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When drawing conclusions from this most important and profound theorem, I wonder if somebody has interpreted its proof of the falseness of local realism as implicitly referring to elementary particles as realistic objects.
Are you asking if the interpretation casts any bearing on whether elementary particles are real, as opposed to something other than real?When drawing conclusions from this most important and profound theorem, I wonder if somebody has interpreted its proof of the falseness of local realism as implicitly referring to elementary particles as realistic objects.
Bell's theorem refers to correlations between "classical" or "macroscopic" experimental outcomes. So as long as one believes that the experimental outcomes in a Bell test are "classical", then the violation of the inequality does rule out local realism.
Are you asking if the interpretation casts any bearing on whether elementary particles are real, as opposed to something other than real?
I don't quite agree with that characterization of Bell's theorem. The theorem doesn't actually mention particles at all. It's a theorem about correlations between detector outcomes. It's agnostic about what causes those correlations.The Bell's inequalities are always mathematically formalized in terms of particle's probabilities, and their effects on detectors wich are identified with the particles themselves.
Hmmm, that is quite a strong statement, isn't it? I thought local realism was a very important and specific assumption about the nature of the variables in the Bell inequalities. And the theorem may be agnostic about the cause of the correlations but it is not agnostic about identifying individual particles with what detectors detect.I don't quite agree with that characterization of Bell's theorem. The theorem doesn't actually mention particles at all. It's a theorem about correlations between detector outcomes. It's agnostic about what causes those correlations.
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Bell's theorem doesn't require any specific assumptions about the nature of the variables.
It makes assumptions about causal influences among variables, but it doesn't say anything about particles.Hmmm, that is quite a strong statement, isn't it? I thought local realism was a very important and specific assumption about the nature of the variables in the Bell inequalities.
But I don't see that Bell's theorem has anything specifically to do with the reality of particles.Quoting the Stanford encyclopedia page on the theorem: "Locality is a condition on composite systems with spatially separated constituents, requiring an operator which is the product of operators associated with the individual constituents to be assigned a value which is the product of the values assigned to the factors, and requiring the value assigned to an operator associated with an individual constituent to be independent of what is measured on any other constituent. From his assumptions Bell proved an inequality (the prototype of “Bell's Inequality”) which is violated by the Quantum Mechanical predictions made from an entangled state of the composite system." (my bold)
I agree the word particles is not mentioned in these assumptions but I think it is clearly implicit as localized realistic individual constituents. And I think that is what Bell and most physicists assumed.
Are you asking whether relativistic QFT is also theoretically predicted to violate the Bell inequalities?The Bell's inequalities are always mathematically formalized in terms of particle's probabilities, and their effects on detectors wich are identified with the particles themselves. But if one separates these, i.e. doesn't identify the detector outcomes with particle entities, it follows that the inequalities hinge on the assumption of the concept of particles as realistic localized objects for the inequalities to impy local realism.
In this sense the violation of the inequalities by the experiments seems to affect just the forms of local realism depending on that specific particle theoretical conception.
I'm not sure what the objections to this reasoning are, other than it seems to lead to seeing the theorem and the results of the experiments based on it as evidence that no theory with particles as fundamental objects is possible, the local hidden variables would be particles themselves as realistic localized objects and their identification with clicks in detectors.
Ok, I see what you mean and it is actually not in contradiction with my point.It makes assumptions about causal influences among variables, but it doesn't say anything about particles.
But I don't see that Bell's theorem has anything specifically to do with the reality of particles.
At the heart of what Bell is doing is assuming that the probability of an outcome can only depend on facts about the causal past of that outcome. Causally separated outcomes can only be correlated due to sharing a common causal past. That's the assumption that Bell used to derive his inequality, and which QM seems to violate.
Local, I'm sure. I think the idea was that there could be forces, particles, or whatever present that could take shapes or forms without specific limit as long as it led to a specification of the system which determined an outcome of a counterfactual measurement. Suppose it was a wave and not a particle? What if there were additional unknown particles present? So no particular requirement other than local variables/rules/forces/waves/particles/etc.I agree the word particles is not mentioned in these assumptions but I think it is clearly implicit as localized realistic individual constituents. And I think that is what Bell and most physicists assumed.
First you need be precise on what you mean by realistic object.When drawing conclusions from this most important and profound theorem, I wonder if somebody has interpreted its proof of the falseness of local realism as implicitly referring to elementary particles as realistic objects.
I don't think you're describing the connection between the many-worlds theory and the Bell inequality very well.Bell's theorem refers to correlations between "classical" or "macroscopic" experimental outcomes. So as long as one believes that the experimental outcomes in a Bell test are "classical", then the violation of the inequality does rule out local realism.
There are some assumptions that go into this conclusion. For example, it assumes that each measurement produces only one outcome. In many-worlds each measurement has more than one outcome, so the Bell test don't rule out that many-worlds is a local realistic theory.
Ok, all those I consider local realistic objects or individual constituents in the words of the Stanford reference above. If those kind of objects are all what is rejected when it is stated that Bell's theorem proves local realism is incompatible with what we observe in quantum experiments I completely agree. But sometimes a broader concept of local realism is used, what I'm saying is that rejecting that broader concept is a bit of a case of throwing the baby with the bathwater.Local, I'm sure. I think the idea was that there could be forces, particles, or whatever present that could take shapes or forms without specific limit as long as it led to a specification of the system which determined an outcome of a counterfactual measurement. Suppose it was a wave and not a particle? What if there were additional unknown particles present? So no particular requirement other than local variables/rules/forces/waves/particles/etc.
I've wondered about it too. Let me give an example of a question I'd like to know the answer to: Is non-relativistic Newtonian gravity local or nonlocal in the sense of the Bell theorems?Ok, all those I consider local realistic objects or individual constituents in the words of the Stanford reference above. If those kind of objects are all what is rejected when it is stated that Bell's theorem proves local realism is incompatible with what we observe in quantum experiments I completely agree. But sometimes a broader concept of local realism is used, what I'm saying is that rejecting that broader concept is a bit of a case of throwing the baby with the bathwater.
For intance, is a classical field in the list of things you consider something local? Because I've seen it sometimes conceptualized as local realistic in the Einsteinian sense, and sometimes as something nonlocal.
No, but QFT in the sense of effective theory or operational tool I don't think that one can reliably answer that question, it doesn't have a well defined ontology, not even enough to have interpretations like quantum mechanics has.Are you asking whether relativistic QFT is also theoretically predicted to violate the Bell inequalities?
There are actually a couple of questions regarding QFT and the Bell inequalities. One is that "local" in QFT is usually defined as operators commuting if they are spacelike, whereas in QM one usually assumes operators that factor according to a tensor product. So the question is whether the Bell inequalities are violated to the same extent in QFT and QM. This is called Tsirelson's problem and is only partially solved.No, but QFT in the sense of effective theory or operational tool I don't think that one can reliably answer that question, it doesn't have a well defined ontology, not even enough to have interpretations like quantum mechanics has.
I don't agree with your characterization of many-worlds. The "splitting" is not something that propagates from one point to another. And there is no useful notion of the "number" of possible worlds--that number is always infinite. And there is no need to "erase" possible worlds.I don't think you're describing the connection between the many-worlds theory and the Bell inequality very well.
A major point behind the many-worlds theory is that whenever there is a QM "coin flip", you create a "heads" universe and a "tails" universe. But the Bell Inequality brings into question whether there really ever are any such coin flips.
Let's look at how many-worlds sees a common Bell experiment. Our two entangled particles A and B, head towards their detectors. In the case of A, we decide to measure along a 30 degree axis - and so as particle A reaches detector A, the universe splits with one getting spin up and the other spin down. Now consider particle B. B will reach detector B without ever knowing what is happening to A. From B's point of view, the world-splitting created at detector A hasn't happened yet. Just before B reaches its detector, we will set detector B to measure either 30 degrees or 120 degrees. If we pick 120 degrees, things are simple. Both A and B create an independent world split and it doesn't really matter which is first.
But if we pick 30 degrees, we have a bit of a problem: both detector A and B need to split the universe in exactly the same way. One solution would be to allow the split at both A and B to occur and to allow all four worlds to be created, but then we would need to erase two of those worlds once the results between A and B were compared. Alternatively, we can allow the splitting at A and B to be coordinated - using non-local mechanisms.
What the Bell Inequality shows us is that as long as we follow the rules of QM, there will be non-local coordination of apparently random events. This takes an awful lot of wind out of the many-worlds sails. Why do we need to split the universe when we know that there are non-local influences on what we think are random events? We already have an explanation for the apparent randomness - that something or everything, anywhere, anytime in the universe is fair game for deciding QM coin flips.
In the sense of Bell's theorem, a classical field counts as a local hidden variable.For intance, is a classical field in the list of things you consider something local? Because I've seen it sometimes conceptualized as local realistic in the Einsteinian sense, and sometimes as something nonlocal.
In the simplest form of Newtonian gravity, it is non-local. Obviously that was already long gone by the time EPR appeared in 1935. Bell was responding to the EPR paradox, in terms that would have mattered in the context of EPR. So definitions of realism (hidden variables or in EPR terms, elements of reality) should be seen in that light.I've wondered about it too. Let me give an example of a question I'd like to know the answer to: Is non-relativistic Newtonian gravity local or nonlocal in the sense of the Bell theorems?
It's nonlocal. The setting of Alice's detector could in principle be determined by sufficiently precise gravitational measurements at Bob's detector, since classical gravity is instantaneous. So the hidden mechanism that determines the outcome of Bob's measurement might very well take Alice's setting into account. The violation of Bell's inequality would not be hard to achieve in that case.I've wondered about it too. Let me give an example of a question I'd like to know the answer to: Is non-relativistic Newtonian gravity local or nonlocal in the sense of the Bell theorems?
Indeed it is.In the simplest form of Newtonian gravity, it is non-local.