I What is the current perspective on quantum interpretation?

[vanhees71]

QM is nonlocal in the Bell's sense, there is no arguing about that. I only argue against the use of the word nonlocal. As to the second, yes, you can take it that particles have positions or you can be agnostic about it, or say that it doesn't matter, or that it is meaningless. Whichever one you prefer.

Of course, particles have positions (provided they have a position observable). As with any other observable positions can be more or less well determined (they are never precisely determined because the specctrum of the corresponding self-adjoint operator is continuous). I also don't think that "my interpretation" of QT is much different from Ballentine's.

I also don't like to say, "quantum theory is nonlocal", because it can be misleading. The most successful physical theory is local (sic) relativistic quantum field theory and the Standard Model based on it, and there the interactions are by construction local (microcausality principle, upon which the unitarity and Poincare invariance of the S-matrix is guaranteed). I'd rather call the phenomena related to entanglement between far-distant parts of a quantum system "long-ranged correlations", because that's what's described, namely a statistical property which goes beyond the statistical properties deterministic "classical" systems can have.

 

[Demystifier]

I also don't like to say, "quantum theory is nonlocal"

I would say that quantum theory is local, but nature isn't.
Quantum theory in its minimal form is incomplete, in the sense that it cannot answer all questions one can ask about nature. To answer such questions one must talk about quantities (e.g. the Bell's $\lambda$) which are not a part of the minimal quantum theory. Quantum theory in its minimal form retains locality by refusing to talk about such quantities. Experimental violation of Bell inequalities shows that nature is nonlocal, irrespective of the theory.

 

[martinbn]

My problem is that I don't get you. It looks as if you don't care about interpretations, yet you like to discuss interpretations and ask questions about them. Is it just a chit-chat for you, or what?

No, I said that I don't have a favorite interpretation. I am not emotionally invested in any of them. That doesn't mean that I am not interested.

 

[martinbn]

Experimental violation of Bell inequalities shows that nature is nonlocal, irrespective of the theory.

NO! It shows that nature is nonlocal in the Bell's sense. It doesn't show that nature is nonlocal period.

 

[martinbn]

Of course, particles have positions (provided they have a position observable). As with any other observable positions can be more or less well determined (they are never precisely determined because the specctrum of the corresponding self-adjoint operator is continuous). I also don't think that "my interpretation" of QT is much different from Ballentine's.

That is not what I am saying. I am saying that you can think of individual particles having exact positions at any time i.e. they are there at a specific point at any given time.

 

[Demystifier]

No, I said that I don't have a favorite interpretation. I am not emotionally invested in any of them. That doesn't mean that I am not interested.

Does it mean that you are "emotionally invested" in the whole field of quantum interpretations?

 

[vanhees71]

That is not what I am saying. I am saying that you can think of individual particles having exact positions at any time i.e. they are there at a specific point at any given time.

You can determine (prepare) the position of a particle with as small an uncertainty as you want but not precisely due to Heisenberg and Robertson's uncertainty relation, $\Delta x \Delta p \geq \hbar/2$. All what's observable on an ensemble of equally prepared particle positions are the probability distributions, $|\psi(t,x)|^2$.

 

[MathematicalPhysicist]

Sounds like an old joke about politics: when three humans get together, they promptly found four political parties.

I heard some variant of it about jews.
Where there are two jews there are three opinions.

I guess this is common for every human...

 

[Buzz Bloom]

I heard some variant of it about jews.
Where there are two jews there are three opinions.

There is a deeper interpretation of this than the joke. Each individually has a different and disagreeing opinion, but together they can find an agreeable mddle ground.

 

[MathematicalPhysicist]

There is a deeper interpretation of this than the joke. Each individually has a different and disagreeing opinion, but together they can find an agreeable mddle ground.

if you have someone arguing for A and the other one for ~A (negation of A), how can you have a third option?!

 

[Buzz Bloom]

if you have someone arguing for A and the other one for ~A (negation of A), how can you have a third option?!

A disagreement between two opinions does not necessarily imply the two opinions are completely opposite. Opinions generally involve a combination of concepts, including opinions about QM interpretatons.

 

[MathematicalPhysicist]

A disagreement between two opinions does not necessarily imply the two opinions are completely opposite. Opinions generally involve a combination of concepts, including opinions about QM interpretatons.

Obviously if it's possible, but not always it's possible...

 

[ObjectivelyRational]

Of course, particles have positions (provided they have a position observable). As with any other observable positions can be more or less well determined (they are never precisely determined because the specctrum of the corresponding self-adjoint operator is continuous). I also don't think that "my interpretation" of QT is much different from Ballentine's.

I also don't like to say, "quantum theory is nonlocal", because it can be misleading. The most successful physical theory is local (sic) relativistic quantum field theory and the Standard Model based on it, and there the interactions are by construction local (microcausality principle, upon which the unitarity and Poincare invariance of the S-matrix is guaranteed). I'd rather call the phenomena related to entanglement between far-distant parts of a quantum system "long-ranged correlations", because that's what's described, namely a statistical property which goes beyond the statistical properties deterministic "classical" systems can have.

Given the arbitrariness of time ordering of space-like separated events, how does one interpret "correlated" microcausality (as a principle)? I'm not proposing "nonlocal" is any better than "correlated" (all things considered), but does thinking "locally" have its own problems?

 

[vanhees71]

It is utmost important to keep in mind that correlations and causal connections are two different things (not only in the context of quantum theory).

The microcausality principle says that any local observable $\mathcal{O}(x)$ ($x$: space-time four-vector) commutes with the Hamilton density, $[\mathcal{O}(x),\mathcal{H}(y)]=0$ for $(x-y)^2<0$, i.e., if $x$ and $y$ are space-like separated. That implies that there are no faster-than light interactions and thus no faster-than light causal effects.

The correlations described by entanglement can refer to space-like separated measurements on an extended quantum object like the usual polarization-entangled two-photon Bell states used to demonstrate the violation of Bell's inequality, teleportation, quantum erasure by postselection, entanglement swapping, ... Here you clearly predict and also empirically confirm stronger correlations between observables (here the polarization of both photons measured at far distance) than is possible within a local deterministic hidden-variable model (according to Bell).

The cause for the correlations in all such cases is not due to the one or the other measurements, which can be space-like separated and thus cannot causally influence one another within local relativistic QFT, and still you observe the correlations due to entanglement predicted by this theory. Within this theory it's also clear that the correlations between the measured polarization observables is due to the preperation of the photon pairs, i.e., they are made as an entangled pair (usually by parametric downconversion using a BBO crystal and a laser). Such Bell states have the amazing property to describe a very "non-classical" situation: Though the single-photon polarizations are completely indetermined when the photon pair is prepared in such a state, there are strong correlations in the outcome of measurements which can be revealed by comparing the measurement protocols of the two space-like separated measurements (which of course can only be done via sending the information of the outcomes between the observers, which cannot be done in any way via faster-than light signals).

With this "minimal interpretation" of the quantum state, i.e., that it describes (and only describes!) the statistical properties of measurement outcomes when measuring observables of the prepared the system, there is no contradiction between microcausality and the observed correlations between space-like separated measurements on an entangled system.

 

[gentzen]

One question raised in the answers to this Quantum Interpretation poll is what it means that "quantum theory is nonlocal". It could mean that Bohmian mechanics is nonlocal, and that any similar deterministic interpretation has to be nonlocal too. But is this really true, and does it help?

For example, Arnold Neumaier's thermal interpretation is deterministic, but less obviously nonlocal than Bohmian mechanics. Its state variables (i.e. properties of the state) includes nonlocal correlations, and the (state of the) one universe may also be seen as nonlocal in character. But being nonlocal is probably more a statement about the evolution of the state than a statement about the state itself. In conclusion, it is unclear to me whether the thermal interpretation is nonlocal or not, or how I could nail down what it means that an interpretation is nonlocal.

This is the context that made me read Nicolas Gisin’s short book Quantum Chance. Gisin somehow goes beyond the notion of true randomness or “bit strings with proven randomness” and tries to capture the experimentally observable nature of quantum chance itself, independent of any interpretation of quantum mechanics (or even the validity of quantum mechanics). Something like that it is a nonlocal randomness, and because the nonlocal correlations of quantum physics are nonsignalling, it has to be random, because otherwise it would allow faster than light communication.

 

[Demystifier]

It could mean that Bohmian mechanics is nonlocal, and that any similar deterministic interpretation has to be nonlocal too.

Similar non-deterministic interpretations also have to be nonlocal. Examples are the stochastic Nelson interpretation and Caticha interpretation.

 

[vanhees71]

The question is what you mean by "local". Relativistic quantum field theory is local by construction. As any quantum theory it allows for strong non-local correlations, i.e., for correlations of outcomes of space-like separated measurements at far distant places on quantum systems where the far-distantly measured observables on parts of this system are entangled (e.g., the single-photon-polarization measurements on polarization entangled photon pairs created by parametric downconversion).

As usual Einstein was much more careful to formulate his quibbles. He didn't like the confusing EPR paper and wrote another one, where he introduced the much better notion of "inseparability" to describe these long-ranged correlations through entanglement, and his true critizism was more against the Copenhagen doctrine (particularly the collapse hypothesis, which is however only part of some flavors of Copenhagen interpretations) to interpret more into the quantum state than the statistical predictions it makes. He considered QT incomplete, because it only makes statistical predictions on the outcome of measurements. For Einstein only a deterministic description, where all values of observables have, at least in principle, a determined value and can be measured. For him the need of statistics (as in classical kinetic theory) should only be due to limited knowledge about the state of the system but not a property of the state. E.g., in classical mechanics the state is a point in phase space, and if you know this state exactly at one time all the observables of the system have a determined value and can be predicted by solving (Hamilton's) equation of motion, while within QT even complete determination of the state (e.g., by determining the values a complete set of compatible observables, defining a unique pure quantum state of the system) does not imply the determination of all observables' values of this system, and the randomness of the outcome of measurements within QT is not due to incomplete knowledge about the state of the system but "irreducible", i.e., within QT there is no state such that all observables take determined values (that's the content of the Heisenberg-Robertson as well as the Schrödinger-Robertson uncertainty relation).

 

[gentzen]

The question is what you mean by "local". Relativistic quantum field theory is local by construction.

I guess not allowing faster than light signaling will be part of it. I could also try to be more specific. For example, in section "8. Locality and Special Relativity" of the SEP article "The Consistent Histories Approach to Quantum Mechanics", Robert Griffiths writes:

In addition, the histories approach makes it possible to establish on the basis of quantum mechanics itself a principle of Einstein locality (Griffiths 2011b):

Objectively real internal properties of an isolated individual system do not change when something is done to another non-interacting system.

However, being too specific risks limiting the meaning of "local" more than necessary. On the other hand, I do believe that it is possible to define exactly in which sense quantum mechanics (or rather relativistic quantum field theory) should be "local", and that it has actually been defined (in a less trivial way than my quote from Griffiths).

However, I do believe that many quantum interpretations (including the thermal interpretation) will be "local" in this sense (or at least compatible with it), even so I am currently unable to define it. But that won't stop those interpretations from being nonlocal, simply because quantum physics itself is nonlocal. Therefore, clarifying what is meant by "quantum theory is nonlocal" remains important. Describing it as nonlocal randomness like in Gisin's book might be wrong, but at least it has some intuitive appeal to me.

 

[vanhees71]

The problem with the debates about interpretation, which is usually a rather philosophical topic without much meaning for physics as a natural science anyway, is that philosophers tend to use fuzzy definitions of their words, particularly the ones we discuss here (locality and reality among them).

Local in the sense of relativistic QFT means that the Hamiltonian density is a function of the field operators and their derivatives at one spacetime point and that local observables commute with the Hamiltonian density at space-like separated arguments, from which unitarity of the S-matrix and the linked-cluster principle follows, including the impossibility for causal effects propagating faster than light (excluding thus faster-than-light signalling).

 

[gentzen]

As usual Einstein was much more careful to formulate his quibbles. He didn't like the confusing EPR paper and wrote another one, where he introduced the much better notion of "inseparability" to describe these long-ranged correlations through entanglement

Can you be more specific about which paper exactly? I have now checked
Physics and Reality (1936)
Considerations concerning the fundamentals of theoretical physics (1940)
Quantum Mechanics and Reality (1948)
but didn't find the word "inseparability" in them (or any suitable substitute).

 

[Demystifier]

The problem with the debates about interpretation, which is usually a rather philosophical topic

Well, I think interpretation of QT is much more religion than philosophy

So which is it?

 

[vanhees71]

Well, I guess both ;-)).

 

[Demystifier]

Well, I guess both ;-)).

Your answer is neither philosophy nor religion. It's politics.

 

[vanhees71]

So it's far from being science. SCNR.

 

[bhobba]

if you have someone arguing for A and the other one for ~A (negation of A), how can you have a third option?!

Because arguments are rarely the A, not A type. They are something like I believe everyone needs a guaranteed income of at least $20,000 a year (statement A). The opposition is nobody should have a guaranteed income. The not A position is a guaranteed income of less than $20,000, or no guaranteed income. A compromise position could be a guaranteed income of $10,000 py which satisfies neither position, but both sides may be able to live with it.

Thanks
Bill

 

[MathematicalPhysicist]

Because arguments are rarely the A, not A type. They are something like I believe everyone needs a guaranteed income of at least $20,000 a year (statement A). The opposition is nobody should have a guaranteed income. The not A position is a guaranteed income of less than $20,000, or no guaranteed income. A compromise position could be a guaranteed income of $10,000 py which satisfies neither position, but both sides may be able to live with it.

Thanks
Bill

Well, how do you know that those type of arguments are rare? you just gave one example of an argument which this is not the case.

 

[bhobba]

Well, how do you know that those type of arguments are rare? you just gave one example of an argument which this is not the case.

You got me there. Just from everyday experience, but we all know how that often collapses when looked at carefully. Actually that is just experience as well - caught in a logical loop.

Thanks
Bill

 

[MathematicalPhysicist]

You got me there. Just from everyday experience, but we all know how that often collapses when looked at carefully. Actually that is just experience as well - caught in a logical loop.

Thanks
Bill

You've caught in a LOOP, and you can't get out of it...

LOOP QG. (used to be my username, but I got outside the LOOP, into another loop).

 

[gentzen]

The problem with the debates about interpretation, ..., is that philosophers tend to use fuzzy definitions of their words, particularly the ones we discuss here (locality and reality among them).

I can fullly share the frustration over the many pointless debates involving the word "reality" provoked both by philosophers (for example Yuval Noah Harari, officially an historician) and physicists alike. There are languages with different words for different aspects of it, for example German has Realität (from res=thing/stuff), Wirklichkeit (from wirken=effect), and Gegebenheit (from gegeben=given). But even those different words won't help much in the end.

Not sure whether it is the fault of philosophers that quantum physics is local and nonlocal at the same time, and that capturing the sense in which it is nonlocal is even more challenging than capturing the sense in which it is local. I think that the word "local" has a sufficiently specific meaning (which is the same in different laguages). Still, it can apply to many different things and situations with meaning slightly adapted to the different contexts.

Thanks for repeating and expanding on the microcausality principle. I have now read a bit about it. Looks like properties of the vacuum state are important too for the consequences related to locality that you gave. Well, I guess this is just related to the fact that the background (like a solid crystal, or a curved spacetime) can affect locality too.

Have you seen my request to be more specific about in which paper exactly Einstein introduced the notion of "inseparability"?

 

[vanhees71]

I'd not use the word "reality" in these debates anymore, because it has practically no clear meaning anymore. For me what's "real" is what physicists measure in the lab, and all I need to provide as a theoretical physicist is to explain how the formalism (Hilbert space, observable algebras, statstical operators,...) describes what can be measured and what one expects to find in the lab.

Concerning locality it's clear that local relativistic QFTs are local (that's why they are called local), and this has a clear mathematical meaning within the formalism: local field operators that describe observables must commute at space like distances with the Hamiltonian density (which itself is also a local field operator, i.e., built out of the field operators and their derivatives at one space-time point). That's also known as the microcausality condition, because it guaranties causality in the sense of the Minkowski space-time structure, particularly that there cannot be within such a theory any causal connection between space-like separated measurements. This principle is pretty strong and leads, together with the boundedness of the Hamiltonian from below, to pretty general conclusions like the spin-statistics connection (half-integer spin fields describe fermions; integer-spin fields bosons), the CPT symmetry, and the linked-cluster principle and unitarity of the S-matrix.

The paper I have in mind is Einstein's own writing about the EPR paradox. In contradistinction to this unfortunately very famous EPR paper it's a masterpiece in scientific prose, as everything Einstein wrote. Recently somebody posted a link to an English translation somewhere here on Physics Forums, but I cannot find it anymore. Here's the original citation:

A. Einstein, Quantenmechanik und Wirklichkeit, Dialectica 2,
320 (1948),
https://doi.org/10.1111/j.1746-8361.1948.tb00704.x

I'm not sure, whether Einstein called it "inseparability" explicitly in this work, but that's what he describes in detail, namely the strong correlations of far-distant properties of an extended quantum system, like two photons which may be registered at very far distant places, being completely unpolarized but still showing 100% correlations of their polarization states.