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

[zonde]

In quantum field theory, there are only symmetrized (or antisymmetrized) multiparticle states. One cannot create any others using creation operators - they are unphysical.

This happens because any state in Fock space is symmetrized (or antisymmetrized) so that output modes are symmetrized simply because they are components of state in Fock space (that describes remote side too), right?

Then the answer to my question:
"Do we automatically view the remote side in this new basis with the same amplitudes as in the local side?"
is yes, right? Because amplitudes at remote side are represented by the same mathematical object (state in a Fock space).

 

[A. Neumaier]

Do we automatically view the remote side in this new basis with the same amplitudes as in the local side?

There is only a single amplitude, namely that for the complete symmetrized state $\psi$. One cannot ascribe the amplitude to a particular region in space. Thus your questions doesn't make sense.

If you want to consider local pieces of the state you need to create them by projection. Thus you need to define projection operators $P_L$ and $P_R$ that project out the local part $P_L\psi$ and the remote part $P_R\psi$. Typically, these do not sum up to $\psi$.

 

[DrChinese]

1. There is no common cause, but there needn't be one in this case.

2. In other words: The probability distributions of Alice and Bob that only depend on local beables (as Bell requires, check out the proof again) don't feature the non-locality and correlations computed from them won't violate Bell's inequality. Only the postselected probability distributions feature non-local correlations, but this is fine, because they don't depend only on local beables.

1. There are perfect correlations, and no opportunity for a common cause. QED.

2. "Local" is an assumption of the usual Bell inequalities. In cases in which this is strictly enforced (for the usual Bell tests), Alice and Bob are non-local to each other (as in the referenced experiment) but they share a common past (unlike the referenced experiment). So I really don't follow your point. When Bell inequalities are violated, under either scenario, no local realistic explanation is possible. This is true whether you accept QM or not.

So to repeat my earlier statement: you are arguing for rejection of classical reality and acceptance of locality. Fine, that is a viable position. But in that quantum ("non-classical) world, there is (still) no causal explanation as you imply. If there were, the time ordering would be different; and it would require Alice and Bob to measure their perfect correlations (and violations of Bell inequalities) within a common light cone (presumably from a common source of entangled pairs) - which they don't.

 

[rubi]

There are perfect correlations, and no opportunity for a common cause.

This is both completely true and completely irrelevant at the same time. Perfect correlations are not problematic if the underlying probability distributions depend on non-local beables. It is only problematic for locality if the local probability distributions of Alice and Bob would satisfy Bell's factorization criterion.

"Local" is an assumption of the usual Bell inequalities. In cases in which this is strictly enforced (for the usual Bell tests), Alice and Bob are non-local to each other (as in the referenced experiment) but they share a common past (unlike the referenced experiment). So I really don't follow your point. When Bell inequalities are violated, under either scenario, no local realistic explanation is possible. This is true whether you accept QM or not.

The postselected probability distributions violate Bell's factorization criterion (because the local probability distributions depend on the beables of photon 2 and 3, which are localized outside the past lightcone of both photon 1 and 4), so a violation of Bell's inequality is not problematic (i.e. the correlations don't require a causal explanation, at least not according to Bell). A violation of Bell's inequality would only be surprising if Bell's factorization criterion did hold. The fact that correlations derived from non-local probability distributions appear to be non-local is not problematic! You might even be able to violate Bell's inequality in a local realistic theory if you use non-local probability distributions, since even in local realistic theories, Bell's inequalities must only hold if Bell's factorization criterion is satisfied.

Bell's factorization criterion holds $\Rightarrow$ Bell's inequality holds
Bell's factorization criterion doesn't hold (as is the case for the postselected probability distributions) $\Rightarrow$ anything can happen

I demand a proof that Bell's inequality is supposed to hold even if the factorization criterion is violated. Otherwise, I'm not going to accept the necessity of a causal explanation.

So to repeat my earlier statement: you are arguing for rejection of classical reality and acceptance of locality. Fine, that is a viable position. But in that quantum ("non-classical) world, there is (still) no causal explanation as you imply.

There is a causal explanation for everything that requires a causal explanation. Your experiment just doesn't require one. I fully agree that there is no causal explanation for your experiment!

There is still non-classical non-locality in the correlations between post-selected photons 1&4, but not of the kind that requires a causal explanation. There is also non-classical non-locality which requires a causal explanation (the correlations between photons 1&2 and 3&4), but there is a causal explanation for them according to quantum reasoning.

If you take non-local correlations that can be explained and combine them in a non-local way, you get non-local correlations again, but these needn't necessarily require an explanation as well. Neither in the case of quantum mechanics nor in the case of classical mechanics.

 

[atyy]

Bell's factorization criterion holds $\Rightarrow$ Bell's inequality holds
Bell's factorization criterion doesn't hold (as is the case for the postselected probability distributions) $\Rightarrow$ anything can happen

I demand a proof that Bell's inequality is supposed to hold even if the factorization criterion is violated. Otherwise, I'm not going to accept the necessity of a causal explanation.

I'm not entirely sure if this is what you had in mind, but the Bell inequalities for entanglement swapping require a slightly different argument than the usual Bell scenario.
http://arxiv.org/abs/0911.1314

 

[DrChinese]

This is both completely true and completely irrelevant at the same time. ...

I demand a proof that Bell's inequality is supposed to hold even if the factorization criterion is violated. Otherwise, I'm not going to accept the necessity of a causal explanation.

There is a causal explanation for everything that requires a causal explanation. Your experiment just doesn't require one. I fully agree that there is no causal explanation for your experiment!
...

Your comments do not make sense to me. In the Bell scheme, all separated observations should be able to factorize. When the results are inconsistent with such factoring, a Bell inequality is violated. Any entangled system does not factorize, according to QM. That includes the usual Bell tests, as well as ones per the supplied references in post #40. Entanglement is entanglement (from swapping) is entanglement (post selected), and that's what you get from entanglement swapping experiments.

According to your argument that classical realism should be rejected when considering quantum systems, there should still be common cause. There isn't, and this is equally true in the usual Bell test regimen. The only difference is that in one group, there is a common source; and in the other group, there isn't. Your distinctions don't hold water. It is good that you agree that "there is no causal explanation for" the referenced experiments; there is no such physical explanation for ordinary Bell tests either. The accepted explanation is that we apply QM and get the correct answer in all cases. And that is as much of which anyone can reasonably be sure.

 

[rubi]

Your comments do not make sense to me. In the Bell scheme, all separated observations should be able to factorize. When the results are inconsistent with such factoring, a Bell inequality is violated. Any entangled system does not factorize, according to QM.

Yes, but in the proof of Bell's inequality, the local probability distributions must only depend on beables in a region that shields the relevant beable from the overlap of the light cones. This is how locality shows up in the proof. The beables of photons 2&3 are not localized in this region, but the postselected probability distribution depends on them nevertheless.

A full specification of the beables in region 3 must determine the probability distribution for region 1 completely. This is not fulfilled for the postselected probability distributions, since they depend on the beables of photons 2&3, which are not even localized within the past lightcone of region 1, let alone region 3.

(@atyy: I hope this clarifies it.)

 

[DrChinese]

Yes, but in the proof of Bell's inequality, the local probability distributions must only depend on beables in a region that shields the relevant beable from the overlap of the light cones. This is how locality shows up in the proof. The beables of photons 2&3 are not localized in this region, but the postselected probability distribution depends on them nevertheless.

A full specification of the beables in region 3 must determine the probability distribution for region 1 completely. This is not fulfilled for the postselected probability distributions, since they depend on the beables of photons 2&3, which are not even localized within the past lightcone of region 1, let alone region 3.

Your diagram and explanation, per your perspective, would not even apply to a normal Bell test. That is because Alice and Bob would both occupy your region 3 in a Bell test. And in strict Bell tests, Alice and Bob are unable to communicate their observation decisions to each other. So no, I disagree with your characterization. Bell actually says that the decision of Alice cannot affect the outcome Bob sees. This is the criteria. This applies to entanglement swapping experiments equally as well.

Basically, you are saying that local realism - where there is a common past - is ruled out by normal Bell tests using entanglement. That is true enough. But it is a special case (there exists a common source) of a more general entanglement scenario in which there is no common source. This is a more far reaching statement, and is a deduction from standard QM. If there *is* something about the requirement of a common source in Bell tests (to achieve its conclusion ruling out local realism), clearly that requirement can be dispensed with. That is what the references I provided tell us. Quantum non-locality (between Alice and Bob) is not dependent on the existence of local beables in a common prior light cone, as you have implied. Because those beables would in the end be classical if there is to be a common cause. Obviously, the experimental results do not change when your hypothetical "common cause" is eliminated. There is no "quantum" (non-classical) local common cause. Drop the common cause entirely, or drop the local part entirely, or both.

 

[rubi]

Your diagram and explanation, per your perspective, would not even apply to a normal Bell test. That is because Alice and Bob would both occupy your region 3 in a Bell test.

This is not true. Alice is localized in region 1 during her measurement and Bob is localized in region 2 during his measurement. Bell requires that a full specification of the beables in region 3 already fully determine Alice's probability distribution. An analogous requirement must hold for Bob.
http://www.scholarpedia.org/article/Bell's_theorem#Bell.27s_definition_of_locality

Obviously, the experimental results do not change when your hypothetical "common cause" is eliminated.

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.

 

[DrChinese]

This is not true. Alice is localized in region 1 during her measurement and Bob is localized in region 2 during his measurement. Bell requires that a full specification of the beables in region 3 already fully determine Alice's probability distribution. An analogous requirement must hold for Bob.
http://www.scholarpedia.org/article/Bell's_theorem#Bell.27s_definition_of_locality

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.

You are mixing a lot of different things here.

First, you are quoting from an article by Norsen (and yes I can read the full author list - but this is mostly Norsen talking). This is a skewed article. Although it is technically correct in most particulars, I don't consider his/their use of terminology to be very good. It causes just the kind of problems in communication that we are having. For example: the use of the word "beable" is most often associated with Bohmians and this article clearly reflects that (see the first sentence if you are not sure). This word causes all kinds of problems. (FYI: A lot of folks do not support Norsen on his interpretations of Bell, so use this article as a source at your own risk. He gets a lot of opposing comments on his articles on the subject from top physicists.)

Second, the diagram (as originally supplied) meant something completely different to me that how it is used in the context of the article (and by you I now presume). So by supplying that context, we can get on the same page on that - so thanks. Norsen uses it to say that to a local realist, observations in area 3 by Alice and Bob cannot be affected by events in area 2. Please, this has little or nothing to do with the usual Bell test. As I said previously, Bell instead says that Alice's outcome should not be influenced by Bob's choice of measurement basis, and vice versa. This is a generally accepted assumption of Bell, and is directly connected to the EPR paper it is addressing.

Last: In reality, your diagram is a better description of a more general conclusion on entanglement described in the references I supplied. That being that local realists assert there cannot be entanglement of photons from sources 1 and 2 in regions that do not overlap (reading the diagram a different way). Obviously, that is wrong (as experiment plainly shows). I would conclude from the experiment that there are no non-local hidden variables either. However, technically such conclusion is still interpretation dependent and is not strictly justified.

 

[stevendaryl]

Any entangled system does not factorize, according to QM.

Bell's factorization criterion is not exactly the same as the criterion that the wave function (or density matrix) factors, because is talking about whether the probabilities for outcomes of measurements factors, rather than whether the wave function factors. Those aren't exactly the same criteria.

I gave an example earlier in this thread, but I'll repeat it: Let |\psi, u\rangle be the one-electron state in which the electron is definitely spin-up along the z-axis, and has probability amplitude \psi(\vec{r}) of being found in position \vec{r}. Let |\phi, d\rangle be the one-electron state in which the electron is definitely spin-down along the z-axis, and has probability amplitude \phi(\vec{r}) of being found in position \vec{r}. Then we can form the two-electron state:

|\Psi\rangle = |\psi, u\rangle \otimes |\phi, d\rangle - |\phi, d\rangle \otimes |\psi, u\rangle

That is an entangled state. But if the two spatial dependencies \phi(\vec{r}) and \psi(\vec{r}) have non-overlapping support (there is no place where both are nonzero), then the corresponding probabilities for spin measurements at two distant locations \vec{r_1} and \vec{r_2}, where \psi(\vec{r_1}) and \phi(\vec{r_2}) are both nonzero, factor:

P(A \& B | \vec{\alpha}, \vec{\beta}) = |\psi(\vec{r_1})|^2 cos^2(\theta_1/2) |\phi(\vec{r_1})|^2 sin^2(\theta_2/2)

(where A is true if an electron is found to have spin-up along \vec{\alpha} at location \vec{r_1}, and B is true if an electron is found to have spin-up along \vec{\beta} at location \vec{r_1}, and \theta_1 is the angle between \vec{\alpha} and the z-axis, and \theta_2 is the angle between \vec{\beta} and the z-axis.)

 

[DrChinese]

Bell's factorization criterion is not exactly the same as the criterion that the wave function (or density matrix) factors, because is talking about whether the probabilities for outcomes of measurements factors, rather than whether the wave function factors. Those aren't exactly the same criteria. ...

OK. The linear polarization observables for any 2 photons entangled on that basis will either be something like H>H>+V>V> or H>V>+V>H> depending on whether they are in the + or - Bell state. Neither of these factor. The photons do not need to be co-existing, may be entangled before/after observation, and can be from the same or different sources.

If you ask: is Alice's outcome independent of Bob's choice of measurement basis, and vice versa? I would answer that under any "reasonable" interpretation of QM the answer is NO. On the other hand, I have no explanation of what influences what, or by what mechanism any of this occurs. Further, given that there is no requirement that Alice and Bob's photons share any prior causal contact (or common contact with any other object), I would be hard pressed to say there is any common preceding cause. And finally, I would say that the only apparent variable which explains the correlations of Alice and Bob is the relationship of their measurement bases, and nothing else.

So in total, the evidence leads us to reject the idea that there is anything objectively real other than the relationship of the observation basis. Everything else (local and nonlocal) appears to reduce to a single random value, if it reduces to anything. Bohmians associate that with a "pilot wave" and MWIers relate that to the world they inhabit.

 

[rubi]

First, you are quoting from an article by Norsen (and yes I can read the full author list - but this is mostly Norsen talking). This is a skewed article. Although it is technically correct in most particulars, I don't consider his/their use of terminology to be very good. It causes just the kind of problems in communication that we are having. For example: the use of the word "beable" is most often associated with Bohmians and this article clearly reflects that (see the first sentence if you are not sure). This word causes all kinds of problems. (FYI: A lot of folks do not support Norsen on his interpretations of Bell, so use this article as a source at your own risk. He gets a lot of opposing comments on his articles on the subject from top physicists.)

I don't agree with Bohmians either (BM clearly is a proof-of-concept conspiracy theory that shows that one can get a realistic theory by dropping locality, but it is not a viable theory of physics) and I don't agree with everything in that article, but the presentation of the locality concept is correct, as it does indeed capture precisely (for a realistic theory) what relativists mean when they talk about locality. The past lightcone around region 1 (or 2 respectively) is called the domain of dependence of region 1 (or 2 respectively). In a local theory, everything that can be known about region 1 (or 2) can only depend on data from the domain of dependence and in fact it even depends only on the data in region 3. Thus, a full specification of all data in region 3 fully determines the data in region 1 (or 2) in every realistic local theory. If you use probability distributions that explicitely depend on non-local beables (I'm using this word only to be consistent with Bell's writing, not because I'm a Bohmian. It refers to the clicks of the detectors, nothing more.), then you shouldn't be surprised about Bell violations.

Assume I gave dice to Alice and Bob and each of them threw them a thousand times. Obviously, their statistics will be completely independent. However, if I know the list of records of both Alice and Bob (this is non-local information) and I remove all entries with unequal results, i.e. I postselect the probability distributions, would you be surprised that the postselected probability distributions feature perfect correlations, although Alice and Bob were spacelike separated when they performed the experiment? Would you require me to find a common cause for that in the intersection of their past lightcones?

Second, the diagram (as originally supplied) meant something completely different to me that how it is used in the context of the article (and by you I now presume). So by supplying that context, we can get on the same page on that - so thanks. Norsen uses it to say that to a local realist, observations in area 3 by Alice and Bob cannot be affected by events in area 2. Please, this has little or nothing to do with the usual Bell test. As I said previously, Bell instead says that Alice's outcome should not be influenced by Bob's choice of measurement basis, and vice versa. This is a generally accepted assumption of Bell, and is directly connected to the EPR paper it is addressing.

Last: In reality, your diagram is a better description of a more general conclusion on entanglement described in the references I supplied. That being that local realists assert there cannot be entanglement of photons from sources 1 and 2 in regions that do not overlap (reading the diagram a different way). Obviously, that is wrong (as experiment plainly shows). I would conclude from the experiment that there are no non-local hidden variables either. However, technically such conclusion is still interpretation dependent and is not strictly justified.

I don't want to defend Norsen's arguments. I only referred to parts of his writings which I think are uncontroversial. If you don't agree that the above description captures locality, can you please point me to the mistake?

 

[DrChinese]

1. The past lightcone around region 1 (or 2 respectively) is called the domain of dependence of region 1 (or 2 respectively). In a local theory, everything that can be known about region 1 (or 2) can only depend on data from the domain of dependence and in fact it even depends only on the data in region 3. Thus, a full specification of all data in region 3 fully determines the data in region 1 (or 2) in every realistic local theory.

2. Assume I gave dice to Alice and Bob and each of them threw them a thousand times. Obviously, their statistics will be completely independent. However, if I know the list of records of both Alice and Bob (this is non-local information) and I remove all entries with unequal results, i.e. I postselect the probability distributions, would you be surprised that the postselected probability distributions feature perfect correlations, although Alice and Bob were spacelike separated when they performed the experiment?

3. Would you require me to find a common cause for that in the intersection of their past lightcones?

1. I follow your notation in this example, and agree that this is what a local realist would assert. Region 3 would receive information (potentially) from an area that is common to both 1 and 2 (which I guess is Alice and Bob in our example).

2. This bears no resemblance to the post-selection done in any Bell tests, including the references I provided. Post-selection criteria is independent of the values that Alice and Bob record. The criteria relates to having pairs arrive at Alice and Bob that can be matched as to time window and Bell State entanglement type (+ or -). Because the criteria is independent of the values Alice and Bob observe, it is a fair test of entanglement. In the swapping-type experiments, a large portion of the photons that Alice and Bob see are not entangled at all. Only some pairs meet the qualifications, because only some pairs are cast into a Bell State. But Alice and Bob have no way to know which photons they see will be a part of a pair. The entanglement can be performed before or after Alice and Bob record anything. Again, these are independently observed and recorded.

3. I would require it if you continue to insist that there is some common cause to what Alice and Bob see. You are the one asserting that you can reject classical realism, maintain locality, and still have a common cause in the past. You can't, that is what all of these experiments show. That, to me, is the point of our discussion.

 

[rubi]

I follow your notation in this example, and agree that this is what a local realist would assert. Region 3 would receive information (potentially) from an area that is common to both 1 and 2 (which I guess is Alice and Bob in our example).

So if a local realist would assert this, then a violation of Bell's inequality, derived from this local realism assumption, let's us discard local realism. However, a violation of Bell's inequality that isn't derived from the local realism assumption tells us nothing, neither about realism nor locality.

This bears no resemblance to the post-selection done in any Bell tests, including the references I provided.

It bears resemblance insofar as it also uses non-local information to make the post-selection.

Post-selection criteria is independent of the values that Alice and Bob record. The criteria relates to having pairs arrive at Alice and Bob that can be matched as to time window and Bell State entanglement type (+ or -). Because the criteria is independent of the values Alice and Bob observe, it is a fair test of entanglement.

In order to be a test for locality, it must also be independent of non-local beables.

I would require it if you continue to insist that there is some common cause to what Alice and Bob see. You are the one asserting that you can reject classical realism, maintain locality, and still have a common cause in the past. You can't, that is what all of these experiments show. That, to me, is the point of our discussion.

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.

 

[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.