Graduate Does the Bell theorem assume reality?

[Demystifier]

So I would say that it's all pretty damn local. What it violates is the assumption that measurement results have a single outcome.

With multiple outcomes, I think "multi-local" is a much better word to describe it than simply "local".

 

[DrChinese]

Local model can produce predictions A, B and C without assuming anything counterfactual. You just perform three calculations with the same $\lambda$ and different measurement angles.

No way. You cannot use formulae involving AB, BC and AC in an equation together unless you assume all 3 have simultaneous validity. You certainly can only measure one pair (AB, BC or C) at a time. You need something counterfactual as an assumption.

The entire idea of the referenced paper is to discuss possible assumptions which go into Bell. One thing I am surprised is not more often mentioned is rotational invariance.

 

[DrChinese]

So which of the Tumulka's (R1)-(R4) would you call realism actually needed to get the Bell result? Or do you think that we need a fifth notion of reality (R5)? If so, can you give a clear definition of (R5)?

I guess my posts were intended to say that Bell did not assume precisely any of (R1), (R2) or (R3). However, you could probably assume (R1) or (R2) and get to it. For (R3), you need to extend it to include simultaneous validity of the 3 expressions:

P(A,B|a,b,λ)
P(A,C|a,c,λ)
P(B,C|b,c,λ)

I realize that the author is trying to locate the "minimal" assumption(s) required to get the Bell result. Others have attempted this too. But I think it never hurts to identify what Bell actually did. Clearly, his inequality (15) depends on the relationships between 3 outcomes that do NOT vary according to which pair is being measured. Any way you wish to express that could be considered (R5). And that step is first introduced immediately after (14), and not before.

 

[DrChinese]

@Demystifier: And if I recall correctly: the Bohmian interpretation does NOT presume counterfactual definiteness. I seem to recall us discussing that previously.

 

[Demystifier]

@Demystifier: And if I recall correctly: the Bohmian interpretation does NOT presume counterfactual definiteness. I seem to recall us discussing that previously.

That is correct. But note that BM is non-local whenever the wave function is entangled, even in cases for which non-locality is not necessary true in the sense of a Bell-like theorem. An example would be the Bell state with spin measurements in z-direction only.

 

[wle]

• (Factorizability): Assume that $P(A,B|a,b,\lambda) = P(A|a,b,\lambda) P(B|a,b,\lambda)$.

The derivations I've seen use Bayes' theorem here, which implies $$P(A, B| a, b, \lambda) = P(A | a, b, \lambda) P(B | A, a, b, \lambda) \,.$$ The locality assumption used after this translates to $P(A | a, b, \lambda) = P(A | a, \lambda)$ and $P(B | A, a, b, \lambda) = P(B | b, \lambda)$.

 

[zonde]

No way. You cannot use formulae involving AB, BC and AC in an equation together unless you assume all 3 have simultaneous validity. You certainly can only measure one pair (AB, BC or C) at a time. You need something counterfactual as an assumption.

Let's say you are in laboratory and you have prepared a state. Your assistant after some time will perform one of the three measurements by his own choice (or using PRNG "choice"). According to protocol you have to produce predictions for all three measurements before any measurement is performed. Let's say you produce them. All three predictions should be unambiguous and valid otherwise your model is not a valid theory. All three predictions should unambiguously exist at the same time - factually. There is nothing counterfactual in such situation.

 

[stevendaryl]

Let's say you are in laboratory and you have prepared a state. Your assistant after some time will perform one of the three measurements by his own choice (or using PRNG "choice"). According to protocol you have to produce predictions for all three measurements before any measurement is performed. Let's say you produce them. All three predictions should be unambiguous and valid otherwise your model is not a valid theory. All three predictions should unambiguously exist at the same time - factually. There is nothing counterfactual in such situation.

In discussions of EPR and Bell's theorem and so forth, you have a number of "trials", where a trial consists of the creation of a particle/antiparticle pair. For each pair of particles, you can only measure spins along a pair of orientations. Alice measures the electron spin along axis $a$ and Bob measures the positron spin along axis $b$. Counterfactuality comes into play if you ask: "What result would Bob have gotten if he had measured his particle along axis $c$ instead?" It is not possible to measure spins along three different orientations.

You can certainly choose to measure along orientations $a, b$ for some trials, and along orientations $a, c$ for other trials. But if we're talking about the possibility of hidden variables affecting the outcomes, we don't know how the variables change from one trial to the next.

 

[zonde]

In discussions of EPR and Bell's theorem and so forth, you have a number of "trials", where a trial consists of the creation of a particle/antiparticle pair. For each pair of particles, you can only measure spins along a pair of orientations. Alice measures the electron spin along axis $a$ and Bob measures the positron spin along axis $b$. Counterfactuality comes into play if you ask: "What result would Bob have gotten if he had measured his particle along axis $c$ instead?" It is not possible to measure spins along three different orientations.

Yes, I understand that. But Bell inequality is calculated for certain hypothetical models. So instead of asking: "What result would Bob have gotten if he had measured his particle along axis $c$ instead?", we ask: "What prediction the model will produce if instead of measurement axis $b$ we will use measurement axis $c$ instead?"
We speak about the map not the territory so to say.

 

[stevendaryl]

The derivations I've seen use Bayes' theorem here, which implies $$P(A, B| a, b, \lambda) = P(A | a, b, \lambda) P(B | A, a, b, \lambda) \,.$$

I think we're talking about slightly different things. The factoring that you are talking about is always true, for any $\lambda$. Reichenbach's Principle claims that there always must be some choice of $\lambda$ such that the factoring looks like this:

$$P(A, B| a, b, \lambda) = P(A | a, b, \lambda) P(B | a, b, \lambda)$$

(no $A$ in the second term).

The distinction is illustrated by my example with twins playing basketball. I have some way to randomly pick a pair of identical twins out of the population. Let $P(A)$ be the probability that the first twin plays basketball. Let $P(B)$ be the probability that the second twin plays basketball. Let $P(A,B)$ be the probability that they both play basketball. Most likely, twins are alike in their basketball playing abilities, or at least more alike than any two random people. So $P(A,B) \neq P(A) P(B)$.

Without understanding anything at all about basketball playing ability, you can, using pure logic, write:

$P(A, B) = P(A) P(B | A)$

That's basically true by definition of conditional probability. So that kind of factoring isn't actually telling us anything about the root causes of basketball ability. On the other hand, let's suppose that we identify a bunch of factors that might come into play. Let $\lambda_1$ be genetics, let $\lambda_2$ be the schools they attend, let $\lambda_3$ be some characterization of their homelife (do they have siblings, do they have two parents, are the parents rich, etc.). Then some collection of such parameters would be a causal explanation of the correlation if:

$P(A, B | \overrightarrow{\lambda}) = P(A | \overrightarrow{\lambda}) P(B | \overrightarrow{\lambda})$

Reichenbach's principle, as formalized as factorability of probabilities, says that if you knew enough about the causes of basketball-playing ability, then it should no longer be necessary to know whether twin $A$ plays basketball to accurately predict whether twin $B$ plays basketball.

(Actually, I realize this example doesn't quite work, because the mere fact that one twin plays basketball might influence the other twin. We can account for this by saying that at some point, before the twins ever play basketball for the first time, we separate the twins and separately try them out on different sports, and decide independently which sport they like the best.)

It's only AFTER you have factored probability distributions by coming up with a complete set of causal factors is it the case that you can apply locality considerations. If you haven't already factored it, then imposing locality is a mistake. We can show this with the basketball players.

We take two twins and take them to distant locations and measure their basketball playing ability. Then using pure logic, we write:

$P(A,B) = P(A) P(B | A)$

If we then say: the basketball tests are far apart, so one twin playing basketball cannot influence the other twin's abilities. So we assume that

$P(B | A) = P(B)$

But that assumption is FALSE. Even though $A$ and $B$ are far apart, that doesn't mean that they are uncorrelated, and therefore it doesn't mean that $P(B | A) = P(B)$

 

[stevendaryl]

Yes, I understand that. But Bell inequality is calculated for certain hypothetical models. So instead of asking: "What result would Bob have gotten if he had measured his particle along axis $c$ instead?", we ask: "What prediction the model will produce if instead of measurement axis $b$ we will use measurement axis $c$ instead?"
We speak about the map not the territory so to say.

Right. It's the models that support or don't support counterfactual claims.

 

[zonde]

It's the models that support or don't support counterfactual claims.

Models always support counterfactual claims, because models don't care if you calculate from it prediction or retrodiction. Models are supposed to be independent from actual reality.

 

[stevendaryl]

Models always support counterfactual claims, because models don't care if you calculate from it prediction or retrodiction. Models are supposed to be independent from actual reality.

No, models don't always support counterfactual claims. A stochastic model, for instance, doesn't have a definite answer to the question: What measurement result would I have gotten, if I had measured this rather than that.

 

[stevendaryl]

No, models don't always support counterfactual claims. A stochastic model, for instance, doesn't have a definite answer to the question: What measurement result would I have gotten, if I had measured this rather than that.

To have definite answers to counterfactual questions, the model needs to be deterministic but not superdeterministic.

 

[zonde]

No, models don't always support counterfactual claims. A stochastic model, for instance, doesn't have a definite answer to the question: What measurement result would I have gotten, if I had measured this rather than that.

Any model would have some scope of things it can say. The point is that if the model have something to say about the future then then it's exactly the same thing it would say about the past or possible past. Just because you know measurement result does not mean that you can get exact result as retrodiction out of stochastic model. There is no difference between prediction and retrodiction even for stochastic model.

 

[stevendaryl]

Any model would have some scope of things it can say. The point is that if the model have something to say about the future then then it's exactly the same thing it would say about the past or possible past. Just because you know measurement result does not mean that you can get exact result as retrodiction out of stochastic model. There is no difference between prediction and retrodiction even for stochastic model.

I guess I agree, but I don't know how that relates to Dr. Chinese' point about counterfactuality.

 

[DrChinese]

EPR said in an entangled system: it would be possible to predict with certainty any possible observable on one (Alice), by measuring the other (Bob) of the pair. That implied that Bob's result was in fact predetermined. The question then is whether all possible observables of Bob were simultaneously predetermined. Only in a world in which there was a subjective realism - Bob's reality is shaped by the choice of measurement basis by Alice - would that NOT be true. They claimed, as an article of faith, such subjective realism - observer shape reality - would be an unreasonable position. So even in 1935, the question on the table was whether there was counterfactual realism.

Bell converted their general conjecture to a specific mathematical argument. He did it by assuming - quietly - that there were in fact predetermined values for non-commuting observables. He showed that these predetermined values could not be consistent with quantum mechanical predictions. And his "quiet" introduction of that conjecture occurs right after Bell's (14). It is NOT, as some believe, in Bell's (2). (2) codifies the argument that the results of Alice and Bob are independent (separable). You could call that the assumption of locality.

You cannot get the Bell result without some kind of counterfactual assumption. You can call it realism or objective reality or whatever, but there is an assumption. And it occurs after (14) - and not before. Whether or not it is (R1) or one of the others, I can't personally say. But I think it is a mistake to consider these independent of Bell. Because the question becomes whether you can assume something OTHER than what Bell assumed, and still get the Bell result.

 

[Demystifier]

You cannot get the Bell result without some kind of counterfactual assumption. You can call it realism or objective reality or whatever, but there is an assumption. And it occurs after (14) - and not before. Whether or not it is (R1) or one of the others, I can't personally say.

Lorentzo Maccone explains it in http://de.arxiv.org/abs/1212.5214 as follows:
"Let us define “counterfactual-definite” [14, 15] a theory whose experiments uncover properties that are preexisting. In other words, in a counterfactual-definite theory it is meaningful to assign a property to a system (e.g. the position of an electron) independently of whether the measurement of such property is carried out. [Sometime this counterfactual definiteness property is also called “realism”, but it is best to avoid such philosophically laden term to avoid misconceptions.]"

Maccone then shows that this counterfactual definiteness is one of the assumptions of the Bell theorem, showing that some kind of "reality" is an assumption of Bell theorem. But Maccone is not sophisticated enough to say whether this reality corresponds to (R1), (R2), (R3) or (R4). As far as as I am aware, the Tumulka's paper is the only paper that clearly distinguishes those 4 versions of reality.

Finally, let me add that (R4) is the same as the Axiom 1 in my "Bohmian mechanics for instrumentalists" linked in my signature below. Unfortunately I didn't cite Tumulka because at the time of writing I was not aware of that paper. I plan to change it in a revised version of the paper.

 

[DrChinese]

Lorentzo Maccone explains it in http://de.arxiv.org/abs/1212.5214 as follows:
"Let us define “counterfactual-definite” [14, 15] a theory whose experiments uncover properties that are preexisting. In other words, in a counterfactual-definite theory it is meaningful to assign a property to a system (e.g. the position of an electron) independently of whether the measurement of such property is carried out. [Sometime this counterfactual definiteness property is also called “realism”, but it is best to avoid such philosophically laden term to avoid misconceptions.]"

Maccone then shows that this counterfactual definiteness is one of the assumptions of the Bell theorem, showing that some kind of "reality" is an assumption of Bell theorem. But Maccone is not sophisticated enough to say whether this reality corresponds to (R1), (R2), (R3) or (R4). As far as as I am aware, the Tumulka's paper is the only paper that clearly distinguishes those 4 versions of reality.

Tumulka:
"(R4): Every experiment has an unambiguous outcome, and records and memories of that outcome agree with what the outcome was at the space-time location of the experiment."

That doesn't sound counterfactual in any sense. I read it as: The outcome of a performed experiment is what we see and record it as. I certainly don't believe Tumulka can recreate the Bell result from that, without one of the others.

 

[DarMM]

Yes, but I think that nobody argues like this: "R3 is wrong, ergo QM is local." It would be nonsense, because saying that R3 is wrong would be saying that probability is not determined by the wave function.

As far as I know, not quite, though it is a subtle thing.

If $\lambda = \psi$ then you have the Beltrametti–Bugajski model, which Leifer describes as "the orthodox interpretation of quantum theory into the language of ontological models". This is saying that $\psi$ is an ontic state of the theory and then Bell's theorem just amounts to a proof that the wavefunction if real (and there isn't multiple worlds) is a nonlocal object.

The way out of this is to reject R3 not by saying that probability is not determined by the wavefunction, but by saying the wavefunction isn't an element of reality/ontic, so the purported proof that it is nonlocal doesn't mean the world is physically nonlocal. This is what AntiRealist/Participatory realist interpretations do (e.g. Copenhagen).

 

[Demystifier]

Tumulka:
"(R4): Every experiment has an unambiguous outcome, and records and memories of that outcome agree with what the outcome was at the space-time location of the experiment."

That doesn't sound counterfactual in any sense.

That's because you don't read between the lines.
In my "Bohmian mechanics for instrumentalists" I have formulated it more explicitly, by stating the Bell theorem as follows:
If the correlated, yet spatially separated, quantum measurement outcomes are there even before a single local observer detects the correlation, then the measurement outcomes are governed by non-local laws.

 

[Demystifier]

The way out of this is to reject R3 not by saying that probability is not determined by the wavefunction, but by saying the wavefunction isn't an element of reality/ontic, so the purported proof that it is nonlocal doesn't mean the world is physically nonlocal. This is what AntiRealist/Participatory realist interpretations do (e.g. Copenhagen).

Fine, but in such interpretations it is not only that the world is not nonlocal. In such interpretations the world is not even real. And yet, adherents of such interpretations deny that they are solipsists. But I think they are solipsists, even if they hide under euphemisms such as "relationalists".

 

[zonde]

He did it by assuming - quietly - that there were in fact predetermined values for non-commuting observables. He showed that these predetermined values could not be consistent with quantum mechanical predictions. And his "quiet" introduction of that conjecture occurs right after Bell's (14). It is NOT, as some believe, in Bell's (2).

He is not assuming that. He infers that from locality and perfect correlations (here he has to assume R4 as well, this indeed is unstated assumption).
And he states this quite clearly before he even starts his derivation:
"Since we can predict in advance the result of measuring any chosen component of $\vec{\sigma}_2$, by previously measuring the same component of $\vec{\sigma}_1$, it follows that the result of any such measurement must actually be predetermined."
Mathematically conclusion of this statement is formulated in (1).

 

[akvadrako]

Fine, but in such interpretations it is not only that the world is not nonlocal. In such interpretations the world is not even real. And yet, adherents of such interpretations deny that they are solipsists. But I think they are solipsists, even if they hide under euphemisms such as "relationalists".

This is the hardest part to understand about QBism, but if they were solipsists that would mean they think only their experience is real. They don't act like that – they act like everybody's own experience is just as real as their own, but only to one's self. So my best guess is they do assume there is a shared arena for experiences to interact but it is not conducive to a mathematical description and certainly isn't QM.

 

[stevendaryl]

He is not assuming that. He infers that from locality and perfect correlations (here he has to assume R4 as well, this indeed is unstated assumption).
And he states this quite clearly before he even starts his derivation:
"Since we can predict in advance the result of measuring any chosen component of $\vec{\sigma}_2$, by previously measuring the same component of $\vec{\sigma}_1$, it follows that the result of any such measurement must actually be predetermined."
Mathematically conclusion of this statement is formulated in (1).

Yes, I think that people (I'm not accusing Dr. Chinese of this) think that Bell's inequality is about deterministic models, and that a nondeterministic model would not be constrained by it. It's true that in Bell's derivation of his inequality, he focuses on deterministic models where, in EPR, the outcome of a measurement is a deterministic function of the hidden variable, $\lambda$ and the detector settings. But that's because he already knows that a nondeterministic model cannot reproduce the perfect correlations/anticorrelations of EPR.

If you start with the assumption that the outcome of a measurement is probabilistically related to the causal factors, then you would have, assuming locality:

$P(A, B | a, b, \lambda) = P_A(A | a, \lambda) P_B(B | b, \lambda)$

(where $P_X(Y | z, \lambda)$ is the probability that observer $X$ will measure result $Y$ when his/her setting is $z$ and the hidden variable is $\lambda$)

Then you take into account the perfect anticorrelation. If $a=b$ and $A = B$, then the probability is zero. The only way for a product of two numbers to be zero is if one of them is zero. So fixing $a, \lambda$, we have four numbers:

1. $P_1 = P_A(+1/2| a, \lambda)$
2. $P_2 = P_A(-1/2 | a, \lambda)$
3. $P_3 = P_B(+1/2 | a, \lambda)$
4. $P_4 = P_B(-1/2 | a, \lambda)$

Since probabilities must add to 1, we have: $P_1 + P_2 = 1$ and $P_3 + P_4 = 1$. Perfect anti-correlation tells us that $P_1 = 0$ or $P_3 = 0$ and that either $P_2 = 0$ or $P_4 = 0$. So there are only two possible assignments:

• $P_1 = 0 \Rightarrow P_2 = 1 \Rightarrow P_4 = 0 \Rightarrow P_3 = 1$
• $P_3 = 0 \Rightarrow P_4 = 1 \Rightarrow P_2 = 0 \Rightarrow P_1 = 1$

So the only possible probabilities consistent with perfect anti-correlation are 0 or 1. So it must be deterministic.

 

[stevendaryl]

This is the hardest part to understand about QBism, but if they were solipsists that would mean they think only their experience is real. They don't act like that – they act like everybody's own experience is just as real as their own, but only to one's self. So my best guess is they do assume there is a shared arena for experiences to interact but it is not conducive to a mathematical description and certainly isn't QM.

If you've ever studied intuitionistic logic, you know that it's basically standard logic in which you reject the "law of the excluded middle" or LEM. LEM is the assumption that either something is true, or its negation is true (there is no third possibility). LEM allows us to do the following kind of reasoning:

• Assume A. Using A, prove B.
• Assume not-A. Using not-A. prove B.
• Conclude B.

To me, it seems that people who feel that quantum mechanics is perfectly adequate are basically being intuitionistic. For certain statements, such as "QM is local", both the statement and its negation lead to conclusions that they reject. When they say that QM is local, what they really mean is that it is not nonlocal, which is different, intuitionistically.

 

[Demystifier]

This is the hardest part to understand about QBism, but if they were solipsists that would mean they think only their experience is real. They don't act like that – they act like everybody's own experience is just as real as their own, but only to one's self. So my best guess is they do assume there is a shared arena for experiences to interact but it is not conducive to a mathematical description and certainly isn't QM.

Perhaps the main problem with them is that they refuse to talk about those questions in a direct and simple manner. By direct and simple, I mean something like what I say in Sec. 2.2 of http://de.arxiv.org/abs/1703.08341 .

 

[atyy]

Fine, but in such interpretations it is not only that the world is not nonlocal. In such interpretations the world is not even real. And yet, adherents of such interpretations deny that they are solipsists. But I think they are solipsists, even if they hide under euphemisms such as "relationalists".

How about allowing the world to be be real, but denying that it is describable by mathematics?

 

[Demystifier]

How about allowing the world to be be real, but denying that it is describable by mathematics?

Perhaps it would be clear what it means, but would be hard to justify by science-friendly arguments.

 

[atyy]

Perhaps it would be clear what it means, but would be hard to justify by science-friendly arguments.

Maybe like a (hypothetical) physical version of the Goedel incompleteness theorem? Which would explain why Bohmian Mechanics is doomed to fail (maybe Lorentz invariance is exact :)

Xiao-Gang Wen's textbook quotes the Tao Te Ching:
"The Dao that can be staled cannot be eternal Dao. The Name that can be named cannot be eternal Name. The Nameless is the origin of universe. The Named is the mother of all matter."

And has fun translating it as:
"The physical theory that can be formulated cannot be the final ultimate theory. The classification
that can be implemented cannot classify everything. The unformulatable ultimate theory does exist
and governs the creation or the universe. The formulated theories describe the matter we see every
day."