On the Fatal Mistake Made by John S. Bell in his theorem

Foundations of physics and/or philosophy of physics, and in particular, posts on unresolved or controversial issues

On the Fatal Mistake Made by John S. Bell in his theorem

Postby Joy Christian » Thu May 26, 2016 4:53 pm

***
I am starting this new thread, triggered by an email I received from someone in response to my new two-page paper posted on Academia.Edu.

In the past some people had difficulty downloading papers from Academia.Edu. In that case you can download the paper directly from my blog:

"On the Fatal Mistake Made by John S. Bell in the Proof of His Famous Theorem": http://libertesphilosophica.info/blog/w ... /Fatal.pdf

Now let me quote the email I received and my response to it in succession:

First, the email:

Dear Dr Christian,

I would have liked to agree with your paper today on [Academia.Edu].

But surely it should be understood in your refs 1 and 2 that the four summations, though over the same range, are over different physical runs, that is k from 1 to n, for the first average, k from n+1 to 2n for the next etc.

Understood in that way, does this not obviate the argument you make in the two lines between your Eqns. 5 and 6?

Or am I missing something here?

Regards

xxx xxxxxxxx

And my reply:

Hi xxx,

Thanks for your comments. I would like to make two points:

(1) Your understanding of Bell-CHSH argument is not correct. Local-realism demands that all of the four summations must be from 1 to k only. The only difference
in the four E's on the LHS of my eq. (4) is in the choice of the pairs of measurement directions. Everything else must remain the same, according to local-realism.
More technically, we are talking about counterfactual definiteness of the outcomes for each run of the experiment, which is often taken as a statement of realism.

(2) If, for the sake of argument, we accept your argument and take k from 1 to n for the first average, k from n+1 to 2n for the next, etc., then that only
strengthens my argument. For that would mean that even the LHS of my eq. (4) is meaningless, and hence the Bell-CHSH argument does not even get off the ground. So you are right about one thing. In that case the standard argument which I spell out between my eqs. 5 and 6 becomes invalid. But again, that is a problem for Bell's argument, not for my argument.

Cheers,

Joy


Admittedly, we have gone through all of these issues in great detail in this forum. And yet the rather obvious point I am making above is worth stressing once again.

***
Joy Christian
Research Physicist
 
Posts: 2793
Joined: Wed Feb 05, 2014 4:49 am
Location: Oxford, United Kingdom

Re: On the Fatal Mistake Made by John S. Bell in his theorem

Postby Joy Christian » Mon May 30, 2016 9:08 pm

***

I have now also incorporated the above two-page refutation of Bell's argument into my "Reply to Gill" paper (see pages 8 and 9): http://arxiv.org/abs/1501.03393.

So now my latest refutation of Bell is also officially published on the arXiv, with a proper date-stamp and everything.

I can only hope that now Bell-followers would finally realize just how badly they have been misled by Bell's manifestly mistaken argument for over fifty years. :(

***
Joy Christian
Research Physicist
 
Posts: 2793
Joined: Wed Feb 05, 2014 4:49 am
Location: Oxford, United Kingdom

Re: On the Fatal Mistake Made by John S. Bell in his theorem

Postby Joy Christian » Sat Jun 04, 2016 5:16 pm

***

Following is an excellent example of how the Bell-believers resort to complete denial of facts when faced with a clear-cut refutation of Bell's ridiculous argument:

I found the following assertion elsewhere on the Internet:

Joy Christian has been trying to disprove Bell's theorem for ages. There is a fundamental mistake in her argument -- She claims that Bell replaces a sum of

expectation values by the expectation value of a sum (see equations D3 and D4 of the paper you reference). But Bell does no such thing: such a replacement

is, of course, invalid, but Bell does not do this.


Now I am sorry to disappoint the author of this assertion, but Joy Christian is a "he", not "she." Please see: http://einstein-physics.org/from-the-director/

More importantly, the assertion made above by the author can be easily shown to be completely false.

My paper being referred to in the quote is this one. Let me reproduce the relevant part from my paper here for convenience:

Image


Now let me reproduce the standard derivation of the CHSH inequality from Wikipedia, which can also be found in Bell's original papers referenced in my paper above:

Image.

Note well that in the derivation of the CHSH above four separate averages in line one are replaced with a single average in line two (albeit in a different notation).

There is no way to derive the upper bound of 2 on the CHSH string without this slight-of-hand.

Now let me re-quote part of the author's assertion above to complete my argument

But Bell does no such thing: such a replacement is, of course, invalid, but Bell does not do this.

Enough said.

***
Joy Christian
Research Physicist
 
Posts: 2793
Joined: Wed Feb 05, 2014 4:49 am
Location: Oxford, United Kingdom

Re: On the Fatal Mistake Made by John S. Bell in his theorem

Postby FrediFizzx » Sat Jun 04, 2016 6:18 pm

Joy Christian wrote:***

Following is an excellent example of how the Bell-believers resort to complete denial of facts when faced with a clear-cut refutation of Bell's ridiculous argument:

I found the following assertion elsewhere on the Internet:

Joy Christian has been trying to disprove Bell's theorem for ages. There is a fundamental mistake in her argument -- She claims that Bell replaces a sum of

expectation values by the expectation value of a sum (see equations D3 and D4 of the paper you reference). But Bell does no such thing: such a replacement

is, of course, invalid, but Bell does not do this.


Now I am sorry to disappoint the author of this assertion, but Joy Christian is a "he", not "she." Please see: http://einstein-physics.org/from-the-director/

More importantly, the assertion made above by the author can be easily shown to be completely false.

My paper being referred to in the quote is this one. Let me reproduce the relevant part from my paper here for convenience:

Image


Now let me reproduce the standard derivation of the CHSH inequality from Wikipedia, which can also be found in Bell's original papers referenced in my paper above:

Image.

Note well that in the derivation of the CHSH above four separate averages in line one are replaced with a single average in line two (albeit in a different notation).

There is no way to derive the upper bound of 2 on the CHSH string without this slight-of-hand.

Now let me re-quote part of the author's assertion above to complete my argument

But Bell does no such thing: such a replacement is, of course, invalid, but Bell does not do this.

Enough said.

***

Well... I will say a bit more. Of course the same mistake can be found in Bell's original 3-term inequality. But the really big question from all of this is why do experimenters and QM prediction people don't know that they are using a different inequality with a bound of 4? It's quite mind boggling since it is such simple mathematics.
***
FrediFizzx
Independent Physics Researcher
 
Posts: 2905
Joined: Tue Mar 19, 2013 7:12 pm
Location: N. California, USA

Re: On the Fatal Mistake Made by John S. Bell in his theorem

Postby Joy Christian » Sat Jun 04, 2016 11:41 pm

FrediFizzx wrote:Well... I will say a bit more. Of course the same mistake can be found in Bell's original 3-term inequality. But the really big question from all of this is why do experimenters and QM prediction people don't know that they are using a different inequality with a bound of 4? It's quite mind boggling since it is such simple mathematics.
***

Indeed. This is all so mind-numbingly simple that one can't help wondering about the honesty and scientific integrity of the Bell-believers.

***
Joy Christian
Research Physicist
 
Posts: 2793
Joined: Wed Feb 05, 2014 4:49 am
Location: Oxford, United Kingdom

Re: On the Fatal Mistake Made by John S. Bell in his theorem

Postby guest1202 » Sun Jun 05, 2016 1:04 am

Many posts on this forum are accessed hundreds or even thousands
of times. But only a half-dozen or so posters account for maybe 90%
of the posts, and these half-dozen "regulars" vehemently espouse views
which I imagine that 99% of practicing physicists would emphatically reject.

Of course, that doesn't imply that the regulars are wrong
(though for other reasons I do think that they are wrong).
But I wonder who might be the hundreds who regularly read
their posts. Are they unconvinced (either of the established views or
of the views of the regulars) and seeking enlightenment? Do they consider
the forum analogous to a "Flat Earth Society" which they read for their
amusement? I have no idea, but in case it is the former, I thought it
might be interesting to try a different way of explaining why what the
regulars deprecatingly call "Bellians" think as they do.

I will illustrate with a parable. An experimenter named Alice
has an instrument with a switch with two positions labeled "A" and "A`".
She believes that it measures one of two physical quantities, with the same
labels. (In physics texts, each of the two quantities is usually the spin of
a particle along a specified axis.) Each measurement yields one
of the two values +1 or -1. Because the switch has two mutually exclusive
positions, she cannot measure both A and A' simultaneously.
Similarly, another experimenter named Bob in a laboratory far
from Alice has an identical instrument which can measure one (and only one)
of two quantities B and B', again obtaining result +1 or -1 for each
measurement.

Alice and Bob can collaborate by prearranging that each will make
one of his (or hers) measurements at a specified time, record the results,
and later compare them. If, say, Alice measures A' and Bob measures B,
denote the joint measurement as A' B. The four possible results of A' B
are (+1, +1), (+1, -1), (-1, +1), (-1, -1), where the first number in
each parenthesis refers to Alice's result and the second to Bob's.

By doing this numerous times, they can estimate
the probability of each possible result (a, b). Thus they can obtain,
to an arbitrary accuracy, a probability distribution which we'll denote
pA' B = pA' B( . , . ) which assigns a probability pA' B(a,b) to each of
the four possibilities (a,b). The TeX facility produces rather ugly
results, so I find it clearer to avoid it when possible, but when
using TeX, I'll write pA' B as



Similarly, Alice and Bob can approximate to arbitrary accuracy three
other possible probability distributions denoted similarly as
pAB, pAB', and pA' B' . These four distributions will be called
"marginal" probability distributions, for reasons which will be made
clear later. They can conveniently be written as matrices, for example
they might find that



which means that p(1,1) = 3/8, p(1,-1) = 1/8, p(-1,1) = 1/8, p(-1,-1) = 3/8,

and that



To skip ahead a bit, these are the (hypothetical) "marginals"
predicted by quantum mechanics for a particular entangled state similar
to the so-called "singlet" state which will be specified later.
The others are



and




Alice and Bob find this method of generating the marginals rather
tedious, and they wonder if with more refined instruments they might be able
to measure all four of the quantities A, A', B, B' simultaneously.
Then super-salesman Gideon (aka "God") appears, claiming to be able to sell
them just such an instrument, which they can barely afford.
He also tries to sell them an expensive course in his self-proclaimed
"Gideon University" to teach them how to use this fantastic instrument.

Then Alice and Bob meet mathematician Mark, who tells them that
he used to work for Gideon and that his instrument and university course
are nothing but a scam. Alice and Bob want to believe Gideon, and so
are skeptical of Mark.

Mark explains that he has a mathematical proof that no such instrument
can exist. It starts as follows.

Suppose there were such an instrument. Then by using it one could
approximate to arbitrary accuracy a probability distribution

p(a, a', b, b')

on four-tuples of variables (a, a', b, b'), where each variable can take the
value +1 or -1, where it is hoped that the notation will seem self-explanatory.
For example,

p(1, -1, -1, 1) = 1/4

represents the probability 1/4 that Gideon's instrument indicates
A = 1, A' = -1, B = -1, B' = 1 .

If Gideon's instrument is measuring what he claims, then from
his measurements we could deduce the four marginals as follows.

,

where the sum ranges over all four possible values for (a' , b' ),
and similarly for the other three marginals.

This explains why the marginals might deserve that name.
ASSUMING THAT GIDEON's CLAIMS ARE CORRECT,
they are slight generalizations of the standard notion of
"marginal distribution" in probability theory. But if we aren't sure
that p actually exists (i.e., that Gideon's instrument works as he claims),
then they really shouldn't be called "marginals", though that name is
still convenient so I won't change the terminology.

[Incidentally, another regular poster has a similar serious omission
in a submitted paper on another topic---he assumes without proof that
a mathematical object which his theory requires must exist. It's
easy to say "let p = p( . , . , . , . ) be a probability distribution
whose marginals are the given pAB( . , . ), pAB', etc.", but just
referring to it in this way doesn't prove that such a p exists!]

That's how Mark's claimed proof starts. The rest is just a usual proof
of some version of Bell's Theorem. From the marginals, we can calculate
the so-called "correlations" like

` C_{AB} := p_{AB}(1,1) + p_{AB}(-1,-1) - p_{AB}(1,-1) - p_{AB}(-1,1)

(These are also often denoted by notation like



or




which you may have seen in books or posts of the regulars.)

Note that the CAB, etc can be obtained
from the corresponding pAB, etc, but not conversely. Thus a theory
that only yields the CAB, etc. (like Dr. Christian's, so far as I know), cannot be said to be
complete unless it is augmented by explanation as to how to obtain the
corresponding pAB, etc. Quantum mechanics does give the pAB, etc.
For example, I calculated the ones given above using the rules of quantum mechanics.

To elaborate a little more, Bell's Theorem states that given
the marginals pAB, etc., a necessary condition that p exists
(hence that Gideon's instrument can do what he claims) is that the
CAB, etc., satisfy some inequality
(there are several, called Bell inequalities).

One such inequality is



and you can easily verify that the marginals given explicitly above
don't satisfy it. Hence Gideon is full of baloney.

I've seen some regulars make puzzling statements on the order of
"a mathematical inequality can NEVER be violated, and therefore quantum
mechanics cannot violate Bell's inequality". I can't imagine that
they mean the words which they have written. I am sure that they are
smarter than that and must have meant something else.

Mathematical inequalities generally make some assumptions which
are necessary for their validity. In our case, the assumption is that
Gideon's instrument actually does what he claims, or more mathematically,
that p can exist. If the inequality is violated, that just means that
the hypotheses for the inequality are violated---in our case that
Mark is right that Gideon's instrument is impossible.

In case the marginals are those predicted by quantum mechanics,
the violation of a Bell inequality just means that quantum mechanics
cannot be reproduced by a theory which assumes that A, A', B, and B'
can all be measured at the same time. This is what almost all physicists
mean by a (local) *realistic* theory. (I wouldn't be surprised if all those
who don't mean that are regulars of this forum.) A (local) "realistic"
theory assumes that what instruments measure is "really" there, whether
measured or not. Even if Alice can't measure A and A' at the same time
because of her antiquated equipment, a "realistic" theory assumes that
someone like Gideon can.


You are probably wondering where the marginals quoted above came from.
The example given above is essentially that of Asher Peres' generally
excellent book Quantum Theory: Concepts and Methods", pp. 162 ff.
Peres assumes the particular quantum state consisting of two entangled
qubits given by




In typical and hopefully self-explanatory physics notation, this state
might be denoted



where the subscript A refers to Alice's part of the qubit and B to Bob's.
(Neither are Peres' notation, which is not as explicit
as it should be.)

Peres only calculates the CAB, etc., not the marginals pAB.
I calculated those. I hope I got them right, but if not it doesn't matter
because the correlations derived from them are the same as Peres'.

To close, I suggest that the hundreds of lurking readers can probably
resolve any disputes to their satisfaction by asking the following questions
of the regulars:

1) Do they agree that the marginals quoted above are predicted by quantum
mechanics?

2) Do they agree that Gideon's p yielding those marginals is logically
impossible?

3) Do they agree that quantum mechanics is not (locally) "realistic"
in the sense of the above definition, i.e., that p cannot exist.

Of course, if the regulars have some different definition of "locally
realistic" the above discussion may not apply to that definition.
You can't argue with a definition ! But the definition used by
the "Bellians" is the one which I just gave.

Under that definition, it seems to me that the regulars should admit that the much-ridiculed
"Bellian" viewpoint is reasonable and consistent and tone down their rhetoric.
If I knew what definition of "realistic" theory the regulars are using,
perhaps I could also admit that their viewpoint is reasonable and consistent.
Should the difference be merely one of definition, no argument is possible,
and insulting rhetoric is inappropriate.
guest1202
 

Re: On the Fatal Mistake Made by John S. Bell in his theorem

Postby Joy Christian » Sun Jun 05, 2016 3:02 am

***

Let me stress again the fatal mistake in Bell's argument to make it clear what I am talking about. Let us look at the standard derivation of the upper bound on CHSH:

Image

Now I have no problem with the first line of the above derivation involving the four C's. Those four experiments can indeed be performed by the God of Spinoza. "He" can simply re-run the entire universe from scratch, four times, allowing Alice and Bob to choose from four different pairs of setting, (a, b), (a, b'), (a', b), or (a', b'), per each re-run. Then "He" can evaluate the four counterfactually possible averages in a sum, as they appear in the first line of the above derivation. So far so good.

But even the God of Spinoza cannot perform the completely different experiment being evaluated in line two of the derivation, where a single average is sneaked in.

Line two might as well be a pink elephant with blue wings. It does not pertain to any physical quantity. It is complete nonsense. It is a Uri Geller-type slight-of-hand.

:shock:
Joy Christian
Research Physicist
 
Posts: 2793
Joined: Wed Feb 05, 2014 4:49 am
Location: Oxford, United Kingdom

Re: On the Fatal Mistake Made by John S. Bell in his theorem

Postby thray » Sun Jun 05, 2016 7:37 am

Joy,

Since Spinoza was Einstein's touchstone for what God can do, it gives all the more importance to the fundamental calculus concepts of limit and function. That which is limited in some direction, may be functionally infinite in another.

Thus there is profound meaning in your statement: "No observation in any experiment was ever made except in some direction."

Quantum theory in principle cannot tame infinity, and in that respect is incomprehensible. A true 4 dimensional quantum theory depends very much on your framework.

Tom
thray
 
Posts: 143
Joined: Sun Feb 16, 2014 6:30 am

Re: On the Fatal Mistake Made by John S. Bell in his theorem

Postby FrediFizzx » Sun Jun 05, 2016 10:47 am

guest1202 wrote:Under that definition, it seems to me that the regulars should admit that the much-ridiculed
"Bellian" viewpoint is reasonable and consistent and tone down their rhetoric.
If I knew what definition of "realistic" theory the regulars are using,
perhaps I could also admit that their viewpoint is reasonable and consistent.
Should the difference be merely one of definition, no argument is possible,
and insulting rhetoric is inappropriate.

I will ask you the same question that I posed to Gordon. Given the CHSH string of expectation terms that can range from -1 to +1 do you think the following as a result for CHSH is possible?

+1 -(-1) + 1 +1 = 4
FrediFizzx
Independent Physics Researcher
 
Posts: 2905
Joined: Tue Mar 19, 2013 7:12 pm
Location: N. California, USA

Re: On the Fatal Mistake Made by John S. Bell in his theorem

Postby Joy Christian » Sun Jun 05, 2016 11:16 am

guest1202 wrote:If I knew what definition of "realistic" theory the regulars are using,
perhaps I could also admit that their viewpoint is reasonable and consistent.

The definition of "realistic" has been provided and explained to guest1202 many times previously, but he or she has failed to understand it. Here it is once again:

Image

This definition of realistic is from the classic and authoritative Report by Clauser and Shimony. It is of course just a reiteration of the definition by Einstein and Bell.

Once again, instead of recognizing the blatant mistake made by Bell and his followers in their derivation of the upper bound 2 on CHSH, guest1202 posts irrelevant details, designed to obfuscate the main issue brought out in this thread.

***
Joy Christian
Research Physicist
 
Posts: 2793
Joined: Wed Feb 05, 2014 4:49 am
Location: Oxford, United Kingdom

Re: On the Fatal Mistake Made by John S. Bell in his theorem

Postby guest1202 » Sun Jun 05, 2016 7:36 pm

FrediFizzx wrote:
guest1202 wrote:Under that definition, it seems to me that the regulars should admit that the much-ridiculed
"Bellian" viewpoint is reasonable and consistent and tone down their rhetoric.
If I knew what definition of "realistic" theory the regulars are using,
perhaps I could also admit that their viewpoint is reasonable and consistent.
Should the difference be merely one of definition, no argument is possible,
and insulting rhetoric is inappropriate.

I will ask you the same question that I posed to Gordon. Given the CHSH string of expectation terms that can range from -1 to +1 do you think the following as a result for CHSH is possible?

+1 -(-1) + 1 +1 = 4




The answer to your question depends on the context in which
you use the word "possible". I can think of only three contexts
that might be relevant for the present discussion. The answers
for each of them are given below.

1) If your context allows any consistent marginals which we can write down,
yes a CHSH sum

CHSH := CAB + CA'B + CAB' - CA'B' = 4

is possible. An example is


together with



This is an example of a kind of marginal(s) called a "Popescu/Rohrlich box",
PR box for short. Quantum mechanics does not permit PR boxes. However,
it does permit a slightly weaker concept which might be described as
a "probabilistic PR box", and the existence of those is sufficient to
prove that quantum mechanics is not local realistic in the sense of
any definition which I have seen.

2) If your context allows only marginals permitted by quantum mechanics,
the answer is that a CHSH sum can never have absolute value greater than
, a result known as the Tsirelson bound.

3) If your context restricts to marginals permitted by local realistic
theories (in the sense of any definition of "local realistic" that I have seen)
then the answer is that the absolute value of any CHSH sum can be no more than 2.
This is one of many so-called "Bell inequalities" (even though Bell didn't prove all of them).
guest1202
 

Re: On the Fatal Mistake Made by John S. Bell in his theorem

Postby FrediFizzx » Sun Jun 05, 2016 8:15 pm

guest1202 wrote:The answer to your question depends on the context in which
you use the word "possible".

The only context I was asking about is that the CHSH string of expectation terms can range from -1 to +1. Nothing else was specified and nothing else needs to be considered for if the result is possible or not. So it doesn't "depend" on anything else. It was a yes or no question. Of course it is easy to see that the answer has to be yes so we will continue anyways without your yes or no answer. What this boils down to is that if the CHSH string of terms are independent from each other, then we can have an inequality,

E(a,b)−E(a,b′)+E(a′,b)+E(a′,b′)≤4.

And that is the inequality that both QM and all experiments to date have used and have never violated. All one has to do is to look and see that all experiments and QM have always used this inequality with independent expectation terms. I have never seen a counter example to this simple demonstration by mathematical inspection. If what Bell says is right, then there ought to be one. Note that we have not said anything about local realistic theories as they are not required for this demonstration. So your task would be to demonstrate to us how QM and the experiments have ever violated Bell's inequalities. You can't because they never have. It is impossible.
FrediFizzx
Independent Physics Researcher
 
Posts: 2905
Joined: Tue Mar 19, 2013 7:12 pm
Location: N. California, USA

Equivalence of Christian's definition of "realistic" and min

Postby guest1202 » Sun Jun 05, 2016 9:19 pm

The definition of (local) "realistic" which Dr. Christian quotes is
equivalent to the one I gave, though the equivalence may
not be obvious at first glance. The earliest reference
stating the equivalence that I have seen is

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

I will restate it below. I think it is unfortunate that
early definitions of "realistic" (such as the one Christian quotes)
used an unnecessarily complicated language of "hidden variables".
It is much easier, clearer, and seemingly (though not actually) more general
to use the language of marginal probability distributions. However, to
make contact with your quoted definition, I will use the old-fashioned
language of "hidden variables" below.

In this language, we imagine a "source" drawing some outcome
from a probability space. The drawn outcome is called a "hidden variable",
often generically denoted by the symbol .
The TeX of this forum requires fussy input (for example, line feeds are
not allowed) and is often hard to read, so I will try to use ordinary
Roman characters wherever possible, and in place of
I will use "t" (suggesting "tuple"). The probability space will be finite.

I will denote Alice's measurement choices as a and a' .
(In my previous post, they were denoted A and A', but the quoted definition
uses capital A for something else.) Bob's choices will be denoted b and b' .

The source sends the hidden variable t to both Alice and Bob.
Encoded in it are instructions for the result of the measurement of each.
Alice's result is denoted

A(a,t) when she measures a, and

A(a', t) when she measures a'.

Bob's similar decoder yields result B(b, t) when he measures b and
B(b', t) when he measures b'.

A hidden variable could be implemented by writing four instructions
on a slip of paper: If Alice measures a , the measurement result is to be
a specified result (say -1); if she measures a' it is to be some
result (say +1) which can be the same or different from the result of
measuring a; and similarly for Bob.

The information contained in the instructions can be summarized
by a four-tuple of numbers, each entry being +1 or -1. For example,
a four-tuple

t = (i, j, k, m) , i,j,k,m = +-1,

could be interpreted as the instruction: If Alice measures a , return
result i (i = +1 or i = -1), if she measures a', return result j ,
if Bob measures b , return result k , and if he measures b', return
result m . By "return result i ", I mean that A(t, i ) = i , etc.

Therefore (and without loss of generality) we can take our
probability space to the the set of all four-tuples (i, j, k, m) with
each entry either +1 or -1. This probability space has 2^4 = 16 outcomes.
The probability

p(i,j,k,m) of the outcome (i, j, k, m)

is the same as the probability which my post expressed as p(a,a' , b, b' ).
For expository reasons I had to change the letters for this post,
but there obviously is no substantive difference between the two.

The bottom line is that Dr. Christian and I are using equivalent definitions
of the "realistic" part of "local realistic theory". If Christian's theory
actually is local realistic, it must yield p(i,j,k,m) for all 16 choices
of (i,j,k,m). More explicitly,

p(i, j, k, m) = prob( t = (i,j,k,m) ).

The "prob" on the right refers to the probability function on the probability space
of hidden variables (which happens to be the same as the "p" of my post).

Anyone wondering whether Christian's claimed local realistic theory really does
reproduce quantum mechanics should ask him what his theory
predicts for p given the marginals quoted in my post. For reference,
these marginals are





They are the predictions of quantum mechanics for the entangled state

( |1>|-1> + |-1>|1>)/\sqrt{2} .

Since I can't do subscripts in ASCII, we have to agree that
the first state in a tensor product like |1>|-1> refer's to Alice,
and the second to Bob. (The TeX rendering
of this is even less readable because it interprets the "minus" in |-1>
as an arithmetic operator; it thinks the expression means "1" subtracted from "|" ! )

Since the above was rather long, I will summarize.
The "hidden variable" contains the information necessary to specify
what results Alice and Bob get for whichever measurements they choose.
This information consists of a four-tuple of numbers t = (i,j,k,m) with each entry +1 or -1.
In principle, the hidden variable could contain additional information as well, but
any such additional information is irrelevant to what Alice and Bob measure, and so can be ignored.
When we do ignore any irrelevant information, we obtain a probability space with 2^4 = 16 outcomes.
This is exactly what the formulation of my post (which is actually the more modern formulation of
Fine and many others) posits. Therefore, the "hidden variable" definition of "realistic" which
Dr. Christian quotes is equivalent to the one I gave.
guest1202
 

Minor correction to quantum state

Postby guest1202 » Mon Jun 06, 2016 12:47 am

guest1202 wrote:Anyone wondering whether Christian's claimed local realistic theory really does
reproduce quantum mechanics should ask him what his theory
predicts for p given the marginals quoted in my post. For reference,
these marginals are





They are the predictions of quantum mechanics for the entangled state

(|1>|-1> + |-1>|1>)/\sqrt{2} .

Since I can't do subscripts in ASCII, we have to agree that
the first state in a tensor product like |1>|-1> refer's to Alice,
and the second to Bob.


The quantum state for which the stated marginals were calculated is

(|1>|1> + |-1>|-1>)/\sqrt{2} ,

not the one stated in the quote. The same error occurred in my previous post.
guest1202
 

Re: On the Fatal Mistake Made by John S. Bell in his theorem

Postby Joy Christian » Mon Jun 06, 2016 1:36 am

***

The detailed probabilistic predictions of my local-realistic model for the singlet state are exhibited here since 2014: http://arxiv.org/abs/1405.2355.

As anyone who bothers to read this paper can see, the probabilistic predictions of my local-realistic model are identical to those of quantum mechanics.

These predictions are also verified in several detailed, event-by-event computer simulations. Here is one of the simulations: http://rpubs.com/jjc/84238.

"guest1202" continues to ignore the blatant mistake made by Bell --- and continue being made by his followers --- in the derivation of the upper bound 2 on the CHSH string of expectation values. There is no way to derive the upper bound of 2 on CHSH without cheating. The correct bound on CHSH is 4, which is less than 2\/2.

The blatant cheating by Bell and his followers has been exposed by me in very simple terms in my latest two-page paper: viewtopic.php?f=6&t=267#p6435.

The physical bound of 2\/2 on the CHSH string within my local-realistic model has been derived by me many times since 2007: viewtopic.php?f=6&t=199#p5485.

Those who continue to cling to Bell's erroneous argument and spread bogus propaganda promoting the ideology inspiered by his work are doing disservice to physics.

***
Joy Christian
Research Physicist
 
Posts: 2793
Joined: Wed Feb 05, 2014 4:49 am
Location: Oxford, United Kingdom

Re: On the Fatal Mistake Made by John S. Bell in his theorem

Postby Joy Christian » Mon Jun 06, 2016 5:07 am

***
A mistake: I meant "The correct bound on CHSH is 4, which is greater than 2\/2."

***
Joy Christian
Research Physicist
 
Posts: 2793
Joined: Wed Feb 05, 2014 4:49 am
Location: Oxford, United Kingdom

Correction of another minor slip

Postby guest1202 » Mon Jun 06, 2016 6:47 pm

guest1202 wrote: The source sends the hidden variable t to both Alice and Bob.
Encoded in it are instructions for the result of the measurement of each.
Alice's result is denoted

A(a,t) when she measures a, and

A(a', t) when she measures a'.

Bob's similar decoder yields result B(b, t) when he measures b and
B(b', t) when he measures b'.

A hidden variable could be implemented by writing four instructions
on a slip of paper: If Alice measures a , the measurement result is to be
a specified result (say -1); if she measures a' it is to be some
result (say +1) which can be the same or different from the result of
measuring a; and similarly for Bob.

The information contained in the instructions can be summarized
by a four-tuple of numbers, each entry being +1 or -1. For example,
a four-tuple

t = (i, j, k, m) , i,j,k,m = +-1,

could be interpreted as the instruction: If Alice measures a , return
result i (i = +1 or i = -1), if she measures a', return result j ,
if Bob measures b , return result k , and if he measures b', return
result m . By "return result i ", I mean that A(t, i ) = i , etc.

Therefore (and without loss of generality) we can take our
probability space to the the set of all four-tuples (i, j, k, m) with
each entry either +1 or -1. This probability space has 2^4 = 16 outcomes.

The last sentence in the next to last paragraph should read:

"By 'return result i', I mean that A(a,t) = i, etc."

While writing, I might also mention that one can think of obtaining the "hidden variable"
from the source as drawing from an urn a slip of paper with a four-tuple (i,j,k,m) written
on it, where the urn contains various such slips.

This seems much more physical than talking about an obscure notion of "hidden variable".
Taken literally, the adjective "hidden" is misleading. The only thing "hidden" about the
slip of paper drawn is that Alice and Bob can't necessarily read it. Their decoders s,t --> A(s,t)
and s,t--> B(s,t) only give them partial information. (Here s represents the setting, a or a' for Alice, etc.)

But in principle, they could have more informative decoders that could allow them to read the entire slip.
Physics papers sometimes try to convey this idea by syntax like "If Charley has access to the hidden variable,
he can do so and so". If one didn't have a physical model in mind such as the one I just described,
such statements could seem very puzzling.

The instrument which Gideon tries to sell to Alice and Bob in my parable is nothing more or less than
a decoder which can read the entire slip. For the given hypothetical marginals, such an instrument is
impossible (so the hypothetical marginals are not true marginals).

The belief of the overwhelming majority of physicist that quantum mechanics cannot be duplicated by any
"local realistic" theory is nothing more or less than the assertion that the hypothetical marginals for some
quantum states can never be true marginals. If someone tells you otherwise, ask them to produce the
p(i,j,k,m) that produces the hypothetical marginals pAB, etc., of my post as true marginals.
guest1202
 

Re: On the Fatal Mistake Made by John S. Bell in his theorem

Postby Joy Christian » Mon Jun 06, 2016 10:27 pm

***

Not surprisingly, more obfuscations and irrelevant nonsense from "guest1202." Please note that "guest1202" is dodging the issue raised at the start of this thread:

There is absolutely no way to derive the upper bound of 2 on CHSH without cheating.

The reader is strongly advised to carefully read these two-pages and recognize that Bell and his followers have been cheating you for the past fifty years.

Joy Christian wrote:***

Let me stress again the fatal mistake in Bell's argument to make it clear what I am talking about. Let us look at the standard derivation of the upper bound on CHSH:

Image

Now I have no problem with the first line of the above derivation involving the four C's. Those four experiments can indeed be performed by the God of Spinoza. "He" can simply re-run the entire universe from scratch, four times, allowing Alice and Bob to choose from four different pairs of setting, (a, b), (a, b'), (a', b), or (a', b'), per each re-run. Then "He" can evaluate the four counterfactually possible averages in a sum, as they appear in the first line of the above derivation. So far so good.

But even the God of Spinoza cannot perform the completely different experiment being evaluated in line two of the derivation, where a single average is sneaked in.

Line two might as well be a pink elephant with blue wings. It does not pertain to any physical quantity. It is complete nonsense. It is a Uri Geller-type slight-of-hand.

:shock:
Joy Christian
Research Physicist
 
Posts: 2793
Joined: Wed Feb 05, 2014 4:49 am
Location: Oxford, United Kingdom

Re: On the Fatal Mistake Made by John S. Bell in his theorem

Postby parnassos2001 » Tue Jun 07, 2016 8:05 am

Relevant to the discussion:

"The irrelevance of Bell inequalities in Physics: Comments on the DRHM paper

"Abstract : It was shown in [1], cited in the sequel as DRHM, that upon a correct use of the respective statistical data, the celebrated Bell inequalities cannot be violated by quantum systems. This paper presents in more detail the surprisingly elementary, even if rather subtle related basic argument in DRHM, and does so together with a few comments which, hopefully, may further facilitate its wider understanding."

https://hal.archives-ouvertes.fr/hal-00824124
parnassos2001
 

Re: On the Fatal Mistake Made by John S. Bell in his theorem

Postby FrediFizzx » Wed Jun 08, 2016 1:34 pm

parnassos2001 wrote:Relevant to the discussion:

"The irrelevance of Bell inequalities in Physics: Comments on the DRHM paper

"Abstract : It was shown in [1], cited in the sequel as DRHM, that upon a correct use of the respective statistical data, the celebrated Bell inequalities cannot be violated by quantum systems. This paper presents in more detail the surprisingly elementary, even if rather subtle related basic argument in DRHM, and does so together with a few comments which, hopefully, may further facilitate its wider understanding."

https://hal.archives-ouvertes.fr/hal-00824124

Here are a couple more papers to contemplate,

http://link.springer.com/article/10.100 ... 010-9461-z
"Is the Contextuality Loophole Fatal for the Derivation of Bell Inequalities?"
Yes it is.

http://iopscience.iop.org/article/10.10 ... 1/1/012021
"EPR paradox, quantum nonlocality and physical reality"
FrediFizzx
Independent Physics Researcher
 
Posts: 2905
Joined: Tue Mar 19, 2013 7:12 pm
Location: N. California, USA

Next

Return to Sci.Physics.Foundations

Who is online

Users browsing this forum: No registered users and 80 guests

cron
CodeCogs - An Open Source Scientific Library