Quantum mechanics is not weird (locality and non-locality weirdness)

[jk22]

Suppose we give up realism to keep locality. Then quantum is treating other thing than reality so why use it to explain real experiments ? There still should be a link to reality in that case.

 

[zonde]

Suppose we give up realism to keep locality. Then quantum is treating other thing than reality so why use it to explain real experiments ? There still should be a link to reality in that case.

Concept of realism as used in QM is different from realism as used in philosophy. This probably goes back to EPR and elements of reality.
And you would have to make a point how you can keep locality by giving up realism (as QM concept).

 

[jk22]

I was thinking about something more human than physics : could it be that the physics community was fed up with Einstein and his rejection of the existence of aether so it played the same game by rejecting the elements of reality ? Else he would be a kind of guru of science everyone saying he is always right.

 

[atyy]

Suppose we give up realism to keep locality. Then quantum is treating other thing than reality so why use it to explain real experiments ? There still should be a link to reality in that case.

In standard Copenhagen style quantum mechanics, the person who uses quantum mechanics and the experimental results he observes are real. However, the wave function itself is not necessarily real. And you are right - in this interpretation, quantum mechanics does not explain reality - quantum mechanics is a calculational tool to predict reality.

 

[jk22]

Could we say that probabilities have no physical reality they are just mathematical informations ?

However quantum mechanics permits to calculate other quantities that are physically real like energy levels.

 

[vanhees71]

Since "realism" is an unsharply defined philosophical concept, it's very easy for physicists to give it up, while locality (in the usual sense of microcausality of relativistic local QFT) is essential for the consistency of quantum theory with the relativistic space-time structure. Thus, I happily give up a murky metaphysical paradigm like "realism". Another argument against "realism" is that all experiments done with entangled states (photons, neutrons, atoms in traps,...) indicate that what's called "realism" is unrealistic, because it contradicts those empirical findings with overwhelming significance.

It's the great achievement of Bell's (in my opinion Nobel-prize quality) work to make the murky concept of "local realism" to a sharply defined scientific question that can be decided experimentally, and the present status of the empirical tests indicate that QT (in its form as a local relativistic QFT) is the correct description, while "local realism" is ruled out with high significance.

 

[atyy]

Since "realism" is an unsharply defined philosophical concept, it's very easy for physicists to give it up, while locality (in the usual sense of microcausality of relativistic local QFT) is essential for the consistency of quantum theory with the relativistic space-time structure. Thus, I happily give up a murky metaphysical paradigm like "realism". Another argument against "realism" is that all experiments done with entangled states (photons, neutrons, atoms in traps,...) indicate that what's called "realism" is unrealistic, because it contradicts those empirical findings with overwhelming significance.

It's the great achievement of Bell's (in my opinion Nobel-prize quality) work to make the murky concept of "local realism" to a sharply defined scientific question that can be decided experimentally, and the present status of the empirical tests indicate that QT (in its form as a local relativistic QFT) is the correct description, while "local realism" is ruled out with high significance.

There are several sharp definitions of realism and locality.

Realism as an alternative to the microcausality of QFT is sharply defined. It is more commonly stated as predetermination.

Not everyone uses the same terminology, but here are equations for all the different definitions of "realism" and "locality", and the several different routes to deriving a Bell inequality: http://arxiv.org/abs/1503.06413.

 

[Ilja]

Since "realism" is an unsharply defined philosophical concept, it's very easy for physicists to give it up, while locality (in the usual sense of microcausality of relativistic local QFT) is essential for the consistency of quantum theory with the relativistic space-time structure.

There is nothing unsharply defined in the EPR criterion of reality. Which is what matters, and not some abstract philosophical ideas about realism.

There is also nothing unsharply defined in Reichenbach's principle of common cause.

Above have been sharp enough to be used in variants of strong mathematical proofs, namely of Bell's theorem. Which is good enough evidence that they are sharp enough.

Instead, "locality" (a misnamed variant of Einstein causality) is nothing which could not be given up easily. All one would have to do would be to go back to classical causality - which is hardly a great difficulty, science has lived centuries nicely with such a concept of causality. Given that relativity is nicely compatible with a preferred frame (essentially the Lorentz interpretation of relativity) there is also no problem with relativistic QFT. At least not a consistency problem.

 

[A. Neumaier]

"local realism" is ruled out with high significance.

Only local particle realism is ruled out. Essentially no foundational investigations exist that do not use a particle concept.

Field theory is seriously underrepresented in foundational studies, although the most fundamental theories of physics are field theories.

 

[Jilang]

Are field theories non-local? If so how can they describe the mechanism?

 

[DrChinese]

Are field theories non-local? If so how can they describe the mechanism?

I think A. Neumaier's point (forgive me if I'm wrong) is that the local realism of Bell's theorem doesn't match current field theory anyway - physicists have moved past that.

In modern quantum field theory, particles aren't point objects anyway and therefore cannot be consider local(ized) in the ordinary sense. The mechanism is not really part of the description.

 

[A. Neumaier]

In modern quantum field theory, particles aren't point objects anyway

Yes. Elementary particles are being referred to as ''pointlike'', but even this cannot be interpreted in classical imagery. For example, renormalization leads to a positive charge radius.

Particles are quantum field excitations in a similar way as water wavelets are excitations of the water surface of a sea. The difference is that the latter have a continuous specrum, hence can be of any size, while the excitations of quantum fields are quantized and can appear only in multiples of an integer (characterizing the representation of the number operator). Thus in a setting where the number operator is diagonal, there is something to count, and tradition calls this something ''particles''.

Are field theories non-local?

It depends on your concept of nonlocality. If you consider the double slit experiment as something nonlocal, yes. (Just consider how water waves go through a double slit.)

 

[vanhees71]

On the other hand locality is constraining our QFTs, and the concept is at the very foundations of the physical interpretation of the theory in terms of the S-matrix, particularly its Poincare invariance. The minimal locality constraint is that the Hamilton density autocorrelation function vanishes for arguments of a space-like separation, i.e. microcausality,
$$[\mathcal{H}(x),\mathcal{H}(y)]_-=0 \quad \text{for} \quad (x-y)^2<0,$$
using the west-coast convention of the metric.

This implies the locality of interactions, i.e., a local event (e.g., the registration event of a photon with Alice's photodetector) cannot have causal effects on another local event which is space-like separted (e.g., the properties of a photon registered by Bob's photodetector far away from Alice).

Now, what's "realism"? According to the original paper, which is not very clearly written (as Einstein lamented about himself; he wrote a much clearer paper in 1948 [*], making clear that his main criticism is against inseparability as encoded in entangled states), it's the assumption that any observable has a well-defined value, while the QT state definition in terms of Born's Rule is explicitly stating that this is not the case. Further, it's a criticism against the naive collapse assumption of (some flavors of the) Copenhagen interpretation.

[*] A. Einstein, Quantenmechanik und Wirklichkeit, Dialectica 2, 320 (1948)
http://onlinelibrary.wiley.com/doi/10.1111/j.1746-8361.1948.tb00704.x/abstract

Of course, "point particles" are strangers in relativistic theories. The idea of a point particle in the mathematical literal sense of a point without any extension is incompatible with relativistic field theories, which are so far the only way enabling a sensible quantum theory. This is well known for about 100 years, when Lorentz tried to formulate his electron theory within classical Maxwell electrodynamics, running in the infamous problems with "radiation reaction", i.e., a fully consistent theory of interacting charged point particles. Point particles are, on the other hand, an abstraction, and what's describable as a classical "point particle" is in reality always something extended, and indeed the description of radiation reaction of extended object, including a careful consideration of the Poincare stresses, leads to physically meaningful fully relativistic equations of motion. The limit to a literal point particle, however, stays always problematic and is possible only in a certain approximation a la Lorentz, Abraham, and Dirac with a modification a la Landau and Lifshitz.

In relativistic QFT one is even more humble, and is just able to define "particles" in a very limited sense as asymptotic states. In QED, where (unconfined) massless gauge bosons are involved, the true asymptotic states are not even the plane waves which have some interpretation of single-particle states in terms of "wave functions" as in the non-relativistic theory, but more something like a "bare charge" surrounded by a "cloud of virtual photons" (coherent states). The formal treatment of these "particle-like states" is a bit inconvenient, which is why we usually start with the naive plane-wave asymptotic states and then realize that there are IR and collinear divergences in the cross sections, which are then cured with a technique called "soft-photon resummation" in the spirit of the old Bloch-Nordsieck procedure (in the non-Abelian case known as the Kinoshita-Lee-Nauenberg theorem).

 

[atyy]

On the other hand locality is constraining our QFTs, and the concept is at the very foundations of the physical interpretation of the theory in terms of the S-matrix, particularly its Poincare invariance. The minimal locality constraint is that the Hamilton density autocorrelation function vanishes for arguments of a space-like separation, i.e. microcausality,
$$[\mathcal{H}(x),\mathcal{H}(y)]_-=0 \quad \text{for} \quad (x-y)^2<0,$$
using the west-coast convention of the metric.

This implies the locality of interactions, i.e., a local event (e.g., the registration event of a photon with Alice's photodetector) cannot have causal effects on another local event which is space-like separted (e.g., the properties of a photon registered by Bob's photodetector far away from Alice).

Now, what's "realism"? According to the original paper, which is not very clearly written (as Einstein lamented about himself; he wrote a much clearer paper in 1948 [*], making clear that his main criticism is against inseparability as encoded in entangled states), it's the assumption that any observable has a well-defined value, while the QT state definition in terms of Born's Rule is explicitly stating that this is not the case. Further, it's a criticism against the naive collapse assumption of (some flavors of the) Copenhagen interpretation.

[*] A. Einstein, Quantenmechanik und Wirklichkeit, Dialectica 2, 320 (1948)
http://onlinelibrary.wiley.com/doi/10.1111/j.1746-8361.1948.tb00704.x/abstract

Of course, "point particles" are strangers in relativistic theories. The idea of a point particle in the mathematical literal sense of a point without any extension is incompatible with relativistic field theories, which are so far the only way enabling a sensible quantum theory. This is well known for about 100 years, when Lorentz tried to formulate his electron theory within classical Maxwell electrodynamics, running in the infamous problems with "radiation reaction", i.e., a fully consistent theory of interacting charged point particles. Point particles are, on the other hand, an abstraction, and what's describable as a classical "point particle" is in reality always something extended, and indeed the description of radiation reaction of extended object, including a careful consideration of the Poincare stresses, leads to physically meaningful fully relativistic equations of motion. The limit to a literal point particle, however, stays always problematic and is possible only in a certain approximation a la Lorentz, Abraham, and Dirac with a modification a la Landau and Lifshitz.

In relativistic QFT one is even more humble, and is just able to define "particles" in a very limited sense as asymptotic states. In QED, where (unconfined) massless gauge bosons are involved, the true asymptotic states are not even the plane waves which have some interpretation of single-particle states in terms of "wave functions" as in the non-relativistic theory, but more something like a "bare charge" surrounded by a "cloud of virtual photons" (coherent states). The formal treatment of these "particle-like states" is a bit inconvenient, which is why we usually start with the naive plane-wave asymptotic states and then realize that there are IR and collinear divergences in the cross sections, which are then cured with a technique called "soft-photon resummation" in the spirit of the old Bloch-Nordsieck procedure (in the non-Abelian case known as the Kinoshita-Lee-Nauenberg theorem).

I hope you realize that the naive collapse in some flavours of Copenhagen is consistent with your definition of locality.

 

[vanhees71]

I hope you realize that the naive collapse in some flavours of Copenhagen is consistent with your definition of locality.

Ok, then define clearly what collapse means in this statement. The naive collapse for me is the sudden reduction of the state into an eigenstate of the self-adjoint operator representing the measured quantity, which is outside of the quantum theoretical dynamics.

 

[atyy]

Ok, then define clearly what collapse means in this statement. The naive collapse for me is the sudden reduction of the state into an eigenstate of the self-adjoint operator representing the measured quantity, which is outside of the quantum theoretical dynamics.

Yes, that is what I mean by the naive collapse. It is consistent with "no superluminal transmission of information", which is what you mean by microcausality. Actually, your definition is a bit stricter than that, but the naive collapse is consistent with your definition of microcausality.

 

[vanhees71]

How can it be? It collapses instantaneously the polarization state of Bob's photon from the mixture $1/2 \einsop_{2}$ to $|H \rangle \rangle H|$, if $A$ meausures her photon to be vertically localized. This is a clear violation of "so superluminal transmission of information", because the entropy of the one state is $\ln 2$ that of the other is $0$. So information is transmitted according to the naive-collapse picture instantaneously.

However, Bob can't observe this information transfer other than knowing what Alice has measured. So it's an empty statement to claim that there was really an instantaneous information transfer by Alice's local measurement to a photon at Bob's place far away. Bob will just measure unpolarized photons (when repeating the experiment with a lot of entangled biphotons). So the assumption of the collapse is unnecessary, because it's unobservable. The predictions concerning the observable facts are the same without it. So you don't need to assume it, and that's preferable for at least 2 reasons: (a) you don't need to invoke dynamics outside of quantum theory, which you necessarily have to do if you assume the collapse, because quantum dynamics is unitary and doesn't change the von Neumann entropy and (b) you don't need to assume faster-than light information transfer.

But this dialogue we have exchanged for an uncountable number of times. I don't understand, why the collapse assumption is so strong in surviving all these debates (not only among us but obviously also in the physics community).

 

[A. Neumaier]

"no superluminal transmission of information", which is what you mean by microcausality.

This is not equivalent. Microcausality is a much stronger statement. It is a mathematically concise expression of the informal statement that there is no theoretical obstacle to prepare states of a local field $\phi(x)$ such that all smeared observables $\int dx f(x)\phi(x)$ with $f(x)$ sufficiently localized around mutually spacelike points have prescribed means and arbitrarily small uncertainty in the corresponding uncertainty relation.

It is a very difficult task to show that this is consistent with state vector collapse, if it can be done at all. Just mumbling "no superluminal transmission of information" is by far not enough.

 

[atyy]

How can it be? It collapses instantaneously the polarization state of Bob's photon from the mixture $1/2 \einsop_{2}$ to $|H \rangle \rangle H|$, if $A$ meausures her photon to be vertically localized. This is a clear violation of "so superluminal transmission of information", because the entropy of the one state is $\ln 2$ that of the other is $0$. So information is transmitted according to the naive-collapse picture instantaneously.

However, Bob can't observe this information transfer other than knowing what Alice has measured. So it's an empty statement to claim that there was really an instantaneous information transfer by Alice's local measurement to a photon at Bob's place far away. Bob will just measure unpolarized photons (when repeating the experiment with a lot of entangled biphotons). So the assumption of the collapse is unnecessary, because it's unobservable. The predictions concerning the observable facts are the same without it. So you don't need to assume it, and that's preferable for at least 2 reasons: (a) you don't need to invoke dynamics outside of quantum theory, which you necessarily have to do if you assume the collapse, because quantum dynamics is unitary and doesn't change the von Neumann entropy and (b) you don't need to assume faster-than light information transfer.

But this dialogue we have exchanged for an uncountable number of times. I don't understand, why the collapse assumption is so strong in surviving all these debates (not only among us but obviously also in the physics community).

It is consistent for exactly the reason you state "Bob can't observe this information transfer other than knowing what Alice has measured".

 

[vanhees71]

But then you can just forget about this collapse assumption. It's empty, because non-observable!

 

[atyy]

But then you can just forget about this collapse assumption. It's empty, because non-observable!

Collapse is needed mathematically. You are welcome to consider it real or not. However, there is no problem with considering collapse to be real and also maintaining your definition of locality.

 

[vanhees71]

Why is it needed mathematically? I just do calculations in QT without ever using it...

 

[stevendaryl]

I do not see how a proof of microcausality (something along the lines that local field at spacelike separated events commute, or anti-commute) answers the question about whether QM (or QFT) is nonlocal. Whether we're talking about QM or QFT, the theory has two parts:

1. There is some notion of "state" that changes deterministically according to some mathematical evolution law.
2. Using the state, we compute probabilities for outcomes of measurements, and when we actually perform a measurement, we get definite values.

Microcausality is about the first aspect of quantum theory, the evolution equations, but the reason people suspect QM is nonlocal is because of the second aspect, measurement (and the Born interpretation of the quantum state). So a rigorous proof of microcausality cannot possibly resolve the issue.

Unless, of course, you adopt the Many Worlds Interpretation, and say that the state is everything, and that measurement and the Born interpretation can somehow be derived from the state evolution equations.

 

[atyy]

Why is it needed mathematically? I just do calculations in QT without ever using it...

How do you show that after Alice measures and receives the outcome up, the state jumps from |uu>+|dd> to |u>?

 

[vanhees71]

One cannot prove that (at least there's no proof known). See Weinberg, Lectures on Quantum Mechanics, Cambridge University Press, but why should such a proof solve the apparent problem. I don't know, where the problem is within the minimal interpretation, because I just take the minimal interpretation and Born's rule as it is. I can predict only probabilities for the outcome of measurements. Then I measure the quantity I've predicted the probabilities for on an ensemble of identically prepared setups and check whether my prediction is right. So far all predictions of QT agreed with experiment. That's it. That a measurement of an observable gives definite values is due to the construction of the measurement apparatus, because otherwise you'd not call it an apparatus that measures the quantity of interest. It's just a technical problem to construct the apparatus, and our experimental colleagues are real wizzards in doing astonishing constructions.

 

[vanhees71]

How do you show that after Alice measures and receives the outcome up, the state jumps from |uu>+|dd> to |u>?

Why do I need to show it? I can make all predictions about the outcome of measurements with the entangled state prepared in the very beginning. No need for the reduction of the state to $|u \rangle$. Why do you need that?

 

[stevendaryl]

How do you show that after Alice measures and receives the outcome up, the state jumps from |uu>+|dd> to |u>?

I think there is a sense in which it's not necessary to consider what happens after a measurement is performed. Alice performs a spin-measurement, and measures spin-up. A short while later, she performs a second measurement, and again measures spin-up. You want to say that the reason she measures spin-up the second time is because the state collapsed into a pure spin-up state following her first measurement. But you could avoid collapse by instead considering the two measurements to be a single, two-part measurement. Pure quantum mechanics without collapse would presumably predict that such a two-part measurement has essentially zero chance of giving the result "up, down" or "down, up".

 

[atyy]

I think there is a sense in which it's not necessary to consider what happens after a measurement is performed. Alice performs a spin-measurement, and measures spin-up. A short while later, she performs a second measurement, and again measures spin-up. You want to say that the reason she measures spin-up the second time is because the state collapsed into a pure spin-up state following her first measurement. But you could avoid collapse by instead considering the two measurements to be a single, two-part measurement. Pure quantum mechanics without collapse would presumably predict that such a two-part measurement has essentially zero chance of giving the result "up, down" or "down, up".

That is not possible. The two measurement outcomes are spacelike separated, so in anyone frame in which one considers them to be simultaneous, there will be another frame in which they are sequential.

 

[atyy]

Why do I need to show it? I can make all predictions about the outcome of measurements with the entangled state prepared in the very beginning. No need for the reduction of the state to $|u \rangle$. Why do you need that?

How do you do the calculation in the Schroedinger picture?

 

[stevendaryl]

That is not possible. The two measurement outcomes are spacelike separated, so in anyone frame in which one considers them to be simultaneous, there will be another frame in which they are sequential.

I was talking about Alice making two spin measurements in succession, with a timelike, not spacelike, separation between them. I wasn't talking about Alice's measurement followed by Bob's.

Anyway, this alternative way of looking at it basically amounts to (as I understand it) the "consistent histories" interpretation of QM, which is like Many-Worlds in avoiding a notion of wave function collapse. The fact that Alice measured spin-up doesn't imply anything about the "wave function of the universe", it just says something about which history she is on.