I How do you understand EPR & Bell's Theorem?

[Blue Scallop]

I'm still looking for the best reference on Aspect experiments in the net. So far I found this good figure https://www.forbes.com/sites/chador...at-show-quantum-physics-is-real/#6ee44ed41ae5:

"Schematic of the third Aspect experiment testing quantum non-locality. Entangled photons from the source are sent to two fast switches, that direct them to polarizing detectors. The switches change settings very rapidly, effectively changing the detector settings for the experiment while the photons are in flight."

When we talk about Bell's Theorem and Bell's Inequality. I think we must discuss in terms of the polarizers and switches changing while the photons are in flight. We mustn't talk about Alice and Bob because it may not give accurate depictions of the Aspect experiment. It may erroneously give one idea that red and blue socks just left the sources and there are simply hidden variables. What happens is the wave function is correlated at initial preparation like what Peterdonis (using vanhess71 context) explained but the wave function still function or work even for entangled particles light years apart. This is the weird part we must not forget that vanhees71 didn't emphasize. I guess the minimal interpretation just smeared this weird part and saying the correlations occur at initial preparations and period.

 

[PeterDonis]

The book says

What book?

When A or B measured the polarization, it has effective of altering the initial conditions.

No, it doesn't. A and B's measurements do not change the initial preparation procedure at all. They can't; the initial preparation procedure is in the past light cone of both measurements.

What you are quoting from the book is using ordinary language in an unusual way--which is not surprising since there is no way to use ordinary language in an ordinary way to describe these experiments. But it means you have to be very, very careful about reading such descriptions.

 

[PeterDonis]

Nick Herbert's proof does not relay on "classical hidden variables" in any way.

Sure it does. They're just not as easily seen because he uses vague ordinary language in his proof instead of precise math the way Bell did.

My reference for Herbert's proof is here (this was a link from the thread linked to earlier):

http://quantumtantra.com/bell2.html

Eberhard's proof does not relay on "classical hidden variables" as well.

Do you have a reference for Eberhard's proof? I'm not familiar with it.

 

[vanhees71]

But 5.3.1 is explained in more detail in Sec. 2.2, where it is pointed that reality exists and is non-local, but that is just not the subject of physics. And I don't think that you agree with that. You think that my claim that "reality exists and is non-local" is meaningless because it cannot be tested in a laboratory. I agree that it cannot be tested in a laboratory, but I don't think that it makes it meaningless. After all, that is based on a sound logic, and logic is meaningful even when it cannot be tested in a laboratory.

No, indeed not. I think that everything (except gravitation) is described by standard QT, and that the all of physics, including both "classical" and "quantum" (where "classical" is an approximation, in principle derivable from "quantum") deals with what we can objectively observe and quantitatively measure in Nature. Everything that goes beyond observable facts is not within the realm of the natural sciences, and whether or not the natural sciences are related to any kind of subjective world views is also not decidable with the methodology provided by the natural sciences, and thus speculating about it is out of the scope of this forum.

 

[PeterDonis]

I think we must discuss in terms of the polarizers and switches changing while the photons are in flight. We mustn't talk about Alice and Bob because it may not give accurate depictions of the Aspect experiment.

Alice and Bob can realize the Aspect experiment--where not just the measurement events but the settings change events are spacelike separated--just fine. The only reason Aspect used high-speed automated devices to do it was that humans act too slowly for such an experiment to fit in an ordinary lab. But if you imagine Alice and Bob out in space, far away from each other, each receiving one of an entangled pair of particles, it's easy for them to manually pick settings at events that are spacelike separated. And none of that changes anything I said.

 

[vanhees71]

Now you effectively claim that when something is known with certainty, then it is real. But EPR proved that this very same criterion of reality, plus assumption of locality, implies that QM is incomplete. Yet, you don't accept that QM is incomplete. Another inconsistency in my view.

I never ever use the word "real" or "reality" in this context since it's not well-defined. I mean, what I wrote: If I have prepared a system in a state, of the form
$$\hat{\rho}=\sum_{\beta} p_{\alpha,\alpha'} |a,\alpha \rangle \langle a,\alpha'|, \quad p_{\alpha,\alpha'}=p_{\alpha',\alpha}, \quad p_{\alpha,\alpha} \geq 0, \quad \sum_{\alpha} p_{\alpha,\alpha}=1$$
where $|a,\alpha \rangle$ is a CONS of eigenstates of the self-adjoint operator $\hat{A}$ with eigenvalue $a$ (labelled with an appropriate set of parameters $\beta$), then the value of the observable $A$, represented by the operator $\hat{A}$, is determined to be $a$. With any proper measurement, I'll find this value $a$ with certainty (as Born's rule tells you).

Concerning any other observable $B$, represented by the self-adjoint operator $\hat{B}$ with CONS of eigenstates with eigenvalues $b$, $|b,\beta \rangle$, the probability to find the value $b$ when properly measuring $b$ is given by
$$P(b|\hat{\rho})=\sum_{\beta} \langle b,\beta|\hat{\rho}|b,\beta \rangle.$$
That's it. QT doesn't imply more but also nothing less. That's also all you need as interpretation of the formalism in order to describe what's observed in the lab/nature (from the point of view of physicists).

QT is incomplete as we don't have a valid description of the gravitational interaction.

 

[zonde]

Sure it does. They're just not as easily seen because he uses vague ordinary language in his proof instead of precise math the way Bell did.

My reference for Herbert's proof is here (this was a link from the thread linked to earlier):

http://quantumtantra.com/bell2.html

I use the quote from this post. It quotes just the proof part.
So if you see where he is using hidden variables please point out the place.

Do you have a reference for Eberhard's proof? I'm not familiar with it.

This paper:
https://journals.aps.org/pra/abstract/10.1103/PhysRevA.47.R747
It contains short proof of Bell type inequalities. Paper is behind paywall so I tried to reproduce this proof for 100% efficiency here.

 

[PeterDonis]

if you see where he is using hidden variables please point out the place.

It's where he assumes that "REALITY IS LOCAL", and then explains what that means. As I said, he does it in ordinary language, so it's not evident how the hidden variables play into it. But if you look at the math corresponding to what he's saying (which you have to do in Bell's paper, since Herbert includes no math--which to me is always a red flag, math is precise and ordinary language isn't), you'll see them there.

(Strictly speaking, I suppose you could implement the factorizability condition that appears in Bell's math without adopting a hidden variable model. But I've never seen anyone try to do it that way. Herbert certainly doesn't; he uses no math at all, he just refers to Bell.)

Paper is behind paywall so I tried to reproduce this proof for 100% efficiency here.

I'll take a look.

 

[PeterDonis]

I tried to reproduce this proof for 100% efficiency here.

The hidden variables are in the "quartets of cards", or more precisely in the functions $\alpha_n(a_k)$, $\beta_n(b_k)$. You say:

value (either H or V) of α_1(a_k), α_2(a_k), β_1(b_k), β_2(b_k) is the same based on our assumptions on all cards from k-th quartet.

This is equivalent to assuming hidden variables: the values of the functions.

 

[Lord Jestocost]

...since Herbert includes no math--which to me is always a red flag...

It seems that some don't or do not want to understand. With all due respect, "...since Herbert includes no math--which to me is always a red flag.." is the worst argument I have ever heard. Nick Herbert's excellent book "Quantum Reality" brings out the amazing and astounding simple and experimentallly established facts which make thinking about quantum phenomena so fascinating. And then, the repeated litanies of the "minimalistic interpretation".

 

[PeterDonis]

With all due respect, "...since Herbert includes no math--which to me is always a red flag.." is the worst argument I have ever heard.

You're entitled to your opinion. But what your claim amounts to is that I should try to learn science from pop science books. Which is not a good strategy. When I say that including no math is a red flag, that's what I mean--that including no math means it's pop science, not science.

 

[Blue Scallop]

What book?
No, it doesn't. A and B's measurements do not change the initial preparation procedure at all. They can't; the initial preparation procedure is in the past light cone of both measurements.

What you are quoting from the book is using ordinary language in an unusual way--which is not surprising since there is no way to use ordinary language in an ordinary way to describe these experiments. But it means you have to be very, very careful about reading such descriptions.

The book is Heinz Pagels The Cosmic Code: Quantum Physics as the Langauge of Nature and Nick Herbert book Quantum Reality.

They have the same example. I think Nick Herbert got the idea from Heinz Pagels although I read too that the idea originated from Bell in his 1980 lecture (I'm looking for the passage where it is said the past 30 minutes and can't find it... and I'm still trying to find it and will share it later).

For those familiar with both of their arguments about setting the calcite by 30 degrees and double error (see Nick website first shared earier). I couldn't understand last time I read them what physically have to happen to the polarizers for them to exhibit the effect. Quoting first Heinz Pagels':

“
A:0001011000101011100011110010110010100100... ...
==]==]================ ]==== ]==========
B:0011001000101011100011010010010010100100...

(where ] is the error or mismatch)

let me quote directly from Pagels:

"In the above example the rate of errors, since there are 4 errors out of 40 detections, is E(theta)=10%.

So far this experiment done with photons resembles that with the nails. Photons are behaving just like the perfectly visualizable experiment with the flying nails. If we assume the state of polarization the photons have at A and B is objective (objectivity assumption) and that what one measures at A does not influence what happens at B(local causality assumption), then Bell’s inequality, E(2theta)<=2E(theta), ought to hold for this experiment. If we double the angle to 2theta=50 degrees, the following records were found:

A: 1000111001100110111001111110110101000100 …
=]]=====]===]====]]]=======]==========]=]]]===
B: 1110111101000111001001110110110101101010 …

This is 12 errors out of 40, so that E(2thetha) = 30%. Now let us compare this result with the requirement of Bell’s inequality. Since E(theta)=10% we have 2E(theta) = 20%; but Bell’s inequality requires that E(2theta)<=2E(theta), so that 30% is supposed to be less than 20% - completely false – 30% is greater than 20%! We conclude that Bell’s inequality is violated by this experiment, as it is for real experiments with photons. Consequently, either the assumption of objectivity or locality or both are wrong. That is very remarkable!”

My question is this paragraph:

“To get an intuitive sense of how objectivity implies nonlocality, compare the records for the angle theta =25 degrees and theta = 50 degrees. There are just too many errors (12) for the 50 degree setting as compared to the number of errors (4) for the 25 degree setting. It seems that by moving A’s polarizer we must have influenced the polarization of the photons about to be detected at B and that produces all those “extra” errors that violate Bell’s inquality. Observer B could be on the Earth and A light-years away, on another galaxy. A, by moving the polarizer, it seems, is sending a signal faster than the speed of light, thus instantaneously changing B’s record. That certainly seems like actions-at-a-distance and the end of locality.

Now that we see what we have been forced into we might want to take a look at this further. Either alternative – a nonobjective or nonlocal reality- is a bit hard to take. Some recent popularizers of Bell’s work when confronted with this conclusion have gone on to claim that telepathy is verified or the mystical notion that all parts of the universe are instantaneously interconnected in vindicated. Others assert that this implies communication faster than the spee of light. That is rubbish, the quantum theory and Bell’s inequality imply nothing of this kind. Individuals who make such claims have substituted a wish-fulfilling fantasy for understanding. If we closely examine Bell’s experiment we will see a bit of sleight of hand by the God that plays dice which rules out actual nonlocal influences. Just as we think we have captured a realiy weird beast – like acausal influences – it slips out of our grash. The slippery property of quantum reality is again manifested”

Ok my questions:

1. Since Pagels example is the same as one used by Nick Herbert in http://quantumtantra.com/bell2.html (refer to the figures). If the degree difference is 60 degrees or (30+30) (Pagels example used 50 degrees or (25+25) and there is supposed to be double errors. How come photons and polarizer can’t produce the errors while classical projective like nails with hidden or unhidden variables can? I mean like do the photons know the polarizer is set up to trick them so they don’t get trick by the double error.. so one of the photons decide not to make errors to produce more errors if they are oriented 60 degrees? This is just my words, mathematicaly how do they know?

2. Is the also what Clauser actually did? Please share simple math to illustrate the point.

3. In this Pagels sentence and wording “It seems that by moving A’s polarizer we must have influenced the polarization of the photons about to be detected at B and that produces all those “extra” errors that violate Bell’s inquality” I got the impression for many years that Bell’s Inequality is additional "long distant" correlations occurring over and above the initial preparation. That is why I want to know what exactly happens to the polarizers in the experiment. This is why I want to see the original Clauser and Aspect experiment in the clearest format so I know what really happens and how they differ to this popularization.

4. How accurate is the population (Nick Herbert and Heinz Pagels) example compared to the actual Clauser experiment?

Thank you!

 

[mikeyork]

They did not. They showed that the result of a measurement on one member of an entangled pair cannot have been determined solely by preexisting properties of that particle.

I like this simple description except for one thing. I would replace "preexisting" by "pre-determinable". If the particle is an electron, it will remain en electron. It is the unknown properties that depend on entanglement that matter. If a particle is part of a pair with entangled spin, the composite spin is known, but the individual spins are not. So the determination of one's spin, also determines the other. This does not mean that it did not have that preexisting property, only that its value was not knowable by any entity in the universe. This is why quantum entanglement differs from pairs of gloves where someone has to put the gloves in separate boxes and so their properties are already known in the universe and any subsequent detection must confirm that. In the quantum case there is no information to confirm.

 

[PeterDonis]

mathematicaly how do they know?

what exactly happens to the polarizers in the experiment

These questions are not answerable. There is no intuitive "machinery" underlying what the photons and polarizers do to produce the correlations that violate the Bell inequalities (or the CHSH inequalities or any other conditions that are said to imply "nonlocality"). There is no intuitive story we can tell that "explains" what the photons and polarizers do. What they are doing has no counterpart in the ordinary language and ordinary experience you are used to. So what you appear to be looking for does not exist.

 

[Nugatory]

I would replace "preexisting" by "pre-determinable".

I think you're right - that's an improvement, better captures what people hoped for in the pre-Bell era but cannot have.

 

[Blue Scallop]

These questions are not answerable. There is no intuitive "machinery" underlying what the photons and polarizers do to produce the correlations that violate the Bell inequalities (or the CHSH inequalities or any other conditions that are said to imply "nonlocality"). There is no intuitive story we can tell that "explains" what the photons and polarizers do. What they are doing has no counterpart in the ordinary language and ordinary experience you are used to. So what you appear to be looking for does not exist.

I also have the book Amir "Aczel Entanglement" but it is popularization too but more complex. But if I'd go directly to the details of the Aspect experiments. I can understand what the photons and polarizers do to produce the correlations that violate the Bell inequalities, right? Like in
http://qudev.phys.ethz.ch/content/courses/QSIT06/pdfs/Aspect81.pdf

Anyway in Nick Herbert book is the passages:

"In quantum theory's formalism, what accounts for strong photon correlation in the twin state is phase entanglement. Whenever quantum system A meets quantum system B, their phases get mixed up. Part of A's proxy wave goes off with B's wave and vice versa. Phase entanglement thereafter instantly connects any two quons which have once interacted. Before Bell's discovery, this strong quantum connection had been recognized (especially by Schrodinger, who considered it quantum theory's most distinctive feature) but regarded by physicists as a kind of mathematical fiction with no roots in reality. Since Bell's theorem demands a superluminal connection and quantum theory provides one - in the form of ubiquitous but presumably "fictitious" phase connections - perhaps these quantum connections are not as fictitious as was once believed.
Since there is nothing that is not ultimately a quantum system, if the quantum phase connections is "real," then it links all the systems that have once interacted at some time in the past - not just twin-state photons - into a single waveform whose remotest parts are joined in a manner unmediated, unmitigated, and immediate. The mechanism for this instant connectedness is not some invisible field that stretches from one part to the next, but the fact that a bit of each part's "being" is lodged in the other. Each quon leaves some of its "phase" in the other's care, and this phase exchange connects them forever after. What phase entanglement really is we may never know, but Bell's theorem tells us that it is no limp mathematical fiction but a reality to be reckoned with."In Big Bang when all is entangled.. after it.. all may still be entangled.. so why is it not right to say I'm entangled with planet Saturn? Why not since during and after the Big Bang.. everything is entangled?

 

[PeterDonis]

But if I'd go directly to the details of the Aspect experiments. I can understand what the photons and polarizers do to produce the correlations that violate the Bell inequalities, right?

I can't say; that's up to you to find out. But I definitely think you should stop looking at pop science and start looking at the actual science, as it is presented in textbooks and peer-reviewed papers.

 

[PeterDonis]

And with that, this thread is closed. @Blue Scallop , before you open another thread on this or a similar topic, please look at valid sources and base your questions on specific scenarios/problems that you come across in those valid sources. This topic is tough enough without bringing all of the vagueness of pop science treatments into the mix.