minkwe wrote:The strongly objective view is that P(H) is the probability of repeatedly tossing the same coin many times, while the "weakly objective" view is that P(H) is the probability of tossing many different "similar" coins each just one time. Once you pick an interpretation, you must consistently use that interpretation, otherwise you shoot yourself in the foot and drown in paradoxes.
...
The short version of the two questions are: What interpretation does Gill use for the terms in Bell's inequality strongly objective or weakly objective? What interpretation does Gill use for the terms from QM strongly objective or weakly objective?
gill1109 wrote:I take the weakly objective interpretation of E(a, b), both with respect to QM and with respect to a possible LHV theory "behind" QM.
minkwe wrote:Are you sure that is your choice, because you just opened Pandoras box.
gill1109 wrote:Yes.
See
https://en.wikipedia.org/wiki/Interpret ... rpretation
It's just the usual frequentist interpretation of probability. It works pretty well in science. See "Introduction to mathematical statistics and data analysis" by John A Rice. Excellent text book with practical introduction to probability theory and then to statistics.
minkwe wrote:Secondly, since you have now committed that you are relying on the "weakly objective" interpretation of those expectation values, could you please explain how "counterfactual definiteness" is relevant to Bell's inequalities. Surely you must understand that there are no counterfactual terms in the "weakly objective" interpretation as opposed to the "strongly objective" one. So since your recent paper spends a lot of ink talking about counterfactual definiteness, please explain how it arises in the "weakly objective view".
minkwe wrote:minkwe wrote:The strongly objective view is that P(H) is the probability of repeatedly tossing the same coin many times, while the "weakly objective" view is that P(H) is the probability of tossing many different "similar" coins each just one time. Once you pick an interpretation, you must consistently use that interpretation, otherwise you shoot yourself in the foot and drown in paradoxes.
...
The short version of the two questions are: What interpretation does Gill use for the terms in Bell's inequality strongly objective or weakly objective? What interpretation does Gill use for the terms from QM strongly objective or weakly objective?gill1109 wrote:I take the weakly objective interpretation of E(a, b), both with respect to QM and with respect to a possible LHV theory "behind" QM.minkwe wrote:Are you sure that is your choice, because you just opened Pandoras box.gill1109 wrote:Yes.
See
https://en.wikipedia.org/wiki/Interpret ... rpretation
It's just the usual frequentist interpretation of probability. It works pretty well in science. See "Introduction to mathematical statistics and data analysis" by John A Rice. Excellent text book with practical introduction to probability theory and then to statistics.minkwe wrote:Secondly, since you have now committed that you are relying on the "weakly objective" interpretation of those expectation values, could you please explain how "counterfactual definiteness" is relevant to Bell's inequalities. Surely you must understand that there are no counterfactual terms in the "weakly objective" interpretation as opposed to the "strongly objective" one. So since your recent paper spends a lot of ink talking about counterfactual definiteness, please explain how it arises in the "weakly objective view".
Gordon Watson wrote:IF Richard Gill's theorem supports Bell's theorem (BT) in some way, please provide a link and commentary to the latest version of that theorem here.
It will then be refuted, as time permits.
Until then, just regard this as prophecy.
gill1109 wrote:Physicists sometimes invent slogans and call them theorems. But Bell never did that.
Joy Christian wrote:Just read Bell's book, written in his own words, where you will find that he repeatedly calls his theorem a "theorem." See, for example, the first edition of his book, page 65, after equation (3), where he writes: "This is the theorem. The proof will not be repeated here."
gill1109 wrote:Theorem. Let A and B be two functions...
Joy Christian wrote:gill1109 wrote:Theorem. Let A and B be two functions...
I would stop right here.
What do you mean by "functions"?
gill1109 wrote:minkwe wrote:Secondly, since you have now committed that you are relying on the "weakly objective" interpretation of those expectation values, could you please explain how "counterfactual definiteness" is relevant to Bell's inequalities. Surely you must understand that there are no counterfactual terms in the "weakly objective" interpretation as opposed to the "strongly objective" one. So since your recent paper spends a lot of ink talking about counterfactual definiteness, please explain how it arises in the "weakly objective view".
Question two: counterfactual definiteness. Local hidden variables implies counterfactual definiteness. If the outcome of Alice's measurement in direction a, when the particle turns up carrying the hidden variable lambda, is A(a, lambda), then it should not be a crime to talk about what the outcome would have been if the setting had actually been b? It seems to me that it's A(b, lambda).
gill1109 wrote:The range of A and B (what you call their co-domain) was assumed to be a point set, {-1, +1}, (two points in R). Later he showed his proof could be adapted so as to allow him to replace {-1, +1} by [-1, +1] (a particular line segment in R) and he had reason to do this in order to accommodate also hidden variables located in the measurement stations.
minkwe wrote:gill1109 wrote:minkwe wrote:Secondly, since you have now committed that you are relying on the "weakly objective" interpretation of those expectation values, could you please explain how "counterfactual definiteness" is relevant to Bell's inequalities. Surely you must understand that there are no counterfactual terms in the "weakly objective" interpretation as opposed to the "strongly objective" one. So since your recent paper spends a lot of ink talking about counterfactual definiteness, please explain how it arises in the "weakly objective view".
Question two: counterfactual definiteness. Local hidden variables implies counterfactual definiteness. If the outcome of Alice's measurement in direction a, when the particle turns up carrying the hidden variable lambda, is A(a, lambda), then it should not be a crime to talk about what the outcome would have been if the setting had actually been b? It seems to me that it's A(b, lambda).
If you are using the weakly objective interpretation, which of the correlations in Bell's or your inequality corresponds to what Alice and Bob got and which one corresponds to what they could have gotten but didn't?
I know you like talking about CFD. There is no crime to talk about it. But it is confusion to introduce the concept into your maths when none of your terms are counterfactual. If you are using the weakly objective view, then none of your terms are counterfactual and you can't reasonably claim at the end that CFD must be false due to violation.
In the weakly objective view, each correlation is measured on a different set of particles so it makes absolutely no sense to talk of what might have been measured but wasn't (CFD). It is only in the Strongly objective view that CFD is present, since all the correlations are measured on the same set of particles, and only one of them can practically be measured, then the others represent what they could have measured but didn't (CFD).
Joy Christian wrote:gill1109 wrote:The range of A and B (what you call their co-domain) was assumed to be a point set, {-1, +1}, (two points in R). Later he showed his proof could be adapted so as to allow him to replace {-1, +1} by [-1, +1] (a particular line segment in R) and he had reason to do this in order to accommodate also hidden variables located in the measurement stations.
[-1, +1] is not the only codomain one could assume to describe the measurement results in any EPRB type experiment. It is a completely ad hoc and physically incorrect assumption of the codomain. The error in Bell's argument thus lies in his very first equation. It contradicts the fact that one is trying to chart the spectrum of the Pauli matrices. An obvious fact which quantum mechanical description correctly takes into account. Bell blundered in his very first equation, and misdirected the course of physics for 50 years. But it is not Bell who should be blamed for this colossal travesty, but the followers of Bell, who should have known better.
gill1109 wrote:Let x be the number of apples and y be the number of oranges ...
The word correlation can mean three different things...
I can explain the meaning of CFD in the context of a simple specific example.
It can be confusing just to say "the correlation E(a, b)".
CFD is clearly true for epr-simple and epr-clocked.
minkwe wrote:There are no counterfactual terms in any of my simulations because my simulations use the weakly objective interpretation -- None whatsoever.Part of the quarrel I've had with you about my simulations has been on this very point. There are no counterfactual terms in any of my simulations. Besides you do not need any simulation to answer the question. You didn't need any simulation to write and publish your article so you should be able to answer the question clearly without one, unless you already know that you can not answer the question.
N <- 10^4
coincWindow <- 0.0004
ts <- pi * 0.03
asym <- 0.98
spin <- 0.5
n <- 2 * spin
phase <- pi * n
alpha <- c(0, 90) * pi / 180 # Alice's possible two settings (degrees)
beta <- c(45, 135) * pi / 180 # Bob's possible two settings (degrees)
a <- sample(c(1, 2), N, replace = TRUE) # Alice setting labels (1, 2)
b <- sample(c(1, 2), N, replace = TRUE) # Bob setting labels (1, 2)
el <- runif(N, 0, 2 * pi)
er <- el + phase
p <- 0.5 * sin(runif(N, 0, pi / 6))^2
ml <- runif(N, asym, 1)
mr <- runif(N, asym, 1)
Cl <- (0.5/pi) * (-1)^n * cos(n * (el - alpha[a]))
Cr <- (0.5/pi) * (-1)^n * cos(n * (er - beta[b]))
tdl <- ts * pmax(ml * p - abs(Cl), 0)
tdr <- ts * pmax(mr * p - abs(Cr), 0)
A <- sign(Cl)
B <- sign(Cr)
# a_CF <- 3 - a
# b_BF <- 3 - b
# Cl_CF <- (0.5/pi) * (-1)^n * cos(n * (el - alpha[a_CF]))
# Cr_CF <- (0.5/pi) * (-1)^n * cos(n * (er - beta[b_CF]))
# tdl_CF <- ts * pmax(ml * p - abs(Cl_CF), 0)
# tdr_CF <- ts * pmax(mr * p - abs(Cr_CF), 0)
# A_CF <- sign(Cl_CF)
# B_CF <- sign(Cr_CF)
AB <- A * B
E11 <- mean(AB[a == 1 & b == 1 & abs(tdl-tdr) < coincWindow])
E12 <- mean(AB[a == 1 & b == 2 & abs(tdl-tdr) < coincWindow])
E21 <- mean(AB[a == 2 & b == 1 & abs(tdl-tdr) < coincWindow])
E22 <- mean(AB[a == 2 & b == 2 & abs(tdl-tdr) < coincWindow])
S <- -(E11 - E12 + E21 + E22)
minkwe wrote:Richard, are you going to answer the question or not?
How is CFD important for your derivation, if you are using the weakly objective interpretation?
gill1109 wrote:Where does CFD come in? Well forget CFD for just a moment, suppose that we have a LHV model. That means that Nature chooses lambda, Alice chooses a and Bob chooses b. Alice and Bob then get to see A(a, lambda) and B(b, lambda). But since A and B are just a couple of functions I can also think of A(a', lambda) for all possible values of a' and B(b', lambda) for all possible values of b', at the same time. Within my mathematical model they are defined, too, even though they don't correspond to anything in the experiment ... well, what they correspond to, is what the outcome would have been, had Alice chosen a' instead of a, while Nature had still made the same choice lambda.
Return to Sci.Physics.Foundations
Users browsing this forum: ahrefs [Bot] and 22 guests