Between Joy Christian and Richard Gill: The middle way?

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

Re: Between Joy Christian and Richard Gill: The middle way?

Postby Heinera » Thu Sep 19, 2019 1:15 am

Gordon Watson wrote:.
It might help us all if you could each provide your definition of an RV. And in the context of Bell's work, if you think it there differs from the definition used in probability and statistics.

PS: I use λ in FUNCTIONS: eg, A(a,λ).

Thanks; Gordon
.

There is already a thread for that topic, and to be honest I don't see that there has been any resolution of the matter in that thread.

But Bell's argument goes through even without the assumption that lambda is a random variable, so I agree with you that there is not much point in explicitly assuming it is random in the context of Bell's theorem.
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Re: Between Joy Christian and Richard Gill: The middle way?

Postby Gordon Watson » Thu Sep 19, 2019 1:31 am

.
I am happy to be on Heinera's side. Especially so if he can see the consequent error in his ways -- and Bell's -- in neglecting my {.}:

From Bell(14a), starting in my terms:

E(a,b) - E(a,c) = ... {A(a,λ)A(b,λ)} - {A(a,λ)A(c,λ)} (1)

= ... etc; as in my paper: avoiding the erroneous step towards Bell(14b).


But in Heinera's terms (as in posts above) as I presently understand them: he now would write, by simplifying (1),

E(a,b) - E(a,c) = ... A(a,λ)[A(b,λ) - A(c,λ)]. (2) [sic]

1. If not, why not, please?

2. Does the above analysis help to show the error in his appreciated Post: Thu Sep 19, 2019 12:26 am ?
For which, many thanks!
.
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Re: Between Joy Christian and Richard Gill: The middle way?

Postby Heinera » Thu Sep 19, 2019 1:50 am

Gordon Watson wrote:.
I am happy to be on Heinera's side. Especially so if he can see the consequent error in his ways -- and Bell's -- in neglecting my {.}:

From Bell(14a), starting in my terms:

E(a,b) - E(a,c) = ... {A(a,λ)A(b,λ)} - {A(a,λ)A(c,λ)} (1)

= ... etc; as in my paper: avoiding the erroneous step towards Bell(14b).


But in Heinera's terms (as in posts above) as I presently understand them: he now would write, by simplifying (1),

E(a,b) - E(a,c) = ... A(a,λ)[A(b,λ) - A(c,λ)]. (2) [sic]

1. If not, why not, please?

2. Does the above analysis help you see the error in your appreciated Post: Thu Sep 19, 2019 12:26 am ?
For which, many thanks!
.


(2) follows from (1), yes. Remember that lambda has the same value in both expressions, so A(a, lambda) has the same value as the other A(a, lambda). This is not a mistake, it is deliberate.
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Re: Between Joy Christian and Richard Gill: The middle way?

Postby Gordon Watson » Thu Sep 19, 2019 1:56 am

Heinera wrote:
Gordon Watson wrote:.
I am happy to be on Heinera's side. Especially so if he can see the consequent error in his ways -- and Bell's -- in neglecting my {.}:

From Bell(14a), starting in my terms:

E(a,b) - E(a,c) = ... {A(a,λ)A(b,λ)} - {A(a,λ)A(c,λ)} (1)

= ... etc; as in my paper: avoiding the erroneous step towards Bell(14b).


But in Heinera's terms (as in posts above) as I presently understand them: he now would write, by simplifying (1),

E(a,b) - E(a,c) = ... A(a,λ)[A(b,λ) - A(c,λ)]. (2) [sic]

1. If not, why not, please?

2. Does the above analysis help you see the error in your appreciated Post: Thu Sep 19, 2019 12:26 am ?
For which, many thanks!
.


(2) follows from (1), yes. Remember that lambda has the same value in both expressions, so A(a, lambda) has the same value as the other A(a, lambda). This is not a mistake, it is deliberate.


So you are deliberately offering us a new Bellian inequality in the form of (2) [sic]?

Where is E(b,c)?
.
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Re: Between Joy Christian and Richard Gill: The middle way?

Postby Heinera » Thu Sep 19, 2019 2:12 am

Gordon Watson wrote:
So you are deliberately offering us a new Bellian inequality in the form of (2) [sic]?

Where is E(b,c)?
.

Sorry, I don't understand your question. If you mean "where is A(b, lambda)A(c, lambda)", then just follow my original derivation in reverse.
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Re: Between Joy Christian and Richard Gill: The middle way?

Postby Gordon Watson » Thu Sep 19, 2019 2:26 am

Heinera wrote:
Gordon Watson wrote:
So you are deliberately offering us a new Bellian inequality in the form of (2) [sic]?

Where is E(b,c)?
.

Sorry, I don't understand your question.


My questions arise from me being surprised that you offered (2) [sic] as a valid result.

It seems to me that, if you study (2) [sic], you will see that you cannot move on to BI; which includes E(b,c).

Which means, it seems to me, that you are offering us a new Bellian inequality; as invalid as all the rest.

So, in not using my mnemonic {.} to help with SIR, you reproduce a similar error to that in your earlier detailed proBellian post.

If it helps: Maybe you have not realised the implications of (2) [sic]?

So probably best to complete the integration and see where we land?

EDIT: I see the added note: "If you mean "where is A(b, lambda)A(c, lambda)", then just follow my original derivation in reverse."

If that's what you want to be in your picture, please show how you get back to BI. But isn't your (2) [sic] a new "BI" in itself?

PS: Have look at the result you get after completing the integration!
.
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Re: Between Joy Christian and Richard Gill: The middle way?

Postby Heinera » Thu Sep 19, 2019 2:38 am

Gordon Watson wrote:EDIT: I see the added note: "If you mean "where is A(b, lambda)A(c, lambda)", then just follow my original derivation in reverse."

If that's what you want to be in your picture, please show how you get back to BI.
.


But I have already shown that, by saying you should follow the derivation in reverse. Which of the steps do you have problems with?
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Re: Between Joy Christian and Richard Gill: The middle way?

Postby Gordon Watson » Thu Sep 19, 2019 2:46 am

Heinera wrote:
Gordon Watson wrote:EDIT: I see the added note: "If you mean "where is A(b, lambda)A(c, lambda)", then just follow my original derivation in reverse."

If that's what you want to be in your picture, please show how you get back to BI.
.


But I have already shown that, by saying you should follow the derivation in reverse. Which of the steps do you have problems with?


Are we talking about the equation that I called (2) [sic]? That's the issue for me for now. For it shows where your analysis now goes astray.

(2) [sic] is the simplest way I have of showing where you -- with Bellians and your earlier longer analysis -- go astray.

Since (2) [sic] is a valid result for you: Please complete the integration of (2) [sic]. What do you get?

E(a,b) - E(a,c) = ?
.
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Re: Between Joy Christian and Richard Gill: The middle way?

Postby Heinera » Thu Sep 19, 2019 2:57 am

Gordon Watson wrote:Are we talking about the equation that I called (2) [sic]? That's the issue for me for now. For it shows where your analysis now goes astray.

(2) [sic] is the simplest way I have of showing where you -- with Bellians and your earlier longer analysis -- go astray.

Since (2) [sic] is a valid result for you: Please complete the integration of (2) [sic]. What do you get?

E(a,b) - E(a,c) = ?
.

I have no idea what you are talking about. Your (2) is just a different way of writing your (1) so we get E(a,b) - E(a,c) = E(a,b) - E(a,c). An utterly trivial result.
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Re: Between Joy Christian and Richard Gill: The middle way?

Postby Gordon Watson » Thu Sep 19, 2019 3:07 am

Heinera wrote:
Gordon Watson wrote:Are we talking about the equation that I called (2) [sic]? That's the issue for me for now. For it shows where your analysis now goes astray.

(2) [sic] is the simplest way I have of showing where you -- with Bellians and your earlier longer analysis -- go astray.

Since (2) [sic] is a valid result for you: Please complete the integration of (2) [sic]. What do you get?

E(a,b) - E(a,c) = ?
.

I have no idea what you are talking about. Your (2) is just a different way of writing your (1) so we get E(a,b) - E(a,c) = E(a,b) - E(a,c). An utterly trivial result.


??? WE were talking about the eqn (2) [sic] --- see below --- that you appeared to endorse under your function-system:

For you replied, "(2) follows from (1), yes."

Can you complete (2) [sic]'s integration and see where it puts you, please?

Heinera wrote:
Gordon Watson wrote:.
I am happy to be on Heinera's side. Especially so if he can see the consequent error in his ways -- and Bell's -- in neglecting my {.}:

From Bell(14a), starting in my terms:

E(a,b) - E(a,c) = ... {A(a,λ)A(b,λ)} - {A(a,λ)A(c,λ)} (1)

= ... etc; as in my paper: avoiding the erroneous step towards Bell(14b).


But in Heinera's terms (as in posts above) as I presently understand them: he now would write, by simplifying (1),

E(a,b) - E(a,c) = ... A(a,λ)[A(b,λ) - A(c,λ)]. (2) [sic]
...............................................................

1. If not, why not, please?

2. Does the above analysis help you see the error in your appreciated Post: Thu Sep 19, 2019 12:26 am ?
For which, many thanks!
.


(2) follows from (1), yes. Remember that lambda has the same value in both expressions, so A(a, lambda) has the same value as the other A(a, lambda). This is not a mistake, it is deliberate.
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Re: Between Joy Christian and Richard Gill: The middle way?

Postby Heinera » Thu Sep 19, 2019 3:22 am

You introduced (2), not me. I merely pointed out that it was equivalent to (1). Which it is. If you think differently, please show us why they are not.
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Re: Between Joy Christian and Richard Gill: The middle way?

Postby Gordon Watson » Thu Sep 19, 2019 3:46 am

Heinera wrote:You introduced (2), not me. I merely pointed out that it was equivalent to (1). Which it is. If you think differently, please show us why they are not.


After the above to-and-fro, I don't know what to think. So please show me why you think that (1) and (2) [sic] are equivalent:

That is, please show by completing the integrals, how

E(a,b) - E(a,c) = -∫dλ ρ(λ)[A(a,λ)[A(b,λ) - A(c,λ)]. (2) [sic]

is equivalent to

E(a,b) - E(a,c) = -∫dλ ρ(λ)[{A(a,λ)A(b,λ)} - {A(a,λ)A(c,λ)}] (1)

under your supposed reduction of (1) to (2) [sic] via the "common function" in (1).

NB: You agree that (1) leads to (2) [sic], so can you please continue on [not via a retreat] and complete the integral.
.
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Re: Between Joy Christian and Richard Gill: The middle way?

Postby Heinera » Thu Sep 19, 2019 4:32 am

What do you mean by "completing the integral", given that we only have an abstract (i.e. unspecified) function A?
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Re: Between Joy Christian and Richard Gill: The middle way?

Postby Gordon Watson » Thu Sep 19, 2019 4:55 am

Heinera wrote:What do you mean by "completing the integral", given that we only have an abstract (i.e. unspecified) function A?


It is via your "common-function" analysis that 'we' arrive at A(a,λ)[ ... ] in (2) [sic].

And 'we' are happy to consider λ to be a random-variable.

So, it seems to me, under your system: ∫dλρ(λ)A(a,λ)[ ...] = 0.

That's why I say that the "equivalence" that you claim is FALSE.

For you have arrived at: E(a,b) - E(a,c) = 0.

Which leads to my main point: you make a similar "common-function" error in your helpful long-form proBellian analysis.

You simply cannot ignore my {.} and the fact that commuting functions in {.} are bound and do not travel: like you suppose they travel when we arrive at A(a,λ)[ ... ] in eqn (2) [sic], and you claim equivalence.
.
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Re: Between Joy Christian and Richard Gill: The middle way?

Postby Heinera » Thu Sep 19, 2019 5:07 am

Gordon Watson wrote:
So, it seems to me, under your system: ∫dλρ(λ)A(a,λ)[ ...] = 0.

.


And WHY should that always equal 0? It is trivial to find a function A that makes a counterexample.
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Re: Between Joy Christian and Richard Gill: The middle way?

Postby Gordon Watson » Thu Sep 19, 2019 5:22 am

Heinera wrote:
Gordon Watson wrote:
So, it seems to me, under your system: ∫dλρ(λ)A(a,λ)[ ...] = 0.

.


And WHY should that always equal 0? It is trivial to find a function A that makes a counterexample.


Thanks. But you need a function that satisfies Bell's analysis; so let's see what triviality you have in mind, please.

PS: If you want to back-track to your original (and very helpful) long-form proBellian analysis, it would be further helpful if you check it to your satisfaction and reproduce it afresh here with each relation numbered (and with comments about how you view the functions).

I recommend you go (H1), (H2) ..., so that we can identify whose relations we are dealing with (in case others want to have a go).

That way I can more easily identify the physical significance of the moves that you make: thus making it clearer where you go astray.

However, please note that (2) [sic] is the quickest way, imho, to spot your error. Since, when you think about it: no Bell-valid function [trivial or not] can eliminate that error.
.
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Re: Between Joy Christian and Richard Gill: The middle way?

Postby Heinera » Thu Sep 19, 2019 5:38 am

Gordon Watson wrote:However, please note that (2) [sic] is the quickest way, imho, to spot your error. Since, when you think about it: no Bell-valid function [trivial or not] can eliminate that error.
.

The only requirement (your "Bell-valid") Bell sets on his function A is that it should take one of two values, +1 or -1. Which one of them depends on the values of the two input parameters. Any function that satisfies this is OK as far as Bell's theorem is concerned.

For instance, as an example in the paper Bell uses . This does not make your integral (2) equal to 0, and is thus a counterexample to your claim.
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Re: Between Joy Christian and Richard Gill: The middle way?

Postby gill1109 » Thu Sep 19, 2019 6:28 am

FrediFizzx wrote:Yeah, I don't know why Gordon keeps harping about some error in the derivation of the inequality. There is no error in the inequality itself as it is mathematically proven. The error arises when you say a, b and c can happen all at the same time. They can't. It is that simple.
.

Indeed, the inequality is trivial.

But nobody says that a, b and c "happen" at the same time. a, b and c are the names of three unit vectors. Alice and Bob are experimenters who may choose which of these three vectors to use as a setting in each of their apparatus. In any one trial of the series of experiments, Alice chooses one of the three, and Bob chooses one of the three.

Repeat many, many times. There are nine possible combinations. Suppose each combination occurs many, many times. Suppose that each time, anew, nature picks a value lambda of the hidden variable, according to the same probability distribution with probability density rho. Then the average of the product of the outcomes on each side, +/-1, when Alice's setting is a and Bob's is b, converges to the integral of A(a, lambda)B(b, lambda) rho(lambda) d lambda.

Not only is Bell's inequality an elementary inequality which can be proven in a hundred different ways and is known under many different names, but the theorem that quantum mechanics is incompatible with local realism is an elementary theorem which also has many different proofs.

I repeat: *nobody* says that those three settings happen at the same time. Any pair can happen at the same time (in either order, if they are different), many times, if we do independent repetitions whereby each time nature picks a value lambda according to the same fixed probability distribution rho (which, please note, does not depend on the settings taken by Alice and Bob).

In conventional probability theory, a real-valued random variable X is represented by a deterministic function X defined on a set Omega and taking values in the set of real numbers. The idea is that Fortuna, Goddess of Chance, picks a value omega in the set Omega. The random variable X then takes on the value x = X(omega). Fortuna's choices are ruled by a probability measure on Omega. The chance that omega is in some subset A of Omega is called P(A) and the function P (taking values in the closed interval [0, 1]) satisfies a little list of rules, or axioms, which I won't repeat here.

You are allowed to think of probability in any way you like. Some people like a subjective interpretation ("degree of belief"), some people like the so-called frequentist interpretation - limiting frequency in many independent repetitions. There is a huge literature about these interpretations and also about other interpretations, and for that matter, about alternative systems of axioms to the Kolmogorov axioms.

In Bell's paper he was thinking about lambda as standing for some kind of complete microscopic description of source, particles, and detectors which makes everything that happens deterministic. The initial conditions. Every time the experiment is repeated the initial conditions can be different, and that is why (with the same settings) the detectors give different outcomes. Think of statistical mechanics.
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Re: Between Joy Christian and Richard Gill: The middle way?

Postby Joy Christian » Thu Sep 19, 2019 6:51 am

gill1109 wrote:
Not only is Bell's inequality an elementary inequality which can be proven in a hundred different ways and is known under many different names, but the theorem that quantum mechanics is incompatible with local realism is an elementary theorem which also has many different proofs.

The first part of the above sentence is correct, but the second part in blue is false. There is no such theorem. And even if there was such a "theorem", there already exists a comprehensive local-realistic model for all quantum correlations. Therefore, the "theorem" would have been either irrelevant or wrong. So, please, stop the false propaganda.

***
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Re: Between Joy Christian and Richard Gill: The middle way?

Postby Heinera » Thu Sep 19, 2019 7:45 am

Anyone who start their argument against Bell's theorem with the experimental fact that each particle can only be measured once, with only one setting for the detector, can merely conclude that experimental data can violate Bell's inequality. Thank you, but we already knew that.
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