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

[DrChinese]

JenniT, I’m sure you mean well, but I can guarantee you that mathematics is not a problem for my_wan.

And yet I get confused by the references my_wan makes to ensembles that add to more than 100%. Maybe JenniT's point is worthy, and if not for my_wan, maybe someone else. Because if you start from a local realistic perspective, you must agree to the mathematical ground rules before Bell makes sense. EPR said these ground rules are "reasonable" as an initial hypothesis, and I agree.

So the first point is: Imagine 360 degrees in a circle. For any of the 360: If you ask the same question of Alice and Bob, you get the same answer. Of course, saying there are 360 possible questions is arbitrary, you could just as easily say a billion. The important thing is that these entangled pairs are polarization clones of each other. We don't know the "how", but we can see that they are.

 

[DevilsAvocado]

And yet I get confused by the references my_wan makes to ensembles that add to more than 100%.

That’s a reasonable point. Not to mess things up, I think it’s safest if my_wan answers the question regarding 'confusion' on "more than 100%".

 

[DrChinese]

Now once you agree that Alice and Bob are ENTANGLED, i.e. they are clones of each other and always yield the same answer to the same question, then you ask: HOW can that happen?

There are 3 basic ways:

a) All measurements give the same answers. We know this isn't true because ONLY entangled pairs have this property, and the answers appear random. So "lucky" guesses are ruled out. If you have collusion between the observers, then this can be gamed. So you have to convince yourself this case is not happening. This is usually handled by a proper experimental setup.

b) Alice and Bob are clones of each other, but otherwise are completely independent. They are local/separate and must therefore have ALL the answers encoded in advance a la EPR. This is the case Bell addresses.

c) Alice and Bob are in communication with each other somehow, and so when Alice answers a question, she shares her answer with Bob. Bell does not address this case. Now, there are other ways to get this result besides instantaneous action-at-a-distance, such as retrocausal and other interpretations. I don't want to discuss any of these in this thread if it can be avoided.

 

[my_wan]

And yet I get confused by the references my_wan makes to ensembles that add to more than 100%.

It's not just 'an' ensemble. In defining an "element of reality" via realism, the argument involves not only the ensemble, but the the set of individual elements that defines that ensemble, and the differences that occur when you switch from detector event "element" counts and individual photon defined count of elements of reality. If the detector count is double counting certain photons, through couterfactual assumptions, then I am removing "ensembles that add to more than 100%". Only the elements of my ensembles is photons, not detector events. To use detector events the photon double counts must be calced, which your negative probabilities can be interpreted as a count of. I've already pointed out your negative "probabilities" are not "probabilities, but case instances, i.e., elements, derived as individual case instances from a probability function. As well as the fact that the definition of those case instances are: when a detection occurs in one, but not neither or both, detectors.

Thus your proof depends on the existence of negative [strike]probabilities[/strike] possibilities. Whereas the interpretation I suggested removes them when the set of individual elements that defines the ensemble is properly counted.

 

[ThomasT]

Thank you ThomasT, but I am confused. Probably I misunderstand your stand on BT? Are you saying Yes (it is irrefutable, it stands forever), Yes, No, Yes? Is your position logical with your other posts? What about

Q1. Are A and B correlated in EPR settings?

Q2. Does Bell use P(AB|H) = P(A|H).P(B|H)?

Q3. Is P(AB|H) = P(A|H).P(B|H) invalid when A and B are correlated?

Q4. Is the mathematical legitimacy of Bell's theorem debatable?

You asked if the mathematical legitimacy of Bell's theorem is irrefutable. The mathematical form of Bell's theorem is the Bell inequalities, and they are irrefutable. Their physical meaning, however, is debatable.

In order to determine the physical meaning of the inequalities we look at where they come from, Bell's locality condition, P(AB|H) = P(A|H)P(B|H).

Then we can ask what you asked and we see that:
1. A and B are correlated in EPR settings.
2. Bell uses P(AB|H) = P(A|H)P(B|H)
3. P(AB|H) = P(A|H)P(B|H) is invalid when A and B are correlated.

Conclusion: The form, P(AB|H) = P(A|H)P(B|H), cannot possibly model the experimental situation. This is the immediate cause of violation of BIs based on limitations imposed by this form.

What does this mean?

P(AB|H) = P(A|H)P(B|H) is the purported locality condition. Yet it is first the definition of statistical independence. The experiments are prepared to produce statistical dependence via the measurement of a relationship between two disturbances by a joint or global measurement parameter in accordance with local causality.

Bell inequalities are violated because an experiment prepared to produce statistical dependence is being modeled as an experiment prepared to produce statistical independence.

Bell's theorem says that the statistical predictions of qm are incompatible with separable predetermination. Which, according to certain attempts (including mine) at disambiguation, means that joint experimental situations which produce (and for which qm correctly predicts) entanglement stats can't be viably modeled in terms of the variable or variables which determine individual results.

Yet, per EPR elements of reality, the joint, entangled, situation must be modeled using the same variables which determine individual results. So, Bell rendered the lhv ansatz in the only form that it could be rendered in and remain consistent with the EPR meaning of local hidden variable.

Therefore, Bell's theorem, as stated above by Bell, and disambiguated, holds.

Does it imply nonlocality -- no.

 

[DrChinese]

It's not just 'an' ensemble. In defining an "element of reality" via realism, the argument involves not only the ensemble, but the the set of individual elements that defines that ensemble, and the differences that occur when you switch from detector event "element" counts and individual photon defined count of elements of reality. If the detector count is double counting certain photons, through couterfactual assumptions, then I am removing "ensembles that add to more than 100%". Only the elements of my ensembles is photons, not detector events. To use detector events the photon double counts must be calced, which your negative probabilities can be interpreted as a count of. I've already pointed out your negative "probabilities" are not "probabilities, but case instances, i.e., elements, derived as individual case instances from a probability function. As well as the fact that the definition of those case instances are: when a detection occurs in one, but not neither or both, detectors.

Thus your proof depends on the existence of negative [strike]probabilities[/strike] possibilities. Whereas the interpretation I suggested removes them when the set of individual elements that defines the ensemble is properly counted.

I guess I have a different idea of what double counting is. If Alice is counted once and only once, that is good and is not double counting. On the other hand, Alice may be "counterfactually" counted an infinite number of times, and this too is OK as long as the H case and the V case add to 100% for each of the counterfactual cases.

I don't know what you are implying when you say something about "when a detection occurs in one, but not neither or both, detectors". We are discussing the ideal case, so every photon is counted somewhere a single time.

 

[DrChinese]

In order to determine the physical meaning of the inequalities we look at where they come from, Bell's locality condition, P(AB|H) = P(A|H)P(B|H).

Then we can ask what you asked and we see that:
1. A and B are correlated in EPR settings.
2. Bell uses P(AB|H) = P(A|H)P(B|H)
3. P(AB|H) = P(A|H)P(B|H) is invalid when A and B are correlated.

This is not correct because it is not what Bell says. You are mixing up his separability formula (Bell's 2), which has a different meaning. Bell is simply saying that there are 2 separate probability functions which are evaluated independently. They can be correlated, there is no restiction there and in fact Bell states immediately following that "This should equal the Quantum mechanical expectation value..." which is 1 when the a and b settings are the same. (This being the fully correlated case.)

 

[Dmitry67]

Ta-da! Aaaaaand the winner is... MWI !

As I said, show me one 'postcard' from any of those +centillion¹⁰⁰⁰ parallel universes, and I’m on the train!

Show me objects behind the cosmological horizon in the telesope, or I claim that nothing exists behind it :)

Do you believe that Universe ends behind the horizon just because we can't see these obejcts (and will never see in some models)? No, you extrapolate the laws of physics to these areas. Exactly what I do.

 

[RUTA]

Show me objects behind the cosmological horizon in the telesope, or I claim that nothing exists behind it :)

Do you believe that Universe ends behind the horizon just because we can't see these obejcts (and will never see in some models)? No, you extrapolate the laws of physics to these areas. Exactly what I do.

I don't think these are equivalent situations. You don't need anything to exist beyond the particle horizon in cosmology to explain what you see within the particle horizon, GR is a local theory (in the sense of differential geometry). In MWI the existence of the extra universes is germane to the explanation.

The main problem I have with MWI is that pointed out by Adrian Kent, "Theory Confirmation in One World and its Failure in Many" (http://www.perimeterinstitute.ca/Events/The_Clock_and_the_Quantum/Plenary_Talks/ ). If you really believe MWI, then you have to admit that there's no way you can ever safely infer the "correct" distribution for experimental outcomes because there's no way to know which branch you reside in.

 

[Dmitry67]

I have what to reply, but I don't want to hijack the thread with MWI.
But what is your personal opinion, how do you explain everything?

 

[RUTA]

I have what to reply, but I don't want to hijack the thread with MWI. But what is your personal opinion, how do you explain everything?

This paper (arXiv 0908.4348) explains where I'm at. It's been accepted for presentation at PSA 2010 and was revised and resubmitted to FoP (decision pending). If you don't want to bother with the formalism (it's messy, discrete path integral over graphs), just look at Figures 1-4.

 

[Dmitry67]

RUTA, thank you. THis is interesting, especially:

Probably the most important aspect of the RBW ontology for the
interpretation of quantum physics is that there are no “quantum Clusters,” so there
are no “quantum Objects,” i.e., all Objects are classical and quantum physics is an
exploration of their relational “composition” (Figure 4). This is in stark contrast to
those interpretations of quantum physics which employ dynamical ontological
constituents of the essentially quantum realm (particles, waves, wave-functions,
fields, etc.) with their strange non-commutative properties and struggle to somehow
compose or realize the essentially classical realm of dynamical ontological
constituents with commutative properties. Thus, there simply is no possibility of a
measurement problem(21) on our view (a problem driven by taking quantum
dynamics realistically), and quantum non-separability is ultimately explained
kinematically by the unity of spacetimematter

So it is in the same camp as SM where macroscopic realty is axiomatic.

Could you answer the list of standard questions for any Interpretation for BRW:

http://en.wikipedia.org/wiki/Interpretation_of_quantum_mechanics#Comparison

If possible?

 

[DevilsAvocado]

Show me objects behind the cosmological horizon in the telesope, or I claim that nothing exists behind it :)

I think RUTA answers the question neatly (thanks RUTA). Personally I think there’s a huge difference between "much more of the same" and "a magic box where anything is possible, including Boltzmann brains".

And in one of those +centillion¹⁰⁰⁰ parallel universes, I must live forever (escaping every last heart attack into a parallel universe) and have proven MWI wrong, right??

 

[Dmitry67]

I think RUTA answers the question neatly (thanks RUTA). Personally I think there’s a huge difference between "much more of the same" and "a magic box where anything is possible, including Boltzmann brains".

And in one of those +centillion¹⁰⁰⁰ parallel universes, I must live forever (escaping every last heart attack into a parallel universe) and have proven MWI wrong, right??

No, there is no difference: in truly infinite universe there are exact copies of you (Max Tegmark had even calculated a distance). In infinite Universe all possibilites are real - you just need to go far enough to find the same Earth where you got a Nobel prize or where you spent all your time in prison for armed robbery and murder.

Unifinite Universe with randomness is equivalent in some sense to MWI, because in both cases it forms FULL UNIVERSUM of all options. But for people (beginning from Newton) it was much easier to accept spatial infinity than other types of infinities.

 

[RUTA]

Could you answer the list of standard questions for any Interpretation for RBW:

http://en.wikipedia.org/wiki/Interpretation_of_quantum_mechanics#Comparison

If possible?

"Deterministic?" As you can see in Figures 1-4, we assume there may well be a definite collection of relations comprising the experimental equipment, but it's impossible to know exactly what all those relations are in practice. As an analogy, different distributions of velocities for the atoms in a gas can give rise to the same pressure and temperature; it's impossible to know what all the velocities are in any particular distribution in practice. So, in doing QM one is simply asking for the probability of finding a particular relation in a particular trial.

"Wave function real?" No.

"Unique history?" Yes.

"Hidden variables?" Uh, yes and no. There is a fact of the matter concerning the experimental equipment, but there is no "screened-off quantum entity" moving through the device, so the "hidden variables," if you want to use that language, would pertain to the experimental equipment.

"Collapsing wavefunctions?" No.

"Observer role?" Computationally, no. Ontologically, yes, because there is no "God's eye view" of a relational reality -- any observer must be part of that which he observes in a relational reality.

 

[Dmitry67]

In general, the answers are the same (with few minor corrections) as SM?

I would even add:
Macroscopic events are basic irreductable notions - SM-Yes, BRW-Yes.

 

[DevilsAvocado]

... to find the same Earth where you got a Nobel prize ...

This sound like a perfect a theory for me!

()

 

[GeorgCantor]

"Observer role?" Computationally, no. Ontologically, yes, because there is no "God's eye view" of a relational reality -- any observer must be part of that which he observes in a relational reality.

It's as if i heard my full name being called out, when i read this. I think there is only one way to 'interpret' the DCE - it must be about the observer's knowledge of the system being measured. And the fact that the measured 'particles' appear to violate both the concepts of time and space, i think you put it right - 'the observer', there is likely just one. Einstein's relativity favors your position nicely, it's only the common-sense that bent to Hell. Most physicists are very naive; most still believe in real waves or particles. This last statement was made by Zeilinger, though.

 

[RUTA]

In general, the answers are the same (with few minor corrections) as SM?

I would even add:
Macroscopic events are basic irreductable notions - SM-Yes, BRW-Yes.

These are very different interpretations, formally and ontologically. In SM, one uses the free-particle propagator. From section 3.4 of 0908.4348, "We point out again that conventional NRQM uses the free-particle propagator for this case while our two-source amplitude is obtained via the discrete, free (Gaussian) theory fundamental to QFT." And SM is applicable only to non-relativistic QM while our path integral is Poincare invariant (see section 4.3).

 

[RUTA]

It's as if i heard my full name being called out, when i read this. I think there is only one way to 'interpret' the DCE - it must be about the observer's knowledge of the system being measured. And the fact that the measured 'particles' appear to violate both the concepts of time and space, i think you put it right - 'the observer', there is likely just one. Einstein's relativity favors your position nicely, it's only the common-sense that bent to Hell. Most physicists are very naive; most still believe in real waves or particles. This last statement was made by Zeilinger, though.

This illustrates your point nicely. From quant-ph/0505187:

Thomas Jennewein: Quoting A.Z., "Photons are just clicks in photon detectors; nothing real is traveling from the source to the detector." — But what about the energy flowing from the source to the detector?

 

[GeorgCantor]

This illustrates your point nicely. From quant-ph/0505187:

Thomas Jennewein: Quoting A.Z., "Photons are just clicks in photon detectors; nothing real is traveling from the source to the detector." — But what about the energy flowing from the source to the detector?

Whoever asked the question about "energy flowing from the source to the detector" must have meant the relativistic "energy flowing from the source to the detector" that can't be unambiguously quantified in a universal frame of reference. Without a context(observer in a FOR), it seems to make very little sense to talk about particular values of measured entities. But conservation laws still apply, the question is how?

What is your opinion on this question?

 

[RUTA]

Whoever asked the question about "energy flowing from the source to the detector" must have meant the relativistic "energy flowing from the source to the detector" that can't be unambiguously quantified in a universal frame of reference. Without a context(observer in a FOR), it seems to make very little sense to talk about particular values of measured entities. But conservation laws still apply, the question is how?

What is your opinion on this question?

Even if you go to M4, as you say, there is the divergence-free nature of the stress-energy tensor to satisfy (local conservation of energy and momentum). The question Jennewein is raising: How can Zeilinger satisfy local conservation principles with his picture? I don't know whether Zeilinger has answered that question.

RBW is fundamentally nonseparable and the separability of classical physics holds only as a statistical approximation, so you'll only have a divergence-free SET when the classical approximation is valid.

 

[DevilsAvocado]

If the wave function is not real, then how do we explain http://en.wikipedia.org/wiki/Afshar_experiment" ??

 

[RUTA]

If the wave function is not real, then how do we explain http://en.wikipedia.org/wiki/Afshar_experiment" ??

As I told DrC in his thread on this subject, in these experiments you construct the wave function for the entire set up -- source, screen, lens, grid, mirrors, detectors. You don't need a story involving any'thing' in addition to the experimental equipment to construct the distribution amplitude of outcomes.

 

[my_wan]

I went through a whole battery of test of LHV. The only one I found to work depended on the polarization of 1 of the detectors to be defined as a 0 angle. Once this condition is imposed, it works without either detector using any information about the other detectors settings. If detector A setting is defined 0 degrees, that could still be 2 different settings as far as the information provided detector B, and B could still be anything from the information provided to A.

It could be argued that this condition implicitly includes the other polarizer setting. But there's a problem with that also. It includes no more information than what can be obtained from a specific photon polarization, knowing that the other is perfectly anti-correlated. Thus not even a FTL mechanism would include more information than can be obtained from a specific correlated/anti-correlated polarization of the photon itself. It seems to be a coordinate property itself.

This could be interpreted as a conflict between coordinate independence and finite non-contextual realism. Any opinions on this issue with LHV's working if we arbitrarily define a 0 setting for 1 detector, or how a FTL mechanism can possibly provide more information than what this does?

 

[zonde]

I went through a whole battery of test of LHV. The only one I found to work depended on the polarization of 1 of the detectors to be defined as a 0 angle.

Why do you think this should work?
To test Bell or let's say rather CHSH inequalities you have to change settings of polarizer. Once you change settings for your reference polarizer then if you change your reference so that new settings remain 0 angle you have to transform whole setup including source (and including photons in transit).
Anyways how does it help with hypothetical additional (counterfactual) measurements that clearly lead to contradictions?

 

[my_wan]

Why do you think this should work?
To test Bell or let's say rather CHSH inequalities you have to change settings of polarizer. Once you change settings for your reference polarizer then if you change your reference so that new settings remain 0 angle you have to transform whole setup including source (and including photons in transit).
Anyways how does it help with hypothetical additional (counterfactual) measurements that clearly lead to contradictions?

Yes, true. It has to do with the way the photon is defined in the model I used. The photon number began with a random polarization and a 180 digit binary number, 1 for each 1/2 degree polarization over 90 degrees. Reversed for some angles over 90 degrees. The photon was assumed to have a particular polarization, defined such that a polarizer at that same angle essentially had a 100% chance of passing that polarizer. If the polarizer detector was offset from that photon polarization, say 22.5 degrees, the binary number at that location had ~85% chance of being a 1 at that binary offset for any given random photon.

The 0 polarization definition condition essentially meant that the side of the formula that was non-zero used the relative offset between the 2 detectors. The 0 setting always returned the first column in the binary number, while the other returned essentially the binary relative offset. Thus any relative settings could be used, as long as 1 of them was defined to be zero.

Any attempt at retrieving the relative offset from settings without a defined 0 polarizer setting required information about the other polarizer setting. Thus this is a situation where, in order for nature to be coordinate independent, only relative settings are meaningful. Yet, for the math to work with finite absolute variables, requires 1 of 2 special coordinate choices. From this perspective, it could be said that coordinate independence requires either a violation of Bell's inequalities, or very different empirical results, from physically identical experiments, simply due to a change in coordinate choices.

I still may be missing something, but I attempted to make only half binary bit in the first column 1's, such that only those with 1's in that location were detected and counted at that detector setting. The detection statistics wouldn't balance out properly to violate Bell's inequalities under arbitrary settings, without or without a 0 degree polarizer setting. These are still absolute finite variables I presupposed, with contextually defined solely in terms of which absolute variables in a set was read. Under relativity this quantization of contextually doesn't follow, but under QM it could in principle.

With these hidden variables it's trivial to define 1 detector or the other as 0 degrees using the photon polarization offset from the first pair of correlated photons at 1 detector, and the perfect anti-correlation defines where that same 0 angle is at the other detector. Thus it's extremely hard to define how a FTL 'real' mechanism would provide more information than already contained here. Which leads me in other directions.

I wonder what classical analogs can be defined, using just coordinate independence and relativity?

 

[DrChinese]

Yes, true. It has to do with the way the photon is defined in the model I used. The photon number began with a random polarization and a 180 digit binary number, 1 for each 1/2 degree polarization over 90 degrees. Reversed for some angles over 90 degrees. The photon was assumed to have a particular polarization, defined such that a polarizer at that same angle essentially had a 100% chance of passing that polarizer. If the polarizer detector was offset from that photon polarization, say 22.5 degrees, the binary number at that location had ~85% chance of being a 1 at that binary offset for any given random photon.

The 0 polarization definition condition essentially meant that the side of the formula that was non-zero used the relative offset between the 2 detectors. The 0 setting always returned the first column in the binary number, while the other returned essentially the binary relative offset. Thus any relative settings could be used, as long as 1 of them was defined to be zero.

Any attempt at retrieving the relative offset from settings without a defined 0 polarizer setting required information about the other polarizer setting. ...

I still may be missing something, but I attempted to make only half binary bit in the first column 1's, such that only those with 1's in that location were detected and counted at that detector setting. The detection statistics wouldn't balance out properly to violate Bell's inequalities under arbitrary settings, without or without a 0 degree polarizer setting. These are still absolute finite variables I presupposed, with contextually defined solely in terms of which absolute variables in a set was read. Under relativity this quantization of contextually doesn't follow, but under QM it could in principle.

With these hidden variables it's trivial to define 1 detector or the other as 0 degrees using the photon polarization offset from the first pair of correlated photons at 1 detector, and the perfect anti-correlation defines where that same 0 angle is at the other detector. Thus it's extremely hard to define how a FTL 'real' mechanism would provide more information than already contained here. Which leads me in other directions.

Good work on creating the simulation. I think these are very helpful in seeing how constraining the Bell work is. That 85% you mention for 22.5 degrees is still 10% too high for local realism (which has a limit of 75%). In other words, your model will show an unusually low correlation between 22.5 degrees and 45 degrees - one which is less than 75% and therefore substantially different than the expected 85% (since 0/22.5 cases should match the 22.5/45 degree cases on average).

You should be able to conclude that your model cannot provide pairs that match the QM rates for arbitrary pairs of angles. Having your model work for 0 degrees is tantamount, of course, to signaling Alice's setting to Bob (which we wish to avoid).

Thanks for taking the time out to run this.

 

[my_wan]

Good work on creating the simulation. I think these are very helpful in seeing how constraining the Bell work is. That 85% you mention for 22.5 degrees is still 10% too high for local realism (which has a limit of 75%). In other words, your model will show an unusually low correlation between 22.5 degrees and 45 degrees - one which is less than 75% and therefore substantially different than the expected 85% (since 0/22.5 cases should match the 22.5/45 degree cases on average).

You should be able to conclude that your model cannot provide pairs that match the QM rates for arbitrary pairs of angles. Having your model work for 0 degrees is tantamount, of course, to signaling Alice's setting to Bob (which we wish to avoid).

Thanks for taking the time out to run this.

This kind of begs the question of what constitutes FTL. I agree that on the surface requiring 0 degrees appears tantamount to signaling Alice's setting to Bob. Yet the information to do that, at least in principle, is contained in the default polarizations of the photon (sort of). Consider 2 factors here, above and this:

When you define 2 arbitrary polarizations, such as 22.5 and 30, this already requires using a common coordinate where both detectors agree on where the settings representing 22.5, 30 and all other settings, including 0 is. So even arbitrary setting requires FTL information of some sort, albeit predefined. We don't consider this FTL because space has covariant symmetries wrt various coordinate systems. Yet, in the EPR case, relative covariance is maintained, i.e., difference in detector settings, but covariance with the numerical labels we put on that coordinate system is broken. It makes our coordinate system look broken in this respect.

I don't care for this, but, extra spatial dimensions can produce this effect. I personally think it's more likely points on our coordinate system are not distinct points, but dynamic vectorial creations (real wavefunction sort of). This, of course, begs the question of why the unit vectors in Hilbert space, in QM, and still allow the limits of calculus.

The way I constructed the HV's in the photons allows any level of violation of Bell's inequalities. I defined photons by a default polarization, followed by a binary digit for each angle available to the detector. So a random number generator, min/max=0/1, that exceeded the Malus' Law for that angle was set to 0. So I did match the QM rates for any arbitrary angle 'difference', but only when the difference was definable. This begs the question, paragraph 2, why the coordinate independent difference requires FTL when 2 coordinate system that must share the same definition of any angle does not. Given the way I defined a default photon polarization, that hits any polarizer at some angle, getting through or not, and the fact that the other photon had exactly the opposite polarization, then a polarization of each detector independently is defined by HV of the photons that hit them. All the information is there, and all that is required to calculate violations of Bell's inequalities is to choose 1 to call 0. It doesn't even matter which 1 is labeled 0, or what actual angle that 0 represents.

This is similar to defining the a relative velocity between 2 inertial observers. You can define the velocity of either inertial observer as 0, but it is senseless to define both as 0 at the same time. If the only way to measure the momentum of an inertial observer was to put something bigger in front of it, then you would have a situation somewhat more like measuring the properties of a photon. In relativity we have Lorentz transformations. In EPR we have QM, or Malus' Law with some added assumptions about properties and interactions like I used.

Given information obtainable from the difference between a presumed default photon polarization and detector setting, plus a partner photon with exactly opposite default polarization, how could a FTL mechanism possibly add more information? In fact the only extra information required is not about polarizations, etc., but which way is "really" up in space, which is nonsensical. Especially given that, even for the LHV, any answer about which way is "really" up is just as good as any other.

 

[DevilsAvocado]

... Given information obtainable from the difference between a presumed default photon polarization and detector setting, plus a partner photon with exactly opposite default polarization, how could a FTL mechanism possibly add more information? In fact the only extra information required is not about polarizations, etc., but which way is "really" up in space, which is nonsensical. Especially given that, even for the LHV, any answer about which way is "really" up is just as good as any other.

Please feel free to laugh (). This is only a layman’s 'feeling' of how we maybe can find a clue to this problem. There are no real mathematical theories behind this, just a "personal guess".

We know that the two entangled photons share the same wave function (I hope!?). In the double-slit experiment, one wave function of one particle (photon) goes thru two slits to create interference with itself.

In EPR we have one wave function with two photons, in each end, going in opposite direction. What if the wave function is the holder of the "default angle reference", i.e. what’s "up and down"??

If we look at this animation of a sine wave, the rotating circle is moving to create a sine wave, but it’s very easy to imagine the circle standing still and rotating, and the sine wave is moving forward to hit at a specific angle.

[URL]http://upload.wikimedia.org/wikipedia/commons/thumb/a/a5/ComplexSinInATimeAxe.gif/450px-ComplexSinInATimeAxe.gif[/URL]

This translated to QM and EPR/BTE would be that the sine wave is the wave function and the probability distribution for a certain outcome.

[URL]http://upload.wikimedia.org/wikipedia/commons/thumb/8/8c/Standard_deviation_diagram.svg/500px-Standard_deviation_diagram.svg.png[/URL]

If this works, there is no need for a FTL mechanism, since the "default angle reference" is in the wave function itself, and travels in both directions simultaneously, and there is no need for LHV, and the outcome is true random.

Pretty nice, huh?

Now the BIG question is – how many are laughing their pants off right now, respective applauding...??

 

[my_wan]

Please feel free to laugh (). This is only a layman’s 'feeling' of how we maybe can find a clue to this problem. There are no real mathematical theories behind this, just a "personal guess".

We know that the two entangled photons share the same wave function (I hope!?). In the double-slit experiment, one wave function of one particle (photon) goes thru two slits to create interference with itself.

In EPR we have one wave function with two photons, in each end, going in opposite direction. What if the wave function is the holder of the "default angle reference", i.e. what’s "up and down"??

If we look at this animation of a sine wave, the rotating circle is moving to create a sine wave, but it’s very easy to imagine the circle standing still and rotating, and the sine wave is moving forward to hit at a specific angle.

[URL]http://upload.wikimedia.org/wikipedia/commons/thumb/a/a5/ComplexSinInATimeAxe.gif/450px-ComplexSinInATimeAxe.gif[/URL]

This translated to QM and EPR/BTE would be that the sine wave is the wave function and the probability distribution for a certain outcome.

[URL]http://upload.wikimedia.org/wikipedia/commons/thumb/8/8c/Standard_deviation_diagram.svg/500px-Standard_deviation_diagram.svg.png[/URL]

If this works, there is no need for a FTL mechanism, since the "default angle reference" is in the wave function itself, and travels in both directions simultaneously, and there is no need for LHV, and the outcome is true random.

Pretty nice, huh?

Now the BIG question is – how many are laughing their pants off right now, respective applauding...??

Yes this is fairly near the way I was modeling it, with some distinct differences.

The rotation you see didn't have to exactly match the polarizer in my LHV modeling. It had some chance of getting through if it was within + or -90 degrees, with a bit set at creation time to determine if it would at any given angle. It's the only (classical) way for 1 polarizer setting to pass 50% of the randomly polarized photons that hit it. The big picture is quiet similar though. It still only works, at least as far as I was able to model, when one of the polarizers was defined to be set at 0. Though it didn't matter what actual angle 0 represented.

Still trying to think up some weird stuff to make it work more clearly, but I'm suspecting it's a more fundamental issue with coordinate independence. Perhaps even a coordinate transform from an element in Hilbert to classical space $$|\psi(x)|^2$$, if we define that as real. It would mean that observables are not direct representations of the 'real' parts of the Universe. I considered defining a bias in the emitter that sets a defined constant angle for all photons somehow. But I'm not really seeing it adding usable information beyond what it already has, because it is a detector angle that must be defined 0. Same reason FTL real mechanisms don't necessarily help.

 

[ThomasT]

Now once you agree that Alice and Bob are ENTANGLED, i.e. they are clones of each other and always yield the same answer to the same question, then you ask: HOW can that happen?

There are 3 basic ways:

a) All measurements give the same answers. We know this isn't true because ONLY entangled pairs have this property, and the answers appear random. So "lucky" guesses are ruled out. If you have collusion between the observers, then this can be gamed. So you have to convince yourself this case is not happening. This is usually handled by a proper experimental setup.

b) Alice and Bob are clones of each other, but otherwise are completely independent. They are local/separate and must therefore have ALL the answers encoded in advance a la EPR. This is the case Bell addresses.

c) Alice and Bob are in communication with each other somehow, and so when Alice answers a question, she shares her answer with Bob. Bell does not address this case. Now, there are other ways to get this result besides instantaneous action-at-a-distance, such as retrocausal and other interpretations. I don't want to discuss any of these in this thread if it can be avoided.

Another alternative is:

Alice and Bob are clones of each other, but otherwise are completely independent. They are local/separate, but the relationship between them is an underlying, or hidden. joint parameter which, when analyzed by a joint measurement parameter (say, the relationship, or angular difference, between crossed polarizers) results in entanglement stats, P(A,B), which are not independent because of what's being measured (the difference between Alice and Bob ... none -- they're clones of each other) and how it's being measured.

Say Alice and Bob are counter-propagating sinusoidal (light) waves that share a cloned property, eg., they're identically polarized. Analyze this cloned property with crossed polarizers and you get entanglement correlation. Cos^2 |a-b| in the ideal. It's just optics. Not that optics isn't somewhat mysterious in it's own right. But we can at least understand that the entanglement stats so produced don't have to be due to Alice and Bob communicating with each other, or that nonseparability means that Alice and Bob are the same thing in the sense that they're actually physically connected when they reach the polarizers..

Bell didn't address this case, because it's precluded by the EPR requirement that lhv models of entanglement be expressed in terms of parameters that determine individual results.

Bell showed that there's an inevitable boundary imposed on formal models that express joint results in terms of individual results. That boundary is expressed in Bell inequalities, and crossed by qm predictions and experimental results.

On the other hand, since a local realistic computer simulation of an entanglement preparation is not the same as a local realistic formal model (in the EPR sense), then it wouldn't be at all surprising if such a simulation could reproduce the observed experimental results, and violate a BI appropriate to the situation being simulated -- and this wouldn't contradict Bell's result, but, rather, affirm it in a way analogous to the way real experiments have affirmed Bell's result.

 

[ThomasT]

This is not correct because it is not what Bell says. You are mixing up his separability formula (Bell's 2), which has a different meaning. Bell is simply saying that there are 2 separate probability functions which are evaluated independently. They can be correlated, there is no restiction there and in fact Bell states immediately following that "This should equal the Quantum mechanical expectation value..." which is 1 when the a and b settings are the same. (This being the fully correlated case.).

Bell illustrated that, for EPR settings, the form (2) can reproduce the qm predictions without assuming nonlocality. For EPR settings, the analogous probability expression doesn't reduce to P(AB|L) = P(A|L)P(B|L).

The form P(AB|L) = P(A|L).P(B|L) is analogous to the form of Bell's (2) wrt at least one salient feature that Bell incorporated in (2). The separability, or independence, of the data sets, A and B. Because it's analogous wrt this feature of (2) it might be used to, say, illustrate the incompatibility of that form wrt the modelling requirements of entanglement experimental situations.

And insofar as the probabilities are conditioned on L, then it seems that it's also analogous to the predetermination feature of Bell's (2).

Bell's (2) isn't just a 'separability formula'. It's the form (which encodes separable predetermination) that any lhv (per EPR elements of reality) model of entanglement has to be rendered in. The main result of his paper involved proving that the form (2) can't possibly reproduce all the qm predictions wrt the experimental (entanglement) situation that he was considering. The EPR requirement that Bell adhered to is that the joint, entangled, experimental situation be modeled in terms of parameters that determine individual results. The proof involved demonstrating that a certain boundary, which he denoted as 'epsilon', can't be made arbitrarily small if you model entanglement situations in terms of parameters that determine individual results.

It was possible for Bell to prove this, formally, precisely because the parameters that determine individual results are different than the parameters that determine joint results.

Here's one way to phrase it. Bell's theorem means that joint experimental situations which are prepared to produce and which do produce (and for which qm correctly predicts) entanglement stats can't be viably modeled in terms of parameters which determine individual results because, simply put, those different experimental situations are measuring different things.

Does Bell's result imply anything about what does or doesn't exist in Nature. No.

What Bell showed is that even if Einstein's ideas about the 'incompleteness' of qm and the contiguity of a fundamental medium (and the principle of local action) are true, it's still also true that lhv theories of entanglement are impossible.

How can both Einstein and Bell be right? The reasons have already been presented. But, we can also look at what Bell did not show.

Bell did not show that local realistic (but not realistic in the sense of the EPR requirement) nonseparable theories of entanglement are impossible. The experimental preparation of entanglement doesn't, per se, require models thereof to be rendered in terms of EPR elements of reality. It isn't constrained by the lhv requirement of modelling the situation in terms of parameters which determine individual results. Entanglement situations can be viably modeled in terms of locally produced underlying relationships between disturbances that are jointly analyzed by global measurement parameters. It's this sort of 'realistic nonseparability' (based on a certain understanding of the actual physics involved, and not some sort of 'nonlocal connection') that is the conceptual foundation on which the qm description of entanglement is based.

 

[DevilsAvocado]

Still trying to think up some weird stuff to make it work more clearly, but I'm suspecting it's a more fundamental issue with coordinate independence.

I always thought of the wave function as 'sine wave' propagating in space, maybe childish and/or wrong. On the other hand, if we look at double-slit experiment, the wave function behaves very much like water wave interference:

Maybe it was misleading with the very strong bound between "the rotating circle and the sine wave", but think of the propagating wave function as 'predefined' probabilities acting in a certain manner, in a certain situation – the wave function 'knows' what it can do, and cannot.

And the entangled partner has the exact, but mirrored, information.

Now, when the wave function reaches Alice polarizer, it doesn’t care one bit about "up & down", it 'knows' the probabilities for any angle Alice polarizer can have – and starts 'executing' that 'probability generator' on Alice’s polarizer.

And the entangled partner executes the exact, but mirrored, 'probability generator' on Bob’s polarizer.

Now how come the entangled photons always and exactly show inverse values when measured along the same axis??

Easy – the entangled photons doesn’t care about Alice or Bob, they only have their probability distribution to care about – and these probability distributions are mirrored!

Meaning, they will always behave in a mirrored way under exactly the same conditions, whatever they may be – i.e. any axis 0º - 360º.


(...I don’t know if this ever going to work in theory and/or practice, but maybe a start for 'something'... )

 

[DevilsAvocado]

As I told DrC in his thread on this subject, in these experiments you construct the wave function for the entire set up -- source, screen, lens, grid, mirrors, detectors. You don't need a story involving any'thing' in addition to the experimental equipment to construct the distribution amplitude of outcomes.

The 'trouble' I see with this explanation is that changes in the set up in a real way (wires), creates real changes in the outcome... To me this indicates the wave function must "be there" to produce these changes... (as much as a water wave is real)

Look at this picture, and hopefully you see what I’m aiming at: