# A How do entanglement experiments benefit from QFT (over QM)?

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#### Auto-Didact

The construction itself is Nelsonian stochastics. All it needs is to work mathematically is that the energy depends quadratically on the momentum variables. So, the mathematics of Nelsonian stochastics can be taken over to bosonic field theories in the same way as this can be done for Bohmian bosonic field theories, with the formulas given in

Bohm.D., Hiley, B.J., Kaloyerou, P.N. (1987). An ontological basis for the quantum theory
The cat is finally out of the bag: I'm a Nelsonian sympathiser, but stochastic mechanics, for all it does - and admittedly it does enormously much, including the full restoration of classical logic in physics - is de facto not standard quantum mechanics, i.e. not part of the canonical mathematical structure of QM as described within the literature and all textbooks: this description is interpretation-free in the sense of how this terminology is used in the foundations literature.

Now the question of whether the canonical description of QM is itself correct, while obviously important, is a completely seperate issue to whether a faithfull description is being given of canonical QM: it seems obvious to me that you are arguing for the former and not the latter, while @DarMM is explicitly arguing for the latter.

In other words, it is you and not @DarMM who is involving their personal philosophy for the right reasons - i.e. a deeper constructive mathematical understanding and a restoration of logic - but at the wrong moment within this discussion. More directly, Smolin also explicitly points out in his latest book how the Nelsonian point of view while almost irresistible does not seem to be capable of being correct.

#### Elias1960

Which doesn't change the fact that this proposition does not have a well-defined truth value for an electron that has just come out of the "up" output of a Stern-Gerlach device oriented in the $z$ direction.
Yes. The information you have is insufficient to identify the truth value. So what? It does not mean that it does not have a truth value.
Not required for what?
For the applicability of the classical propositional calculus, in particular, the applicability of Boolean logic, so that the set of propositions defines a Boolean algebra, the application of Stone's theorem to construct a unique sample space, and the logic of plausible reasoning - classical probability theory - on this space of elementary events.
Not required for QM, sure; but QM does not claim that there is a single Boolean algebra that captures all of these propositions.
It is sufficient that any scientific discourse is based on applying classical logic on propositions about QM as well as about other theories. If you cannot talk about a theory you propose using the language of logical propositions with meaningful truth values, you simply don't have a well-defined theory.

This is my point all the time: The rules of logic (inclusive the logic of plausible reasoning) are part of the scientific method, they are theory-independent and beyond particular theories, and in particular not subject to empirical falsification.
You are claiming that, so you can't wave your hands and say it's "not required" to test them both. Not being able to test them both is precisely what prevents there from being a single sample space.
No. There is no such requirement neither in classical logic nor in the logic of plausible reasoning.

A standard proceeding in a criminal investigation would be the evaluation of different possibilities. Some of them appear in conflict with the available data, all others give the conclusion that the accusation is correct. Is this sufficient, even if we cannot identify, given the available information, which of the many scenarios for the crime is the correct one, for a conviction? Yes, it is.

But the advocate of the accused would be happy to be able to apply quantum strangeness in the defense of his client. Once we cannot find out if his T-shirt was yellow or green, there is no single sample space for the colors of his T-shirt, so one cannot apply classical plausible reasoning, thus, one cannot prove that the accused has done it.

(Aside: The rules of scientific reasoning are open to criticism too. But if one proposes to reject the rules of scientific reasoning and to modify them, then one has to do this consistently, theory-independent, and reject the invalid rules of reasoning in everyday reasoning too. This is behind my examples regarding tobacco industry and that criminal case.)

#### Elias1960

The cat is finally out of the bag: I'm a Nelsonian sympathiser, but stochastic mechanics, for all it does - and admittedly it does enormously much, including the full restoration of classical logic in physics - is de facto not standard quantum mechanics, i.e. not part of the canonical mathematical structure of QM as described within the literature and all textbooks: this description is interpretation-free in the sense of how this terminology is used in the foundations literature.
I agree. The point being? Note the context where I have introduced it:
No, these are the metaphysical choices you have made by choosing your preferred interpretation of QM. You are aware that there exist other interpretations of QM which have a different view. A piece of mathematical machinery does nothing without your interpretational choices. Here, in particular, you make the assumption that that $C^∗$ structure is something fundamentally important, and not a nice accidental consequence of [the way it is interpreted in Nelsonian stochastics]
Now the question of whether the canonical description of QM is itself correct, while obviously important, is a completely separate issue to whether a faithfull description is being given of canonical QM: it seems obvious to me that you are arguing for the former and not the latter, while @DarMM is explicitly arguing for the latter.
What is the "canonical description of QM"? There is the minimal interpretation, which remains silent over such questions as if the $C^∗$ structure is something fundamentally important. Those who claim that the $C^∗$ structure is something fundamentally important support an interpretation beyond the minimal one and involve their personal QM philosophy. And naming this "canonical description of QM" (instead of giving it the appropriate name, like "Copenhagen interpretation" or whatever) could be even suspected to be an attempt to hide this. A description as "canonical" and "of QM" I can accept only for the minimal interpretation, and the claims I have questioned are obviously not part of the minimal interpretation.
More directly, Smolin also explicitly points out in his latest book how the Nelsonian point of view while almost irresistible does not seem to be capable of being correct.
Any open link to it? If it contains more than the standard arguments (necessity of preferred frame, the Pauli argument in favor of p-q symmetry, and Wallstrom), what is his point?

#### DarMM

Gold Member
It wasn't clear to me that you were referring to different sample spaces in each theory
I'm referring to the sample spaces each theory actually has.

Well, perhaps a point of error or maybe just not understanding your terminology. I have not understood till now why you say BM has a single sample space, but QM does not - to me neither have a single sample space in only the variables defined in Fine's theorem.
Bohmian Mechanics does have a single sample space for the variables for Fine's theorem. The variables can be modelled as random variables $\Gamma_{E,M}(\lambda)$, often called Response functions in the Foundation literature. The difference is that they are contextual, i.e. arbitrary identity partitions $M$ appear.

Anyway, if you mean QM rejects decorrelating explanation, then I understand what you mean (and yes, I do agree with Wiseman). I would, however, disagree on terminology. I would say QM is neutral on the rejection of decorrelating explanation, and it is neutral on the general issue of having no single sample space in arbitrary variables.
I don't agree with this. The formalism itself does not have a single sample since it has a non-commutative C*-algebra. This isn't interpretational. The number of sample spaces is a mathematical fact.

Bohmian Mechanics is an alternate formalism and ultimately a different theory. As a different formalism different mathematical statements are true about it. It has a single sample space of the form:
$$\mathcal{H}\times Q^{\otimes n}$$
where $Q$ is some manifold (generally orbifold) of particle positions.

This simply is mathematically a very different set up. QM itself has no such Hilbert-Orbifold state space.

One can be neutral on which formalism is physically correct, but not on the mathematical facts of each formalism. And it is a mathematical fact that QM has multiple sample spaces. Nobody in the actual literature phrases this as or considers it as interpretational.

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#### Tendex

BM interpretation making the same predictions (otherwise it wouldn't be a QM interpretation) also has multiple sample spaces for its predictions and that doesn't prevent it from having one sample space for the much bigger set of all possible outcomes. Having multiple sample spaces for predictive subsets is not equivalent to discard having a single sample space for a bigger set of elementary outcomes that can be used to conform the subsets that correspond to predictions.
Also clearly as one can check reading descriptions of different QM interpretations with the same predictions whether to reject locality, or counterfactuals or not is purely interpretational, not part of the formalism as falsely claimed by DarMM.

#### DarMM

Gold Member
What is the "canonical description of QM"? There is the minimal interpretation, which remains silent over such questions as if the $C^∗$ structure is something fundamentally important. Those who claim that the $C^∗$ structure is something fundamentally important support an interpretation beyond the minimal one and involve their personal QM philosophy. And naming this "canonical description of QM" (instead of giving it the appropriate name, like "Copenhagen interpretation" or whatever) could be even suspected to be an attempt to hide this.
This is daft though. QM has a C*-algebra structure, that's just the mathematical formalism. If we can't say the mathematical formalism has properties because there might ultimately be another deeper theory one can basically say nothing about any theory.

"Does General Relativity have differentiable manifolds? Who knows there might be a deeper theory."

Statements like these mix up mathematical facts of the formalism with claims about ontology. I'm not interested in the latter. I'm saying the actual formalism that is used by most physicists, the actual C*-algebra set up of QM, has multiple sample spaces.

#### DarMM

Gold Member
BM interpretation making the same predictions (otherwise it wouldn't be a QM interpretation)
It possibly makes the same predictions as non-relativistic QM (there is no fully general proof that it does) ignoring Wigner's friend scenarios.

It simply doesn't make the same predictions with regard to QFT.

also has multiple sample spaces for its predictions and that doesn't prevent it from having one sample space for the much bigger set of all possible outcomes
It doesn't. See the random variables/response functions I mentioned to @atyy above.

#### Elias1960

The formalism itself does not have a single sample since it has a non-commutative $C^*$-algebra. This isn't interpretational. The number of sample spaces is a mathematical fact.

Bohmian Mechanics is an alternate formalism and ultimately a different theory. As a different formalism different mathematical statements are true about it. It has a single sample space of the form:
$$\mathcal{H}\times Q^{\otimes n}$$
where $Q$ is some manifold (generally orbifold) of particle positions.

This simply is mathematically a very different set up. QM itself has no such Hilbert-Orbifold state space.
While I agree that BM is ultimately a different theory (simply because the QM states are only a small subset of states of BM theory, namely quantum equilibrium states), what distinguishes different theories are different empirical predictions, not a different mathematical apparatus. In fact, one can use the mathematical apparatus of non-commutative $C^*$-algebra in BM too if one likes, the math formalism does not have patents or require licenses. So, BM restricted to quantum equilibrium states is the same theory as Schrödinger theory, given that it makes the same empirical predictions.

Of course, for particular quantum experiments, one can use the correspondingly reduced sample spaces restricted to the particular experiment. So the existence of these reduced versions is a triviality which proves nothing. And, given that the combination of all this into a single big sample space is a quite straightforward and trivial exercise if one recognized how it has to be done appropriately, and this construction is essentially theory-independent and works even for metatheoretical considerations, the point that such a common sample space exists is not even part of a theory, it is part of logical reasoning about such theories.

The choice of what defines the ontology is clearly interpretational. It exists only in realistic interpretations, and not in the mathematical apparatus itself.

#### Tendex

It possibly makes the same predictions as non-relativistic QM (there is no fully general proof that it does) ignoring Wigner's friend scenarios.

It simply doesn't make the same predictions with regard to QFT.
This is irrelevant for your own point, it is enough with the predictions of NRQM, the noncommutative algebra applies to them.
It doesn't. See the random variables/response functions I mentioned to @atyy above.
See the construction of random outcomes by Kochen and Specker quoted above and valid for any theory.

#### DarMM

Gold Member
In fact, one can use the mathematical apparatus of non-commutative $C^*$-algebra in BM too if one likes, the math formalism does not have patents or require licenses. So, BM restricted to quantum equilibrium states is the same theory as Schrödinger theory, given that it makes the same empirical predictions.
It is a conjecture that it is the same theory for a particular subset of non-rel QM. It's completely proven. As I've said it's acknowledged by Bohmians that it's not the same in Wigner's friend scenarios.

QM is distinguished from Bohmian Mechanics because it only has the C*-algebra strucutre and states upon it. Thus QM has multiple sample spaces.

#### DarMM

Gold Member
This is irrelevant for your own point
It is not. The most general type of algebraic structures we see even in non-relativistic physics are type-$III$ C*-algebra factors which Bohmian Mechanics cannot replicate. It is a conjecture that it replicates a Wigner Friend excluding subset of non-relativistic finite degree of freedom Quantum mechanics. This is what I mean, it's an alternate formalism that has a lot of work to do to replicate QM and we know it won't replicate QM in Wigner's friend scenarios. Thus it is a different theory, so why are we using it to object to facts about the mathematical structure of QM?

See the construction of random outcomes by Kochen and Specker quoted above and valid for any theory.
This is a complete non-sequitur. That construction shows what I am saying, an alternate formalism with infinitely many contextual variables for each variable in QM, all defined on a single sample space. It doesn't show Bohmian Mechanics also has multiple sample spaces.

#### Tendex

It is not. The most general type of algebraic structures we see even in non-relativistic physics are type-$III$ C*-algebra factors which Bohmian Mechanics cannot replicate. It is a conjecture that it replicates a Wigner Friend excluding subset of non-relativistic finite degree of freedom Quantum mechanics. This is what I mean, it's an alternate formalism that has a lot of work to do to replicate QM and we know it won't replicate QM in Wigner's friend scenarios. Thus it is a different theory, so why are we using it to object to facts about the mathematical structure of QM?

This is a complete non-sequitur. That construction shows what I am saying, an alternate formalism with infinitely many contextual variables for each variable in QM, all defined on a single sample space. It doesn't show Bohmian Mechanics also has multiple sample spaces.
By definition of QM interpretation, (you are referring to an alternative Bohmian theory, not to the QM interpretation then) all QM interpretations make the same predictions and they can apply the noncommutative C*-algebra to them, so they have multiple sample spaces for their predictions.
Additionally, as Kochen&Specker assert explicitly, their single sample space can be applied to ANY theory(as long as it follows mathematical logic and deals with probabilities of course)

#### atyy

I don't agree with this. The formalism itself does not have a single sample since it has a non-commutative C*-algebra. This isn't interpretational. The number of sample spaces is a mathematical fact.

Bohmian Mechanics is an alternate formalism and ultimately a different theory. As a different formalism different mathematical statements are true about it. It has a single sample space of the form:
$$\mathcal{H}\times Q^{\otimes n}$$
where $Q$ is some manifold (generally orbifold) of particle positions.

This simply is mathematically a very different set up. QM itself has no such Hilbert-Orbifold state space.

One can be neutral on which formalism is physically correct, but not on the mathematical facts of each formalism. And it is a mathematical fact that QM has multiple sample spaces. Nobody in the actual literature phrases this as or considers it as interpretational.
It's just a matter of language, so I won't argue with that.

But consider orthodox QM with either wave function and collapse to be real, or not real. When the wave function is not real, the mathematics of orthodox QM is a non-commutative C*-algebra. Now take the wave function and collapse to be real, is the langauge of naive QM no longer a non-commutative C*-algebra?

#### Elias1960

It possibly makes the same predictions as non-relativistic QM (there is no fully general proof that it does) ignoring Wigner's friend scenarios.
The simple straightforward proof is sufficient. Wigner's friend scenarios are artificial constructions which are irrelevant for the comparison of empirical predictions.
It simply doesn't make the same predictions with regard to QFT.
Wrong. Once again the reference

Bohm.D., Hiley, B.J., Kaloyerou, P.N. (1987). An ontological basis for the quantum theory, Phys. Reports 144(6), 321-375

This is daft though. QM has a C*-algebra structure, that's just the mathematical formalism. If we can't say the mathematical formalism has properties because there might ultimately be another deeper theory one can basically say nothing about any theory.
You are free to say whatever you like about the mathematical formalism. Of course, a single sample space for the whole theory can be reduced to much smaller subspaces for particular experiments, so, there is nothing strange with multiple sample spaces. The nonsensical part is the claim that there does not exist a single one, if it has been explicitly constructed and presented.

You can also say that there exist no single sample space with particular additional properties related with that C*-algebra structure. No problem. But in this case, the objection that the C*-algebra structure may be of no fundamental interest is a reasonable objection. The single sample space which does not care about the C*-algebra structure has been explicitly presented. Moreover, the construction is essentially part of logic, not of the particular theory (it is the Stone space of the Boolean algebra of the meaningful propositions of the theory).

Why the non-existence of such a sample space with some additional properties, like some compatibility with some C*-algebra structure, is something worth to be mentioned, is something which has to be explained by the one who makes this claim.
I'm saying the actual formalism that is used by most physicists, the actual C*-algebra set up of QM, has multiple sample spaces.
And this information is quite irrelevant because for a given particular experiment one can always reduce the single sample space to various much smaller ones which fix all the information about that particular experiment. The information which would be problematic would be that no single one exists. The information that no single one with particular additional properties exists would be uninteresting too, if presented without any arguments that the additional structure is somehow fundamentally important.

#### DarMM

Gold Member
By definition of QM interpretation, (you are referring to an alternative Bohmian theory, not to the QM interpretation then
I'm referring to what Bohmian Mechanics is actually like. The meaning of the English word "interpretation" doesn't alter the mathematical facts. One could argue if "interpretation" is the correct word, but that's a separate issue.

Additionally, as Kochen&Specker assert explicitly, their single sample space can be applied to ANY theory
The resulting construction is not part of QM. One can use the machinery of the generalized Nash's embedding theorem to construct a 231-D Minkowski space in which to embed any spacetime from General Relativity, but the resulting Minkowski space is not part of GR.

Sure you can apply the construction, one can imagine building structures out of almost anything in QM by applying some construction to them. If the resulting object isn't part of the theory though, why does it matter?

#### DarMM

Gold Member
Wrong. Once again the reference
That doesn't replicate QFT. Even Bohmians say they cannot replicate QFT. Show me that being used to compute a weak force cross section.

And this information is quite irrelevant
The actual mathematical structure of the commonly used formalism is irrelevant? Well there is little I can say to that.

#### DarMM

Gold Member
But consider orthodox QM with either wave function and collapse to be real, or not real. When the wave function is not real, the mathematics of orthodox QM is a non-commutative C*-algebra. Now take the wave function and collapse to be real, is the langauge of naive QM no longer a non-commutative C*-algebra?
We know what you call "orthodox QM with wave function collapse as real" is self-contradictory.

Non-self contradictory approaches that have the wave-function as real require supplementation with additional variables and thus are different theories.

It's just a matter of language, so I won't argue with that.
I don't think it is. A formalism either has a mathematical property or it does not. Something being a mathematical property of a formalism is not a matter of language I would have said.

#### DarMM

Gold Member
I think at this point everything possible has been said.

I think it should be clear that QM the formalism itself is a generalized probability theory with a non-commutative C*-algebra.
(Opinions here that such a generalization is not sensible are crankish internet opinions not found in the literature)

This then causes there to be multiple sample spaces, which prevent decorrelating explanations and thus allows violations of Bell's inequality.

I'll close with that.

#### Tendex

I'm referring to what Bohmian Mechanics is actually like. The meaning of the English word "interpretation" doesn't alter the mathematical facts. One could argue if "interpretation" is the correct word, but that's a separate issue.
The mathematical fact I was pinpointing in the usual way is that all theories making the same predictions as QM regardless of their ontology can have multiple sample spaces, you got a problem with this?
The resulting construction is not part of QM. One can use the machinery of the generalized Nash's embedding theorem to construct a 231-D Minkowski space in which to embed any spacetime from General Relativity, but the resulting Minkowski space is not part of GR.

Sure you can apply the construction, one can imagine building structures out of almost anything in QM by applying some construction to them. If the resulting object isn't part of the theory though, why does it matter?
GR is(as I already told you) so far about 4-dimensional spacetimes so I guess you can leave out a 231-dimensional space but last I checked Hilbert spaces such as the used by Kochen&Specker with quantum observables and quantum states and explicitly claiming is a QT construction might have something to do with QM and be part of the theory, but who knows?

#### Elias1960

That doesn't replicate QFT. Even Bohmians say they cannot replicate QFT. Show me that being used to compute a weak force cross section.
Why would that be a problem? You somehow seem to think that Bohmians are not allowed all the mathematical apparatus of standard QFT. (It seems to be a property of many of your claims that you confuse interpretational questions with mathematical formalism which has nothing to do with the interpretation.)
The actual mathematical structure of the commonly used formalism is irrelevant? Well there is little I can say to that.
No, not the actual mathematical structure, but the claim that there exist multiple sample spaces. It is irrelevant because it is a triviality too. One can always reduce the single sample space for multiple particular experiments to multiple particular sample spaces. So, please read what I write, and don't cut necessary context in your quotes which already answers your polemical rhetorical question.

#### Morbert

Yes. The information you have is insufficient to identify the truth value. So what? It does not mean that it does not have a truth value.
A Boolean logic is an event algebra that follows from a sample space of elementary event propositions. If you construct a Boolean logic around a sample space appropriate for the $S_x$ measurement you made, you cannot include propositions like $S_z = \uparrow$, as you cannot construct a sample space that contains all the necessary elementary propositions about $S_x$ and $S_z$. I.e. It's not just that the truth of the proposition is unknown. The proposition itself cannot be made.

You can, of course, build an alternative Boolean logic around an alternative sample space that contains elementary propositions like $S_z = \uparrow$, but this logic necessarily excludes propositions logically equivalent to the measurement outcome you just observed, and so cannot be used in the context of the measurement result you are analysing.

#### Jimster41

Gold Member
The information you have is insufficient to identify the truth value. So what? It does not mean that it does not have a truth value.
I thought it was more like @Morbert is saying. Re the the cat being either dead, alive or dead and alive - There are a incompatible clauses in Boolean algebra else why the XOr and it’s not the same as the t-shirt being red or green or red and green.

Additionally, as Kochen&Specker assert explicitly, their single sample space can be applied to ANY theory(as long as it follows mathematical logic and deals with probabilities of course)
That’s what I thought experiments in QM show (and our empirical reality reinforces) there are justifications for taking a set of proposable propositions and carving them down to plausible ones via formalism. Your positions feels like it’s advocating for The supremacy of the first important Cantor-like metafying step - the collection of all proposals we can propose (including “the perp was a cat that was entirely red and entirely green”). Sure it’s an important step but so is the sorting out of what the algebra of empirical reality supports.

The simple straightforward proof is sufficient. Wigner's friend scenarios are artificial constructions which are irrelevant for the comparison of empirical predictions
I’m a bit surprised to hear you say this. To me it seems like you’ve been taking the exactly opposite position w/respect to dinosaur guy the whole time. He’s saying a sharp description of QM formalism w/respect to the algebra type empirical observations support is key to discourse about it and you’ve been saying general propositional set building can be done on the propositions about observables to embed whatever distinction that process makes into a common and indistinguishable set.

Sometime I wish there was like a supermoderator who could come along and when closing these great (albeit contentious) threads do a bit of summarizing for the listeners - maybe some sound healing, a little deep breathing.

#### DrClaude

Mentor
This thread has ran its course. Time to close.

Thanks to all that have participated.

#### DrClaude

Mentor
As a closing note, @*now* would like to point out the following paper:

https://arxiv.org/pdf/1806.08150.pdf

The notion of locality in relational quantum mechanics
P. Martin-Dussaud, C. Rovelli, and F. Zalamea

The term ‘locality’ is used in different contexts with different meanings. There have been claims that relational quantum mechanics is local, but it is not clear then how it accounts for the effects that go under the usual name of quantum non-locality. The present article shows that the failure of ‘locality’ in the sense of Bell, once interpreted in the relational framework, reduces to the existence of a common cause in an indeterministic context. In particular, there is no need to appeal to a mysterious space-like influence to understand it.