Quantum Entanglement: Exploring the Limits of Faster-Than-Light Information

[Paper]

So from what I understand of Quantum Entanglement:
1. Two particles are produced which are linked somehow so as to have the opposite spins

2. By measuring one particle, the entanglement is broken - however that you then also know the state of the other particle. This is said to be faster-than-light action

3. It can't be used as a communication pathway as the original state of either particle is unknown before they are measured - and once they're measured the entanglement breaks down. Some argue therefore that there is no faster-than-light action, others argue though that there is still information about particle states that is being gained faster-than-light.


I have an idea. Let's say I had two pieces of paper, one red and one blue. I put each into it's own envelope, and give the envelopes randomly to two travellers. I send one traveller to London and the other to Sydney. They are both told that if they have the red one, the other had the blue, and vice versa. Now, it could be said that as soon as either opens their envelope, they know not only their own colour but also, instantaneously, the colour of the other person's paper.

Would this determination of the other's colour be faster-than-light information?

 

[netheril96]

Your "analogy" is totally different from quantum entanglement. It has a formal name local hidden variable theory and been refuted by experiments.

See http://en.wikipedia.org/wiki/Bell's_inequality for more information.

 

[DrChinese]

I have an idea. Let's say I had two pieces of paper, one red and one blue. I put each into it's own envelope, and give the envelopes randomly to two travellers. I send one traveller to London and the other to Sydney. They are both told that if they have the red one, the other had the blue, and vice versa. Now, it could be said that as soon as either opens their envelope, they know not only their own colour but also, instantaneously, the colour of the other person's paper.

Would this determination of the other's colour be faster-than-light information?

To add to what netheril96 said:

This is not FTL communication. No information is transferred from point A to point B instantaneously in this example. And this is NOT how entanglement operates, which is why this example does not really apply. Now, keep in mind that this was an open question for some time in the sense that after EPR and before Bell it was considered a "possiblity". But after Bell it was obvious that something had to give.

 

[Paper]

I think I might give physics a miss...

 

[StevieTNZ]

To add to what netheril96 said:

This is not FTL communication. No information is transferred from point A to point B instantaneously in this example. And this is NOT how entanglement operates, which is why this example does not really apply. Now, keep in mind that this was an open question for some time in the sense that after EPR and before Bell it was considered a "possiblity". But after Bell it was obvious that something had to give.

That's cause the red and blue paper existed already before one of the envelopes was opened, right?

 

[thenewmans]

I think I might give physics a miss...

No! Don’t give it a miss. You’re so close. What you say is exactly what Einstein thought up 80 years ago. I know it’s hard to get through the mumbo jumbo. It’s just that we like to take conversational shortcuts and we forget how hard it is to make sense of it. Let me see if I can guide you in the right direction.

So when Einstein said what you are saying, the quantum mechanics physicists knew he was wrong but they only had untestable arguments. It took 30 years for Bell to come up with a good test. And even then it took a while to actually do the test. Bell didn’t figure out what was actually going on. All he could do is prove that the envelope idea is a bad analogy. They call this a No-Go theory.

First of all, let me change the analogy. Let’s say you came up with the hideous idea that an electron is something like a baseball. And if you take a picture of a pitch, you can figure out if it’s spinning up or spinning down. Now if you take a second picture of the same pitch but tilt the camera, you might get a different answer. You could even come up with a nice formula that predicts the probability that the 2 photos disagree based on the amount of tilting.

Quantum mechanics predicts that 2 entangled electrons will have opposite spin. Einstein said the spin is set when they leave the emitter. This is like your envelopes or my baseball analogy. The effect of tilting the camera should be very predictable. Bell’s argument is that any kind of formula you come up with using this kind of analogy will not be as accurate as the predictions of quantum mechanics.

Now that Wikipedia page will make more sense to you http://en.wikipedia.org/wiki/Bell's_inequality

What this means is that we are now sure that the spin is not set at the emitter. So far it looks as if it must get set when the electron is measured. So how can the measurements match for two distant electrons? Here’s where the faster than light idea comes in. And a lot of the discussions here are on that.

I hope you decide to ask lots of follow up questions.

 

[Gordon Watson]

No! Don’t give it a miss. You’re so close. What you say is exactly what Einstein thought up 80 years ago. I know it’s hard to get through the mumbo jumbo. It’s just that we like to take conversational shortcuts and we forget how hard it is to make sense of it. Let me see if I can guide you in the right direction.

So when Einstein said what you are saying, the quantum mechanics physicists knew he was wrong but they only had untestable arguments. It took 30 years for Bell to come up with a good test. And even then it took a while to actually do the test. Bell didn’t figure out what was actually going on. All he could do is prove that the envelope idea is a bad analogy. They call this a No-Go theory.

First of all, let me change the analogy. Let’s say you came up with the hideous idea that an electron is something like a baseball. And if you take a picture of a pitch, you can figure out if it’s spinning up or spinning down. Now if you take a second picture of the same pitch but tilt the camera, you might get a different answer. You could even come up with a nice formula that predicts the probability that the 2 photos disagree based on the amount of tilting.

Quantum mechanics predicts that 2 entangled electrons will have opposite spin. Einstein said the spin is set when they leave the emitter. This is like your envelopes or my baseball analogy. The effect of tilting the camera should be very predictable. Bell’s argument is that any kind of formula you come up with using this kind of analogy will not be as accurate as the predictions of quantum mechanics.

Now that Wikipedia page will make more sense to you http://en.wikipedia.org/wiki/Bell's_inequality

What this means is that we are now sure that the spin is not set at the emitter. So far it looks as if it must get set when the electron is measured. So how can the measurements match for two distant electrons? Here’s where the faster than light idea comes in. And a lot of the discussions here are on that.

I hope you decide to ask lots of follow up questions.

QUOTE: Here’s where the faster than light idea comes in. You're right, but can we bury such craziness, once and for all?

QUESTION: Why does such a crazy idea come in when we have the following less-crazy idea?

In each electron-pair, the electrons have equal and opposite total angular momentum; so each pair of electrons is in a spherically symmetric state, since total angular momentum is conserved in their paired creation.

Now the total angular momentum for each electron is the sum of their extrinsic and intrinsic spin.

And a Stern-Gerlach magnet "burns off" the extrinsic spin and re-orients the intrinsic spin.

So the resultant correlations, for any setting of the magnets, follow from the spherical symmetry of each pristine electron-pair.

QED; no FTL.

 

[StevieTNZ]

Maybe this will be a good thread to pose this question:
I was reading Philosophical Concepts in Physics by Cushing. I quote:

What is it about the formalism of quantum mechanics that makes it so difficult to tell a story that we feel we understand about fundamental physical phenonema? The heart of the problem is the entanglement of quantum states that gives rise to the measurement problem and to nonlocality. ... but such entanglement is a generic feature of quantum systems (except under very special cirumstances that do not usually obtain).

What would those special circumstances be?

 

[DrChinese]

QUESTION: Why does such a crazy idea come in when we have the following less-crazy idea?

In each electron-pair, the electrons have equal and opposite total angular momentum; so each pair of electrons is in a spherically symmetric state, since total angular momentum is conserved in their paired creation.

Now the total angular momentum for each electron is the sum of their extrinsic and intrinsic spin.

And a Stern-Gerlach magnet "burns off" the extrinsic spin and re-orients the intrinsic spin.

So the resultant correlations, for any setting of the magnets, follow from the spherical symmetry of each pristine electron-pair.

QED; no FTL.

What you are describing, JenniT, is inaccurate and you are savvy enough to know it. This is completely contradicted by Bell and Aspect.

 

[thenewmans]

QUOTE: Here’s where the faster than light idea comes in. You're right, but can we bury such craziness, once and for all?

QUESTION: Why does such a crazy idea come in when we have the following less-crazy idea?

In each electron-pair, the electrons have equal and opposite total angular momentum; so each pair of electrons is in a spherically symmetric state, since total angular momentum is conserved in their paired creation.

Now the total angular momentum for each electron is the sum of their extrinsic and intrinsic spin.

And a Stern-Gerlach magnet "burns off" the extrinsic spin and re-orients the intrinsic spin.

So the resultant correlations, for any setting of the magnets, follow from the spherical symmetry of each pristine electron-pair.

QED; no FTL.

Yeah, I agree. That FTL stuff is crazy. But from Paper’s question, I think it’s best to stick established theory before going into interpretations. That said, if you’re really married to locality, there are a few interpretations that maintain it. I’m partial to locality, so I’m with you there. But as far as a theory with the spin set at the source, well then that’s testable. And the test has already been done. Unless you can come up with test results that disagree with Bell’s theory, it’s too marginal a topic.

 

[thenewmans]

What is it about the formalism of quantum mechanics that makes it so difficult to tell a story that we feel we understand about fundamental physical phenonema? The heart of the problem is the entanglement of quantum states that gives rise to the measurement problem and to nonlocality. ... but such entanglement is a generic feature of quantum systems (except under very special circumstances that do not usually obtain).

StevieTNZ, I’d say there are several flaws in that snipit you provided. Entanglement is a particularly good example of the philosophical trickiness in QM. But it’s not the only one. Check out quantum tunneling. And QM doesn’t require nonlocality. But if you keep locality then something else has to give. I’m not sure what role entanglement plays when we’re not observing it. What I mean is that entanglement is only useful to us when we know we have generated it and we plan to measure it. On top of that, I don’t know what those very special circumstances are.

 

[Gordon Watson]

What you are describing, JenniT, is inaccurate and you are savvy enough to know it. This is completely contradicted by Bell and Aspect.

Thank you, DrC, but:

Why two? If my idea were wrong, one would have been enough.

All of us being helped, of course, by some added explanation of a better rational idea.

Note that I was responding to another post, and thus tangentially to the OP's idea; hoping to suggest that the offered classical example cannot match the symmetry associated with the QM example. Hopefuly encouraging Paper to seek a better analogy; hoping such as you might respond to the valid question: Would this determination of the other's colour be faster-than-light information?

PS: Please see my next reply; in case you are jumping to a false conclusion about the nature of my elements of physical reality.

Thanks again,

JenniT

 

[Gordon Watson]

Yeah, I agree. That FTL stuff is crazy. But from Paper’s question, I think it’s best to stick established theory before going into interpretations. That said, if you’re really married to locality, there are a few interpretations that maintain it. I’m partial to locality, so I’m with you there. But as far as a theory with the spin set at the source, well then that’s testable. And the test has already been done. Unless you can come up with test results that disagree with Bell’s theory, it’s too marginal a topic.

QUOTE: "But as far as a theory with the spin set at the source, well then that’s testable."

Yes, I am wedded to locality; and very pleased to learn of your partiality in that direction.

But please note: My idea does not imply that (loosely) "the spin" is set at source, because for me, we need to be more judicious in our use of language here: There are three spins (angular momenta) involved with each electron: The total, the extrinsic, the intrinsic.

1. Being electrons, they have the same intrinsic spin of one-half.

2. Being pair-wise created in the spherically symmetric singlet state, they have equal but opposite total spin.

3. Hence my idea: We just need to understand what a Stern-Gerlach magnet (SGM) does to each spin, and to each electron.

4. Noting that, AFAIK and for Paper's benefit, the spherical symmetry of the singlet state is not matched by any classical analogy.

5. Also noting: AFAIK, the spherical symmetry of the singlet state is reflected in the paired SGM outcomes and their correlations.

QED.

 

[DrChinese]

...hoping such as you might respond the the valid question: Would this determination of the other's colour be faster-than-light information?

No, and I say that because learning about a far away object does not require any information to be transmitted FTL.

 

[DrChinese]

5. Also noting: AFAIK, the spherical symmetry of the singlet state is reflected in the paired SGM outcomes and their correlations.

QED.

This is false, so your QED doesn't work. I say this because the statistics (outcomes and their correlations) are a function of BOTH SGMs. That wouldn't be true unless there were *quantum* non-locality OR an FTL signal was sent from one SGM to the other.

That does not mean that SR need be abandoned, however. I kinda like it, actually.

 

[Gordon Watson]

From JenniT:

5. Also noting: AFAIK, the spherical symmetry of the singlet state is reflected in the paired SGM outcomes and their correlations.

QED.

A: This is false, so your QED doesn't work. I say this because the statistics (outcomes and their correlations) are a function of BOTH SGMs. That wouldn't be true unless there were *quantum* non-locality OR an FTL signal was sent from one SGM to the other.

B: That does not mean that SR need be abandoned, however. I kinda like it, actually.

A and B added for clarity in responding.

RE A: Well; the idea is this:

A1. We can check the spherical symmetry over many many pairs by setting the SGMs to be parallel or anti-parallel at any random orientation.

A2. Then the reason that both SGMs come into the correlations (whether the SGMs are parallel or not) is straight-forward:

A3. Each SGM interacts (locally and realistically) with a pristine electron and perturbs it -- so that, in any pair, each electron emerges from its SGM with a property that it did not have prior to the interaction.

A4. In accounting for the consequent correlations, we must allow for this double-perturbation in any pair by recognizing both SGMs. Seems a sensible idea to me.

RE B: But, IMHO: Oh what a distortion of SR you require!? And, IMHO, just to accommodate *quantum* non-locality OR an FTL signal! That is: Seemingly invoking no known mechanism or, alternatively: a mechanism known to be impossible. But I digress ...

 

[thenewmans]

QUOTE: "But as far as a theory with the spin set at the source, well then that’s testable."

Yes, I am wedded to locality; and very pleased to learn of your partiality in that direction.

But please note: My idea does not imply that (loosely) "the spin" is set at source, because for me, we need to be more judicious in our use of language here: There are three spins (angular momenta) involved with each electron: The total, the extrinsic, the intrinsic.

1. Being electrons, they have the same intrinsic spin of one-half.

2. Being pair-wise created in the spherically symmetric singlet state, they have equal but opposite total spin.

3. Hence my idea: We just need to understand what a Stern-Gerlach magnet (SGM) does to each spin, and to each electron.

4. Noting that, AFAIK and for Paper's benefit, the spherical symmetry of the singlet state is not matched by any classical analogy.

5. Also noting: AFAIK, the spherical symmetry of the singlet state is reflected in the paired SGM outcomes and their correlations.

QED.

JenniT,

I have a challenge for you. I worked on this for over an hour so I hope you take it seriously. You’re idea sounds interesting. But there’s one thing missing. It doesn’t take into account the angle at which a measurement is made. This is an important part of Bell’s theory. I’ve devised an experiment that demonstrates the problem.

Let’s start with classic polerizers. The offset angle between 2 polarizers cuts the light that get through by Cos(Angle)^2. If the polerizers are at the same angle, all the light gets through. Cos(0)^2=1. At 90 degrees, no light gets through. Cos(90)^2=0. At 45 degrees, half the light gets through. Cos(45)^2=.5. Finally, at 22.5 degrees, 85% of the light gets through. Cos(22.5)^2=.85.

Using the correspondence principle, this should turn out just the same on average even if 1 photon at a time goes through. Individually, you can’t get 85% of a 1 photon. It either gets through or it doesn’t. So if you send 10,000 photons through 2 polerizers offset by 22.5 degrees, roughly 8500 make it through.

With entanglement, 2 photons go through separate polerizers. With the polerizers at the same angle, if a photon gets through one, it gets through the other. That counts as a match with 100% correlation. But if the polerizers are offset by 22.5 degrees, the correlation is roughly 85%. Results like this have been tested to a very high precision.

In an experiment, let’s say 20 pairs of entangled photons are sent through with the polerizers at particular angles. The detection results are listed below. The number of matches should match the prediction. I’ll do an example here for you. The polerizers are set at 0 and 22.5 degrees.
Set A - 0 degrees - 1 0 1 1 0 1 0 0 1 0 0 1 1 1 0 1 0 1 0 0
Set B - 22.5 degrees - 1 0 1 1 0 1 1 0 1 0 0 1 0 1 0 1 1 1 0 0
17 out of 20 pairs match. So that’s an 85% correlation as expected.

Here’s your challenge. I want you to come up with 3 sets of data; A, B and C. Set A has the polarizer set at 0 degrees. Set B has the polarizer at 22.5 degrees. And Set C has the polarizer at 45 degrees. Sets A and B should match 85% of the time. Sets B and C should match 85% or the time. And sets A and C should match 50% of the time.
Set A - 0 degrees -
Set B - 22.5 degrees -
Set C – 45 degrees -

 

[Gordon Watson]

JenniT,

I have a challenge for you. I worked on this for over an hour so I hope you take it seriously. You’re idea sounds interesting. But there’s one thing missing. It doesn’t take into account the angle at which a measurement is made. This is an important part of Bell’s theory. I’ve devised an experiment that demonstrates the problem.

Let’s start with classic polerizers. The offset angle between 2 polarizers cuts the light that get through by Cos(Angle)^2. If the polerizers are at the same angle, all the light gets through. Cos(0)^2=1. At 90 degrees, no light gets through. Cos(90)^2=0. At 45 degrees, half the light gets through. Cos(45)^2=.5. Finally, at 22.5 degrees, 85% of the light gets through. Cos(22.5)^2=.85.

Using the correspondence principle, this should turn out just the same on average even if 1 photon at a time goes through. Individually, you can’t get 85% of a 1 photon. It either gets through or it doesn’t. So if you send 10,000 photons through 2 polerizers offset by 22.5 degrees, roughly 8500 make it through.

With entanglement, 2 photons go through separate polerizers. With the polerizers at the same angle, if a photon gets through one, it gets through the other. That counts as a match with 100% correlation. But if the polerizers are offset by 22.5 degrees, the correlation is roughly 85%. Results like this have been tested to a very high precision.

In an experiment, let’s say 20 pairs of entangled photons are sent through with the polerizers at particular angles. The detection results are listed below. The number of matches should match the prediction. I’ll do an example here for you. The polerizers are set at 0 and 22.5 degrees.
Set A - 0 degrees - 1 0 1 1 0 1 0 0 1 0 0 1 1 1 0 1 0 1 0 0
Set B - 22.5 degrees - 1 0 1 1 0 1 1 0 1 0 0 1 0 1 0 1 1 1 0 0
17 out of 20 pairs match. So that’s an 85% correlation as expected.

Here’s your challenge. I want you to come up with 3 sets of data; A, B and C. Set A has the polarizer set at 0 degrees. Set B has the polarizer at 22.5 degrees. And Set C has the polarizer at 45 degrees. Sets A and B should match 85% of the time. Sets B and C should match 85% or the time. And sets A and C should match 50% of the time.
Set A - 0 degrees -
Set B - 22.5 degrees -
Set C – 45 degrees -

I'm pleased to see that you want to take this idea seriously. So let me assure you that there is nothing missing.

I suggest, for starters, that you re-think your challenge along the following lines. Since your example is text-book Bell stuff, this suggestion is not limited to your example:

1. Please note that, with my idea, you must initially focus on the total angular momentum of each particle.

2. To simplify our discussion, without any loss of generality whatsoever, let us ignore the magnitude of the total angular momentum and work with its orientation only.

3. Let that orientation be Tk for particle k, where k is the number allocated to the particle-pair that you test. Its twin can then be denoted by k'. Say k = k' = 1 for the first tested particle-pair, k = 2 for the second pair, etc.

4. Your example is based on photons, so let us now stay with them throughout this discussion. Electrons follow similar analysis; you just put their intrinsic spin (S) -- 1/2 -- into the cosine argument used for your photon example, where the photon's intrinsic-spin 1 is implicit.

5. Now here's an important point that is much neglected in Bell-studies. No two input (pristine, untested) particle-pairs are the same! NB: For this simple reason: The orientations that we are discussing are orientations in ordinary 3-space, and there are an infinity of them. So the probability that any two photon-pairs have the same T is ZERO. That is:

(1) P[Tk = T(k' + n)] = 0, where n = 1, 2, 3, ... .

YET

(2) P[Tk = Tk'] = 1.

6. So in your example, where you correctly have a 0 or 1 for the paired dichotomous outputs, you must be aware that the paired INPUTS are NEVER the same! We are working with just four paired-output combinations [00, 01, 10, 11] from an infinite, non-replicated, set of paired inputs: Tk = Tk', k = 1, 2, 3, ..., ... ; Tk ≠ Tk' if k ≠ k'.

7. SO: When you want a third set of paired-outputs, for that third angular differential between the polarizers, they will be drawn from a completely different set of paired-inputs. There is no requirement -- nor possibility -- that any third output-string even if it had the same sequence as an earlier string, has the same input-string.

8. Of course, this is not a problem. Just use this third angular differential between the polarizers to calculate the third correlation coefficient that will apply to your third set of paired-tests.

9. As I wrote earlier, the paired-test devices perturb the pristine particle-pairs locally, realistically AND individually. So we need to work with the angular differentials to bring both perturbations to account in deriving the twinned correlations.

PS. With this idea, there is an underlying gyroscopic-style mechanism that can be brought to bear on this discussion. But first let's see if you understand how my idea responds, correctly, to your challenge -- delivering in every case (s = 1/2 or S = 1) the correct experimental results.

QED.

 

[thenewmans]

JenniT,

You’re just going to have to run the gauntlet and answer people’s questions. And expect follow-ups too. That’s because nobody’s going to spend time on your idea if you’re unwilling to answer all these questions.

So either your idea takes the angle of measurement into account or you can answer my previous post. It’s time for you to fish or cut bait.

 

[Gordon Watson]

JenniT,

You’re just going to have to run the gauntlet and answer people’s questions. And expect follow-ups too. That’s because nobody’s going to spend time on your idea if you’re unwilling to answer all these questions.

So either your idea takes the angle of measurement into account or you can answer my previous post. It’s time for you to fish or cut bait.

Uh? See #8.

 

[Gordon Watson]

Uh? See #8.

A. Clarification: That is, see the point numbered 8 in

https://www.physicsforums.com/showpost.php?p=3134494&postcount=18


B. Question: So, dear thenewmans, what part of your challenge is not answered?

JenniT

 

[DrChinese]

A3. Each SGM interacts (locally and realistically) with a pristine electron and perturbs it -- so that, in any pair, each electron emerges from its SGM with a property that it did not have prior to the interaction.

A4. In accounting for the consequent correlations, we must allow for this double-perturbation in any pair by recognizing both SGMs. Seems a sensible idea to me.

These are just a bunch of words where you conclude you are correct without bothering to provide a derivation. In fact, Bell showed WHY this idea is plain wrong. When you try to supply the "sensible" perturbation into a formula, it falls apart. Exactly as thenewmans has described in detail above.