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Bell's theorem is often interpreted to have destroyed local realism. This means something like the properties of the particle do not exist until they are being measured. I am not sure what does this exactly mean. Can there still be an algorithm to predict those measurements? Can anyone give me an example of a toy theory that is local but non-realist? How such "unreal" variable would be computed and what would the difference with local hidden variables be.

I am not asking for a quantum mechanical theory, just a local no real theory, how is a prediction made? is there an algorithm at all? if there is no algorithm, then what is it, a noncomputable law? a random law? what other options am I missing?

glS
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  • Possibly related: https://physics.stackexchange.com/questions/591578/how-does-relaxing-counterfactual-definiteness-allows-for-chsh-inequality-violati/591824#591824 – Cream Nov 30 '20 at 14:47
  • Did you already took a look at Aspect experiment: https://en.wikipedia.org/wiki/Aspect%27s_experiment ? – Mauricio Nov 30 '20 at 17:48
  • @Mauricio I was aware of it. But my question is not about experiments, but about what is meant by ruling out local realism, what kind of local hidden variables theory can be left after you exclude "realism"? –  Nov 30 '20 at 18:53
  • Can anyone give me an example of a toy theory that is local but non-realist?, well, quantum mechanics? – glS Dec 01 '20 at 00:25
  • @gls I disagree, qm might be just non-local, what does exactly mean non-real in an algorithm or rule of nature? –  Dec 05 '20 at 22:28
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    @brucesmitherson I'm not sure what algorithms have to do with it, but QM is literally where the concept of "non-realism" came from. It is non-realist in the sense that measurement results cannot be attributed to/determined by some hidden variable existing before the measurement itself. That's the typical way to express QM anyway, as a local non-realist theory. If you use a different formalism such as bohmian mechanics you can equivalently describe it as realist but non-local. Both choices are equivalent as far as I'm aware – glS Dec 06 '20 at 18:31
  • @gls it seems to me that non-realism is just an empty word used to avoid the word "non-local" –  Dec 06 '20 at 18:34
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    @brucesmitherson no, as I said above, these are different concepts. Bohmian mechanics is non-local but realist (it is fully deterministic, but admits action-at-a-distance). Standard QM is local (no instantaneous causal influences) but non-realist (no hidden variable explanations). See the answer below – glS Dec 06 '20 at 18:41
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    I think Tim Maudlin argues there is no such thing as "local nonrealism," so you may appreciate reading What Bell did. There is a reply article that gives counterarguments and argues for how there can be "local nonrealist" theories. At the least, I suspect the reply article would provide you with an understanding of what people are trying to convey. – Maximal Ideal Dec 06 '20 at 22:52
  • @brucesmitherson I love these conceptual questions, and your suspicion that “non-realism is just an empty word used to avoid the word "non-local"“ is understandable; however these two concepts aren’t the same, there are indeed toy examples of local non-realist theories (see my answer). Maximal Ideal, thanks for the link to Tim Maudlin’s article! He says “any world that displays violations of Bell's inequality ... must be non-local. Since the world we live in displays such violations, actual physics is non-local.” Note this is *not* saying there couldn't be a local non-realist world. – ReasonMeThis Dec 06 '20 at 23:37
  • @gIS there can't be faster than light communication of information, but that doesn't mean that quantum mechanics is a local theory (see the addendum in my answer). Tim Maudlin, as I just discovered, seems to agree (see my previous comment). – ReasonMeThis Dec 06 '20 at 23:46
  • @glS thanks a lot, I will read it! –  Dec 07 '20 at 03:25
  • @ReasonMeThis yes, thank you, I am still evaluating the answers –  Dec 07 '20 at 03:26
  • @ReasonMeThis "but that doesn't mean that quantum mechanics is a local theory" I'd say that's quite close to the definition of the theory being local. The existence of a way to describe things via a non-local theory doesn't affect the standard framework being a local one. – glS Dec 07 '20 at 09:19
  • @gIS The OP is asking about "local realist" as defined in the context of Bell's theorem (see OP’s very first sentence). That definition of "local", which is also the same used in the EPR paper, makes quantum mechanics a non-local theory. – ReasonMeThis Dec 07 '20 at 10:02
  • @ReasonMeThis I'm just using the standard terminology used in this context, see e.g. https://arxiv.org/abs/1303.2849 – glS Dec 10 '20 at 08:31
  • @gIS their abstract says "quantum theory cannot be accounted for by any local theory" but you say: "Standard QM is local". – ReasonMeThis Dec 10 '20 at 22:24
  • Any world would violate Bell's inequality because his concept of particles and what they can do is very limited. Two particles can easily be correlated and tested to produce any QM prediction if you take them seriously and allow for all the proper principles. – Bill Alsept Dec 10 '20 at 23:05
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    @ReasonMeThis Indeed, I should have been more careful with the terminology. QM produces nonlocal correlations. Nevertheless, it is local, in the sense of the theory being no-signaling. I'd say in general there is a difference between saying "QM is nonlocal" (which is generally taken to mean it allows for instantaneous causal influences) and saying "QM allows for nonlocal correlations (assuming a non-FTL description)", which is e.g. proven via Bell, CHSH etc. See sections (II.A.1) and (II.A.2) in the linked paper. QM is local, but predicts nonlocal correlations. – glS Dec 11 '20 at 08:43
  • What is wrong with local, real and deterministic? – Bill Alsept Dec 11 '20 at 11:00
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    @gIS by their notion of locality, QM is not local (“ quantum theory cannot be accounted for by any local theory", see also the very first sentence in their introduction, and elsewhere in the paper). Of course both notions are meaningful, but their notion of locality is identical to the one in my answer, and more importantly to Bell’s. – ReasonMeThis Dec 12 '20 at 06:13
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    @ReasonMeThis look, that's all just semantics. Until you precisely define your words you can say one thing or the other. The way I see it, the only meaningful statement is that QM cannot be described by a theory allowing only for correlations writable as $p(ab|xy)=\sum_\lambda p_\lambda p_\lambda(a|x)p_\lambda(b|y)$. The rest is chatter – glS Dec 12 '20 at 11:00

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Short answer: the question puts into sharp focus the fact that there are various definitions of the term "local" and "realist", which are in need of careful disambiguation.

It's not possible to give a thorough treatment, but let's give a quick review of the most common definitions.

What is a local theory?

There are two main meanings given to the term local:

  1. Local in the sense of EPR and Bell. This means "no spooky action at a distance", i.e. the probabilities for the results of a process/procedure are not dependent on procedures performed far away (at space-like separations).

  2. Local in the sense of no-signaling. This means no information can be communicated faster than light from one observer to another.

Quantum theory is non-local in the first sense and local in the second. In particular, it's noteworthy that Bohm's pilot wave theory is deterministic and local (in the 2nd sense).

What is a realist theory?

Here there is even more definitional confusion. Let's list a few noteworthy definitions:

  1. Realist in the sense of preexisting information about measurement results.

This means that the system "knows" the value of any property, such as position, momentum etc. prior to measurement. This corresponds to Einstein's notion of "elements of reality".

Another way to say it would be: measurements of properties have definite numerical outcomes, which follow deterministically from the prior state of the system.

A shorthand would be to say that the theory includes hidden variables. Copenhagen quantum mechanics is not realist, but the pilot wave theory is realist in this sense.

  1. Realist in the sense of determinism.

You might be wondering how the previous definition is different from determinism. The big difference is that determinism does not presuppose that measurements of properties have definite numerical outcomes.

For example, the many world theory is deterministic, but not realist in the first sense, because measurements do not result in definite numerical outcomes, but instead in the branching of the world, with all numerical outcomes existing simultaneously.

A further distinction is that strictly speaking the first definition does not require that the time evolution between measurements be deterministic, only that measurements be deterministic.

  1. Realist in the sense of "indistinguishable from realist".

Unlike the first definition, where the theory's formalism must already include hidden variables, according to this definition a theory is realist if its predictions can be reproduced by another theory with hidden variables. According to this definition, Copenhagen quantum mechanics would be realist because its predictions are indistinguishable from those of the pilot wave theory.

Any physical theory can be reproduced by a realist2 (deterministic) theory because any source of randomness in the theory's formalism can be reproduced by a deterministic "simulation" of randomness. Therefore any physical theory that has a notion of definite numerical measurement outcomes (so not the many worlds theory) is realist in this third sense.

  1. Philosophical realism.

To satisfy this definition, the theory needs to be interpreted as describing the actual reality, as opposed to, for example, our subjective experience or epistemological state.

This is not so much an attribute of the theory itself, but a philosophical position on what a theory is, or an interpretation of the relationship between a given theory and reality.

What is local realism?

With so many definitions of the two separate terms floating around (and I certainly haven't covered them all!), it might seem like the combined term is even more ambiguous. However, the situation is not as dire. There seems to be far less disagreement on the meaning of the combined term.

A local realist theory is typically understood to be a theory which is Bell-local (i.e. local in the first sense) and realist in the first sense (measurements are not "chancy"). A shorthand would be to say that the theory includes local hidden variables.

(One alternative definition in the literature involves, instead of “normal", deterministic local hidden variables, having local but stochastic ones. I won't spend too much time on the explanation, but it's not too hard to show that this definition reduces to the theory just being Bell-local.)

What did Bell prove?

There are two opinions floating around. Bell's own opinion was that he proved that the results of quantum mechanics cannot be reproduced by a local (in the sense of Bell/Einstein, i.e. the first sense) theory.

Others think that he proved that they cannot be reproduced by a local realist theory.

Philosopher Tim Maudlin, among others, agrees with Bell. I also agree (see my other answer and comments below it for more details).

What about the original question, about a toy example of a local theory which is not realist?

Now that we have disambiguated the definitions, it should not be too hard to find such an example once we decide which exact definition we will be using.

If we decide to use the first definitions of both terms, then the Mystery Particle would be a good example of a simple local non-realist theory. This particle would be a local object that doesn't have a definite color before we shine our flashlight on it. Once we do, it randomly "chooses" the color to become/show.

Further reading.

Great reading resources have been provided by @MaximalIdeal and @gIS in the comments below the original question.

ReasonMeThis
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    Ok this disambiguating of local explains a lot! It seems clear Bell proved in a mathematical sense that you can’t have any theory that’s local in the 1st sense explain the result of the CHSR experiments. So i was then surprised to hear people saying that QM is local — because it’s mathematically impossible for it to be and to describe the actual outcome of the experiments. But now I see that that’s using local in a different sense :) – Cloudyman Oct 29 '22 at 21:41
  • Isn't Many Worlds the textbook example of a local non-realistic interpretation? – Peter Moore Dec 09 '22 at 20:51
  • @PeterMoore Thanks for posting, it was nice to return to this question and refresh my recollection of these tricky concepts. Many Worlds wouldn't be an example of local non-realism, because it's non-local (in the relevant sense of "local"). More specifically: quantum theory - whether it's Many Worlds or some other interpretation - is non-local in the 1st sense and local in the 2nd sense (as I described in my answer). The 1st sense is the relevant one here because that's the sense used in the expression "local realism". – ReasonMeThis Dec 10 '22 at 01:43
  • @Claudiu Precisely! It's a bit of an unfortunate situation that the term "local" has these two senses - no doubt this has caused lots and lots of confusion in academic discussions. – ReasonMeThis Dec 10 '22 at 01:49
  • My pleasure. :) But I'm gonna have to push back on saying MWI is non-local even in the first sense. Again I could be wrong, but I thought that MWI's answer to EPR is that the "action" that results in the spooky correlation between two measurements doesn't take place until the measurements are compared, which results in another branch forming. That is when you see the result at A, you have one branching, then when you go compare it to B (which must happen STL), you branch again, and that is the moment the "spooky" correlation gets enforced by the laws of physics, but not before. – Peter Moore Dec 10 '22 at 16:13
  • @PeterMoore The crucial part is - what exactly does it mean for a theory to be local in the 1st sense, in the sense of Bell/EPR? It means that the theory's ontology can be specified location by location: "here's the situation at A (which fully determines probabilities of all possible A measurements) - AND - here's the situation at B". This is what Bell assumed to derive his inequality. But a state like |up dn> + |dn up> can't be specified in the above form, therefore any theory whose ontology includes such states (and Many Worlds is fundamentally committed to them) is not Bell-local. – ReasonMeThis Dec 11 '22 at 11:44
  • @PeterMoore Bell proved that if we take any theory that satisfies the above assumption (Bell-locality) then it will predict that the Bell inequality will hold. But we know that QM predicts that the Bell inequality is violated. Combining these two facts, we get the conclusion: QM is inconsistent with any Bell-local theory. Note that it's a much stronger statement than saying QM is not Bell-local - we don't need Bell's theorem for that, we just need what I said in the comment above. – ReasonMeThis Dec 11 '22 at 12:19
  • @ReasonMeThis Ah ok. See to me what you're calling Bell non-local is what I'm thinking of as non-real, but I guess this is the inherent danger in talking about this in words rather than not math. And MWI (which I don't endorse BTW, though I tend to flip on this every few years ;)) makes no predictions different from vanilla QM, which is really what matters. – Peter Moore Dec 11 '22 at 19:18
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An explanation is local if the behavior in one part doesn't depend on the actions in the other part. For example, local operations should commute if they are spacelike separated. You should be able to create two (classical) computer programs that simulate the system, and they don't need to communicate the actions they are taking to each other to produce correct output.

An explanation is realist if the state of the whole system can be described by some probability distribution. You should be able to reproduce the behavior of a local realist system by tallying up how the local computer programs you wrote from before respond to each of the probabilistic cases from the distribution.

An example of a non-realist system is... instead of the various cases from the probability distribution being independent, and adding up the usual linear way, they interact with each other in complicated ways. For example, you might see the system perform behavior like "if the chance that X happened is greater than 10%, cut the chance that Y happened in half" (which is not a valid probabilistic operation because it isn't linear; there is no way to turn it into a stochastic matrix with X and Y as basis vectors).

Craig Gidney
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  • My interpretation is that you mean that non-realist is equivalent to non markovian? Am I correct? –  Dec 07 '20 at 17:15
  • I think there might be a couple different definitions of markovian, but yes basically I mean it can be modelled by a state machine with probabilistic transitions. I don't know if that's the generally accepted definition but that's my reading of realism. – Craig Gidney Dec 07 '20 at 17:27
  • What would make a nonmarkovian process help reproduce the nonclassical correlations of QM as opposed to a markovian process? –  Dec 07 '20 at 17:35
  • @brucesmitherson I think you need the locality constraint or else you can do pretty much anything with a Markov process plus some hidden information. It's the combination of the two that's limiting. – Craig Gidney Dec 07 '20 at 17:41
  • Thus, in your opinion, could in principle a local non-markov process reproduce the QM correlations? –  Dec 07 '20 at 17:48
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    @brucesmitherson Yes. For example, quantum mechanics is a local non-markov process that reproduces the QM correlations. (QM is local in the sense that spatially separated operators commute.) More generally, the space of non-markov processes include some effects that allow faster than light signalling so the locality constraint doesn't really mean anything if you're allowing non-markov. Post-selection is an example of a non-markov process that can be used for retroactive FTL signalling. – Craig Gidney Dec 07 '20 at 17:57
  • Do you have any references about the subject? –  Dec 08 '20 at 03:11
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The simplest and most used example would be, within quantum mechanics, the standard scenario of Bell's inequalities (in the CHSH form, for simplicity).

You have two boxes. Each one has two buttons, and according to some internal rule, it can respond to pressing a button with one of two outcomes (think two led lights on top of each box turning on or off). Denote the probability of observing the outcomes $a$ and $b$ when you press the buttons $x$ and $y$ with $p(ab|xy)$.

You can prove that there are probability distributions $p(ab|xy)$ which cannot be described by any kind of local, realist theory. This means that there is no hidden variable $\lambda$ with distribution $p(\lambda)$ such that $$p(ab|xy) = \sum_\lambda p_\lambda p_\lambda(a|x) p_\lambda(b|y),\tag1$$ where $p_\lambda(a|x)$ is the the probability of observing the outcome $a$ on the first box when you pressed the input $x$ and the hidden variable is $\lambda$.

One can prove that an entangled quantum state such as $|00\rangle+|11\rangle$, when using appropriate measurement bases, results in a probability distribution which cannot be written as (1). This proves that to describe measurement results in QM you need a theory that is either non-local or non-realist. See e.g. here for the proof.

glS
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  • Thus, to you non-realist means no-hidden variables. Do you have any idea why a nonhidden variable model might result in nonclassical correlations? what advantage would a lack of hidden variables would give? –  Dec 07 '20 at 17:42
  • @brucesmitherson I'm not sure what you mean. The lack of a nonhidden variable model is almost the definition of "nonclassical correlation". It's nonclassical because you cannot reproduce it classically. These is all standard terminology by the way, see e.g. https://arxiv.org/abs/1303.2849 – glS Dec 10 '20 at 08:29
  • See Scholarpedia, it's a common misunderstanding that "Bell's theorem proves the impossibility of "local realism"". More accurate is that "Bell's theorem states that the predictions of quantum theory (for measurements of spin on particles prepared in the singlet state) cannot be accounted for by any local theory." Locality is the only assumption that leads to e.g. the CHHS inequality. – Cloudyman Oct 31 '22 at 13:54
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    not sure what you're referring to. Words aside, the point is that Bell-like inequalities (CHSH or others) rule out factorisations of the conditional probability distribution of the form (1). Of course it's a statement about specific kinds of states, not every state will violate nonlocality inequalities. – glS Nov 01 '22 at 10:03
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It' important to understand the exact question:

Can anyone give me an example of a toy theory that is local but non-realist?

It seems some people have misinterpreted it as asking for just a non-realist theory, but the question crucially asks that the example also be local.

Here is very familiar example of such a theory, which most people seem to hold to: libertarian free will. This theory says:

  1. Your decision (for example to choose between vanilla and chocolate ice cream) is caused by YOU (your brain/soul), and not by something or somebody far away - locality.

  2. Your decision is not completely deterministic. Your exact prior state doesn't completely rob you of a "free choice", there is still a chance that you will choose either option - non-realism.

The trouble with this, and any other local non-realist theory, is that it cannot be distinguished from a local theory with hidden variables. For example, maybe there is some kind of invisible deterministic computer above your head that is responsible for your seemingly purely "free", random choices.

Of course, we could come up with many other examples of local non-realistic theories, and they don’t have to involve complicated entities like free agents.

For example: suppose there is a Mystery Particle, and whenever you shine your flashlight on it you can see its color. The colors of ordinary objects are determined before you look at them, but suppose this Mystery Particle is different. Suppose that before you shine your flashlight on it it's in some specific definite state O, but the moment you shine the flashlight it probabilistically "decides" to become/show a random color.

But again, if you encountered such a local non-realist particle, you could never rule out that maybe there is some kind of hidden variable, which is responsible for the seemingly random colors.

Finally, you asked about the possibility of predicting the results of measurements:

how is a prediction made? is there an algorithm at all?

Sure, for example by observing many Mystery Particles we can learn that if we prepare it in state O, then whenever we shine a flashlight on it it will become green with probability 12.5%, red with probability 73%, etc.

ADDENDUM. This is less relevant to the actual question, but if you know about Bell’s inequalities, you might be wondering if they contradict this claim I made:

“The trouble with this, and any other local non-realist theory, is that it cannot be distinguished from a local theory with hidden variables“.

To contradict this claim, we would need to have an example of a theory with two properties:

  1. It’s local non-realist
  2. It cannot be a result of some deeper, local hidden variable theory.

So didn't Bell prove that quantum mechanics is such an example?

No, he proved that quantum mechanics has the second property, not both properties! In fact, not only did he not prove property 1, he actively advocated for its exact opposite - namely for Bohmian pilot wave theory, which is non-local and deterministic!

Note that a pair of entangled particles separated by a large distance is not described in QM by a combination of two local states, i.e. the entangled state is not a tensor product of two one-particle states. (Also note that this statement is not just an idiosyncrasy specific to the Copenhagen interpretation.)

Here is what Wikipedia has to say on the matter:

Quantum nonlocality has been experimentally verified under different physical assumptions.[1][2][3][4][5] Any physical theory that aims at superseding or replacing quantum theory should account for such experiments and therefore must also be nonlocal in this sense; quantum nonlocality is a property of the universe that is independent of our description of nature. Quantum nonlocality does not allow for faster-than-light communication,[6]

tpg2114
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ReasonMeThis
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  • "The trouble with this, and any other local non-realistic theory, is that it cannot be distinguished from a local theory with hidden variables." -- Bell inequalities? – Norbert Schuch Dec 06 '20 at 20:49
  • @NorbertSchuch No, Bell inequalities prove that the results of QM can't be reproduced by a local realist theory, which doesn't contradict the claim you quoted. Note that a pair of entangled particles separated by a large distance is not described in QM by a combination of two local states, i.e. the entangled state is not a tensor product of two one-particle states. – ReasonMeThis Dec 06 '20 at 21:02
  • Your example of a mystery particle looks like a markov process. Do you mean markov processes are non realist? –  Dec 07 '20 at 17:22
  • Also, your claim that a nonrealist local is not distinguishable from hidden local may or may be not true, I dont think any one has a prove of that. Actually, part om my question is that, what is it a nonrealist theory in the first place, and then figure out the answer to your thesis –  Dec 07 '20 at 17:29
  • @Reason Bell inequalities allow to disambiguate theories which do allow for a local hidden variable description from those which don't. Your statement which I quote claims the opposite: That it cannot be distinguished. This is incorrect. – Norbert Schuch Dec 07 '20 at 22:00
  • @NorbertSchuch My claim is not the opposite of what Bell proved. Bell: "*Certain* theories don't admit local hidden vars". Me: "All local non-realist theories do admit local hidden vars". My claim would contradict Bell only if there exists a local non-realist theory that falls within the set of these *certain* theories. See my addendum for a fuller explanation. (Oh, and by local I mean what Einstein and Bell meant) – ReasonMeThis Dec 07 '20 at 22:12
  • @brucesmitherson Essentially, a non-realist theory is one where Nature "doesn't know" the value of a property until it's measured. As for how to prove my claim, if you were clear on the example with the invisible computer, then it's easy to adapt. Basically if a theory is local, then we can attach this "computer"/hidden var to every particle, or alternatively to every point in space. In other words, a field of hidden vars. – ReasonMeThis Dec 07 '20 at 22:22
  • @ReasonMeThis How do you define "non-realist", if not "there is no hidden variable description"? – Norbert Schuch Dec 09 '20 at 22:36
  • @NorbertSchuch That’s fine (provided we are clear on what we mean by "no description") and consistent with how I defined it in my above comment (…"doesn't know"…). Here is the crucial distinction: Copenhagen QM is non-realist, we can say it's not described in terms of hidden variables, the measurement is "chancy". But its results admit an alternative, deterministic, description, namely the pilot wave theory. So non-realist is completely different from not admitting an alternative realist description, which is what my claim concerns with (along with the property of locality). – ReasonMeThis Dec 10 '20 at 21:58
  • @NorbertSchuch Also, my bad, please accept my apology about the downvoting comments, they weren't meant to be mean, but a lighthearted jab for prematurely, imo, concluding that I made a silly mistake. I am more used to poker strategy forums, which are more informal, but I recognize I need to get a better grip on the SE community standards. – ReasonMeThis Dec 10 '20 at 22:04
  • @ReasonMeThis I thought a theory is non-realist if it does not admit a hidden-variable description, by definition. (Or not local realist if it does not admit a local hidden variable description, like QM.) You're definition would be about how the theory is phrased, not what it predicts? This is "hyper-realist", in that you assign reality to the way you formulate the theory rather than its predictions. – Norbert Schuch Dec 10 '20 at 22:11
  • @NorbertSchuch So, in your understanding of the term realist, Copenhagen QM is realist (because Bohmian QM reproduces its results)? – ReasonMeThis Dec 10 '20 at 22:19
  • Well, quantum mechanics can be explained by a non-local realist theory. So yes, it is realist. Both are interpretations, which make the same predictions. The theory is determined by its predictions, anything else is interpretation. – Norbert Schuch Dec 10 '20 at 23:02
  • @NorbertSchuch I think we've pinpointed the difference in our definitions. I won't claim that yours is " wrong", but I think it's unusual: mostly because it seems every theory is realist in your sense. For suppose some theory says event A will occur with prob. 0.73. Then we can always account for this randomness by proposing an alternative description: that the event will occur if and only if some hidden variable x, which has existed since time immemorial, is < 0.73. So if the results of any theory can be explained by some non-local hidden var. theory, then any theory is realist. – ReasonMeThis Dec 11 '20 at 03:41
  • @NorbertSchuch This is less crucial, but a countable number of hidden variables between 0 and 1 can be encoded with just a single hidden variable between 0 and 1. Also, I think it's also somewhat unusual to say that any two theories with the same predictions for observations are actually the exact same theory. Because then, for example, the theory of evolution would be the same theory as the theory that there was no evolution and the world is only 5 minutes old (created with all the dinosaur bones already in the ground). – ReasonMeThis Dec 11 '20 at 03:51
  • Exactly - those are interpretations: Whether the world has been created 5 mins ago or not cannot be experimentally tested and is a completely valid interpretation of world. I'm not sure whether there are physical theories which don't allow for a realist (i.e., hidden variable) interpretation. I can't think of one, but lack of imagination is not an argument. – Norbert Schuch Dec 11 '20 at 13:34
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I am not sure what you mean by "unrealism", unless it is the philosophy (adopted by many physicists) that the reality underlying quantum mechanics cannot be described, and that we should not even try to describe it. In this case one accepts the algorithm that probabilities for the results of measurement are given by the calculations of quantum mechanics (sometimes known as "shut up and calculate").

However, one should distinguish between realism and naive realism. Bell's theorem does not actually refute realism (local or otherwise) but it does refute naive realism, which I think is what you mean by "local realism". Indeed naive realism is already refuted by the mathematical structure of quantum mechanics even without Bell's theorem. Bell's theorem just underlines the fact in a way which is harder to dispute.

Naive realism means that reality is modelled by our perception, or our classical understanding, that particles always have location in space. Quantum mechanics shows that this is not true. The properties we observe (including the property of position) are not the inherent properties of particles, but they are properties of the way in which particles interact with other matter to produce our observations (and in particular the results of measurements).

Realism simply means that there exists a material reality which is responsible for our perceptions, but it does not say that this material reality is as described by our perceptions. This distinction was made as early as Plato, in his allegory of the cave. I think what you mean by an "unrealist" theory is what I would call a realist theory, but not a naive realist theory.

Perhaps the first such model was Levcippus' notion of atoms in the void. In the original form of this theory the void has no properties. In particular it contains no notion of place, or location.

Interestingly enough, this corresponds precisely to the view (held by Feynman himself) that Feynman diagrams actually do describe underlying reality. Mathematically Feynman diagrams are graphs. A graph means a collection of vertices or nodes and a collection of edges represented as lines connecting pairs of vertices. In a graph, only the connections between lines and vertices have meaning. The position on the paper of the nodes and lines is meaningless (a familiar graph is a map of the London underground, which does not show the geographical relationship of stations). Feynman diagrams are graphs showing a consistent physical structure in which space has no properties. This is a local theory in the sense that particles only have contact when they interact (as shown in vertices).

Then I think that the type of theory you are looking for is that underlying reality is described in this diagram, and the algorithms for predicting measurement results are as given in quantum electrodynamics.

enter image description here

I have given a mathematical account of this view in Mathematical_Implications_of_Relationism

Charles Francis
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  • Our observations are a result of the way particles interact with matter. As I said in the first comments, Any world would violate Bell's inequality because his concept of particles and what they can do is very limited. Two particles can easily be correlated and tested to produce any QM prediction if you take them seriously and allow for all the proper principles. Just add one extra principle such as oscillation and you can correlate any two real objects. – Bill Alsept Dec 10 '20 at 23:17