An argument against Bohmian mechanics?

[stevendaryl]

So you find that locality split from realism is the same as local realism? You might be missing a later paper by Bell after his famous 1964 one.

Definitely there is a distinction between "No FTL communication" and Bell's notion of "local realism". I would not say that Bell ever suggested that "No FTL communication" is his definition of "local". If that's somebody's idea of "local", it's not Bell's. What Bell claimed is this: (first line of section 5 of the chapter "The theory of local beables" in the book "Speakable and unspeakable in quantum mechanics")

Quantum mechanics, however, gives certain correlations which do not satisfy the locality inequality (16).

But I suppose it doesn't matter what Bell's definition of "local" was--it's clear there are two (or more) subtly different concepts.

 

[Demystifier]

First of all what's a "realstic part". Note that after all these years in this forum, I still haven't get a clear-cut definition, what's meant by "realistic" in this context. As far as I can see, it's usually synonymous with deterministic.

Let me again use the magic trick as an example. Reality is the claim that the rabbit exists even when the spectators do not see him. Determinism is the claim that the behavior of the rabbit is not random. Clearly, reality and determinism are totally independent.

 

[stevendaryl]

First of all what's a "realstic part". Note that after all these years in this forum, I still haven't get a clear-cut definition, what's meant by "realistic" in this context. As far as I can see, it's usually synonymous with deterministic.

No, I definitely do not consider it synonymous with deterministic. A stochastic process is nondeterministic, but locally realistic.

To me, realism is the assumption that there is a physical "state" of the universe at any given time (or to be consistent with relativity, there is a state associated with any spacelike slice of spacetime), and the probability of any future event depends only on the state "now". "Local realism" further requires that the state of the universe factors into local states, so that the probabilities for any localized event depends only on the local state. "No FTL" implies yet another constraint, which is that the local state at any time can only depend on the local states in the backward light-cone.

The connection between realism and determinism is that if there is any realistic model, then there is another deterministic realistic model that makes the same predictions.

 

[RockyMarciano]

Definitely there is a distinction between "No FTL communication" and Bell's notion of "local realism".

Please read my posts without prejudging.That is exactly what I'm saying. There is a clear distinction between "No FTL communication" and "local realism".
It is only when "local realism" is split in two other different concepts locality and realism, which Bell himself did in later years that locality(not local realism) when separated from classical determinism is equivalent to "no FTL communication" or "c limit to causal influences" as defined above. It is sad that the same term("locality") is usually used indistinctively for the former concept of local realism or local hidden variables and for the meaning in QFT ("no FTL communication") giving rise to confusion like the one here.

 

[RockyMarciano]

Let me again use the magic trick as an example. Reality is the claim that the rabbit exists even when the spectators do not see him. Determinism is the claim that the behavior of the rabbit is not random. Clearly, reality and determinism are totally independent.

You are free to make your own distinction of realism and deterrminism but in the context of Bell's theorem realism is usually referring to classical determinism. It is regretable that the term realism, with so many different meanings is used but that is what traditionally was used.

 

[stevendaryl]

I think, it's just that we are so used to the classical worldview that we cannot emotionally accept that there's no more to know about the electron than the probabilistic content of the quantum formalism.

That might be the case for some people, but my problems with the quantum formalism is not about any emotional preference for determinism. It's a technical question as to whether the minimal interpretation is in fact consistent. I'm not convinced that it is. If you have rules for macroscopic objects that are not derivable from the rules for microscopic objects, then to me, that implies that the microscopic rules are not completely true--they leave something out, or they are false.

My complaint with discussions of interpretations of quantum mechanics is that the same people who say they want to avoid philosophical discussions are the ones who constantly make interpretation into philosophy (just a matter of opinion, or emotional preference). There are issues that are, as I said, technical, independent of your philosophical or emotional biases.

 

[stevendaryl]

Please read my posts without prejudging.That is exactly what I'm saying. There is a clear distinction between "No FTL communication" and "local realism".

But Bell was not the one who said that "local" means "No FTL communication". So I'm just objecting to your saying that "in Bell's terminology...". It's not Bell's terminology that equates "No FTL" with "local".

 

[RockyMarciano]

No, I definitely do not consider it synonymous with deterministic. A stochastic process is nondeterministic, but locally realistic.

This is another regretable semantic confusion, the concept of "classical determinism" is broader that the usaul concept of dertministic as opposed to stochastich. For instance, classical probabilities are contained in the concept of "classical determinism". If the EPR experiments gave statistics compatible with the classical probabilities it would follow the Bell inequalities and therefore be local realistic.

 

[vanhees71]

To me, realism is the assumption that there is a physical "state" of the universe at any given time (or to be consistent with relativity, there is a state associated with any spacelike slice of spacetime), and the probability of any future event depends only on the state "now". "Local realism" further requires that the state of the universe factors into local states, so that the probabilities for any localized event depends only on the local state. "No FTL" implies yet another constraint, which is that the local state at any time can only depend on the local states in the backward light-cone.

The connection between realism and determinism is that if there is any realistic model, then there is another deterministic realistic model that makes the same predictions.

Hm, but also in QT you have states, which precisely fulfill what you use to define "realism", but I thought that the apparent problem is that QT is not realistic. Again puzzled :-(.

 

[RockyMarciano]

But Bell was not the one who said that "local" means "No FTL communication". So I'm just objecting to your saying that "in Bell's terminology...". It's not Bell's terminology that equates "No FTL" with "local".

It did in his paper from the 70's and 80's when he separated the classical deterministic part from what he called "causal locality".
EDIT: actually you are right that it is not exactly Bell's terminology. Bell rethinked several times his notion of locality after 1964, for instance in 1976 and in 1990 with his "Nouvelle cuisin" paper, but he never defined locality as "no ftl communication". He did conclude that violating his inequalities was not the same as "ftl communication".

 

[ShayanJ]

This is starting to annoy me. Its becoming a steady pattern in discussions of this type that @Demystifier, @atyy and @stevendaryl insist on the necessity of collapse axiom and existence of measurement problem and @vanhees71 insists that the collapse axiom is not needed and there is no problem. Physics discussion aren't supposed to be like this. We're not supposed to have problems that don't exist according to some people. There should be some way to settle this and I think @vanhees71 should pay attention to an important point. If it was only some people who were just clinging to the old classical notions, I wouldn't call this a problem either but its not only this. Its true that as long as we apply QM to only an ensemble of equally prepared systems and obtain the probability distribution of different quantities, there is no problem and no collapse and interpretation is needed. The problem appears when we try to apply QM to a single quantum system. Claiming that QM can't be applied to a single quantum system isn't a solution to this problem and doesn't give people the right to say that concepts defined to solve this problem are outside the scope of physics.

 

[vanhees71]

That might be the case for some people, but my problems with the quantum formalism is not about any emotional preference for determinism. It's a technical question as to whether the minimal interpretation is in fact consistent. I'm not convinced that it is. If you have rules for macroscopic objects that are not derivable from the rules for microscopic objects, then to me, that implies that the microscopic rules are not completely true--they leave something out, or they are false.

My complaint with discussions of interpretations of quantum mechanics is that the same people who say they want to avoid philosophical discussions are the ones who constantly make interpretation into philosophy (just a matter of opinion, or emotional preference). There are issues that are, as I said, technical, independent of your philosophical or emotional biases.

I don't know any evidence, that the behavior of macroscopic objects contradict QT. Then of course QT would be wrong or at least incomplete in not desribing parts of observable facts about macroscopic objects. However there's no evidence for that.

What are the technical issues you are referring to? If I just accept that there are the probabilities described by QT and nothing else and find them to be accurate when testing them on ensembles of equally prepared systems then there are no technical problems on the level of physics left. So the only quibbles with QT can be of philosophical nature, and that I don't like to discuss, because it doesn't lead to anything useful in my experience.

 

[vanhees71]

This is starting to annoy me. Its becoming a steady pattern in discussions of this type that @Demystifier, @atyy and @stevendaryl insist on the necessity of collapse axiom and existence of measurement problem and @vanhees71 insists that the collapse axiom is not needed and there is no problem. Physics discussion aren't supposed to be like this. We're not supposed to have problems that don't exist according to some people. There should be some way to settle this and I think @vanhees71 should pay attention to an important point. If it was only some people who were just clinging to the old classical notions, I wouldn't call this a problem either but its not only this. Its true that as long as we apply QM to only an ensemble of equally prepared systems and obtain the probability distribution of different quantities, there is no problem and no collapse and interpretation is needed. The problem appears when we try to apply QM to a single quantum system. Claiming that QM can't be applied to a single quantum system isn't a solution to this problem and doesn't give people the right to say that concepts defined to solve this problem are outside the scope of physics.

This is not a physics discussion anymore. It's philosophy, and in philosophy you must live with endless disputes, where nobody is sharply right or wrong.

Concerning the physics part in your posting, I don't see a problem with single quantum systems either. If you accept that nature cannot be described by a deterministic theory there's no problem that you can't predict the outcome of measurements on a single quantum system. The measured observable is just not determined due to the preparation of the system, and that's it.

 

[stevendaryl]

You are free to make your own distinction of realism and deterrminism but in the context of Bell's theorem realism is usually referring to classical determinism.

I don't think that's true. Determinism follows from local realism + perfect correlations in EPR. It's not an assumption of local realism.

Bell only considered deterministic realistic models in his theorem because if there is no deterministic theory, then there is no nondeterministic theory, either. You can prove quite easily that the assumption of local realism implies determinism.

In an EPR type experiment, Alice chooses a detector setting, $\alpha$ and gets a measurement result, $A$. Bob chooses a detector setting, $\beta$ and gets a measurement result, $B$. We perform the experiment over and over, for different values of $\alpha$ and $\beta$, and we get a probability distribution:

$P(A, B|\alpha, \beta)$ (the probability Alice gets $A$ and Bob gets $B$, given that Alice chose setting $\alpha$ and Bob chose setting $\beta$)

The assumption of local realism is that Bob's outcome should depend only on conditions local to him (in his past lightcone) and Alice's outcome should depend only on conditions local to her (in her past lightcone). This implies that the probability distribution should factor into the form:

$P(A,B|\alpha, \beta) = \sum_{c_a} \sum_{c_b} \sum_\lambda P(\lambda) P(c_a) P(c_b) P(A | \alpha, \lambda, c_a) P(B | \beta, \lambda, c_b)$

where $\lambda$ represents conditions in the common past lightcone of Alice and Bob, $c_a$ represents conditions local to Alice's detector, $c_b$ represents conditions local to Bob's detector. So Bob's outcome only depends on $\lambda$ and $c_b$ and Alice's outcome only depends on $\lambda$ and $c_a$.

The perfect correlations (or anti-correlations) from EPR allow us to show that $c_a$ and $c_b$ are irrelevant, so we can simplify to the form:

$P(A,B|\alpha, \beta) = \sum_\lambda P(\lambda) P(A | \alpha, \lambda) P(B | \beta, \lambda)$

We can further show that perfect correlations imply in fact that $P(A |\alpha, \lambda) = 0$ or $P(A |\alpha, \lambda) = 1$. In other words, $A$ is determined by $\alpha$ and $\lambda$. Furthermore, $B$ must be determined by $\beta$ and $\lambda$.

Determinism is not an assumption of local realism, but a derivable conclusion from local realism.

 

[stevendaryl]

This is not a physics discussion anymore. It's philosophy, and in philosophy you must live with endless disputes, where nobody is sharply right or wrong.

I would say that you are making it into a philosophical discussion by assuming that there is no technical answer. The question of whether something does not follow from certain assumptions is a technical question, not a philosophical question.

 

[stevendaryl]

Concerning the physics part in your posting, I don't see a problem with single quantum systems either. If you accept that nature cannot be described by a deterministic theory there's no problem that you can't predict the outcome of measurements on a single quantum system. The measured observable is just not determined due to the preparation of the system, and that's it.

The issue is not determinism. There is a tendency in discussions such as this one to have some stock responses, and to assume that they address what has been said, whether or not they actually do.

My problem with quantum formalism has nothing to do with determinism.

 

[stevendaryl]

I don't know any evidence, that the behavior of macroscopic objects contradict QT.

But you are assuming facts about macroscopic objects that are not assumed about the microscopic objects. So either you are introducing new phenomena, or you're being redundant---the facts are (in some complicated way) derivable from the microscopic facts.

 

[RockyMarciano]

I don't think that's true. Determinism follows from local realism + perfect correlations in EPR. It's not an assumption of local realism.

Bell only considered deterministic realistic models in his theorem because if there is no deterministic theory, then there is no nondeterministic theory, either. You can prove quite easily that the assumption of local realism implies determinism.

In an EPR type experiment, Alice chooses a detector setting, $\alpha$ and gets a measurement result, $A$. Bob chooses a detector setting, $\beta$ and gets a measurement result, $B$. We perform the experiment over and over, for different values of $\alpha$ and $\beta$, and we get a probability distribution:

$P(A, B|\alpha, \beta)$ (the probability Alice gets $A$ and Bob gets $B$, given that Alice chose setting $\alpha$ and Bob chose setting $\beta$)

The assumption of local realism is that Bob's outcome should depend only on conditions local to him (in his past lightcone) and Alice's outcome should depend only on conditions local to her (in her past lightcone). This implies that the probability distribution should factor into the form:

$P(A,B|\alpha, \beta) = \sum_{c_a} \sum_{c_b} \sum_\lambda P(\lambda) P(c_a) P(c_b) P(A | \alpha, \lambda, c_a) P(B | \beta, \lambda, c_b)$

where $\lambda$ represents conditions in the common past lightcone of Alice and Bob, $c_a$ represents conditions local to Alice's detector, $c_b$ represents conditions local to Bob's detector. So Bob's outcome only depends on $\lambda$ and $c_b$ and Alice's outcome only depends on $\lambda$ and $c_a$.

The perfect correlations (or anti-correlations) from EPR allow us to show that $c_a$ and $c_b$ are irrelevant, so we can simplify to the form:

$P(A,B|\alpha, \beta) = \sum_\lambda P(\lambda) P(A | \alpha, \lambda) P(B | \beta, \lambda)$

We can further show that perfect correlations imply in fact that $P(A |\alpha, \lambda) = 0$ or $P(A |\alpha, \lambda) = 1$. In other words, $A$ is determined by $\alpha$ and $\lambda$. Furthermore, $B$ must be determined by $\beta$ and $\lambda$.

Determinism is not an assumption of local realism, but a derivable conclusion from local realism.

Again we agree, how does this mean my sentence is not true? becauseonce again local realism is not the same as just realism.
Let me ask you directly, do you agree that Bell's theorem leaves us with the choice between "no ftl communication"(let's not call it locality anymore to avoid confusions) or "classical determinism"(defined as "existence of predetermined values at all possible measurements", let's not call it realism if you prefer) but never both as explained in DrChinese post quoted above?

 

[RockyMarciano]

This is starting to annoy me. Its becoming a steady pattern in discussions of this type that @Demystifier, @atyy and @stevendaryl insist on the necessity of collapse axiom and existence of measurement problem and @vanhees71 insists that the collapse axiom is not needed and there is no problem. Physics discussion aren't supposed to be like this. We're not supposed to have problems that don't exist according to some people. There should be some way to settle this and I think @vanhees71 should pay attention to an important point. If it was only some people who were just clinging to the old classical notions, I wouldn't call this a problem either but its not only this. Its true that as long as we apply QM to only an ensemble of equally prepared systems and obtain the probability distribution of different quantities, there is no problem and no collapse and interpretation is needed. The problem appears when we try to apply QM to a single quantum system. Claiming that QM can't be applied to a single quantum system isn't a solution to this problem and doesn't give people the right to say that concepts defined to solve this problem are outside the scope of physics.

I share that annoyance feeling but this thread is about arguments against Bohmian interpretation, so I don't even know how is that discussion on topic here.

 

[stevendaryl]

What are the technical issues you are referring to? If I just accept that there are the probabilities described by QT.

But what does that mean? It means that you're assuming that

If you perform a measurement, then the result is some eigenvalue of the operator corresponding to the quantity being measured, with probabilities given by the Born interpretation.​

That's an assumption about measurements that is not assumed about microscopic interactions. That is potentially inconsistent. If measurements are just complicated combinations of microscopic interactions, then any fact about measurements should be derivable from corresponding facts about microscopic interactions.

As I said, it's as if you said, in the 19th century: "All particles move deterministically according to Newton's laws, and the only interactions are gravitational and electromagnetic. And snowflakes have 6 points." The statement about snowflakes can't be a fundamental law of nature. Either in some complicated way, it's derivable from the facts about particles, or else it points to physics beyond what was assumed about particles.

 

[stevendaryl]

Again we agree, how does this mean my sentence is not true?

Because you seemed to be saying that local realism is classical determinism. It's not. There can be locally realistic theories that are not deterministic. But such a theory cannot explain perfect correlations.

 

[RockyMarciano]

Because you seemed to be saying that local realism is classical determinism. It's not. There can be locally realistic theories that are not deterministic. But such a theory cannot explain perfect correlations.

No, I just clarified I wasn't saying this. Could you maybe address my question on that same post?

 

[stevendaryl]

No, I just clarified I wasn't saying this. Could you maybe address my question on that same post?

Okay, you said:

Let me ask you directly, do you agree that Bell's theorem leaves us with the choice between "no ftl communication"(let's not call it locality anymore to avoid confusions) or "classical determinism"(defined as "existence of predetermined values at all possible measurements", let's not call it realism if you prefer) but never both as explained in DrChinese post quoted above?

What I assume you meant was this:

Bell's theorem, together with the fact that EPR violates his inequality, implies that either there are FTL interactions, or else classical determinism is false.

Yes, I agree with that. I'm not sure what you mean by "never both". You could have classical determinism and FTL interactions.

My point is that the use of the phrase "classical determinism" is unnecessarily restrictive. There is no realistic nondeterministic model possible, either. By using the word "determinism", it gives the mistaken impression that violations of Bell's inequality simply mean that the world is nondeterministic. Local nondeterministic models satisfy Bell's inequality, also.

 

[stevendaryl]

I'm not sure what you mean by "never both". You could have classical determinism and FTL interactions.

Never mind. I take it that you mean that you can't have both "no FTL" and "determinism". I think I agree with that.

(Actually, there is yet another loophole, which is superdeterminism, but that's usually dismissed as a possibility, although some people, such as t'Hooft, take it as a serious possibility.)

 

[DrChinese]

Sure, I'm not saying it is Bell by itself. It is basically Bell plus the cluster decomposition theorem from QFT plus their experimental confirmation of course.

Ah. There are a number of attempts to pin the Bohmians down; but as you can see there are just enough "outs" to not be convincing to that group. Hopefully someone will come up with something to tip it one way or the other eventually.

 

[RockyMarciano]

Okay, you said:What I assume you meant was this:
Bell's theorem, together with the fact that EPR violates his inequality, implies that either there are FTL interactions, or else classical determinism is false.

Yes, I agree with that. I'm not sure what you mean by "never both". You could have classical determinism and FTL interactions.

Ok. By "never both" I just mean that if you had both classical determinism and FTL interactions, Bell's inequalities wouldn't be violated. Thus the choice one must make.
So te get away from semantics as much as possible and come back to the thread's theme, in QFT the choice is made that classical determinism is false, but classical determinism is the main content of Bohmian mechanics. So why wouldn't you agree that Bell's theorem plus "no ftl communication" QFT implies Bohmian interpretation is not compatible with what we have confirmed about quantum theory?

 

[RockyMarciano]

Ah. There are a number of attempts to pin the Bohmians down; but as you can see there are just enough "outs" to not be convincing to that group.

Well, that is understandable if not very scientific taking into consideration human nature and its attachment to pet ideas, but I think it should be clear for those not in that "group". And of course I wouldn't oppose to any toy interpretation used as a sort of sparring of new ideas as in brainstorming as long as one is aware of it.

Hopefully someone will come up with something to tip it one way or the other eventually.

I honestly think there are enough elements to tip it one way already.

 

[stevendaryl]

So te get away from semantics as much as possible and come back to the thread's theme, in QFT the choice is made that classical determinism is false, but classical determinism is the main content of Bohmian mechanics. So why wouldn't you agree that Bell's theorem plus "no ftl communication" QFT implies Bohmian interpretation is not compatible with what we have confirmed about quantum theory?

Well, Bohm's original theory was an interpretation of nonrelativistic quantum mechanics. And it was designed to reproduce the same predictions as the usual Copenhagen interpretation. I don't know anything about extending Bohm's model to relativistic quantum mechanics (QFT). I suspect that such an extension is possible, but I don't know whether there is one.

 

[stevendaryl]

Well, Bohm's original theory was an interpretation of nonrelativistic quantum mechanics. And it was designed to reproduce the same predictions as the usual Copenhagen interpretation. I don't know anything about extending Bohm's model to relativistic quantum mechanics (QFT). I suspect that such an extension is possible, but I don't know whether there is one.

In Chapter 19 of "Speakable and unspeakable in quantum mechanics", Bell sketches what might be turned into a Bohmian version of QFT. I don't know whether anyone has followed up on his ideas, or not. Maybe Demystifier knows?

 

[RockyMarciano]

Well, Bohm's original theory was an interpretation of nonrelativistic quantum mechanics. And it was designed to reproduce the same predictions as the usual Copenhagen interpretation.

Fine, thus my initial question, why do everyone acts in these debates as if we were in 1928 and NRQM was the last word about quantum things. I suspect one reason is that not very many people of the already not so big set that is comfortable with NRQM knows enough about QFT.

I don't know anything about extending Bohm's model to relativistic quantum mechanics (QFT). I suspect that such an extension is possible, but I don't know whether there is one.

Well, what I'm saying is that such an extension would have to renounce to the basic tenet of Bohm's original theory and therefore it would be a different interpretation altogether. If this is not a definite argument against Bohmian mechanics I don't know what it is.