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The present posting replies to the following quote of Fredifizzx

2. It is a proven fact that Joy Christian's local-realistic model is a valid counter example to Bell's so-called "theorem". Therefore all of Bell's arguments are invalid. It is junk physics now.
FrediFizzx
Independent Physics Researcher

I doubt that there is substantial agreement that Dr. Christian's
model can be considered "local-realistic". By a "realistic" model,
I think most people mean a model in which all measurements are detecting
something which is "really" there. By "really there",
we mean that the model allows us to measure,
in principle, all measurable quantities simultaneously.

For example, suppose Alice can measure quantities named and ,
obtaining in each measurement (say) +1 or -1. But she may not be able
to measure them simultaneouly, due to limitations in her equipment
or to some physical law. If she cannot, one could argue that
when she measures does not exist in any verifiable sense, and vice versa.

In that case, when she measures , there will exist a probability function
which gives a probability that she measures and a probability
that she measures . If we idealize to assume that there
are no "dud" measurements which yield no result, we will have
Of course, there will exist a similar probability
function for when she chooses to measure
BUT THERE WILL BE NO OBVIOUS REASON TO ASSUME THAT THERE EXISTS A JOINT
PROBABILITY FUNCTION for which and are marginals.

Such a joint probability function would give, for example,
a probability that and etc.
To say that is a marginal for means, for example,
that

A model for which there does exist such a joint probability function
is called a *realistic* model, because it allows the possibility
that both and have definite values even if in practice we can't observe
these values simultaneously.

It is a simple exercise to derive a necessary and sufficient
condition for two given and to be the marginals of some
It turns out that the condition is always satisfied, so for this simple
case, every model is "realistic". But in the more general case which will
be considered next, this will not hold.

Next consider two observers Alice and Bob, each of whom can make
measurements or for Alice, or or for Bob, as described above.
Then there are four possible measurements for both together, which we may
denote , , , , with corresponding joint probability distributions
, etc. The generally accepted definition
of a "realistic" model is one for which corresponding to these four given
joint distributions, there exists a probability distribution
for which the given are marginals.
This means, for example, that the probability that is and that

where the symbols i and j range over the set .
and similarly for , etc.

The usual proof of the CHSH "Bell'' inequalities shows that
a necessary condition for the existence of is for the CHSH
inequalities to hold. That is, CHSH is a necessary condition for the
existence of a "realistic" model, as "realistic" is usually defined.
The model of quantum mechanics does not satisfy the CHSH inequalities,
and therefore, by this definition, is not "realistic". Neither is Christian's
model "realistic" according to this definition, since it makes predictions identical to
quantum mechanics (at least for the singlet state, which seems to be all that is considered
in this forum). These are simple mathematical facts about which, so far as I know,
there is no controversy whatsoever.

Apparently, some of the posters in this group believe that
Christian's model is "locally realistic" (hence "realistic"). For this to
be correct, they have to be using a different definition of "realistic",
which has never been made explicit, so far as I know.

Readers interested in exploring this further may find the following
of interest:

A. Fine, "Hidden variables, joint probability and the Bell inequalities"
Phys. Rev. Lett. 48 (1982), 291-295

A. Fine, "Joint distributions, quantum correlations, and commuting
observables", J. Math. Phys. 23 (1982), 1306-1310

For the discussion above, these papers merely validate that our definition
of a "realistic" model is a commonly accepted one. Actually, Fine
proves in both papers the converse of the mathematically trivial fact
that the CHSH inequalities are a necessary condition for a realistic model.
Fine proves the much more difficult result that satisfaction of
the CHSH inequalities is sufficient for a model to be "realistic" in
the sense described above. The mathematical contents of the above two
papers are similar, but I think that the second is much easier to read.

guest1202 wrote:The usual proof of the CHSH "Bell'' inequalities shows that
a necessary condition for the existence of is for the CHSH
inequalities to hold. That is, CHSH is a necessary condition for the
existence of a "realistic" model, as "realistic" is usually defined.
The model of quantum mechanics does not satisfy the CHSH inequalities,
and therefore, by this definition, is not "realistic". Neither is Christian's
model "realistic" according to this definition, since it makes predictions identical to
quantum mechanics (at least for the singlet state, which seems to be all that is considered
in this forum). These are simple mathematical facts about which, so far as I know,
there is no controversy whatsoever.

Apparently, some of the posters in this group believe that
Christian's model is "locally realistic" (hence "realistic"). For this to
be correct, they have to be using a different definition of "realistic",
which has never been made explicit, so far as I know.

Joy's model is deterministic. IOW, if you know what the hidden variable is at the time of the singlet creation, you know the outcome of A, A', etc. That seems pretty realistic to me. Of course since QM has no hidden variables, it can't do that. So it must be false that CHSH is some kind of condition for "realistic".

guest1202 wrote: Apparently, some of the posters in this group believe that
Christian's model is "locally realistic" (hence "realistic"). For this to
be correct, they have to be using a different definition of "realistic",
which has never been made explicit, so far as I know.

My model for the quantum correlations, including that of the EPR-Bohm correlation, is local and realistic in the sense espoused by Einstein and further explicated by Bell. As is well known, Bell's definition of local-realism does not depend on any dubious inequalities involving mutually exclusive incompatible experiments, does not conflate counterfactually possible with actually occurring measurement events, and dispenses entirely with extrenuous concepts borrowed from a probability theory.

More explicitly, here is how Bell defined a local, realistic, and deterministic model for the EPR-Bohm correlation (for further details see, e.g., this paper by Shimony):

Let A(a, h) = +/-1 and B(b, h) = +/-1 be two functions such that their product AB(a, b, h) = +/-1 is factorizable as follows:

AB(a, b, h) = A(a, h) x B(b, h),

where the initial or complete state h is a shared randomness between A and B, and "a" and "b" are freely chosen, "non-hidden" parameters. Note that A(a, h) does not depend on either B or b, and B(b, h) does not depend on either A or a. Thus A(a, h) and B(b, h) are manifestly local functions. It is easy to see that A(a, h) and B(b, h) are also realistic and deterministic functions. Given a freely chosen parameter a and an initial state h, the function A(a, h) yields a definite result, either +1 or -1, and likewise for the function B(b, h). I do not think anyone would doubt that the functions A(a, h) and B(b, h) so defined by Bell are realistic and deterministic functions.

Bell then claimed that with such local-realistic functions it is mathematically impossible to reproduce the strong correlations, such as the singlet correlation -a.b,
where "correlation" E(a, b) simply means an ordinary average of the product A(a, h_i) x B(b, h_i) over a large number N of initial states h_i :

E(a, b) = (1/N) Sum_i A(a, h_i) x B(b, h_i) = -a.b.

However, it is not difficult to see that Bell's mathematical claim above about the strong correlations -a.b is simply false. It is, in fact, quite easy to reproduce the strong correlation -a.b with the functions A(a, h) and B(b, h), as anyone can verify for themselves by studying some of my papers, for example the following two:

https://www.academia.edu/19235737/Macro ... fied_Proof.

https://www.academia.edu/7024415/Local_ ... _Spacetime

Joy Christian

Joy Christian wrote

More explicitly, here is how Bell defined a local, realistic, and deterministic model for the EPR-Bohm correlation (for further details see, e.g., this paper by Shimony):

Let A(a, h) = +/-1 and B(b, h) = +/-1 be two functions such that their product AB(a, b, h) = +/-1 is factorizable as follows:

AB(a, b, h) = A(a, h) x B(b, h),

where the initial or complete state h is a shared randomness between A and B, and "a" and "b" are freely chosen, "non-hidden" parameters. Note that A(a, h) does not depend on either B or b, and B(b, h) does not depend on either A or a. Thus A(a, h) and B(b, h) are manifestly local functions. It is easy to see that A(a, h) and B(b, h) are also realistic and deterministic functions. Given a freely chosen parameter a and an initial state h, the function A(a, h) yields a definite result, either +1 or -1, and likewise for the function B(b, h). I do not think anyone would doubt that the functions A(a, h) and B(b, h) so defined by Bell are realistic and deterministic functions.

This well illustrates why Dr. Christian's papers are hard to read. It is a tautology that for any two functions,
A and B, AB is factorizable! By definition, a function h (usually a function of a particular kind) is factorizable if there exist two functions f and g (usually of the same kind) such that
h = fg. By definition, for any functions f and g, fg is factorizable! By definition, AB is always factorizable.

I am sure that Dr. Christian knows this. I am sure that the meaning he was trying to convey is something different than that tautology. But I have no clue as to what it might be!

Regarding the question as to whether quantum mechanics can be reproduced by a local-realistic model, the answer
will obviously depend on one's definitions of "local" and "realistic". The definition that I gave is not only mine, but a commonly used definition (actually, almost universally used in my experience). Let's give it the name "1202realistic",
to distinguish it from other possible definitions. Dr. Christian must also have a definition of "realistic", though I haven't been able to extract it from his papers. Let's call that definition "Crealistic". I am perfectly willing to admit the possibility that quantum mechanics might be Crealistic, but not 1202realistic !

To argue over which definition is "correct" is philosophy, not physics or mathematics. There is nothing wrong with philosophical discussions, but a lot of acrimony could be avoided if the participants realized that they were presenting points of view, not propositions which could be labeled definitely true or false.

guest1202 wrote:This well illustrates why Dr. Christian's papers are hard to read.

I believe you were the one complaining about uncivil behavior on the forum so why do you want to instigate that kind of behavior with such a comment?

Topic was split off from viewtopic.php?f=6&t=230

FrediFizzx wrote:

guest1202 wrote:This well illustrates why Dr. Christian's papers are hard to read.

I believe you were the one complaining about uncivil behavior on the forum so why do you want to instigate that kind of behavior with such a comment?

Topic was split off from viewtopic.php?f=6&t=230

I have made it quite clear in my post at the above link that I am using the standard definition of local realism, as espoused by Einstein and later explicated by Bell.

If anyone has any doubt about this then they are welcome to consult Eq. (3.4) of the Clauser-Shimony report (Rep. Prog. Phys., Vol. 41, 1978), which is the standard reference on the subject (see the image below). The claim that I have somehow invented my own concept of local realism is ridiculous.

My submission "More on definition of 1202realistic" was mistakenly posted as a quote. The problem with that (other than that it makes it harder to read), is that TeX symbols did not print, making part of it seem like nonsense.
For example, what was printed included

If it is false that A=B (i.e., if sometimes Alice and Bob get different
results), we write A B. Note that A B isn't the same as saying
that A and B have opposite results (Alice measures +1 and Bob -1, or Alice
measures -1 and Bob +1). When A and B have exactly opposite results,
we shall write A = (not B).

The phrase "if sometimes Alice and Bob get different results, we write A B" was originally submitted as:

"if sometimes Alice and Bob get different results, we write A B".

The inequality symbol did not print in the posted version.

Would it be possible to remove the incorrectly posted version, and replace it by the one previously
submitted?

I'm submitting this as a post to alert readers that the version now online would be too hard to read as printed; just don't bother. There isn't a lot of TeX in it, but the omissions sometimes make it look crazy. I hope that the moderators will post this correction even if they replace the incorrectly posted version. It's a question of credibility.

Regarding the question of possible incivility that FrediFizzx raised, I'm not sure it's uncivil to say that one finds certain papers hard to read. And is it uncivil to point out that a comment doesn't seem to make sense, while making clear that one recognizes that its author must have meant something different from what he wrote? I was hoping for a clarification, in which case the matter would have come gracefully to an end. I'm deliberately not quoting the tautologous comment here in order to avoid prolonging the matter.

My previous complaint about incivility referred to a thread entitled
"Are Gill and Moldeveanu disingenuous or incompetent" , along with many other slurs in individual posts. I don't think that should have been allowed by the moderators, particularly since Gill is said to be banned from replying. Those comments are of an entirely different nature than saying that one personally finds some papers hard to read.

Incidentally, I am neither Gill nor Moldeveanu, nor have I ever had any contact with either.

Oops, I copy and pasted wrong. Please post the correct version with the tex; I will delete the other one but will leave it up until you post the correct version so you can just copy it then fix the tex. The original is gone.

What you posted about "hard to read" is considered a minor flame comment. IOW, meant to inflame the other poster though you might not have meant it that way. You were the one complaining so try to set a good example in your posts. We should all try to do better.

Following is something close to what I originally posted under the title "More on definition of `1202realistic' ".
In a previous post I had coined the terms "1202realistic" and "Crealistic" to refer to different definitions of
the "realistic" part of "local-realistic" (model).

BEGIN REPRODUCTION OF PREVIOUSLY SUBMITTED POST

I have wondered if there might be readers who would be interested
in a more extensive explanation of what I think is the almost universally
accepted meaning of the "realistic" part of a "local-realistic" model.
The elaboration below is based on the wonderful exposition:

P.G. Kwiat and L. Hardy, "The mystery of the quantum cakes",
Am. J. Physics 68 (2000), 33-36.

Start with the familiar scenario of a researcher Alice who
can measure one of two quantities, A and A', but not necessarily both
at once. Each measurement yields either +1 or -1. Add another researcher
Bob who can similarly measure two quantities B or B'.

The Kwiat/Hardy paper introduces a (somewhat contrived but possible)
real-life setting as follows. A cake takes two hours to bake. After one
hour, an experimenter can open the oven to see if it has risen earlier than
usual. This is like Alice measuring quantity A, or Bob measuring quantity B
(early risen = +1, not early risen = -1). (Each has his or her own oven and cake.)
However, opening the oven will disturb the rest of the baking.

Another experiment that can be done is to let the cake bake the
full two hours without opening the oven, and see if it tastes good
(tastes good = +1, doesn't taste good = -1). This is like Alice measuring
A' or Bob measuring B'.

Although Alice cannot measure A and A' simultaneously (because
opening the oven disturbs the baking), a "realist" thinks that
it still makes sense to talk about the possibility that the cake is
early risen even if the oven is not opened. That is, when Alice measures A,
she is measuring something which has a "real" existence whether or not
it is measured.

The rest of the explanation will not follow this analogy further;
it was presented only to give a real life flavor to the more abstract (and
more concise) version of Kwiat/Hardy to be presented below.

Together, Alice and Bob have four possible measurements, which
we'll denote AB, A' B, AB', A' B'. Suppose it happens that whenever
Alice measures A and Bob measures B, they always get the same result:
if Alice gets +1, Bob also gets +1, and if Alice gets -1, Bob also gets -1.
Let us denote this situation by writing

A = B .

If it is false that A = B (i.e., if sometimes Alice and Bob get different
results), we write A B . Note that A B isn't the same as saying
that A and B have opposite results (Alice measures +1 and Bob -1, or Alice
measures -1 and Bob +1). When A and B have exactly opposite results,
we shall write A = (not B).

Suppose further that besides A = B, also, B = A' and A' = B'. Written on one line
this looks like:

A = B = A' = B'.

It actually isn't permissible to write it all on one line because each
equality refers to a different experiment, but it would be permissible
under an assumption that the measurements are measuring
things that are "really" there, whether they are measured or not.
In that case, from normal logic (transitivity of equality) we would conclude that

A = B'.

But if we take an opposite stance that only the above four measurements
AB, A' B, AB', A' B' can be made and that quantities not actually measured
cannot be assumed to exist, then

A B'

would be conceivable. Such a seemingly contradictory situation is sometimes
called a "Popescu/Rohrlich box", abbreviated "PR box". In summary, a PR box
describes a situation for which

A = B and B = A' and A' = B' and A B' .

This does not imply a logical contradiction if only the four measurements AB, A' B, AB', A' B' can
be made, and if we do not assume that the measurements are measuring "real" things
that exist independently of the measurement.

It would be hard to believe both in a physical theory
which permits Popescu/Rohrlich boxes and in the "reality" of the measured
quantities A, B, etc. If someone claims that he has a "local-realistic"
model for such a theory, most would probably reject his definition of
the "realistic" part of "local-realistic".

Quantum mechanics does not permit the existence of Popescu/Rohrlich
boxes. However, it does allow what we could call "probabilistic
Popescu/Rorhlich boxes". More precisely, it allows situations in which

A = B and A'= B'

and with nonzero probability, when Alice measures A' and Bob measures B,
they get the same result and also,

A = (not B' ) .

(Recall that A = (not B' ) means that when Alice measures A and Bob measures B',
they always get opposite results.)

This is a bit complicated, but when thought through one sees that
it is essentially the same as a Popescu/Rohrlich box. To see this clearly,
restrict attention to the cases in which Alice measures A', Bob measures B,
and they get the same result, which happens with nonzero probability.
What would we expect for the values of A and of B', assuming that it
makes sense to talk about them even though they haven't been measured (that is,
assuming "realism")?

Well, A' and B have yielded the same value, which is also the value
of A (because A = B ) and of B' (because A' = B' ). So,
all four of A, B, A', and B' have the same value. In particular,
A and B' have the same value, which contradicts A = (not B' ).
This is just like a Popescu/Rohrlich box, except that for a PR box
the probability of occurence is 1 rather than merely nonzero.

If we agree that PR boxes violate "realism" (e.g., it isn't permissible
to talk about the value of A when only A' B or A' B' has been measured),
then we should also agree that quantum mechanics similarly violates realism.

To conclude, let me make clear that I am presenting a point of view
with which the reader may or may not agree, not a mathematical theorem.
I believe that this is the point of view of the vast majority of the
technical literature. Someone who has a different point of view is welcome
to explain it in a friendly spirit of mutual inquiry.

***

I have addressed the issue of "realistic" raised by guest1202 in my posts here and here. I have used the standard definition of "realistic" in my work. End of the story.

***

What is realistic? How about sticking with the EPR criteria:

If, without in any way disturbing a system, we can predict with certainty (i.e., with probability equal to unity) the value of a physical quantity, then there exists an element of reality corresponding to that quantity.

It does not say the value is there before measurement, just that we can predict it without disturbing the system. It also does not say, the measurement is simply passively revealing the value. The value could very well be a combined result of pre-existing conditions plus measurement context.

In short, any theory that can predict any value with certainty, without disturbing the system is realistic according to EPR. That includes QM, which can predict expectation values with certainty.

In fact, in the EPR experiment, QM predicts with certainty that if Alice measures along "a" and obtains +1, Bob MUST, also obtain -1 if he measures the sibling particle along "a". QM is realistic according to the EPR criteria. It high time people recognised that and start focusing on the real issue.

minkwe wrote:What is realistic? How about sticking with the EPR criteria:

If, without in any way disturbing a system, we can predict with certainty (i.e., with probability equal to unity) the value of a physical quantity, then there exists an element of reality corresponding to that quantity.

It does not say the value is there before measurement, just that we can predict it without disturbing the system. It also does not say, the measurement is simply passively revealing the value. The value could very well be a combined result of pre-existing conditions plus measurement context.

In short, any theory that can predict any value with certainty, without disturbing the system is realistic according to EPR. That includes QM, which can predict expectation values with certainty.

In fact, in the EPR experiment, QM predicts with certainty that if Alice measures along "a" and obtains +1, Bob MUST, also obtain -1 if he measures the sibling particle along "a". QM is realistic according to the EPR criteria. It high time people recognised that and start focusing on the real issue.

That looks perfect to me for a definition of realistic. Thanks.

Thanking Fred for this excellent new topic, I bring the following from viewtopic.php?f=6&t=230:

FrediFizzx wrote:

Gordon Watson wrote:(ii) New clue re CH74 error: Look at the unnumbered equation (the old Bellian trick) on p.528; call it (3a). Now look at their (4), same page.

I don't see anything wrong in going from eq. (3a) to eq. (4) in the CH74 paper. Looks like pretty standard math stuff.

Fred, with apologies (and aware that my response is overdue), this note is conditional under "E and OE" due to current time pressures. NB: For clarity, I use P instead of their p:

So, seeing nothing wrong, we note that (4) in CH74 is wholly amenable to analysis under ordinary probability theory (OPT). In particular, the following dissection can never be wrong under OPT and CH74; ie, from CH74 eqn. (4):

-1 ≤ P1(a)P2(b|a) - P1(a)P2(b'|a) + P1(a')P2(b|a') + P1(a')P2(b'|a') - P1(a') - P2(b) ≤ 0. (4a)

Then, since λ is a random variable, we have:

P1(a) = P1(a') = P2(b) = 1/2. (4b)

So from (4a) we have: -1 ≤ (1/2) [P2(b|a) - P2(b'|a) + P2(b|a') + P2(b'|a') - 1 - 1] ≤ 0. (4c)

So: CH74' = |P2(b|a) - P2(b'|a) + P2(b|a') + P2(b'|a')| ≤ 2. (4d)

However, under EPRB (using Ps that are readily derived), (4d) delivers:

CH74' = | sin^2((a,b)/2) - sin^2((a,b')/2) + sin^2((a',b)/2) + sin^2((a',b')/2)| ≤ 2. (4e)

Now a, b, a', b' are unrestricted! So let (a,b) = (a',b) = (a',b') = (a,b')/3 = 3π/4.

Then CH74' is absurd, for we find:

CH74' = 2 + (√2 - 1) >> 2. (4f) QED; E and OE!

So questions arise: (i) Where does CH74 go wrong? (ii) What definition of realism do they rely on? (iii) What alternative definition of realism is warranted under QM?

And since these are good questions under this excellent new topic, I bring them here as well.

guest1202 wrote:… ... By a "realistic" model, I think most people mean a model in which all measurements are detecting
something which is "really" there. By "really there", we mean that the model allows us to measure, in principle, all measurable quantities simultaneously. … ...

Hi guest1202, and welcome to SPF! I credit both you and Fred with starting a truly important thread: so I apologise for opening with some serious concerns.

From my point of view, given the material shown above: I see trouble ahead.

(i) By a "realistic" model, do you mean something physical?

(ii) I'm much more interested in what you mean by "realistic" -- rather what you think most people mean.

(iii) To me, the term "measurement" is problematic. I know too well that a "measurement" may perturb the measured system.

(iv) You then talk of a model in which all measurements are "a detection of something that is really there". Moving from the model to the physical: If I send you a photon of unknown-to-me-but-discoverable linear polarisation, I'm sure you can detect the photon. But can you measure the linear polarisation?

(v) When you conjoin "really there" with "the model allows us to measure ...", then the model must be physical, a model of the subject physical reality; right?

(vi) But to "… to measure, in principle, all measurable quantities simultaneously" ?? (On a friendly endnote: Do I smell fish?)

Excuse me for now; must run; looking forward to some good clarifying discussion.
.

I don't think there is any reason to go beyond what Michel and Joy have posted for the meaning of realistic. Of course by realistic we mean physical.

Joy Christian wrote:

FrediFizzx wrote:I don't think there is any reason to go beyond what Michel and Joy have posted for the meaning of realistic. Of course by realistic we mean physical.

LOL! I like it. Ain't it the truth?

From viewtopic.php?f=6&t=230&p=6012#p6012

Via CH74, (4e*) becomes: 0 ≤ 3sin^2(θ/2) - sin^2(3θ/2) ≤ 2. (4f*)

For comparison, also under EPRB, CHSH69 is: |cos(3θ)-3cosθ|≤ 2. (4g*)

For Bell's supporters: (4f*) and (4g*) are identically absurd for more than 75% of the range -π < θ < π!

So the same questions arise: (i) Where do CHSH69 and CH74 go wrong? (ii) What definition of realism do they rely on? (iii) What alternative definition of realism is warranted under QM?

With apologies (as a warning): E and OE!

***
Below is the central derivation of the EPR-Bohm correlation from my latest paper, which predicts exactly what quantum mechanics predicts for such correlations.

Anyone still concerned about my use of "realistic", please tell us where in my derivation there is "non-reality", non-locality", or lack of determinism creeping in:

Joy Christian wrote:***
Below is the central derivation of the EPR-Bohm correlation from my latest paper, which predicts exactly what quantum mechanics predicts for such correlations.

Anyone still concerned about my use of "realistic", please tell us where in my derivation there is "non-reality", non-locality", or lack of determinism creeping in:

No problem. Reality never is represented with bad math. You conveniently but quite mathematically incorrectly use s in both limits s->a and s->b to allow you to combine the two L's in s. This would only be possible only if a=b.

Yet another blatantly obvious math error.

Disagree? Justify your math. sorry but "Lockyer is disingenuous, made a math error, does not understand your work, does not understand physics, etc, etc, etc" is non-responsive.