I New experimental support for pilot wave theory?

[N88]

So you accept that there are spatially separated observables which are correlated. And yet, you do not accept nonlocality. Then how do you explain the correlation? Again, let me offer you a few answers so that you can choose one of them:

1.1) One of the observables (say A) influences the other (say B).

1.2) Both A and B are influenced by a third entity (call it C).

1.3) The correlations are not a result of any influence between the entities. The correlations happen for no reason.

1.2) Call C the Correlative Consequences of the initial pair-wise Conservation of total-spin; and recall that, in Bell (1964), the correlated detectors and the correlated test outcomes relate to spin.

Our discussion might be helped by your mathematical answer to this question: How do you move from LHS of Bell's (1964) equation (3) to the RHS?

 

[bhobba]

Does BM use operators and eigenvectors?

Its an interpretation so obviously has all the standard formalism.

Thanks
Bill

 

[N88]

Its an interpretation so obviously has all the standard formalism.

Thanks
Bill

Bill,
How do you move, mathematically, from LHS of Bell's (1964) equation (3) to the RHS? I would like to compare your approach with Demystifier's BM approach. Thanks.

 

[bhobba]

Bill,How do you move, mathematically, from LHS of Bell's (1964) equation (3) to the RHS? I would like to compare your approach with Demystifier's BM approach.

Please post the full detail then me or someone else can comment - just saying Bells (1964) equation 3 is pretty meaningless. And when I say full detail - that's what I mean - generally asking people to decipher papers without formulating a precise issue is not productive. That said if its an equality then you have your answer.

My approach? BM approach? My approach, and the standard approach, is the usual QM formalism which BM also has. There is no difference.

But Bell is simple - our own doctor Chinese explains it very very clearly:
http://www.drchinese.com/Bells_Theorem.htm

Its simply this. QM allows correlations different to those of classical theory. The reason is in classical probability theory objects have properties at all times. QM is silent on the issue. That is the crucial difference. All Bell shows is if you want it to be like classical theory and have properties at all times then superluminal signalling is required. Its not hard. If you can live with things not having properties until observed then you don't need it. Also there is the issue of if locality is a meaningful concept for correlated systems because the cluster decomposition property, which is locality in QFT, precludes correlated systems. But that is way off topic and requires its own thread.

Also a lot of water has passed under the bridge since Bell wrote that paper - much better to refer to more modern presentations if you want the full mathematical detail:
http://arxiv.org/pdf/1212.5214v2.pdf

I would appreciate you going through the above paper which I have gone through a lot more recently than Bells original paper and then we can have a meaningful discussion.

Added Later:
I had a look at the equation. Since its a singlet state the outcomes are correlated so the expectation on the RHS is simple - it simply the values eg if its 1/2 and -1/2 and you multiply them together its exactly the same as the other way around ie -1/2 and 1/2. Since they are correlated that's the only possibilities.

But, please, please do not discuss that paper. Modern treatments like the paper I linked to will almost certainly be clearer - it would be better to go through it.

Thanks
Bill

 

[Demystifier]

1.2) Call C the Correlative Consequences of the initial pair-wise Conservation of total-spin; and recall that, in Bell (1964), the correlated detectors and the correlated test outcomes relate to spin.

So you do accept that there is some extra entity, which here we call C, while Bell calls it $\lambda$. And like Bell, you assume that this extra quantity is local. But unlike Bell, you don't see a contradiction with QM. Am I right?

Our discussion might be helped by your mathematical answer to this question: How do you move from LHS of Bell's (1964) equation (3) to the RHS?

So are you questioning this particular mathematical step in the Bell's derivation? Fine, now we know where exactly do you disagree with Bell. But Eq. (3) is a consequence of standard QM. People, like Zeilinger, who question the Bell's conclusions, do not question Eq. (3). So are you sure that Eq. (3) is the crucial issue for you? In other words, if you could prove (3), would you then accept nonlocality?

Anyway, the proof of (3) is straightforward but slightly tedious and boring. So let me just give you a few hints. You should use the singlet state defined in
https://en.wikipedia.org/wiki/Singlet_state
and properties of $\sigma$ matrices presented in
https://en.wikipedia.org/wiki/Pauli_matrices

 

[stevendaryl]

Alice's knowledge is a property of Alice's consciousness.

Well, yes. But for a property of Alice's consciousness to count as knowledge, it has to be about something in the real world. In this case, it's about the outcome of Bob's future measurement.

Given the correlation of the photons, the correlation of the detectors and her knowledge of physics: Alice can anticipate the outcome that will soon be known to Bob.

In other words, she can deduce something about Bob from (1) the initial conditions of the EPR, together with (2) her observations.

Predicting a future test result means that you know something about the future reaction of a photon when tested by a detector. False realism is to have an over-developed sense of realism (based on an inappropriate classicality - from a typical classical-world-view) and attribute the outcome (H-polarization) to the pre-test photon.

The issue is: When Alice makes an observation of her photon, does she learn something about Bob's future measurement result that she didn't know already?

Paraphrasing Zeilinger, "This inference to classicality is based on a mis-interpretation (an inappropriate classically-based interpretation) of the information. If you don't assume this, you don't need nonlocality."

I can't make any sense of that, which is why I'm trying to understand what you (and Zeilinger) mean by that.

Our discussion might be helped by the mathematical answer to this question: How do you move from LHS of Bell's (1964) equation (3) to the RHS?

I'm not talking about Bell's theorem, I'm asking about the nature of Alice's knowledge of Bob's future measurement result. Is that knowledge about the physical world, or not?

 

[N88]

Please post the full detail then me or someone else can comment - just saying Bells (1964) equation 3 is pretty meaningless. And when I say full detail - that's what I mean - generally asking people to decipher papers without formulating a precise issue is not productive. That said if its an equality then you have your answer.

"Bells (1964) equation 3 is pretty meaningless"? See https://cds.cern.ch/record/111654/files/vol1p195-200_001.pdf

I am seeking to link the discussion to the OP. So your own mathematical moves from the LHS to the RHS are of interest to me: I am keen to see where nonlocality and a pilot-wave might enter into your analysis.

My approach? BM approach? My approach, and the standard approach, is the usual QM formalism which BM also has. There is no difference.

BM has no difference? I thought BM was decidedly nonlocal. Are you implying that all mathematical approaches are nonlocal?

But Bell is simple - our own doctor Chinese explains it very very clearly:
http://www.drchinese.com/Bells_Theorem.htm

Its simply this. QM allows correlations different to those of classical theory. The reason is in classical probability theory objects have properties at all times. QM is silent on the issue. That is the crucial difference. All Bell shows is if you want it to be like classical theory and have properties at all times then superluminal signalling is required. Its not hard. If you can live with things not having properties until observed then you don't need it. Also there is the issue of if locality is a meaningful concept for correlated systems because the cluster decomposition property, which is locality in QFT, precludes correlated systems. But that is way off topic and requires its own thread.

Also a lot of water has passed under the bridge since Bell wrote that paper - much better to refer to more modern presentations if you want the full mathematical detail:
http://arxiv.org/pdf/1212.5214v2.pdf

I would appreciate you going through the above paper which I have gone through a lot more recently than Bells original paper and then we can have a meaningful discussion.

You misunderstand. Bell's (1964) equation (3) is pure QM. That was the limit of my question to you.

Added Later:
I had a look at the equation. Since its a singlet state the outcomes are correlated so the expectation on the RHS is simple - it simply the values eg if its 1/2 and -1/2 and you multiply them together its exactly the same as the other way around ie -1/2 and 1/2. Since they are correlated that's the only possibilities.

But, please, please do not discuss that paper. Modern treatments like the paper I linked to will almost certainly be clearer - it would be better to go through it.

Thanks
Bill

Bill, in the context of the OP, and your comments here about ± 1/2, it seems that you do not understand Bell's (1964) equation (3). Do you not have a short mathematical procedure to move from its LHS to its RHS?

 

[Demystifier]

Are you implying that all mathematical approaches are nonlocal?

Actually, they are. All mathematical approaches use a wave function (or something equivalent), and wave function for entangled particles is a nonlocal object. For a 2-particle entangled wave function $\Psi({\bf x}_1,{\bf x}_2)$, you cannot say what is the value of wave function at the position ${\bf x}_1$.

 

[bhobba]

"Bells (1964) equation 3 is pretty meaningless"?

The equation is not meaningless - what's meaningless is your asking someone to explain it without context.

I am seeking to link the discussion to the OP. So your own mathematical moves from the LHS to the RHS are of interest to me: I am keen to see where nonlocality and a pilot-wave might enter into your analysis.

The pilot wave has nothing to do with it. Its a general analysis.

BM has no difference? I thought BM was decidedly nonlocal. Are you implying that all mathematical approaches are nonlocal?

What I said - and I will state it as clearly as I can, BM is an interpretation. All interpretations have exactly the same QM formalism. There is no difference - only in interpretation. The QM formalism is silent on locality - BM being an interpretation makes a statement about it (the pilot wave is explicitly non local). That's the sort of thing interpretations do by the definition of interpretations. They fill in things.

Do you not have a short mathematical procedure to move from its LHS to its RHS?

I gave you the answer. I will repeat it. The spins are correlated that means you will get the same answer when multiplied regardless of outcome. It simple when you think about it. If you want me to go deeper you will need to explain precisely what you don't understand about it. The LHS is a statement about expectations. The RHS is what you must get regardless because the singlet state is 100% correlated.

But I again urge you to study the modern link I gave before delving into Bells paper.

Thanks
Bill

 

[stevendaryl]

Actually, they are. All mathematical approaches use a wave function (or something equivalent), and wave function for entangled particles is a nonlocal object. For a 2-particle entangled wave function $\Psi({\bf x}_1,{\bf x}_2)$, you cannot say what is the value of wave function at the position ${\bf x}_1$.

Right. I would say that the formalism of QM is nonlocal, in the sense that there are facts about the state that are non-localized--they aren't facts about any particular locality. That's why realism comes into play, though. Classical probability theory is also nonlocal in this sense: You can have a situation of the form:

• Probability 1/2 that Alice has a left shoe and Bob has a right shoe
• Probability 1/2 that Alice has a right shoe and Bob has a left shoe

That probability distribution is nonlocal in exactly the same sense the wave function is. However, in the case of classical probability theory, the probability distribution is (usually) not considered to be a property of the world, it's considered to be a property of our knowledge about the world.

 

[bhobba]

Actually, they are. All mathematical approaches use a wave function (or something equivalent), and wave function for entangled particles is a nonlocal object. For a 2-particle entangled wave function $\Psi({\bf x}_1,{\bf x}_2)$, you cannot say what is the value of wave function at the position ${\bf x}_1$.

Exactly. Interpretations simply interpret the formalism - not change it.

All Bell is saying is if you want properties to exist independent of observation (technically called counterfactual definiteness - although its slightly more subtle than that - but no need to go into that here) then you must have non-locality. That's one reason I asked N88 to study my linked paper - it carefully explains the assumptions.

It applies to any interpretation - not just BM. BM has properties real at all times, so must be non local - which it explicitly is due to the pilot wave.

Thanks
Bill

 

[Demystifier]

Exactly. Interpretations simply interpret the formalism - not change it.

Yes. And one possible attempt of interpretation is this: Wave function is nonlocal, but reality should be local, so wave function is not real.

But that's not enough. If one claims that wave function is not real, then one has to say what is real? One can be very flexible about that, but the Bell theorem says that, whatever one chooses to be real, it is almost inevitable that this reality will have some nonlocal features.

 

[bhobba]

Yes. And one possible attempt of interpretation is this: Wave function is nonlocal, but reality should be local, so wave function is not real.

Yes - but a (reasonably) obviously flawed one eg it does not follow from our current understanding of physics that reality must be local - only that its not possible to sync clocks FTL. However people are often not careful about that sort of thing and you get flawed arguments like that.

Thanks
Bill

 

[Ilja]

The paper as well as Motl's attack is discussed in http://ilja-schmelzer.de/forum/showthread.php?tid=45 too.

But "realism" is (from my readings) the UNrealistic view that each photon had the "measured" polarisation before it was "measured". So, on this point, I find it best to stick to the Copenhagen interpretation and reject such false "realism" (such "quantum classicality") and retain locality in all its forms. So (I wonder):
Is the claimed "experimental nonlocality" a by-product of their Bohmian unrealism?
Is my subscription to "locality in all its forms" sustainable?

Your subscription to "locality in all forms" is unsustainable. Because you have to give up causality to preserve it (at least any meaningful notion of causality, in particular Reichenbach's principle of common cause). But in this case what remains of causality is reduced to signal causality (you cannot send signals faster than light), and this holds in non-local realistic interpretations too.

Thus, you give up a lot (realism, causality) but win nothing (the week causality you can preserve is not endangered anyway).

That one can really experimentally establish such nonlocal influences I doubt. Because dBB is an interpretation. And experiments supporting interpretations are, hm, ..., interpretations of the experiments.

 

[naima]

Its an interpretation so obviously has all the standard formalism.

If BM accept (unknown) trajectories, there wold be an associated set of orthogonal eigen vectors associated with each point of the trajectory. At every moment in the hilbert space the vector would have to skip to an orthogonal vector. This would imply collapse at every moment.

 

[Ilja]

If BM accept (unknown) trajectories, there wold be an associated set of orthogonal eigen vectors associated with each point of the trajectory. At every moment in the hilbert space the vector would have to skip to an orthogonal vector. This would imply collapse at every moment.

Simply wrong. Learn de Broglie-Bohm theory before talking about it, sorry. In dBB theory there is no collapse at all, there is a wave function and a trajectory. Once the trajectory defines what we observe, there is no need to introduce any collapse - the wave function may present the cat in a superposition, the trajectory of the cat is what matters in reality.

 

[naima]

Please do not only say: Learn. If you know what is wrong about these othogonal vectors, tell it.

 

[Ilja]

I say "learn" because I have the impression that you know almost nothing about dBB theory. The wave function evolves in dBB theory following the same equation as in usual quantum theory, namely the Schrödinger equation. And without any collapse. So your "collapse at every moment" strongly suggest that you don't know even the basics of dBB theory. Sorry, but this is my impression based on your post. And the "learn" means that every introduction into dBB theory will tell you that you are wrong.

 

[bhobba]

If BM accept (unknown) trajectories, there wold be an associated set of orthogonal eigen vectors associated with each point of the trajectory. At every moment in the hilbert space the vector would have to skip to an orthogonal vector. This would imply collapse at every moment.

As Ilja says that's incorrect:
http://arxiv.org/abs/quant-ph/0611032

Thanks
Bill

 

[bhobba]

there is no need to introduce any collapse

Technically its because, in BM, after decoherence the mixed state is a proper mixed state.

Thanks
Bill

 

[naima]

There are many things that i do not want to study. I do not want to waste time with the fractal QM of Nottale or to learn C++.
But when i wonder if there are recursive call in this language, i appreciate a yes/no answer.

My question was about the use of operators and eigenvectors in BM. Bhobba said that it is just an interpretation an thar it uses the Hilbert space machinary.
It seems that it is different. There a wave which obeys the Schrodinger equation but my question was mainly about the particles.
If there is no vector state in the Hilbert space associated to a position in the configuation space write it. Is there even a supperposition principle for particle states?

 

[bhobba]

My question was about the use of operators and eigenvectors in BM. Bhobba said that it is just an interpretation an thar it uses the Hilbert space machinary.

Your error in logic is assuming that it doesn't have more than operators and Hilbert space machinery.

In BM the usual QM formalism emerges from its assumptions rather than simply being assumed. It also has a different interpretation eg its probabilistic nature is due to lack of knowledge of initial conditions rather than being inherent and you don't have improper mixed states, they are all proper.

That's what interpretations do - they add more stuff to the formalism, but the formalism doesn't change.

Thanks
Bill

 

[naima]

Does it use superposition principle for particles? yes? no?
When you read a text it is not easy to find the words which are avoided

 

[bhobba]

Does it use superposition principle for particles? yes? no?
When you read a text it is not easy to find the words which are avoided

The superposition principle is simply that states form a vector space. Since that is part of the standard QM machinery it must.

Thanks
Bill

 

[Demystifier]

If there is no vector state in the Hilbert space associated to a position in the configuation space write it. Is there even a supperposition principle for particle states?

In Bohmian mechanics there is an eigenstate associated with the position operator, but there is no eigenstate associated with the actual position. Likewise, superposition principle is valid for wave functions, but not for actual positions. In Bohmian mechanics there are two kinds of "position" and your confusion seems to emerge from a failure to understand the difference between them.

 

[Demystifier]

Does it use superposition principle for particles? yes? no?

No. Only for wave functions.

 

[naima]

Likewise, superposition principle is valid for wave functions, but not for actual positions.

Thanks
So there is only superposition for the pilot wave.

 

[Demystifier]

Yes, exactly.

 

[stevendaryl]

John Bell wrote a short article about the relationship between Bohmian mechanics and Many-Worlds that was kind of interesting. But here's my take on it:

Many-Worlds starts with the not-too-radical assumption that quantum mechanics (or rather, the Schrodinger equation) applies to arbitrarily large systems, such as the entire universe. So there is no "wave function collapse" if you include the entire universe as your "system". That means that there is no obvious way to interpret the wave function as giving probabilities (via the Born rule), because for the universe as a whole, there are no measurements performed.

Bohmian mechanics, in a way of looking at it, starts in the same place, with a wave function for the universe that evolves unitarily. But it doesn't consider this universal wave function to be "the world". Instead, the world is basically a point in 3N-dimensional configuration space (configuration space being the set of simultaneous positions of each of the N particles in the universe --- this description might only make sense nonrelativistically, where we can think of the number of particles in the universe as a constant). The role of the wave function, then, is to give a probability distribution for the location of the world in phase space.

As an aside---something that's aesthetically unpleasing to me about Bohmian mechanics is the fact that it lacks the symmetry of standard quantum mechanics. The way that standard quantum mechanics is formulated using Dirac's abstract bra-ket notation, there is a kind of "coordinate independence"; the formalism has the same form in any basis. So you don't have to consider configuration space to be primary, you can work in momentum space, or you can work in a basis of harmonic oscillator eigenstates, or you can assume the existence of abstract internal variables such as spin that have no translation into configuration space. In contrast, Bohmian mechanics insists that configuration space is what's "real". The Born probability rules applied to observables besides position are not considered fundamental; if the observable does not relate to position, then it has no direct physical meaning.

Here's where Bell departs from the usual Bohmian mechanics. For the usual formulation of Bohmian mechanics, the relationship between the wave function and a probability distribution in configuration space is dynamic: You assume that that is true initially, and you propose equations of motion for configuration space that preserves this relationship. What Bell pointed out is that trajectories in configuration space are not (directly) observable. The only thing you know about the past history of the universe is whatever is recorded in persistent records. But those persistent records are part of the present state of the universe. So there is a sense in which trajectories are redundant. In light of this, Bell proposed an interpretation of quantum mechanics that was a kind of unification of the Bohmian and Many-Worlds interpretations. In his unified interpretation, the only dynamics is the unitary evolution of the universal wave function. There is no secondary equations of motion for configuration space. Instead, he proposed that at each moment, the world had a probability of being at any point in configuration space, according to the Born rule. So there are no trajectories, the universe just hops from point to point in configuration space randomly.

 

[N88]

… … I gave you the answer. I will repeat it. The spins are correlated that means you will get the same answer when multiplied regardless of outcome. It simple when you think about it. If you want me to go deeper you will need to explain precisely what you don't understand about it. The LHS is a statement about expectations. The RHS is what you must get regardless because the singlet state is 100% correlated.

But I again urge you to study the modern link I gave before delving into Bells paper.
Thanks, Bill

A. Delving into Bell's paper is neither relevant nor my intention here. But I again note that, despite my providing the context, you do not give me the way that you mathematically link the LHS to the RHS of Bell (1964), eqn (3). I expected your math would allow us to discuss where "non-locality" (allegedly) arises in such math.

B. As for the paper that you favour http://arxiv.org/pdf/1212.5214v2.pdf: it makes my point explicitly (p.2, with my emphasis):

"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.]
Bell’s theorem can be phrased as “quantum mechanics cannot be both local and counterfactual-definite”. A logically equivalent way of stating it is “quantum mechanics is either non-local or non counterfactual-definite.”​

My interest is in learning about local and non counterfactual-definite QM.