Is action at a distance possible as envisaged by the EPR Paradox.

[SpectraCat]

This is important and I have to be sure.

Causal locality
If we set LHV to be +1 & -1 before sending the photons, we are not violating any locality. It’s just a matter of sending away 'predefined letter' in an 'envelope', and we know the outcome in advance, right...?

Constitutive locality
The receivers of the 'envelope' are physically separated in space-time, i.e. they have no connection FTL, right...?

Okay, can we 'refine' this and say – According to SEP the 'cause' of EPR is not "spooky action at a distance", it’s 'something else', but SEP can’t say anything about that. (right?)

Okay, thanks.

No worries mate! It was just a (terribly silly) joke!



>> This is extremely interesting! <<
Wow! I thought we only had one "problem" with the "spooky action at a distance", but this proves it’s much worse²!

Let’s see now... IF we assume there ARE "spooky action at a distance" AND the values of the Particles are 100% RANDOM, and the OTHER Particle must obtain the OPPOSITE value instantly. THIS CAN’T BE DONE DUE TO RoS??

Sweet jeees... I’m feeling dizzy...

Does DrChinese or Frame Dragger or anyone else have a solution to this...?

AFAICS, RoS is a non-issue for this case. There is no question of causality here, only comparison of measurement. There is no logical inconsistency in a frame where B was measured before A or vice-versa, because the results are perfectly correlated. IOW, if you measure B first, you determine the value of A, if you measure A first, you determine the value of B. This holds in all frames, for all observers, so IMO there is no problem. Furthermore, when observers in different frames compare answers (as is required for a Bell test), they may disagree on the ordering of events, but they will always agree that there is a Bell violation for the results.

 

[DevilsAvocado]

Welcome to the counterintuive nature of QM!

... I need coffee ... or maybe ... a vacation ... in the sun ... something real ... anything ... booze ... girls ...


()

 

[DevilsAvocado]

... IOW, if you measure B first, you determine the value of A, if you measure A first, you determine the value of B.

IMO I see a weakness here, "spooky action at a distance" introduces another 'spooky thing' – An instant and universal NOW (that’s probably what made AE want to 'throw up').

... but that’s maybe the whole solution?? Einstein WAS wrong, there is a universal NOW!?

I dunno...

 

[SpectraCat]

IMO I see a weakness here, "spooky action at a distance" introduces another 'spooky thing' – An instant and universal NOW (that’s probably what made AE want to 'throw up').

... but that’s maybe the whole solution?? Einstein WAS wrong, there is a universal NOW!?

I dunno...

No, that is just the same as saying that there is a "preferred reference frame". As RUTA said, there are people exploring that possibility, but I don't think it is necessary to resolve this issue.

It is important to realize that this is strictly an interpretational "what is going on behind the scenes" question at this point. AFAIK, there is no way to make any testable predictions based on different theories of *how* the Bell inequality occurs (i.e. how particle A "knows" that a measurement was performed on particle "B").

Most of the problems that are raised in this vein would only be real issues if FTL communication was possible using entangled pairs, but it's not, so we are ok. The causality relationship between the measurements at A and B is one example of this ... if it were somehow possible for Alice to know what Bob was doing at the time she made her measurement (assuming a space-like separation between them), then causality would be a problem, and you could potentially have a logical contradiction, because Alice would have access to information that was not available to all observers, i.e. she would be in a preferred reference frame. But that is equivalent to speculating about how things might change if SR is wrong ... as far as we know it isn't, so let's not worry about all of that .. physics is hard enough to understand as it is .

To reiterate, from a QM point of view, there are two measurements performed on the members of an entangled pair. Since the results are always perfectly correlated, it fundamentally does not matter which measurement comes first, at least for the purposes of Bell tests. All observers in all frames agree on the results of the measurements, once they have communicated them by normal sub-lightspeed channels for comparison.

 

[DevilsAvocado]

Okay SpectraCat, I get back to you on that ASAP. NOW one part of my nonseparable body tells me it’s time for food...

 

[DrChinese]

IMO I see a weakness here, "spooky action at a distance" introduces another 'spooky thing' – An instant and universal NOW (that’s probably what made AE want to 'throw up').

... but that’s maybe the whole solution?? Einstein WAS wrong, there is a universal NOW!?

I dunno...

A lot of the Bohmians believe there is such, a preferred frame. Demystifier covers this well, but I will pass this along:

a) In the most common versions of BM, a preferred frame is required;
b) tests to discover such a preferred frame have so far found nothing resembling that;
c) most Bohmians do not accept the premise of those tests in the first place (I believe their idea is that these tests apply to the G-R-W class of non-local theories but not the Bohmian);
d) some Bohmians do not advocate a preferred frame, and I believe Demystifier has written extensively on that possibility.

As to the Relativity of Simultaneity: If you accept an acausal interpretation such as RBW, that goes away as an issue. It also is not an issue if you simply accept the quantum formalism.

 

[DevilsAvocado]

A lot of the Bohmians believe there is such, a preferred frame. ...

Thanks for the info DrC. I continue my reasoning, and relate to some of the 'interpretation issues', in next post.

 

[DevilsAvocado]

No, that is just the same as saying that there is a "preferred reference frame". As RUTA said, there are people exploring that possibility, but I don't think it is necessary to resolve this issue.

Okay, I think DrC covers the 'basic'.

It is important to realize that this is strictly an interpretational "what is going on behind the scenes" question at this point. AFAIK, there is no way to make any testable predictions based on different theories of *how* the Bell inequality occurs (i.e. how particle A "knows" that a measurement was performed on particle "B").

Very true! I agree! (with 'some' objections below )

Most of the problems that are raised in this vein would only be real issues if FTL communication was possible using entangled pairs, but it's not, so we are ok. The causality relationship between the measurements at A and B is one example of this ... if it were somehow possible for Alice to know what Bob was doing at the time she made her measurement (assuming a space-like separation between them), then causality would be a problem, and you could potentially have a logical contradiction, because Alice would have access to information that was not available to all observers, i.e. she would be in a preferred reference frame. But that is equivalent to speculating about how things might change if SR is wrong ... as far as we know it isn't, so let's not worry about all of that .. physics is hard enough to understand as it is .

Okay, I know this is true, but I’m going to 'challenge' you a little (so you can show where I go wrong):

Let’s say Bob is a cruel bastard, and Alice is a cat. Bob have arranged a "Schrödinger Box" for Alice so that if the spin is up at Bob, and down at Alice, the "Box" will kill Alice!

Now, it’s hard to argue that Bob don’t know what Alice 'is doing'. He knows if she’s dead or alive...
(of course, Bob cannot control the outcome...)

To reiterate, from a QM point of view, there are two measurements performed on the members of an entangled pair. Since the results are always perfectly correlated, it fundamentally does not matter which measurement comes first, at least for the purposes of Bell tests.

I agree on the 'interpretation issues', but at the same time – if we cannot describe in fairly simple and understandable words what’s 'going on', and make logical attachments to current understandings – we’re in deep sh*t, IMO.

That would most probably mean that the true nature of the world is illogical, and that would be the worst outcome of all...

All observers in all frames agree on the results of the measurements, once they have communicated them by normal sub-lightspeed channels for comparison.

Well yes, but let’s have a look at the flip side of the coin... Let’s suppose we have arranged a Bell test where the photons run parallel, with a 'photon barrier' between them. Now, after x amount of time the photons hits the polarizer’s. Who is going to decide which one arrives first? The photons!? And if they arrives at exactly the same time (which they should do according to current understanding of physics)? Who is going to do the 'negotiation'?? "The United Council of Photons"?

This is a fairly simple logical problem. Two physically separated entities are going to obtain the opposite outcome 100% random, and ONLY ONE can decide. Who decides? And how is this accomplished on distances FTL?

It does not help if the observers agree. The photons must 'agree' first!

I don’t think this is an 'interpretation issues'. This must be at the 'core' of nature. And I don’t think mixing past, present & future, is going to help us much either.

The answer is most definitely not easy. Just let’s hope it’s logical...


Talking about interpretations, I found this IMO interesting video where Alain Aspect talks about EPR, Albert Einstein & Niels Bohr. Aspect concludes that Einstein & Bohr trusted their interpretations completely, but in the end John Bell showed that they were both wrong!

In the end of the video Anton Zeilinger talks about Quantum Teleportation (entanglement-assisted). Would you enter such a 'machine' without a fundamental understanding of the process?? Talk about FTL transfer/communication!?

Conference Clips With Scientists in Quantum Tamers (2)
https://www.youtube.com/watch?v=<object width="480" height="385"><param name="movie" value="http://www.youtube.com/v/m8P--jFe3vM&hl=en_US&fs=1&rel=0&color1=0x006699&color2=0x54abd6"></param><param name="allowFullScreen" value="true"></param><param name="allowscriptaccess" value="always"></param><embed src="http://www.youtube.com/v/m8P--jFe3vM&hl=en_US&fs=1&rel=0&color1=0x006699&color2=0x54abd6" type="application/x-shockwave-flash" allowscriptaccess="always" allowfullscreen="true" width="480" height="385"></embed></object>

 

[DevilsAvocado]

Here are the other 2 clips with Alain Aspect, Anton Zeilinger, Ray Laflame and Joseph Emerson at WCSJ 2009 London, providing more interesting 'aspects' on EPR, measurement and entanglement.

Conference Clips With Scientists in Quantum Tamers (1)
https://www.youtube.com/watch?v=<object width="480" height="385"><param name="movie" value="http://www.youtube.com/v/kWasiW_UiMI&hl=en_US&fs=1&rel=0&color1=0x006699&color2=0x54abd6"></param><param name="allowFullScreen" value="true"></param><param name="allowscriptaccess" value="always"></param><embed src="http://www.youtube.com/v/kWasiW_UiMI&hl=en_US&fs=1&rel=0&color1=0x006699&color2=0x54abd6" type="application/x-shockwave-flash" allowscriptaccess="always" allowfullscreen="true" width="480" height="385"></embed></object>

Conference Clips With Scientists in Quantum Tamers (3)
https://www.youtube.com/watch?v=<object width="480" height="385"><param name="movie" value="http://www.youtube.com/v/sLsFN3jQ1SE&hl=en_US&fs=1&rel=0&color1=0x006699&color2=0x54abd6"></param><param name="allowFullScreen" value="true"></param><param name="allowscriptaccess" value="always"></param><embed src="http://www.youtube.com/v/sLsFN3jQ1SE&hl=en_US&fs=1&rel=0&color1=0x006699&color2=0x54abd6" type="application/x-shockwave-flash" allowscriptaccess="always" allowfullscreen="true" width="480" height="385"></embed></object>

 

[Frame Dragger]

Interesting stuff, I've got to look over this later when I get the chance. Thanks DA, you know how to keep a fun discussion going.

 

[DevilsAvocado]

Thanks FD! Do check out the videos, interesting stuff!

(And I just love when Aspect, with French 'intensity', shouts – The wool! )

 

[eveo]

University of Waterloo! That's where I'm off to next year for nanotech engineering :D

 

[Frame Dragger]

University of Waterloo! That's where I'm off to next year for nanotech engineering :D

Hey, congrats on that!

 

[DevilsAvocado]

University of Waterloo! That's where I'm off to next year for nanotech engineering :D

Lucky you!

 

[eveo]

Thank you :D
Well, I'm still staying back a year to get higher marks and take a few extra courses to get an increase in scholarship funds :P

 

[SpectraCat]

Okay, I think DrC covers the 'basic'.


Very true! I agree! (with 'some' objections below )


Okay, I know this is true, but I’m going to 'challenge' you a little (so you can show where I go wrong):

Let’s say Bob is a cruel bastard, and Alice is a cat. Bob have arranged a "Schrödinger Box" for Alice so that if the spin is up at Bob, and down at Alice, the "Box" will kill Alice!

Now, it’s hard to argue that Bob don’t know what Alice 'is doing'. He knows if she’s dead or alive...

This "knowledge" is illusory ... if there is a space-like separation between Alice and Bob, then after he has made his measurement in his frame, he cannot know with certainty anything beyond the value of the measurement at Alice, and (this is crucial) he cannot know that Alice's measurement has even taken place until it has been confirmed on a "normal" communication band. The state of Alice's particle is not determined until it is measured, and he cannot be sure that Alice's measurement was not performed first, and that the value he measured was pre-determined because her measurement had already happened. This last point is what we really mean when we say that entangled pairs cannot be used for FTL communication.

Now, Bob may have tried to place external controls on Alice's environment by trapping her in a box with a death-device, but how did he set up the measurement that was to take place. Whatever arrangements he made, once he goes away to make his measurement (at a suitably large distance to make this test case meaningful and interesting), he can only assume without knowing that his arrangements went off without a hitch. Confirmation must wait for the information to arrive by normal light-speed comms.

(of course, Bob cannot control the outcome...)

Yep, and that's the point, as I mentioned above.

I agree on the 'interpretation issues', but at the same time – if we cannot describe in fairly simple and understandable words what’s 'going on', and make logical attachments to current understandings – we’re in deep sh*t, IMO.

Hmmm .. not sure why it should be 'simple and understandable' .. and to whom should it be so? What level of education and familiarity with physics should they have? How many years of schooling?

Well yes, but let’s have a look at the flip side of the coin... Let’s suppose we have arranged a Bell test where the photons run parallel, with a 'photon barrier' between them. Now, after x amount of time the photons hits the polarizer’s. Who is going to decide which one arrives first? The photons!? And if they arrives at exactly the same time (which they should do according to current understanding of physics)? Who is going to do the 'negotiation'?? "The United Council of Photons"?

This is a fairly simple logical problem. Two physically separated entities are going to obtain the opposite outcome 100% random, and ONLY ONE can decide. Who decides? And how is this accomplished on distances FTL?

See .. this is why you should have listened to your mother and not gotten involved with those seedy looking QM interpretations!

It does not help if the observers agree. The photons must 'agree' first!

I don’t think this is an 'interpretation issues'. This must be at the 'core' of nature. And I don’t think mixing past, present & future, is going to help us much either.

The answer is most definitely not easy. Just let’s hope it’s logical...

All joking aside, I guess I see what you are saying here, and suppose it might be a real issue. I am not sure, because I am not sure what "arriving at the same time" means in this context. I'll think about it some more, but it seems like the only way you might be able to define it absolutely is when both photons were impingent on the same detector. Even in that case I think you get into trouble with the HUP when you try to nail things down precisely for the two measurement events. Like I said .. I need to think about it more ...

On final point is that it seems to me that all of your objections are inherently local in character ... don't they all just go away if you accept that the wavefunction of the entangled pair is inherently non-local?

P.S. the vids look cool .. I will check them out when I have time

 

[Phrak]

I'm going to ressurect the opening question, hoping for insight:

Is action at a distance possible as envisaged by the EPR Paradox?

Is it action at a distance, or local action based on concepts of locality had by habitual and provably useful methods of mapping spacetime to a coordinate system with expectations extrapolated from Euclidean geometry?

 

[ThomasT]

All performed Bell test experiments clearly show that it’s impossible to use local 'entities', whether it’s variable or constant – it just doesn’t work, due to the fact that the receiving polarizer’s are randomly rotated *AFTER* the photons left the source...

Whether the polarizer settings are not varied during a run, or varied nonrandomly, or varied randomly, or varied randomly after emission, the result (the correlation between the angular difference of the polarizers and rate of coincidental detection) doesn't vary.

So, the fact that Bell's lhv ansatz "just doesn't work" is NOT "due to the fact that the receiving polarizers are randomly rotated 'AFTER' the photons left the source".

The problem with getting an lhv formulation that fits the experimental results has nothing to do with loopholes.

-------------------------

Try to come up with a set of data points for a Bell test in the Mermin format (I have that on one of my pages). So that is at 0, 120, 240 degrees. You will see that NO realistic theory - local or otherwise - can account for this. Just try to put together the dataset and you will quickly see none is possible. So that seems to rule out all hidden variable theories right there. Let's call this the MAIN RESULT: no hidden variable formulations are possible without outside help.

Ok, let's use a two photon setup where polarization entanglement is produced when two photons are emitted in opposite directions by the same atom. Due to conservation of angular momentum, they're polarized identically.

For the purpose of discussion we can assume an ideal setup (perfect efficiency, all loopholes closed).

The hidden variable is the polarization angle, and it's the same for each member of any pair of entangled photons (though it varies randomly from pair to pair).

Malus Law applies in this situation. We can denote the individual detection rates as,

P(A) = cos²(|a - L|) and
P(B) = cos²(|b - Ll|)

where a and b are polarizer settings and L is the polarization angle of the optical disturbances incident on a and b.

Since the average angular difference between the polarizer setting and L is 45^o, then the expected normalized individual detection rates are,

P(A) = .5 and
P(B) = .5

which agrees with QM prediction and experiment.

For the joint detection situation Malus Law also applies since we have crossed polarizers analyzing identically polarized optical emissions.

The relevant independent variable is the angular difference of the polarizer settings, |a-b|, which can be expressed as (||a-L| - |b-L||).

So, we can denoted the joint detection rate as

P(A,B) = cos²(||a-L| - |b-L||)

which agrees with QM prediction and experiment.


Even though this expression for the joint expectation, per se, doesn't explicate locality (as, say, Bell's ansatz purports to but actually doesn't), it is nonetheless a local hidden variable account of entanglement insofar as it (1) incorporates the hidden variable, and (2) the assumptions underlying it are in accord with the principle of local causality.

 

[zonde]

Well yes, but this is only your personal 'speculations', right? And I do think you got it somewhat wrong... check my https://www.physicsforums.com/showpost.php?p=2685669&postcount=108".

I do not see connection with your post #108 but yes this is my personal speculation that illustrates problems with your personal speculation about this overlapping effect.

About your statement in post #108

The superposition of the particle (photon) is when it passes both slits simultaneously.

Particle = superposition
Wavefunction <> superposition

From wikipedia - http://en.wikipedia.org/wiki/Superposition_principle" states that, for all linear systems,
The net response at a given place and time caused by two or more stimuli is the sum of the responses which would have been caused by each stimulus individually.

So I would restate what you said this way: The condition for superposition of the particle (photon) is that it should pass both slits concurrently.

You make the assumption that the pros making the experiments are 'fighting in the dark', to get some 'exiting results' to flash to the world... anything...

I do not make such assumption.

I’m not in the 'business', but I do know that if a scientist says "Hey! I can prove some weird stuff!", he or she is going to be scrutinized by a lot of very smart people, trying to find any weakness in the claim.

Of course there are swindlers, who make every effort to fool the whole world, but they are rare, and they do not survive the fight against reality, in the long run.

First, scientist do not to say things like "Hey! I can prove some weird stuff!" because they relay on http://en.wikipedia.org/wiki/Scientific_method" . They say things like "Results of experiment is in agreement with some weird hypothesis." This is because you can not prove theory with experiment but only disprove competing theories.

Second, you don't have to be considered swindler if you make some error. Everybody makes errors but not everybody is swindler.

There is nice picture that I spied in another thread:

So, what have we got? Well, we have a theory that all agrees is mathematical correct and reliable. This theory makes a prediction:

Either X is true or, Y or Z must be violated.

X = Local Hidden Variables
Y = Counterfactual Definiteness (Heisenberg Uncertainty Principle)
Z = Locality

You are not very careful with your statement.
The theory states that if X, Y, Z and determinism then certain inequalities hold.
Besides Counterfactual Definiteness is in conflict with Heisenberg Uncertainty Principle contrary to what you are implying.

Now, we know from the theory that X is not true if we accept that QM is a correct theory (and we all agree that QM is the most precise theory we have). To reverse X to true, we have to abandon QM, and start from scratch.

This is quite loose statement. There are things in QM that are not very strictly established like correspondence between certain things in mathematical formalism and physical reality. Because of that QM still can accommodate quite different interpretations.
So I would say that with some minor changes in interpretation it can still be compatible with (contextual) LHV.

Therefore, the most healthy choice between QM=true/X=false or QM=false/X=true, must naturally be QM=true/X=false.

Y (Heisenberg Uncertainty Principle) is a fundamental part of QM, which we have conclude true, then naturally Y must also be true!

All this is achieved by natural reasoning, common sense, and a very solid theory.

Now, when we start to perform Bell test experiments, every experiment indicates that Y or Z is violated!

What’s the most logical to do in this situation?? Well, it’s not start a "Denial Camp" to reintroduce X as true – it’s way too late for that!

We are getting the 'expected' results from the experimentalists, and it’s not sound to start questioning if the scientists making the experiments are 'retards' or 'swindlers'...

Come on!

Okay! Let’s start with not throwing the logic away in the evaluation of Bell test experiments!

 

[RUTA]

This is important and I have to be sure.

Causal locality
If we set LHV to be +1 & -1 before sending the photons, we are not violating any locality. It’s just a matter of sending away 'predefined letter' in an 'envelope', and we know the outcome in advance, right...?

Constitutive locality
The receivers of the 'envelope' are physically separated in space-time, i.e. they have no connection FTL, right...?

Causal locality is the "no FTL communication." Constitutive locality is that spacetime events are separable.

Okay, can we 'refine' this and say – According to SEP the 'cause' of EPR is not "spooky action at a distance", it’s 'something else', but SEP can’t say anything about that. (right?)

SEP "doesn't" say anything about what that "something else" is. I don't know that they "can't" say; the author of that definition of nonseparability might have some examples, but they didn't share them :-)

>> This is extremely interesting! <<
Wow! I thought we only had one "problem" with the "spooky action at a distance", but this proves it’s much worse²!

Let’s see now... IF we assume there ARE "spooky action at a distance" AND the values of the Particles are 100% RANDOM, and the OTHER Particle must obtain the OPPOSITE value instantly. THIS CAN’T BE DONE DUE TO RoS??

RoS doesn't bear on the nonseparability option. I was pointing out: FTL causes + RoS = a problem, because then you can have event A causing event B even though A occurs after B.

 

[DrChinese]

...
Malus Law applies in this situation. We can denote the individual detection rates as,

P(A) = cos²(|a - L|) and
P(B) = cos²(|b - Ll|)

where a and b are polarizer settings and L is the polarization angle of the optical disturbances incident on a and b.

Since the average angular difference between the polarizer setting and L is 45^o, then the expected normalized individual detection rates are,

P(A) = .5 and
P(B) = .5

which agrees with QM prediction and experiment.

For the joint detection situation Malus Law also applies since we have crossed polarizers analyzing identically polarized optical emissions.

The relevant independent variable is the angular difference of the polarizer settings, |a-b|, which can be expressed as (||a-L| - |b-L||).

So, we can denoted the joint detection rate as

P(A,B) = cos²(||a-L| - |b-L||)

which agrees with QM prediction and experiment.

Sorry, this most definitely does NOT agree with experiment and the math is wrong. In fact the coincidence rate varies between .25 and .75 per your example. Experiment has it varying between 0 and 1.

See where your P(A)=.5 and p(B)=.5? That is correct. But it does not lead to your result. For example, where A=0 and B=0, you will NOT get correlation of 100% UNLESS you have entangled photons. Unentangled photons would have the same math as you describe but yield Product statistics. They are NOT the same. Yet they should be, according to you.

This is a frequent mistake that folks make in attempting to come up with local hidden variable models. You must model BOTH of these following cases successfully:

a) Polarization entangled photon pairs yield perfect correlations and entangled state statistics (the cos^2(theta) rule);

b) Polarization UNentangled photon pairs - coming from the same PDC crystal as in a) - yield Product State statistics (.25 + .5(cos^2(theta)). With these, the polarization is known, which is why they are not entangled.

Your example models b) and not a). If I need to, I will be glad to derive this for you in a later post. Or you can do it, but you must put in the correct values for the expansion.

 

[ThomasT]

Sorry, this most definitely does NOT agree with experiment and the math is wrong. In fact the coincidence rate varies between .25 and .75 per your example.

I think you've got it backwards.

As the angular difference, |a - b| = ||a - L| - |b - L||, goes from 0^o to 90^o, the cos² of that angular difference goes from 1 to 0.

Experiment has it varying between 0 and 1.

The experiments I've seen have it varying between 0 and .5, and it never quite reaches those limits. It can't go to 1 if the individual detection rates never exceed .5 .

The correct expression for an idealized setup, normalized joint detection rate is, then,

.5 (cos²(|a-b|) ,

which would be modified depending on whatever inefficiencies are involved in the actual production of the data.

By the way, the normalization is wrt the detection rate with no polarizers present.

See where your P(A)=.5 and p(B)=.5? That is correct. But it does not lead to your result.

It can't. Isn't that what we've been discussing?

For example, where A=0 and B=0, you will NOT get correlation of 100% UNLESS you have entangled photons. Unentangled photons would have the same math as you describe but yield Product statistics. They are NOT the same. Yet they should be, according to you.

If you mean A and B to refer to detection rates, then the normalized individual rates with polarizers in place at both ends is always, in the ideal, A = .5 and B = .5 . If not, then I don't know what you're saying.

a) Polarization entangled photon pairs yield perfect correlations and entangled state statistics (the cos^2(theta) rule);

b) Polarization UNentangled photon pairs - coming from the same PDC crystal as in a) - yield Product State statistics (.25 + .5(cos^2(theta)). With these, the polarization is known, which is why they are not entangled.

Your example models b) and not a).

It accounts for a) in the assumptions underlying the application of Malus Law and the model(s) of the production of the entanglement via the emission process. Keep in mind that the perfect correlation/anticorrelation corresponding to angular differences of 0^o and 90^o have always been explainable assuming a local common cause for the entanglement.

 

[RUTA]

AFAICS, RoS is a non-issue for this case.

Correct, RoS doesn't bear on nonseparability. It does, of course, bear on the nonlocality issue, as I pointed out in post #140.

There is no question of causality here, only comparison of measurement. There is no logical inconsistency in a frame where B was measured before A or vice-versa, because the results are perfectly correlated.

QM predicts the correlations between space-like separated experimental outcomes that violate Bell inequalities, that's not the issue. The question QM doesn't answer is, "What is the nature of reality such that correlations between space-like separated experimental outcomes violate Bell inequalities?" For some people, the answer is FTL communication between the measurement events. For those people, RoS becomes an issue.

IOW, if you measure B first, you determine the value of A, if you measure A first, you determine the value of B. This holds in all frames, for all observers, so IMO there is no problem.

The problem with "if you measure B first, you determine the value of A" when A and B are space-like separated is that, per RoS, there is no absolute temporal ordering of A and B. So, what does "if you measure B first" really mean?

Furthermore, when observers in different frames compare answers (as is required for a Bell test), they may disagree on the ordering of events, but they will always agree that there is a Bell violation for the results.

Correct.

 

[RUTA]

To reiterate, from a QM point of view, there are two measurements performed on the members of an entangled pair. Since the results are always perfectly correlated, it fundamentally does not matter which measurement comes first, at least for the purposes of Bell tests. All observers in all frames agree on the results of the measurements, once they have communicated them by normal sub-lightspeed channels for comparison.

The strange nature of the correlated outcomes is not illucidated by the measurements for which there is 100% correlation alone. One can imagine there is a "fact of the matter" for the outcomes corresponding to those measurement settings (like settings). But, if you assume there is a "fact of the matter" for the outcomes corresponding to like settings (in order to account for the 100% correlation), then you don't obtain the correct (QM predicted) correlation rate for outcomes in unlike settings. Thus, some people invoke FTL communication of settings between measurements so the particles can "give the right outcomes" no matter how they're measured.

 

[DrChinese]

I think you've got it backwards.

As the angular difference, |a - b| = ||a - L| - |b - L||, goes from 0^o to 90^o, the cos² of that angular difference goes from 1 to 0.

The experiments I've seen have it varying between 0 and .5, and it never quite reaches those limits. It can't go to 1 if the individual detection rates never exceed .5 .

The correct expression for an idealized setup, normalized joint detection rate is, then,

.5 (cos²(|a-b|) ,

which would be modified depending on whatever inefficiencies are involved in the actual production of the data.

By the way, the normalization is wrt the detection rate with no polarizers present.

It can't. Isn't that what we've been discussing?

If you mean A and B to refer to detection rates, then the normalized individual rates with polarizers in place at both ends is always, in the ideal, A = .5 and B = .5 . If not, then I don't know what you're saying.

No. It models a). Keep in mind that the perfect correlation/anticorrelation corresponding to angular differences of 0^o and 90^o have always been explainable assuming a local common cause for the entanglement.

OK, first let's agree that there are 2 types of PDC. We can discuss either one, but I personally think it is easier to discuss Type I. With Type I, both photons have identical polarization. With Type II, the photons have anti-symmetric/orthogonal/crossed/opposite polarization.

It makes no difference to the result whether we are going from 0 to 1 or 1 to 0, when moving from 0 to 90 degrees apart. So I will use the Type I example.

Second: the joint detection rate is NOT cos^2(theta) in your example. It is actually .25+.5(cos^2(theta)) which is obviously different. This is the Product State statistics.

Remember: we are talking about your example. IF you take a pair of PDC photons at any KNOWN angle (the hypothesized L in your example) and actually check their polarizations at any angle settings A and B, THEN you will get .25+.5(cos^2(A-B)). That is an experimental fact.

What may be confusing is that PDC photon pairs can come out either polarization entangled or not. Either way, they have identical polarization! If the polarization is known, it is not entangled. You hypothesize that there is a definite polarization L associated with the photons. If there were such, then the expected statistics are PRODUCT state.

If, on the other hand, you specify that there is no definite polarization L, then you would have entanglement. But of course, then you would be accepting that no LHV can reproduce the predictions of QM - exactly what you wish to avoid. Of course, everyone else (save a diehard few) already accepts this.

 

[DrChinese]

Keep in mind that the perfect correlation/anticorrelation corresponding to angular differences of 0^o and 90^o have always been explainable assuming a local common cause for the entanglement.

Yes and No. YES: there have been models that could explain some situations such as these special cases. But NO: your model is NOT one of those. Those models are different. In effect, they postulate that there are a large (and perhaps infinite) number of hidden variables associated with the range of polarization settings. For simplicity, imagine that there is: HV(1), HV(2),... HV(359, HV(360).

Of course, this model "fixes" the problem with your model. But at a cost. Because now you just fell prey to Bell and the problem of being able to provide a realistic resultset for the 3 angles I specified (0/120/240 a la Mermin). You cannot do it - but please feel free to try!

 

[RUTA]

Ok, let's use a two photon setup where polarization entanglement is produced when two photons are emitted in opposite directions by the same atom. Due to conservation of angular momentum, they're polarized identically.

For the purpose of discussion we can assume an ideal setup (perfect efficiency, all loopholes closed).

The hidden variable is the polarization angle, and it's the same for each member of any pair of entangled photons (though it varies randomly from pair to pair).

Malus Law applies in this situation. We can denote the individual detection rates as,

P(A) = cos²(|a - L|) and
P(B) = cos²(|b - Ll|)

where a and b are polarizer settings and L is the polarization angle of the optical disturbances incident on a and b.

Since the average angular difference between the polarizer setting and L is 45^o, then the expected normalized individual detection rates are,

P(A) = .5 and
P(B) = .5

which agrees with QM prediction and experiment.

For the joint detection situation Malus Law also applies since we have crossed polarizers analyzing identically polarized optical emissions.

The relevant independent variable is the angular difference of the polarizer settings, |a-b|, which can be expressed as (||a-L| - |b-L||).

So, we can denoted the joint detection rate as

P(A,B) = cos²(||a-L| - |b-L||)

which agrees with QM prediction and experiment.

Even though this expression for the joint expectation, per se, doesn't explicate locality (as, say, Bell's ansatz purports to but actually doesn't), it is nonetheless a local hidden variable account of entanglement insofar as it (1) incorporates the hidden variable, and (2) the assumptions underlying it are in accord with the principle of local causality.

I don't see how you obtained your P(A,B) other than by fiat.

Suppose you say the photons pass a polarizer (vertically polarized wrt the setting, typically denoted V) if their polarization L is within 45 deg of the setting. Between 45 deg and 90 deg the photons are blocked (horizontally polarized wrt the setting, typically denoted H). This is a reasonable assumption and leads to an overall 50% rate for V at each detector. Now, what is the probability of a VV outcome for settings A and B? The answer is 0.5 - |A - B|/pi, which you can obtain by simply drawing the 45-deg cones about settings A and B and looking at their overlap. For a detailed explanation, see equation 19, p 907, of section VIII. Local Realistic Hidden Variable Theory, in "Entangled photons, nonlocality, and Bell inequalities in the undergraduate laboratory," Dietrich Dehlinger and M.W. Mitchell, Am. J. Phys. 70 (9), Sep 2002.

 

[ThomasT]

OK, first let's agree that there are 2 types of PDC. We can discuss either one, but I personally think it is easier to discuss Type I. With Type I, both photons have identical polarization. With Type II, the photons have anti-symmetric/orthogonal/crossed/opposite polarization.

It makes no difference to the result whether we are going from 0 to 1 or 1 to 0, when moving from 0 to 90 degrees apart. So I will use the Type I example.

Second: the joint detection rate is NOT cos^2(theta) in your example. It is actually .25+.5(cos^2(theta)) which is obviously different. This is the Product State statistics.

Remember: we are talking about your example. IF you take a pair of PDC photons at any KNOWN angle (the hypothesized L in your example) and actually check their polarizations at any angle settings A and B, THEN you will get .25+.5(cos^2(A-B)). That is an experimental fact.

What may be confusing is that PDC photon pairs can come out either polarization entangled or not. Either way, they have identical polarization! If the polarization is known, it is not entangled. You hypothesize that there is a definite polarization L associated with the photons. If there were such, then the expected statistics are PRODUCT state.

If, on the other hand, you specify that there is no definite polarization L, then you would have entanglement. But of course, then you would be accepting that no LHV can reproduce the predictions of QM - exactly what you wish to avoid. Of course, everyone else (save a diehard few) already accepts this.

If you reread the post where I introduced this you'll see that I wasn't talking about SPDC photons.

The counter-propagating photons emitted by the same atom in my example are always entangled in polarization due to conservation of angular momentum. This entanglement means that members of an entangled pair are polarized identically. However, the value of L, the polarization angle of any given pair, is varying randomly.

 

[ThomasT]

I don't see how you obtained your P(A,B) other than by fiat.

Not by fiat. Malus Law is applied and the angular difference is simply rendered in terms of the hidden variable.

 

[RUTA]

Not by fiat. Malus Law is applied and the angular difference is simply rendered in terms of the hidden variable.

Why did you apply Malus Law?