spin-down.

Would be more properly stated as "We know that for spin-entangled particles if one particle is measured as having spin up then if/when the second particle is measured for spin, it will be measured to have spin down."

 

[entropy1]

Would be more properly stated as "We know that for spin-entangled particles if one particle is measured as having spin up then if/when the second particle is measured for spin, it will be measured to have spin down."

I don't agree that it will be measured spin down. It depends on the orientation of the measurement, as I mentioned in #1.

 

[Doc Al]

I don't agree that it will be measured spin down. It depends on the orientation of the measurement, as I mentioned in #1.

Obviously. To say something is measured to be "spin down" is meaningless unless a direction is specified.

In some popularized discussions of entanglement, you often hear that:

"IF particle A is found to be spin-up, "we know that" particle B "has" spin-down."

This only makes sense if both particles have their spins measured in the same direction. Obviously, if the second particle is measured in a completely different direction you may get different results.

 

[phinds]

I don't agree that it will be measured spin down. It depends on the orientation of the measurement, as I mentioned in #1.

Yes. I was assuming the same orientation, but assumptions ...

 

[entropy1]

This only makes sense if both particles have their spins measured in the same direction. Obviously, if the second particle is measured in a completely different direction you may get different results.

I agree. But that still says nothing about the ontology of the spin that particle B has before measurement. So then I feel the quote is incorrect.

Just today I heard Sean Carroll say "The only probabilites for anything are 0%, 100% and 50/50." I guess this would be a case of 50/50.

 

[AndreiB]

I agree. But that still says nothing about the ontology of the spin that particle B has before measurement.

If you make the assumption that physics is local (the measurement of A does not disturb B) it follows that B had that spin (DOWN in your example) not only before B is measured but even before A is measured.

Given that we have strong evidence that physics is local it follows that we have equally strong evidence that B was in a DOWN state before any measurement took place.

Obviously, we are speaking about same-direction measurements.

 

[vanhees71]

Would be more properly stated as "We know that for spin-entangled particles if one particle is measured as having spin up then if/when the second particle is measured for spin, it will be measured to have spin down."

More precisely: If two spin-1/2 particles are prepared in a spin singlet state and A measures spin up in $z$-direction she knows that B will find spin down with certainty when also measuring his particle's spin in $z$-direction.

 

[entropy1]

More precisely: If two spin-1/2 particles are prepared in a spin singlet state and A measures spin up in $z$-direction she knows that B will find spin down with certainty when also measuring his particle's spin in $z$-direction.

That is a good description I think. But I find that often the description is not that accurate in more popular media. Figures.

 

[Doc Al]

Just today I heard Sean Carroll say "The only probabilites for anything are 0%, 100% and 50/50." I guess this would be a case of 50/50.

By choosing the appropriate angles for measuring the spins, you can arrange for any probability, not just those three.

 

[Doc Al]

If you make the assumption that physics is local (the measurement of A does not disturb B) it follows that B had that spin (DOWN in your example) not only before B is measured but even before A is measured.

Given that we have strong evidence that physics is local it follows that we have equally strong evidence that B was in a DOWN state before any measurement took place.

You might want to review Bell's Theorem and the work done to confirm the violation of Bell's inequalities.

 

[entropy1]

By choosing the appropriate angles for measuring the spins, you can arrange for any probability, not just those three.

I think he means that any angle is not perfectly 0% or perfectly 100%. Then, any probability between those can be weighted to be equivalent to 50%.

 

[AndreiB]

You might want to review Bell's Theorem and the work done to confirm the violation of Bell's inequalities.

I know Bell's work. What's your point?

 

[Doc Al]

I know Bell's work. What's your point?

My point is that what you posted was incorrect.

 

[AndreiB]

My point is that what you posted was incorrect.

Can you be more specific about what is incorrect about my post? Just quote the relevant part and explain what's wrong!

 

[Doc Al]

Can you be more specific about what is incorrect about my post? Just quote the relevant part and explain what's wrong!

We can start here, where you seem to assume what you wish to conclude:

Given that we have strong evidence that physics is local

But let's not do it here, as this is not relevant to the thread. If you dispute Bell and its experimental tests, perhaps you should publish a paper.

 

[AndreiB]

If you dispute Bell and its experimental tests, perhaps you should publish a paper.

So, you disagree that we have strong evidence that physics is local? I also don't get what is circular about that. I assume locality to prove that the particle was in a spin DOWN state before the measurement. I'm not assuming locality to prove locality, which would be circular, indeed.

If you dispute Bell and its experimental tests, perhaps you should publish a paper.

I do not dispute any experimental test. I also do not dispute the validity of Bell's theorem. But since you didn't tell me what it is you think Bell proved I can't say if I dispute "Bell" or not.

 

[vanhees71]

Bell assumed a general type of local deterministic hidden-variable theories and proved an inequality for certain correlation measures. This inequality is predicted to be violated by QT, including local relativistic QFTs, and all experimental tests disfavored with overwhelming significance the local deterministic HV theories and confirmed local relativistic QFT. For me the conclusion is clear.

 

[AndreiB]

Bell assumed a general type of local deterministic hidden-variable theories...

He assumed a type of local deterministic hidden-variable theories in which the hidden variables are independent of measurements' settings. Those are indeed ruled out. The others still remain on the table.

 

[PeterDonis]

He assumed a type of local deterministic hidden-variable theories in which the hidden variables are independent of measurements' settings. Those are indeed ruled out. The others still remain on the table.

The type of model in which the hidden variables are not independent of the measurement settings is called "superdeterminism". In such a model, you have to accept that, for example, in all of the experiments we have run on entangled particles that have shown violations of the Bell inequalities, the measurement settings for each individual particle were not independent of the process that produced the particles themselves. Those physical processes had some hidden connection between them that ensured that only certain combinations of particle states and measurement settings occurred, in order to make it seem like the world works according to quantum mechanics even though the actual underlying model is very different.

To say that such a model seems implausible is a vast understatement. But if you are going to take the position you are taking in what I quoted above, that is the kind of model you are committed to.

 

[AndreiB]

The type of model in which the hidden variables are not independent of the measurement settings is called "superdeterminism".

Indeed.

In such a model, you have to accept that, for example, in all of the experiments we have run on entangled particles that have shown violations of the Bell inequalities, the measurement settings for each individual particle were not independent of the process that produced the particles themselves.

True.

Those physical processes had some hidden connection between them that ensured that only certain combinations of particle states and measurement settings occurred, in order to make it seem like the world works according to quantum mechanics even though the actual underlying model is very different.

The connection is not necessary hidden. What you need is an interaction (with infinite range) and we know for a fact that the source and detectors interact. They interact gravitationally (which is probably not that important) but they also interact electromagnetically (since they are composed of charge particles). Bell's statistical independence assumption is in fact a non-interaction assumption. In the general case, if N bodies interact their state would be described by a solution to the N-body problem, not by N solutions of the 1-body-problem, so their states are not independent. A Bell test is a particular case of an N body electromagnetical problem, where N is the number of charged particles (electrons and nuclei) taking part in the experiment, so, I would say, the statistical independence assumption is (almost) clearly false. I say almost, because it might be the case that independence is restored at the statistical level. At the level of single states there is no independence since the state of each object clearly depends on all N objects, that's a mathematical fact.

To say that such a model seems implausible is a vast understatement.

1. How do you estimate the probability of such a model to be true? Based on what?
2. Even if you can prove that this type of model is unlikely it doesn't mean much if the alternative (non-locality) isn't more likely. Can you tell me why would you ascribe a greater probability for the non-locality to be true? I would say the opposite is more reasonable, since superdeterminism does not violate any known physical principle, whyle non-locality does.

But if you are going to take the position you are taking in what I quoted above, that is the kind of model you are committed to.

Sure.

 

[PeterDonis]

What you need is an interaction (with infinite range) and we know for a fact that the source and detectors interact.

An interaction by itself is not enough. You need an interaction whose effects are very precisely tailored to make it look like quantum mechanics is correct, when in fact the underlying laws are very different. Ordinary gravitational or electromagnetic interactions will not do that.

How do you estimate the probability of such a model to be true?

"Implausible" is a judgment, not an estimate of probability. You are free to disagree with such a judgment; I am simply pointing out what such a disagreement commits you to. You appear to be fine with that.

superdeterminism does not violate any known physical principle, whyle non-locality does.

What "known physical principle" does non-locality (in the sense of violating the Bell inequalities) violate? Note that quantum mechanics, including quantum field theory, predicts Bell inequality violations, so you are claiming that QM/QFT violates some "known physical principle", which is a very, very strong claim.

 

[vanhees71]

Again we have the problem that you and @AndreiB did not specify what you mean with "non-locality". The standard relativistic local QFTs are local, as the name local QFT says, and here locality means that local observables fulfill the microcausality constraint. It's also a realization of what Bell means by "locality" at least in his original papers containing his inequalities based on local deterministic hidden-variable models.

Of course local relativistic QFTs don't violate any known physical principles but are by construction a realization of those principles as far as causality in accordance with (special) relativity and the fundamental spacetime symmetries following from the spacetime model (proper orthochonous) Poincare invariance as well as the unitarity of the quantum-theoretical time-evolution is concerned.

 

[PeterDonis]

Again we have the problem that you and @AndreiB did not specify what you mean with "non-locality".

If you are referring to me, I did specify what I meant by it in post #22.

 

[vanhees71]

There you just claim the violation of Bell's inequality implies non-locality. Relativistic local QFT violates Bell's inequality too and it's local (in the sense of no FTL propagating causal effects).

 

[PeterDonis]

There you just claim the violation of Bell's inequality implies non-locality.

I am saying that it is one possible definition of "non-locality".

 

[bhobba]

This issue has been discussed many times on this forum. I have only recently reached a view I am pleased with. It has to do with the is the issue of Outcome Independence and Parameter Independence. QFT is compatible with SR and violation of OI but not a violation of PI. Bells theorem is viewed as showing QM violates OI but not PI. See:
https://plato.stanford.edu/entries/qm-action-distance/#AnaFac

Also, as Peter correctly emphasises, a lot of confusion about this has to do with what one means by locality. The above is my meaning of it.

Thanks
Bill

 

[gentzen]

QFT is compatible with SR and OI but not necessarily PI. Bells theorem show QM violates PI but not OI. See:

But that SEP article says that it is the other way round, i.e. you should exchange OI and PI in your statement.

 

[bhobba]

But that SEP article says that it is the other way round, i.e. you should exchange OI and PI in your statement.

Ok, I see what you mean. I have changed my post to fix the bad way I expressed it. To be clear, let's be careful. The article says:

'Assuming λ-independence (see section 2), any empirically adequate theory will have to violate OI or PI. A common view has it that violations of PI involve a different type of non-locality than violations of OI: Violations of PI involve some action-at-a-distance that is impossible to reconcile with relativity (Shimony 1984, Redhead 1987, p. 108), whereas violations of OI involve some holism, non-separability and/or passion-at-a-distance that may be possible to reconcile with relativity.'

A simple way of looking at it is Bell shows entangled systems can not be considered two separate systems but are in some way a holistic single system. That is a violation of OI but does not violate relativity. However, we can keep PI because it would violate relativity. My previous view had to do with the Cluster Decomposition property of QFT, but I find the above more satisfactory. As Peter has emphasised, it depends on what you think locality means in this context.

Thanks
Bill

 

[vanhees71]

I am saying that it is one possible definition of "non-locality".

I don't understand, why it is not possible to stick to one definition at least within one thread. It's really bad that one has to explain all the time again and again what locality means. There's a clear definition in standard mainstream physics, and it's the one used by Bell: Locality means that there is no causal influence between space-like separated events. The violation of Bell's inequality is due to correlations between far-distant entangled parts of a quantum system. At least within science it should be clear that correlations are not necessarily due to causal connections.

 

[vanhees71]

This issue has been discussed many times on this forum. I have only recently reached a view I am pleased with. It has to do with the is the issue of Outcome Independence and Parameter Independence. QFT is compatible with SR and violation of OI but not a violation of PI. Bells theorem is viewed as showing QM violates OI but not PI. See:
https://plato.stanford.edu/entries/qm-action-distance/#AnaFac

Also, as Peter correctly emphasises, a lot of confusion about this has to do with what one means by locality. The above is my meaning of it.

Thanks
Bill

The important point is that for each local observer both OI and PI hold. If you have, e.g., two spins in the singlet state, A and B both simply find unpolarized particles when measuring a spin component, no matter which spin component the other experimenter chooses to measure. Only by comparing the outcomes of their measurements they find the correlations due to the entanglement, and of course the statistics depends on which spin components they measure (the conditional probability distribution for an outcome of A given a certain outcome of B depends on the relative angle between the measured spin measurements in this case), which indeed is the content of these correlations. In this sense of course QM violates OI.

 

[PeterDonis]

I don't understand, why it is not possible to stick to one definition at least within one thread.

I gave my definition in response to @AndreiB's claim that "non-locality" violates "known physical principles"; I gave the definition because he didn't give one at all, and the one I gave is the one Bell used. If @AndreiB meant something different by "non-locality", he's welcome to clarify what he meant.

 

[AndreiB]

An interaction by itself is not enough.

It is. If there is an interaction you cannot assume that distant equipments are independent and Bell's inequalities can't be derived.

You need an interaction whose effects are very precisely tailored to make it look like quantum mechanics is correct, when in fact the underlying laws are very different.

Sure, if you want the theory to be true. But if you only ask for a minimum requirement so that the theory passes Bell's theorem you need not provide any other evidence.

Ordinary gravitational or electromagnetic interactions will not do that.

How do you know that?

"Implausible" is a judgment, not an estimate of probability. You are free to disagree with such a judgment; I am simply pointing out what such a disagreement commits you to. You appear to be fine with that.

OK.

What "known physical principle" does non-locality (in the sense of violating the Bell inequalities) violate?

By non-locality I mean the statement that space-like events cause each other. Without hidden variables the only way to explain the perfect correlations in an EPR-Bohm experiment is to assert that the A measurement caused B's result. The argument is really simple.

Say the A measurement was "UP". This let's B in a "DOWN" state. If the A measurement did not disturb B (locality assumption) it follows that B was in a spin "DOWN" state even before the A measurement. So, you either have non-locality (A measurement disturbed/caused B) or deterministic hidden variables (the spins were predetermined).

Note that quantum mechanics, including quantum field theory, predicts Bell inequality violations, so you are claiming that QM/QFT violates some "known physical principle", which is a very, very strong claim.

The argument applies to "complete"/fundamental theories. QM/QFT can be local if they are statistical approximations to a hidden-variable theory. Otherwise, they are non-local.

 

[AndreiB]

There you just claim the violation of Bell's inequality implies non-locality. Relativistic local QFT violates Bell's inequality too and it's local (in the sense of no FTL propagating causal effects).

Can you prove that in QFT it is impossible for the A measurement to cause the result at B (A and B are space-like)? It seems to me that microcausality is a weaker condition than locality.

 

[gentzen]

By non-locality I mean the statement that space-like events cause each other. Without hidden variables the only way to explain the perfect correlations in an EPR-Bohm experiment is to assert that the A measurement caused B's result. The argument is really simple.

You use the word 'cause' is a strange way. For me, C might cause both A and B, or A might cause B, but to say that A and B cause each other seems to be meaningless.

Another confusion in your language for me is that you talk about 'the A measurement', but don't distinguish between the measurement outcome and the mere fact that a measurement with some specific settings gets performed. Do you mean that the "the A measurement outcome is causing the B measurement outcome"?

 

[AndreiB]

You use the word 'cause' is a strange way. For me, C might cause both A and B, or A might cause B, but to say that A and B cause each other seems to be meaningless.

Right, my formulation is not correct. I intended to say that non-locality implies that either A causes B or B causes A. Indeed, it doesn't make sense to say that they both cause each other.

Another confusion in your language for me is that you talk about 'the A measurement', but don't distinguish between the measurement outcome and the mere fact that a measurement with some specific settings gets performed. Do you mean that the "the A measurement outcome is causing the B measurement outcome"?

I mean that the A measurement outcome causes the B measurement outcome.

 

[PeterDonis]

If there is an interaction you cannot assume that distant equipments are independent

You can if the interaction is limited to the speed of light and the measurements are spacelike separated. That is precisely the case that Bell was interested in.

if you only ask for a minimum requirement so that the theory passes Bell's theorem

A theory which makes correct predictions about experimental results will violate the Bell inequalities, not satisfy them.

How do you know that?

Because ordinary gravitational and electromagnetic interactions (i.e., the kind we can describe with the classical theories of those interactions) cannot produce violations of the Bell inequalities.

By non-locality I mean the statement that space-like events cause each other.

Which is meaningless unless you can give an operational definition of "cause", i.e., some way to test whether there is a causal connection between two events. That's why I very carefully defined "non-locality" to be something that we know is testable: violation of the Bell inequalities.

The argument is really simple.

Only because your argument includes a number of unstated premises. Some of which QM is known to violate.

QM/QFT can be local if they are statistical approximations to a hidden-variable theory.

No local hidden variable theory can produce violations of the Bell inequalities. That's what Bell's theorem proved. We do have at least one example of a hidden variable theory that does produce Bell inequality violations--the Bohmian interpretation of standard QM--but that theory is explicitly non-local.

 

[AndreiB]

You can if the interaction is limited to the speed of light and the measurements are spacelike separated. That is precisely the case that Bell was interested in.

In classical electromagnetism the interactions are limited by the speed of light.

A theory which makes correct predictions about experimental results will violate the Bell inequalities, not satisfy them.

I didn't say anything about "satisfying the inequalities". I said a theory should pass (not be ruled out) by Bell's theorem.

Because ordinary gravitational and electromagnetic interactions (i.e., the kind we can describe with the classical theories of those interactions) cannot produce violations of the Bell inequalities.

Or so you claim. Where is the proof for this assertion?

Which is meaningless unless you can give an operational definition of "cause", i.e., some way to test whether there is a causal connection between two events.

In the argument I presented one either assumes or rejects a causal connection, each choice implying some consequences. So, there is no need to perform any test.

That's why I very carefully defined "non-locality" to be something that we know is testable: violation of the Bell inequalities.

The theory of relativity forbids space-like events being causally related. Any theory that denies that is in contradiction with SR, so this is the definition of locality which is relevant here.

Only because your argument includes a number of unstated premises. Some of which QM is known to violate.

Please state those premises then!

No local hidden variable theory can produce violations of the Bell inequalities.

...except for the case when the statistical independence assumption is denied. This is the case I am arguing for.

 

[Sunil]

...except for the case when the statistical independence assumption is denied. This is the case I am arguing for.

To give up the assumption that decisions of experimenters what to measure can be made independent of the initial state means the end of experiments in science. Because without this assumption experiments are useless, they cannot be used to show anything nontrivial. Every observed correlation allows an explanation - it is a consequence of the special choices of the experimenters.

 

[Sunil]

It seems to me that microcausality is a weaker condition than locality.

It is indeed weaker. It is essentially only about the impossibility to send signals FTL, but allows violations of Bell inequalities. Bell locality forbids violations of the Bell inequalities.

 

[AndreiB]

It is indeed weaker. It is essentially only about the impossibility to send signals FTL, but allows violations of Bell inequalities. Bell locality forbids violations of the Bell inequalities.

Exactly my point. Relativity does not distinguish between events that can be used to send signals and events that cannot be used to send signals. So, showing that in QFT you cannot send signals it's not enough to guarantee compatibility with SR.

 

[AndreiB]

To give up the assumption that decisions of experimenters what to measure can be made independent of the initial state means the end of experiments in science.

I think there are situations where the initial state is indeed independent of the experimenters' decisions and other situations where it's not. One has to analyze the physics of the situation and decide one way or another. More exactly, if the experiment involves long-range interactions between the experimenter and the system, the state of the system would be perturbed by the experimenter. For example, if our experimenter wants to study some delicate gravitational interaction between two small objects he should not move around that place. If he does so, the mass of his body would change the state of the system. This does not mean "the end of experiments in science".

Every observed correlation allows an explanation - it is a consequence of the special choices of the experimenters.

Such an explanation only works if the influence of the experimenter on the system can be established, based on the physics of the situation. One should not make unjustified assumptions, one way or another.

 

[Sunil]

I think there are situations where the initial state is indeed independent of the experimenters' decisions and other situations where it's not.

Of course, given that one cannot exclude that the experimenter decides to have such a dependence on the given initial data, or that this happens by bad design, the mere possibility of such a dependence exists. But there are ways to make sure that there are no such dependencies, and such ways have been used in Bell tests. Simply make the local measurements dependent on local random numbers, or input coming from the opposite direction by light from far galaxies, or combinations of several such things.

More exactly, if the experiment involves long-range interactions between the experimenter and the system, the state of the system would be perturbed by the experimenter. For example, if our experimenter wants to study some delicate gravitational interaction between two small objects he should not move around that place. If he does so, the mass of his body would change the state of the system.

And, of course, the two experiments are event which are space-like separated to exclude any physical influences by whatever. According to GR gravity has the limiting speed c too.

This does not mean "the end of experiments in science".

It does if a.) you insist on such dependencies even if extraordinary means have been used to exclude such influences, like in the Bell experiments, and b.) behave after this consistently, thus, don't use the independence assumption anywhere else, instead of ignoring what you think about BI violations.

Such an explanation only works if the influence of the experimenter on the system can be established, based on the physics of the situation. One should not make unjustified assumptions, one way or another.

The independence assumption is the default, the zero hypothesis. That means, you can make it even if you have no knowledge about this. (That's so in objective Bayesian probability.)

 

[AndreiB]

Of course, given that one cannot exclude that the experimenter decides to have such a dependence on the given initial data, or that this happens by bad design, the mere possibility of such a dependence exists.

Great.

But there are ways to make sure that there are no such dependencies, and such ways have been used in Bell tests.

I disagree. There is nothing you can do so that an electron/nucleus stops interacting electromagnetically and gravitationally with other electrons/nuclei. it's a direct consequence of mass/energy and charge conservation.

Simply make the local measurements dependent on local random numbers, or input coming from the opposite direction by light from far galaxies, or combinations of several such things.

As long as the equipment is made out of atoms, it does not really matter. The equipment interacts with the source electromagnetically and gravitationally, the state of the source and the state of the detector+whatever you use to set the detector are still not independent. They are solutions to the N-body problem, where N is the total number of charged/massive particles in the experiment.

And, of course, the two experiments are event which are space-like separated to exclude any physical influences by whatever. According to GR gravity has the limiting speed c too.

The instantaneous positions of the Earth and the Sun are not independent, even if GR is local. The correlations are a result of their past gravitational interaction. The same is true for electromagnetic systems. So, space-like separation does not give you independence.

It does if a.) you insist on such dependencies even if extraordinary means have been used to exclude such influences, like in the Bell experiments

As explained above, those "extraordinary means" are ineffective here. An N body system remains an N body system regardless of the specific arrangement of those bodies.

, and b.) behave after this consistently, thus, don't use the independence assumption anywhere else, instead of ignoring what you think about BI violations.

I am consistent. The EM interaction between objects that are neutral on average (same number of positive and negative charges) is not going to influence average properties, like the position and momentum of their center of mass, their temperature, chemical composition and so on because the EM interactions cancel at the statistical level. So, you can use the independence assumption in Newtonian mechanics, chemistry, biology and so on.

In a Bell test you are not interested in average quantities. The hidden variables (say photons' polarisations) depend on the specific arrangement of charged particles and EM fields at the locus and time of the emission. And those properties do depend on the state of the detectors.

The independence assumption is the default, the zero hypothesis. That means, you can make it even if you have no knowledge about this. (That's so in objective Bayesian probability.)

But we have knowledge about this. We know that massive/charged particles interact and we know that the experiment depends on a specific charge/fields distributions. So, we need to reject the independence assumption hypothesis.

 

[Sunil]

I disagree. There is nothing you can do so that an electron/nucleus stops interacting electromagnetically and gravitationally with other electrons/nuclei. it's a direct consequence of mass/energy and charge conservation.

So what? Some influence does not necessarily lead to dependence. Say, the parameter you want to control is $0 \le A \le 1$. To compute A, take the fractional part of several different ways to generate random numbers, each of which has an approximately even distribution over $[0,1]$. Then, if some parts of this sum are somehow influenced by B, it does not matter. The resulting A will be nonetheless independent of B.

As long as the equipment is made out of atoms, it does not really matter. The equipment interacts with the source electromagnetically and gravitationally, the state of the source and the state of the detector+whatever you use to set the detector are still not independent. They are solutions to the N-body problem, where N is the total number of charged/massive particles in the experiment.

Ok, let's start with an angle of the detector which depends completely on the source. Then turn it by $2\pi A$. The resulting angle will be independent on the influence of the source.

The instantaneous positions of the Earth and the Sun are not independent, even if GR is local. The correlations are a result of their past gravitational interaction. The same is true for electromagnetic systems. So, space-like separation does not give you independence.

My random number generator initialized with the time when I had decided to restart my computer last time may be also dependent on the location of the Sun. For example, I don't restart computers if I sleep and my sleeping mode is somewhat correlated with the position of the Sun as visible from my window. The influence on the parts of the second of the time, which is what is given as the seed to the pseudorandom number generator, will be already minimal.

In a Bell test you are not interested in average quantities. The hidden variables (say photons' polarisations) depend on the specific arrangement of charged particles and EM fields at the locus and time of the emission. And those properties do depend on the state of the detectors.

But choosing the final configuration of the detector using random numbers obtained and computed only after the initial emission makes the imaginable influence of the detectors before the final preparation on the emission irrelevant. Same for influences of the emission device on the detectors. That would be simply adding yet another error to the already used random rotation.

But we have knowledge about this. We know that massive/charged particles interact and we know that the experiment depends on a specific charge/fields distributions. So, we need to reject the independence assumption hypothesis.

As my consideration shows, these interactions do not destroy statistical independence if a sufficiently safe design is used.

 

[AndreiB]

So what? Some influence does not necessarily lead to dependence. Say, the parameter you want to control is $0 \le A \le 1$. To compute A, take the fractional part of several different ways to generate random numbers, each of which has an approximately even distribution over $[0,1]$. Then, if some parts of this sum are somehow influenced by B, it does not matter. The resulting A will be nonetheless independent of B.

I think you misunderstood my point. Yes, you can do whatever you want with the detectors, but:

1. Whatever you do is encoded in the past state, as we are speaking about deterministic theories.
2. This past state is part of a solution to the N-body problem that also includes the particles in the source.

When you change your past state (say, by using a different seed for your random number generator) you "jump" to a different solution of the N-body problem, and the part of that solution which is relevant to the source is also different. It doesn't really matter how intricate is your algorithm for choosing the settings.

Ok, let's start with an angle of the detector which depends completely on the source. Then turn it by $2\pi A$. The resulting angle will be independent on the influence of the source.

In order to be able to perform that turn you need to have a suitable initial state that necessarily determines you to perform that turn. This again gives you a different initial state for the N-body system, with a different solution for the hidden variables.

My random number generator initialized with the time when I had decided to restart my computer last time may be also dependent on the location of the Sun. For example, I don't restart computers if I sleep and my sleeping mode is somewhat correlated with the position of the Sun as visible from my window. The influence on the parts of the second of the time, which is what is given as the seed to the pseudorandom number generator, will be already minimal.

Again, it does not matter how minimal the influence of a different initial state appears to you. The only thing that matters is that a changed initial state would give you a different solution to the N-body problem. And this implies a change of the hidden variable.

But choosing the final configuration of the detector using random numbers obtained and computed only after the initial emission makes the imaginable influence of the detectors before the final preparation on the emission irrelevant.

Not so, if you just look at the physics of the situation. You don't "choose" the final configuration, the final configuration is determined, together with the hidden variables, by the initial state of the experiment (position/momenta of charges, electric/magnetic fields). Each such initial state evolves uniquely into the final measurement settings AND the hidden variables. In another run of the experiment the initial state is different, you get another set of measurement settings AND hidden variables. And so on for every run of the experiment. Unless you don't solve those 6N equations or so there is no way to know how likely a certain value of the hidden variable is, given a certain detector setting.

 

[Sunil]

I think you misunderstood my point. Yes, you can do whatever you want with the detectors, but:

1. Whatever you do is encoded in the past state, as we are speaking about deterministic theories.
2. This past state is part of a solution to the N-body problem that also includes the particles in the source.

When you change your past state (say, by using a different seed for your random number generator) you "jump" to a different solution of the N-body problem, and the part of that solution which is relevant to the source is also different. It doesn't really matter how intricate is your algorithm for choosing the settings.

First, no, it matters. If the algorithm is complicate enough, there will be no correlation.

Correlations do not appear out of nothing. Instead, they have causal explanations. If, by modifying the seed for my random number generator, I modify the angles of my devices, but by whatever way also influence the emitter, this will not lead to a correlation.

If you think it leads to a correlation, and, moreover, even think that doing this in many different ways will not destroy this correlation (else, it could influence only one experiment, but not consistently distort many experiments in the same way, namely toward a violation of the Bell inequality), you follow a universe-wide conspiracy theory of universal control of everything. This ultimate conspiracy theory is named superdeterminism, and those who believe it ... ok, self-censored.

But in this case I have to repeat the objection that you have to give up science in general. And you cannot invent a situation where the independence assumption would be justified, thus, no scientific experiment can prove anything.

 

[PeterDonis]

In classical electromagnetism

This is the quantum interpretations forum, not the classical physics forum. In any case, classical electromagnetism cannot produce Bell inequality violations on measurements of entangled particles, so it is clearly a non-starter as far as the subject of this thread is concerned.

I said a theory should pass (not be ruled out) by Bell's theorem.

Bell's theorem is not the final arbiter of what theories get "ruled out". Experiment is. Experiment has clearly shown that in the real world, the Bell inequalities are violated. So any theory that cannot produce violations of the Bell inequalities is ruled out by experiment. Whether you want to call that also being ruled out by Bell's theorem is a matter of words, not physics.

Or so you claim. Where is the proof for this assertion?

The burden of proof is on you, not me, since you are the one who is claiming that a classical theory like classical EM or classical gravity can account for Bell inequality violations on measurements of entangled particles, a claim which, as far as I know, no physicist has made in the literature. At this point you are the one who needs to either back up this claim with references, or drop it, or be banned from further posting in this thread.

The theory of relativity forbids space-like events being causally related.

The classical theory of relativity says this. But we are not talking about the classical theory of relativity. Quantum field theory, which is the quantum theory of relativity, does not say this. All it says is that spacelike separated measurements must commute. It takes no position on whether this precludes such measurements being "causally related", since there is no testable criterion in QFT for "causally related", whereas testing whether spacelike separated measurements commute is simple.

except for the case when the statistical independence assumption is denied. This is the case I am arguing for.

Please give a reference for the specific kind of model you are referring to.

 

[AndreiB]

First, no, it matters. If the algorithm is complicate enough, there will be no correlation.

OK, let's make this more clear:

let S0 be the microscopic state (position/momenta of charge particles+electric/magnetic fields) of the source at a certain (initial) time before the experiment. Let D10 and D20 be the corresponding microscopic states of the detectors. Since all charged particles interact, the hidden variable, lambda (the polarisations of the emitted EM waves at some later time) would be given by a very complicated function like:

lambda = f(S0,D10,D20).

So, lambda cannot be independent of either D10 or D20, it's a function of them.

Since the theory is deterministic, the final state of the detectors, at the moment of measurement (D1f, D2f) will also be a function of their initial states (D10 and D20), so lambda cannot be independent of D1f and D2f. In other words, the hidden variable is not independent on the measurement settings.

Correlations do not appear out of nothing. Instead, they have causal explanations. If, by modifying the seed for my random number generator, I modify the angles of my devices, but by whatever way also influence the emitter, this will not lead to a correlation.

If you modify the seed, you modify D10 to D10'. In this case you will have:

lambda'=f(f(S0,D10',D20).

There is no reason to assume that lambda' = lambda, as the argument of the function is different, so a change of the seed implies a change of the hidden variable. Again, the independence assumption fails.

If you think it leads to a correlation, and, moreover, even think that doing this in many different ways will not destroy this correlation...

I have no idea what correlations, if any, can be generated in this way. I have no intuitive grasp on how the solution to those 10^26 equations looks like. What I know is that the hidden variables and detector settings can't be independent, so Bell's theorem can't rule out any theory with long-range interactions. I do not claim that such theories can reproduce QM (maybe they can't), but the opposite claim, that they cannot reproduce QM, is also lacking any evidence. We just don't know.

This ultimate conspiracy theory is named superdeterminism, and those who believe it ... ok, self-censored.

There is no need to posit any conspiracy. Interacting objects are not independent, this is the only point I am trying to make. Since one premise of Bell's theorem is not fulfilled, the conclusion does not follow. The conclusion might still be true, but not necessarily so.

But in this case I have to repeat the objection that you have to give up science in general.

As explained, the above argument applies only to interacting systems. Even in a Bell test, the macroscopic settings of the detectors are independent parameters (since the interaction between their constituent particles cannot determine a macroscopic rotation of the device). So, you can assume independence in all experiments where the microscopic arrangement is not relevant, which includes almost everything except Bell tests and a few other quantum experiments.

I also think that the importance of the independence assumption is greatly exaggerated. Most experiments do not depend on it.

And you cannot invent a situation where the independence assumption would be justified, thus, no scientific experiment can prove anything.

It's not about inventing anything. You analyze the situation and determine, based on what we know, what is independent and what is not. It's a scientific, objective criteria.

 

[AndreiB]

This is the quantum interpretations forum, not the classical physics forum.

I don't see how one can talk about Bell's theorem without mentioning hidden variables. My arguments do not depend specifically about electromagnetism, they hold for any theory with long-range interactions.

In any case, classical electromagnetism cannot produce Bell inequality violations on measurements of entangled particles

Can you provide a reference to back up this assertion? And again, this is not only about EM, it's about a class of theories with long-range interactions. EM is just a member of this class.

Bell's theorem is not the final arbiter of what theories get "ruled out". Experiment is.

I agree.

Experiment has clearly shown that in the real world, the Bell inequalities are violated.

Agreed.

So any theory that cannot produce violations of the Bell inequalities is ruled out by experiment.

Agreed.

The burden of proof is on you, not me, since you are the one who is claiming that a classical theory like classical EM or classical gravity can account for Bell inequality violations on measurements of entangled particles...

The burden of proof is on the one who makes the claim. I did not claim that EM violates the inequalities, I claimed that one cannot prove, based on Bell's theorem that EM cannot violate them, an important distinction.

You, on the other hand, claimed that EM cannot violate the inequality, the burden of proof is on you to justify this claim.

The classical theory of relativity says this.

There is no other theory of relativity.

Quantum field theory, which is the quantum theory of relativity, does not say this. All it says is that spacelike separated measurements must commute. It takes no position on whether this precludes such measurements being "causally related", since there is no testable criterion in QFT for "causally related", whereas testing whether spacelike separated measurements commute is simple.

OK, let's assume for the sake of the argument that A caused B. In this case you need to specify an absolute reference frame, to show that A happened first. Since QFT does not specify this frame, it's predictions would be inconsistent (different observers would disagree on how the same experiment happened).