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

[jlcd]

I mean that one projects the Hilbert space to a smaller space in which position no longer figures. One hardly ever sees an exposition of experiments involving entanglement in which position is an observable in the tensor product structure assumed silently in the discussion. Usually the state space in is finite-dimensional in the exposition. But in the interpretation of certain experiments position suddenly plays a decisive role. Weirdness introduced by sloppiness.

Let's use an experimental example to better picture the concepts you are expressing. When an em wave spread from a electron concentrically and hit a detector located anywhere around it and detect it. Do you interpret it as the wave hitting all areas of the circle equally or do you believe in the convensional idea it is the wave function that travels and upon detection anywhere in the circle.. all the rest of the wave function collapse instantaneously?

 

[DrChinese]

I thought I made it perfectly clear that I don't insist on a common cause for an experiment that uses entanglement swapping, precisely because the postselected probability distributions depend on non-local information. Non-local correlations are only weird, if they are obtained from data that is collected locally. Otherwise, it is perfectly fine to have non-local correlations without common cause. Not even a local realist would insist on a common cause for non-local correlations that have been postselected using non-local data.

You are not making sense. There are no common causes! That is the talk of the local realist. And yes, a local realist would definitely deny: there can be perfect correlations (and violations of Bell inequalities) for apparently random photon polarization detections lying outside each others' light cones when Alice and Bob can freely choose their measurement parameters. You can't even do that with a standard Bell test when there the detection is done within a light cone - you will violate a Bell inequality. Post selection is not an issue from a scientific perspective in any scenario; and I mentioned at the beginning of this discussion that you are free to reject the generally accepted results of the references I provided. Obviously you have done so, and I really don't see any point to further discussion.

I would simply say that you should preface every statement you make about the existence of "common causes" for quantum events with: "My personal opinion, which is not generally accepted science, is..." Rejection of classical reality means that we live in an observer dependent world; and how we choose to measure shapes the outcomes in some manner.

 

[rubi]

You are not making sense. There are no common causes!

I don't understand you. Are we still talking about the same thing? I'm referring to the paper you referenced that uses entanglement swapping. I fully agree that there is no common cause! And even a local realist would not require a common cause in this situation. My point is that your paper is not relevant to the discussion, because nobody in the universe sees a necessity for a common cause for that paper.

I can even have perfect correlations between socks that have never coexisted and it would be perfectly fine if no common cause could be found (both for a local realist and a quantum physicist):
Assume there is a sock factory that produces pairs of red and blue socks randomly. It sends the first sock to Alice at the speed of light (imagine massless socks, or think of classical red or blue light pulses). The second sock is sent to Charlie. Alice records the color of her sock and burns it before the second sock arrives ar Charlie. Also before the second sock arrives at Charlie, but after Alice burned her sock, another sock factory produces another pair of red and blue socks. It sends one sock (let's call it sock #3) to Charlie and another sock (sock #4) to Bob, again at the speed of light. The third sock arrives at Charlie before the fourth sock arrives at Bob. Charlie records the color of the third sock. Then he destroys both the second and the third sock. Later, sock #4 arrives at Bob and he records the color. Now Alice and Bobs socks are totally uncorrelated, but we can use Charlies non-local data to postselect Alice and Bobs socks, by counting only those events, where the socks that arrived at Charlie had the same color. Then automatically, the postselected probability distributions of Alice and Bob's socks show perfect correlations, although the socks have never coexisted! And there is no common cause, although this is a completely classical experiment without any quantum effect. And if you replace the sock factory with a generation of entangled particles, you get exactly the experiment from your paper.

you are free to reject the generally accepted results of the references I provided. Obviously you have done so, and I really don't see any point to further discussion.

You misunderstood me. I fully accept the paper, everything in it is 100% correct! The calculation is right and I'm sure that the experiment agrees with the calculated statistics! The paper just doesn't support your argument against common causes and you failed to realize this! And this is not because the paper is wrong, but because the experiment doesn't need a common cause explanation in the first place! You may still disagree that common causes can be found in a quantum mechanical world, but you will have to use different arguments.

 

[vanhees71]

Your wave packets can have an arbitrary energy not necessarily related to the frequency. But I said:

Which means that a coherent state whose mode (= normalizable solution of the Maxwell equation) consists of a sequence of N pulses each with the energy of ##\hbar\omega## is considered to contain N photons. (In contrast to the most orthodox view, where a coherent state is a superposition of N-photon states of all N, independent of its mode.)

I'd not call a coherent state a photon. I think, by definition in the quantum-optics community a photon is a single-photon state of the (non-interacting) electromagnetic field.

The momentum-helicity eigenstates are generalized states, which are not realizable in nature, because they are not normalizable to 1. A lot of misunderstandings occur because often the difference between Hilbert-space vectors and generalized eigenstates, which are "distributions", is not made carefully clear enough. A true single-photon state indeed does not have a sharp energy and momentum.

 

[vanhees71]

I don't understand you. Are we still talking about the same thing? I'm referring to the paper you referenced that uses entanglement swapping. I fully agree that there is no common cause! And even a local realist would not require a common cause in this situation. My point is that your paper is not relevant to the discussion, because nobody in the universe sees a necessity for a common cause for that paper.

Entanglement swapping is no problem for the minimal interpretation either. You prepare a pair of entangled bi-photons in a state, which factorizes. Then you perform measurements, leading to the observation of correlations which are due to this very preparation. There's again no state collapse necessary to explain the correlations but just the preparation of the four photons in this specific state before the meausurement was done.

 

[A. Neumaier]

I'd not call a coherent state a photon. I think, by definition in the quantum-optics community a photon is a single-photon state of the (non-interacting) electromagnetic field.

Did you read my slides? I noticed that there are different usages of the word, not clearly distinguished in practice since it is anyway only talk, and the real communication about physics happens on the formal level.
Of course not every coherent state is a photon but only a monochromatic coherent state whose mode is highly localized and has a total energy of ##\omega\hbar## where ##\omega## is the frequency.

 

[stevendaryl]

I can even have perfect correlations between socks that have never coexisted and it would be perfectly fine if no common cause could be found (both for a local realist and a quantum physicist):
Assume there is a sock factory that produces pairs of red and blue socks randomly. It sends the first sock to Alice at the speed of light (imagine massless socks, or think of classical red or blue light pulses). The second sock is sent to Charlie [stuff deleted]
Then automatically, the postselected probability distributions of Alice and Bob's socks show perfect correlations, although the socks have never coexisted!

Thanks for that analogy. Just for clarification about the meaning of the analogy: Your "socks" example is explaining how a classical notion of correlation can be established by post-selection, even when the two correlated objects had no common origin. But (do I understand this correctly?) there is a corresponding quantum effect whereby similarly, post-selection can bring about a purely quantum notion of correlation (namely, spin-entanglement or polarization-entanglement) between objects with no common origin.

I think I agree that this shows that post-selection creation of entanglement should be no more mysterious (and no less!) than creation of entanglement through a common origin. The only relevance to discussions of realism or nonlocality is whether the way of understanding quantum spooky action at a distance for the latter case (common origin) equally well helps in the former case (no common origin).

 

[rubi]

Thanks for that analogy. Just for clarification about the meaning of the analogy: Your "socks" example is explaining how a classical notion of correlation can be established by post-selection, even when the two correlated objects had no common origin. But (do I understand this correctly?) there is a corresponding quantum effect whereby similarly, post-selection can bring about a purely quantum notion of correlation (namely, spin-entanglement or polarization-entanglement) between objects with no common origin.

Yes, exactly. We have two pairs of correlated objects. By post-selection, I can transport these correlations to members of the pairs that had not been correlated before. The statistical features of the post-selected correlations are just inherited from the statistics of the correlated pairs. So if I had classical non-locality before, the post-selected probability distributions will also exhibit classical non-locality. If I apply post-selection to pairs that exhibit quantum non-locality, then the post-selected probability distribution will inherit quantum statistics.

By the way: There is nothing wrong with post-selection. It can be applied in quantum communication and is thus very useful in practice. I'm just arguing that it can't be used for drawing conclusions about locality. Quantum cryptographers usually don't care about locality. They only need the typical quantum statistics for their communication protocols to work. The protocols also works if the origin of the statistics isn't a non-local phenomenon.

I think I agree that this shows that post-selection creation of entanglement should be no more mysterious (and no less!) than creation of entanglement through a common origin. The only relevance to discussions of realism or nonlocality is whether the way of understanding quantum spooky action at a distance for the latter case (common origin) equally well helps in the former case (no common origin).

Yes, the purpose of my argument with DrChinese was to establish that we can focus on quantum statistics that is generated from a common origin for the discussion of locality.

 

[vanhees71]

Did you read my slides? I noticed that there are different usages of the word, not clearly distinguished in practice since it is anyway only talk, and the real communication about physics happens on the formal level.
Of course not every coherent state is a photon but only a monochromatic coherent state whose mode is highly localized and has a total energy of ##\omega\hbar## where ##\omega## is the frequency.

Which slides?

Again, that's NOT a photon in the modern meaning of the word. Such a state is mostly vacuum with some small admixture of the one-photon and higher-photon number states. Nowadays quantum opticians have well-defined single-photon sources ("heralded photons").

 

[zonde]

This class of experiments is very difficult for many QM interpretations - regardless of what one's favorites are. Because they don't fit naturally with either the Many Worlds or the Bohmian Mechanics groups. That doesn't stop those groups from claiming they are not ruled out, but again there is nothing natural about how they address this. MW says there is a splitting of worlds upon observation (its signature feature), but clearly that doesn't help much when entanglement is performed AFTER the splitting of worlds. And BM says there are non-local guide waves (its signature feature), which seemingly fails to explain why a photon that no longer exists is entangled with one that exists now - but is not entangled with anything else.

I don't know Bohmian Mechanics so well to analyze this experiment from perspective of this interpretation but I can explain what in entanglement swapping is more problematic and what is less problematic if we explain entanglement via some generic non-local (FTL) model.

We can draw three different diagrams for the sequence of three measurements in preferred simultaneity foliation:

"S" stands for two sources and bold point for three measurements.

The middle diagram that correspond to experiment you quoted is actually least problematic for non-local entanglement model as Alice's and Bob's measurement outcomes (and measurement bases) can already be "known" to Charlie's photons when we perform BSA measurement. So we can sort all pairs in appropriate subsets.
The last one does not seem problematic too as measurement outcome (and measurement basis) for one of the Charlie's photon's can be known so that we can "collapse" the state of second photon and sort results in subsets by outcomes. Unmeasured photon then can "find out" his state from it's measured entangled twin photon.
The first case is most problematic as it actually requires entanglement between Alice's and Bob's photons in respective subsets before they perform measurement. It would be nice to see experimental results of such experiment. Of course Alice's and Bob's measurements would have to be timelike separated from Charlie's BSA measurement in order to conclude that it unequivocally corresponds to first case.

What I see as interesting in entanglement swapping is that by postselection that splits the ensemble of photons in respect to only two discrete degrees of freedom (H/V and +/-) we can observe entanglement type correlations in each of four subsets.

 

[A. Neumaier]

Which slides?

I had analyzed a particular experiment from the literature, creating single photons on demand in these slides (sorry, my old link in the PF post here should have contained this, is now corrected), and found them to be states of the kind I described, not true 1-photon states. I's be surprised if heralded photons would be essentially different, though I haven't analyzed them in detail. But I'll do so if you think it is different.

 

[vanhees71]

Heralded photons use entangled biphotons from parametric down conversion. Then you can measure one of the photons and be sure to have precisely one photon for further use. That's why it's "heralded".

If I understand your slides right, on p. 26 you show that you don't have a single-photon source but one which describes an (approximate) coherent state, the superposition of the vacuum state with the single photon state. As far as I know, this is not considered a true single-photon source anymore.

 

[DrChinese]

I can even have perfect correlations between socks that have never coexisted and it would be perfectly fine if no common cause could be found (both for a local realist and a quantum physicist):
Assume there is a sock factory that produces pairs of red and blue socks randomly. It sends the first sock to Alice at the speed of light (imagine massless socks, or think of classical red or blue light pulses). The second sock is sent to Charlie. Alice records the color of her sock and burns it before the second sock arrives ar Charlie. Also before the second sock arrives at Charlie, but after Alice burned her sock, another sock factory produces another pair of red and blue socks. It sends one sock (let's call it sock #3) to Charlie and another sock (sock #4) to Bob, again at the speed of light. The third sock arrives at Charlie before the fourth sock arrives at Bob. Charlie records the color of the third sock. Then he destroys both the second and the third sock. Later, sock #4 arrives at Bob and he records the color. Now Alice and Bobs socks are totally uncorrelated, but we can use Charlies non-local data to postselect Alice and Bobs socks, by counting only those events, where the socks that arrived at Charlie had the same color. Then automatically, the postselected probability distributions of Alice and Bob's socks show perfect correlations, although the socks have never coexisted! And there is no common cause, although this is a completely classical experiment without any quantum effect. And if you replace the sock factory with a generation of entangled particles, you get exactly the experiment from your paper.

Come on, yours is a classical example so you must know it cannot explain quantum action.

So no, you can't have perfect correlations and apparently randomness with socks that are separated as I describe (i.e. like the experiment). The flaw in your argument is the idea that socks have 1 color; photons have an infinite number (because polarization can be measured at any angle across 360 degrees).

In your (classical) analogy:

1. Let's assume post selection occurs as you say - Charlie post selects when matches occur of either both red (0 degrees) or both blue (90 degrees). How is it that Alice and Bob now get the same answer when they check their socks at ANY angle across 360 degrees? The only way that is possible is if they were clones of each other and had been identically manufactured to yield the same color answers at any angle.

2. OK, fine, that is technically feasible I guess. But hello, we are now back to Bell's Theorem! There is NO manufacturing template in which a Bell Inequality can be violated! And yet that is precisely what happens in the referenced experiment.

3. And by the way, post selection per 1 does not work as we assumed anyway. That is because post selection by casting into a Bell State is a process that affects the results at Alice and Bob. Charlie can match Blue-Blue and Red-Red 2 different ways: he can check without casting into a Bell State, and he can check by casting into a Bell State. Only 1 of those creates entanglement at Alice and Bob that will generate perfect correlations. The other creates a random agreement dependent on the choice of measurement angles by Alice and Bob.

If you look at 2 and 3 closely, you will see that your example is factually incorrect. There is no common cause. A local realist wants that.

 

[atyy]

If I choose not to produce entangled particles in the past, I will not see non-local correlations in the future and the other way around. From this I conclude that the cause of the correlations is my choice in the past. We can agree to disagree that this is a valid way of reasoning.

I think it's ideas like this that DrChinese is objecting to. Here you still use the word "cause". It ordinary language, a "cause" does require realism, since what can an "unreal cause" mean? So this is where you are still assuming realism. Of course, you can say that you mean an "unreal cause", which would be fine.

 

[DrChinese]

I think it's ideas like this that DrChinese is objecting to. Here you still use the word "cause". It ordinary language, a "cause" does require realism, since what can an "unreal cause" mean? So this is where you are still assuming realism. Of course, you can say that you mean an "unreal cause", which would be fine.

So correct! I realize my pursuit of the details on this is a bit dogged. But there are a lot of people who follow these various thread that can pick up the wrong impression easily.

When you accept Bell (as we all should), the evidence says we must give up either locality or realism (or both). So if you give up (classical) realism, you give it up. For some, that means giving up on the simultaneous existence of quantum observables that do not commute. For others, that means giving up the idea that causes precede effects. For yet others, it means both of these. The moral is: you can't have your cake and eat it too.

 

[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!