Curious about an idea of a modified polariser to send signals with QE

[tade]

I've very often expressed my opinion on this topic. For me it is very clear that there's no possibility to send signals faster than light using quantum entanglement. The reason is that this impossibility is implemented in relativistic quantum field theory by the socalled microcausality principle. In my scientific community, high-energy particle/nuclear physics, that's what's called "locality", and this excludes any causal connections between space-like separated events.

The observed long-ranged correlations between space-like separated measurements are due to the preparation of the system in the entangled state and not due to any "spooky action at a distance" of one measurement apparatus at position A on the part of the system at B or the measurement apparatus used at B.

Since thus relativistic local QFT realizes locality via the microcausality constraint on local observables, what one has to give up according to Bell's theorem is "realism", i.e., the assumption that all observables always take determined values, which are only appearing probabilistic because of our ignorance of some "hidden variables".

Whether there are non-local deterministic (realistic) relativistic models in accordance with the observations I don't know.

thanks, an interesting informative post
so is it that there's no 'spooky action at a distance' occurring?

 

[vanhees71]

Not according to relativistic local QFT.

 

[tade]

Not according to relativistic local QFT.

and that's pretty interesting, because I think that one of this year's Nobel winners, John Clauser, said that he was initially distressed by the results of his own groundbreaking experiments, because he was more of an Einsteinian in his personal metaphysical notions. In fact I think even now, he's still not too happy about having experimentally proven the incredible properties of quantum mechanics.
Though maybe the way that you describe it could be a way for Clauser to be at peace with both his experimental results and his metaphysical notions.

 

[vanhees71]

Well, I think also Bell was not too happy about the outcome of these experiments. For me it's hard to understand that a first-rank QFT expert like Bell was a proponent of Bohmian QM (which in my opinion only works in non-relativistic QM, and in non-relativistic physics there's anyway no problem with actions at a distance but it's rather the standard Newtonian way to describe interactions as in the Newtonian theory of gravity). Microcausality is at the very foundation of local relativistic QFT precisely because it's a viable realization of the causality principle in relativistic QT, and it's till today the only realization. Whether there are non-local Einstein-causal relativistic theories, I don't know.

 

[Nugatory]

oh i see, maybe can you elaborate more about the basis behind the Born rule and its exclusion of nudging, thanks

I did link to the Wikipedia article, but that is somewhat heavy going. If you are really interested in this stuff but not up for a serious college-level intro to quantum mechanics you might give Giancarlo Ghirardi’s book “Sneaking a look at God’s cards” a try.

 

[DrChinese]

so you said that Bob's ratio of random outcomes only depends on the setting of Bob's polarizer, not on the setting of Alice's, and I was wondering about the entanglement between Alice and Bob, so I was thinking that maybe you could explain about the entanglement together with why Bob's ratio doesn't depend on Alice's settings, and/or about how the inclusion of the special 52/48 polariser may or may not affect things

A couple of points, some of which are reiterations of earlier ones:

a. It is possible for Alice to have a polarizer which produces outcomes different than the usual 50-50. For obvious reasons, manufacturers of polarizing beam splitters work very hard to achieve as close to 50-50 as possible. Further, it is not unusual for the outcomes of actual Bell tests to evidence a slight variance from 50-50. This has no practical effect on the experimental conclusion (which is normally to exclude local realistic theories).

b. All Alice ever sees is a stream of random bits (H/T, U/D, 0/1 or whatever you label it). If Alice has a typical polarizer, the outcomes will average 50-50. If she has a less accurate polarizer, the percentage could be skewed (say 48-52 for purposes of discussion). The stream will still be random. If Alice changes from one polarizer to another, she can send a signal to herself (since one polarizer stream will be 50-50, the other will be 48-52, and she can eventually detect the difference).

c. All Bob ever sees is a stream of random bits (H/T, U/D, 0/1 or again whatever you label it). Here's the important point: nothing Alice does changes this fact! Even IF Alice could somehow change the stream of Bob, then Bob's stream would still be completely random. So Bob has no way to detect or otherwise sense any change by Alice.

d. In the most extreme scenario, Alice removes her polarizer completely and she see a stream that is 0-100. This too changes nothing for Bob's statistics, which never change.

e. The only thing that changes when Alice acts is the CORRELATION between Alice's results and Bob's results. These vary according to the predictions of quantum mechanics, and have values between 0 and 100% correlation. This is what is studied in Bell tests. If you study Bell (or Clauser or Aspect or Zeilinger) you will see that the quantum prediction is incompatible with all hidden variable theories - unless such theories allow for faster-than-light action. There is no known example of faster-than-light action that allows for signaling,

I should point out that PeterDonis and Nugatory are quantum forum moderators, and they are actually being very nice to you (and patient!). While you may feel your questions are not being addressed... the issue is that you aren't actually varying your questions. In every one, there are entangled pairs and in all cases the results are described by my points a-e above. And there is no possibility of FTL signaling because Bob always sees the same thing - a random stream. And a random stream, by definition, lacks any information by itself.

 

[tade]

I did link to the Wikipedia article, but that is somewhat heavy going. If you are really interested in this stuff but not up for a serious college-level intro to quantum mechanics you might give Giancarlo Ghirardi’s book “Sneaking a look at God’s cards” a try.

yeah, thanks, so I'm thinking of like a streamlined explanation of the exclusion of 'nudging' and such

 

[tade]

The only thing that changes when Alice acts is the CORRELATION between Alice's results and Bob's results. These vary according to the predictions of quantum mechanics, and have values between 0 and 100% correlation.

thanks, are these correlations the correlations of Alice and Bob randomly selecting spin directions to measure in?
and also kinda confused because I think Nugatory's suggesting that the issue is that the nudging is unphysical

 

[tade]

Well, I think also Bell was not too happy about the outcome of these experiments. For me it's hard to understand that a first-rank QFT expert like Bell was a proponent of Bohmian QM (which in my opinion only works in non-relativistic QM, and in non-relativistic physics there's anyway no problem with actions at a distance but it's rather the standard Newtonian way to describe interactions as in the Newtonian theory of gravity). Microcausality is at the very foundation of local relativistic QFT precisely because it's a viable realization of the causality principle in relativistic QT, and it's till today the only realization. Whether there are non-local Einstein-causal relativistic theories, I don't know.

and oh yeah, i was wondering how does microcausality/localism fit into Bell's theorem(s) about quantum mechanics

 

[PeterDonis]

you said that Bob's ratio of random outcomes only depends on the setting of Bob's polarizer, not on the setting of Alice's

Yes.

I was wondering about the entanglement between Alice and Bob

The entanglement is between Alice's and Bob's photons, not between Alice and Bob. The statement you quoted above is true when the photons are entangled.

I was thinking that maybe you could explain about the entanglement together with why Bob's ratio doesn't depend on Alice's settings

Because that's how entanglement in QM works. If Alice's and Bob's photons are entangled, that means their polarization measurement results are correlated, but the only way to see the correlations is to compare Alice's and Bob's results, which means Alice and Bob need to communicate those results to each other. @DrChinese already explained this in post #2.

and/or about how the inclusion of the special 52/48 polariser may or may not affect things

A 52/48 polarizer is still a polarizer. If it's Alice's polarizer, which is what you said before, you should be able to deduce what effect it will have on Bob's ratio of random outcomes from the statement I've already given.

 

[PeterDonis]

are these correlations the correlations of Alice and Bob randomly selecting spin directions to measure in?

Read the very sentence you quoted from @DrChinese. What does it say the correlations are correlations of? It's right there in the quote.

 

[tade]

The entanglement is between Alice's and Bob's photons, not between Alice and Bob.

Well I would hope not, otherwise someone might get slapped in the face at the Oscars

the only way to see the correlations is to compare Alice's and Bob's results

so I was thinking that Bob might notice a shift from 50/50 to 52/48 without him having done anything special, though I guess you've already ruled that out, and is there an underlying explanation/mechanism for why it doesn't occur

 

[tade]

Read the very sentence you quoted from @DrChinese. What does it say the correlations are correlations of? It's right there in the quote.

hmm, sorry I'm still really not sure

 

[Nugatory]

so I was thinking that Bob might notice a shift from 50/50 to 52/48 without him having done anything special, though I guess you've already ruled that out, and is there an underlying explanation/mechanism for why it doesn't occur

it is indeed ruled out. As for the underlying reason….

The state (you may have heard it called the wavefunction) of the entangled two-particle system can be written as $|\psi\rangle=\frac{1}{\sqrt{2}}|HV\rangle+ \frac{1}{\sqrt{2}}|VH\rangle$. The $|\rangle$ thingies are called “kets” and they are abstract mathematical objects that add like vectors. The ket $|HV\rangle$ represents the state “Alice’s particle will pass through a horizontal polarizer and Bob’s particle will pass through a vertical polarizer”, and vice versa for the ket ket $|VH\rangle$. The overall state is the ket $|\psi$ and the sum indicates that it is a superposition that will collapse to either $|HV\rangle$ or $|VH\rangle$ when the system interacts with a polarizer in any way. (Using abstract mathematical objects to represent the physics is not as weird as it seems - numbers are abstract mathematical objects but we’re comfortable using them to represent physical quantities like speeds. It’s just that here we have more complicated physics so we need more complicated mathematical objects to represent it).

So that’s the essence of entanglement. If Alice’s measurement is H then the wave function has collapsed to $|HV\rangle$; when and if Bob measures his particle he will get V. If Alice’s measurement is V the wave function has collapsed to $|VH\rangle$ and Bob will get H. But what is the probability of either outcome?

This is where the Born rule comes in. It says that the probability of the wavefunction collapsing to a given state is the square of the coefficient of that state in the superposition. Here both coefficients are $\frac{1}{\sqrt{2}}$, and when we square that we get $\frac{1}{2}$ - both possibilities occur with 50% probability, it is completely random which one we get for any particular entangled pair, and until you introduce your hypothetical modified polarizer both just see an endless series of random H and V results. It’s only when they get together after the fact and compare notes that they see that whenever one of them measured H the other measured V so they must have been working with entangled pairs.

And now we’ve gotten to where we can introduce your hypothetical modified polarizer. There are two possibilities:
1) The modified polarizer violates the Born rule: even though the coefficients and their squares are equal the probability of collapse to either state are not equal. But the Born rule is a fundamental axiom of quantum mechanics, like energy conservation is in classical physics. A device that violates it is impossible the same way that perpetual motion machines violating conservation of energy are impossible. So this line of thought takes us to the logically hopeless situation of trying to apply the laws of physics while assuming that they don’t apply.
2) The modified polarizer doesn’t violate the Born rule, but after the collapse it sometimes changes Alice’s H in the $|HV\rangle$ to a V leaving the system in the state $|VV\rangle$. That will give her the 52/48 ratio you’ve been looking for. However, that doesn’t change Bob’s V/H ratio because he’s still getting the same V and H results. (This, BTW, is why the first measurement on an entangled system breaks the entanglement - once that initial superposition collapses the two sides evolve independently).

 

[PeterDonis]

I was thinking that Bob might notice a shift from 50/50 to 52/48 without him having done anything special, though I guess you've already ruled that out

Definitely.

sorry I'm still really not sure

Here's what you quoted from @DrChinese:

The only thing that changes when Alice acts is the CORRELATION between Alice's results and Bob's results. These vary according to the predictions of quantum mechanics, and have values between 0 and 100% correlation.

Read the first sentence. Then read it again. And again. And keep doing so until you realize what the answer to your question is. The word "correlation" is right there (it's even capitalized) followed by description of what the correlation is a correlation of.

 

[tade]

followed by description of what the correlation is a correlation of.

yeah i see it, though I'm wondering if they are from Alice and Bob randomly selecting spin directions to measure in

 

[tade]

2) The modified polarizer doesn’t violate the Born rule, but after the collapse it sometimes changes Alice’s H in the $|HV\rangle$ to a V leaving the system in the state $|VV\rangle$. That will give her the 52/48 ratio you’ve been looking for. However, that doesn’t change Bob’s V/H ratio because he’s still getting the same V and H results. (This, BTW, is why the first measurement on an entangled system breaks the entanglement - once that initial superposition collapses the two sides evolve independently).

thanks, quite a detailed informative response, and is this changing of Alice's H to a V meaning a breaking of the entanglement? oh wait, nevermind, i got it now

 

[PeterDonis]

i'm wondering if they are from Alice and Bob randomly selecting spin directions to measure in

The correlations between Alice's and Bob's measurements are due to the entangled state that the pairs of photons are in, and the spin directions in which the measurements are made. There is no requirement that Alice and Bob have to randomly select spin directions in order for the measurements to be correlated.

 

[tade]

The correlations between Alice's and Bob's measurements are due to the entangled state that the pairs of photons are in, and the spin directions in which the measurements are made. There is no requirement that Alice and Bob have to randomly select spin directions in order for the measurements to be correlated.

and so i'd like to ask about how the correlation changes
and also wondering if we're applying what Nugatory has said about the Born rule, or if its a different issue

e. The only thing that changes when Alice acts is the CORRELATION between Alice's results and Bob's results. These vary according to the predictions of quantum mechanics, and have values between 0 and 100% correlation.

 

[tade]

This is where the Born rule comes in. It says that the probability of the wavefunction collapsing to a given state is the square of the coefficient of that state in the superposition. Here both coefficients are $\frac{1}{\sqrt{2}}$, and when we square that we get $\frac{1}{2}$ - both possibilities occur with 50% probability

and also i was wondering about the maths of the situation at the moment when the wave encounters the molecules of the polariser, the interaction of the target particle with the polariser molecules, or also the maths of the transition when and as the wavefunction is collapsing as it encounters and interacts with the molecules of the polariser, and I think resources on this would be swell

and as DrChinese has said: "It is possible for Alice to have a polarizer which produces outcomes different than the usual 50-50. For obvious reasons, manufacturers of polarizing beam splitters work very hard to achieve as close to 50-50 as possible.", so that sounds pretty interesting, like, perhaps they could go in the opposite direction, and deliberately manufacture a wonky polariser, and try testing quantum entanglement with that

 

[PeterDonis]

i'd like to ask about how the correlation changes

How much background do you have in the math of QM?

 

[tade]

How much background do you have in the math of QM?

i think let's go with an intermediate level, thanks

 

[PeterDonis]

i think let's go with an intermediate level, thanks

Then you should be able to write down the entangled photon wave function and the basic action of a polarizer. Can you do that?

 

[tade]

Then you should be able to write down the entangled photon wave function and the basic action of a polarizer. Can you do that?

hmm ok, maybe not, maybe first can you give a brief description of how the correlation changes, thanks

 

[PeterDonis]

hmm ok, maybe not

Then you don't really have an "I" level background in this subject, and it's hard for me to see how you would be able to follow any explanations more complicated than "well, that's just how it works". Which is basically what you've already been told.

maybe first can you give a brief description of how the correlation changes

How the correlation changes with what?

 

[tade]

Then you don't really have an "I" level background in this subject, and it's hard for me to see how you would be able to follow any explanations more complicated than "well, that's just how it works". Which is basically what you've already been told.How the correlation changes with what?

oh no worries, i think i would be able to

as DrChinese said, "The only thing that changes when Alice acts is the CORRELATION", so it'd be Alice swapping the polarisers

 

[Motore]

oh no worries, i think i would be able to

Can you show some effort yourself?
At least check a textbook, post the math and then ask about that math.
You are responding very quickly and it seems to me you are not digesting the answers because your follow up questions are all pretty much the same.

 

[vanhees71]

If you have a Bell state, e.g., the spin-0 state,
$$|\Psi \rangle=\frac{1}{\sqrt{2}} (|HV \rangle-|VH \rangle),$$
then the single photons are precisely unpolarized, i.e.,
$$\hat{\rho}_A =\mathrm{Tr}_B |\Psi \rangle \langle \Psi|=\frac{1}{2} \hat{1}, \quad \hat{\rho}_B=\mathrm{Tr}_A |\Psi \rangle \langle \Psi|=\frac{1}{2} \hat{1},$$
and thus if Alice measures 48% H and 52% V, her polarization experiment is somehow inaccurate. As has been correctly stressed over and over again that cannot be used to transmit a signal, because all that B has are also precisely unpolarized photons. With a correctly working polarization measurement he'll simply get a random sequence of H and V polarized photons with the 50%:50% probabilities, no matter what A does with her photons. Only if both detectors work precisely you can figure out the correlations predicted by QED given the two-photon Bell state, and this can be done only by comparing A's and B's measurement protocols, which is possible only by exchange of this information, which is possible only with real-world signals, which propagate at most at the speed of light.

 

[tade]

Can you show some effort yourself?
At least check a textbook, post the math and then ask about that math.
You are responding very quickly and it seems to me you are not digesting the answers because your follow up questions are all pretty much the same.

Well, from my perspective, I am examining the answers and it seems to be pretty roundabout, you can pick anyone of my replies and I can explain it.

And you've been following the thread right, and I think that the main issue is that you're "skeptical" right

and anyway, also since you've been following, hope you don't mind if I ask you, what do you think are the changes which DrChinese is referring to in "The only thing that changes when Alice acts is the CORRELATION"

Because to be clear its just that I'm interested to know what they are.

 

[tade]

If you have a Bell state, e.g., the spin-0 state,
$$|\Psi \rangle=\frac{1}{\sqrt{2}} (|HV \rangle-|VH \rangle),$$
then the single photons are precisely unpolarized, i.e.,
$$\hat{\rho}_A =\mathrm{Tr}_B |\Psi \rangle \langle \Psi|=\frac{1}{2} \hat{1}, \quad \hat{\rho}_B=\mathrm{Tr}_A |\Psi \rangle \langle \Psi|=\frac{1}{2} \hat{1},$$
and thus if Alice measures 48% H and 52% V, her polarization experiment is somehow inaccurate. As has been correctly stressed over and over again that cannot be used to transmit a signal, because all that B has are also precisely unpolarized photons. With a correctly working polarization measurement he'll simply get a random sequence of H and V polarized photons with the 50%:50% probabilities, no matter what A does with her photons. Only if both detectors work precisely you can figure out the correlations predicted by QED given the two-photon Bell state, and this can be done only by comparing A's and B's measurement protocols, which is possible only by exchange of this information, which is possible only with real-world signals, which propagate at most at the speed of light.

oh sorry, to be crystal clear, is this explanation with the assumption that the 52/48 nudge is unphysical or impossible?

 

[tade]

I've very often expressed my opinion on this topic. For me it is very clear that there's no possibility to send signals faster than light using quantum entanglement. The reason is that this impossibility is implemented in relativistic quantum field theory by the socalled microcausality principle. In my scientific community, high-energy particle/nuclear physics, that's what's called "locality", and this excludes any causal connections between space-like separated events.

The observed long-ranged correlations between space-like separated measurements are due to the preparation of the system in the entangled state and not due to any "spooky action at a distance" of one measurement apparatus at position A on the part of the system at B or the measurement apparatus used at B.

Since thus relativistic local QFT realizes locality via the microcausality constraint on local observables, what one has to give up according to Bell's theorem is "realism", i.e., the assumption that all observables always take determined values, which are only appearing probabilistic because of our ignorance of some "hidden variables".

Whether there are non-local deterministic (realistic) relativistic models in accordance with the observations I don't know.

and I came across this article from Quanta Magazine titled "How Bell’s Theorem Proved ‘Spooky Action at a Distance’ Is Real", seems like they're really affirmative on it

https://www.quantamagazine.org/how-...spooky-action-at-a-distance-is-real-20210720/

 

[vanhees71]

It's a pop-sci article on a subject, which cannot be communicated on that level in all details appropriately, and given that constraint it did a good job. Generally I think, QUANTA is a pretty good pop-sci source, although quite often I don't understand their articles and only when reading the scientific papers I understand what they want to say (provided, I've enough expertise in the subject discussed in that papers ;-)).

The point is that, as soon as you simply accept that in Nature there is inherent randomness as described by the minimal statistical interpretation of the QFT formalism that what's described by entangled states of the kind we discuss here are correlations of observables on far-distantly measured parts of the entangled quantum system (e.g., two photons in an entangled state). These correlations are there, because of the preparation of the system in such an entangled state, and thus nothing in the QFT description needs a faster-than-light-signal propagation between the two spacelike separated measurement events (e.g., clicks of the far-distant photon detectors in our example). Within relativistic local (i.e., microcausal) QFT by construction such faster-than-light signals are excluded, and as long as QFT (in our example it's QED, the best-tested QT ever) can explain the phenomena, you have at least one theory describing these phenomena, and this implies that what has to be abandoned of Bell's class of realistic local hidden-variable theory is reality (i.e., the assumption that all observables always take determined values), because local QFT is by construction local (i.e., space-like separated events cannot be causally connected within this theory).

 

[DrChinese]

1. and also i was wondering about the maths of the situation at the moment when the wave encounters the molecules of the polariser, the interaction of the target particle with the polariser molecules

2. also the maths of the transition when and as the wavefunction is collapsing as it encounters and interacts with the molecules of the polariser...

3. and as DrChinese has said: "It is possible for Alice to have a polarizer which produces outcomes different than the usual 50-50. For obvious reasons, manufacturers of polarizing beam splitters work very hard to achieve as close to 50-50 as possible.", so that sounds pretty interesting, like, perhaps they could go in the opposite direction, and deliberately manufacture a wonky polariser, and try testing quantum entanglement with that

1. This has nothing to do with entanglement. And in some ways has nothing to do with quantum mechanics. The full details of how a PBS works requires a working knowledge of quantum optics, and explaining that is far outside the scope of any PF thread. Although the following reference is not a summary in any way, I think you would benefit from studying it. It is specifically about entangled particles encountering a polarizing beam splitter as a demonstration of the existence of photons (as a nonclassical field).

http://people.whitman.edu/~beckmk/QM/grangier/Thorn_ajp.pdf2. The concept of collapse is interpretation dependent. There is no known quantum explanation of collapse that fits into what you are asking. If quantum collapse does occur, no one can pinpoint when or how it does experimentally. (Nor even theoretically, for that matter, since in principle collapse can be reversed.)3. As mentioned, no scientific manufacturer will intentionally manufacture "wonky" instrumentation. Any more than a toaster manufacturer will make toasters that don't cook your bread.

Keep in mind that in principle, you could yourself construct a black box device that is inefficient at performing the T and R operations of a PBS - and presents any combination of output percentages you care to work with. However, the problem is that none of this actually allows any meaningful exploration of quantum entanglement (as far as I can imagine, although I am far from the authority on such). As is always the case in the experimental world: scientists experiment to prove/disprove/quantify specific ideas they feel have value. They don't normally spend their days working on "interesting" speculations by non-professionals.

 

[tade]

Although the following reference is not a summary in any way, I think you would benefit from studying it. It is specifically about entangled particles encountering a polarizing beam splitter as a demonstration of the existence of photons (as a nonclassical field).

http://people.whitman.edu/~beckmk/QM/grangier/Thorn_ajp.pdf

oh i see, because i was thinking about and hoping for literature on the maths and mechanics of photon-polariser interactions at the quantum-molecular level, to take a look at the limits of what the Born probabilities might possibly be at the moment of interaction

Keep in mind that in principle, you could yourself construct a black box device that is inefficient at performing the T and R operations of a PBS - and presents any combination of output percentages you care to work with. However, the problem is that none of this actually allows any meaningful exploration of quantum entanglement

hmmm, I was thinking about the possible meaningfulnesses of my OP example, though is it that its ruled-out like Nugatory saying in #49

 

[tade]

These correlations are there, because of the preparation of the system in such an entangled state, and thus nothing in the QFT description needs a faster-than-light-signal propagation between the two spacelike separated measurement events (e.g., clicks of the far-distant photon detectors in our example).

man that's really mind-bending