minkwe wrote:Zero. Now where is the dataset?
samplecommon <- (sample11 & sample12 & sample21 & sample22)
LGdelta <- sum(samplecommon)/sum(sample11)
LGdelta
[1] 0
gill1109 wrote:delta is defined in formula (7), which refers to the population (ie to the model, not to the outcomes of a simulation experiment), and it refers to events defined in terms of counterfactual measurement of spin in both directions on both particles at once.
The problem here is that the ensemble on which the correlations are evaluated changes
with the settings, while the original Bell inequality requires that they stay the same. In effect,
the Bell inequality only holds on the common part of the four different ensembles ΛAC′ , ΛAD′ ,
ΛBC′ , and ΛBD′ , i.e., for correlations of the form
E(AC′|ΛAC′ ∩ ΛAD′ ∩ ΛBC′ ∩ ΛBD′ ). (8)
Unfortunately our experimental data comes in the form
E(AC′|ΛAC′),
so we need an estimate of the relation of the common part to its constituents:
δ = inf_settings P(ΛAC′ ∩ ΛAD′ ∩ ΛBC′ ∩ ΛBD′ )/P(ΛAC′ )
= inf_settings P(ΛAD′ ∩ ΛBC′ ∩ ΛBD′ |ΛAC′).
...
ΛI = ΛAC′ ∩ ΛAD′ ∩ ΛBC′ ∩ ΛBD′
This ensemble may be empty, but only when δ = 0
It is not difficult however to add the complete set of counterfactual measurement outcomes in the simulation code, and to compute the "empirical" analogue of (7).
I have extended the script. There is indeed also a violation of (7) in this particular experiment.
dataSet <- data.frame(settingAlice = settingAlice, spinAlice = spinAlice, timeAlice = timeAlice,
settingBob = settingBob, spinBob = spinBob, timeBob = timeBob)
delta <- abs(timeAlice - timeBob)
sample11 <- (delta < 1.5) & (settingAlice == 1) & (settingBob == 1)
rho11 <- mean((spinAlice*spinBob)[sample11])
dataSet <- data.frame(settingAlice = settingAlice, spinAlice = spinAlice, timeAlice = timeAlice,
settingBob = settingBob, spinBob = spinBob, timeBob = timeBob)
delta <- abs(timeAlice - timeBob)
sample12 <- (delta < 1.5) & (settingAlice == 1) & (settingBob == 2)
rho12 <- mean((spinAlice*spinBob)[sample12])
(S <- rho11 + rho12 + rho21 - rho22)
all <- sum(sample11 & sample12 & sample21 & sample22)
delta11 <- all / sum(sample11)
delta12 <- all / sum(sample12)
delta21 <- all / sum(sample21)
delta22 <- all / sum(sample22)
delta <- min(c(delta11, delta12, delta21, delta22))
bound <- 4 - 2 * delta
S-bound
[1] -0.005963789
Note: one cannot violate a theorem. But sample analogues can violate population inequalities, of course. To look at (7) we need to extend the simulation so as to simulate the complete set of counterfactual outcomes of all possible measurements. The model allows us to do so, easily, by definition (it is a LHV model).
minkwe wrote:You claim that violation of such a bound is a privileged property of QM/non-local theories/non-real theories but impossible for LHV models.
gill1109 wrote:I did what you asked me to do, Michel. You owe me a beer, if ever we meet somewhere.
The theorem in my paper is a true theorem.
The difference between population mean and sample average still eludes you
minkwe wrote:No future experiment will ever violate it either.
minkwe wrote:Richard, you do not understand how to apply mathematics to experiments or physics. That is what we have discovered.
minkwe wrote:(1) How can it be that two particles are "entangled" at the stations if they were not "entangled" at the source?
OR
(2) Why do we need a single source (as opposed to two separate sources) to begin with if we do not believe the source imparts shared hidden properties to the particle pairs?
gill1109 wrote:minkwe wrote:(1) How can it be that two particles are "entangled" at the stations if they were not "entangled" at the source?
OR
(2) Why do we need a single source (as opposed to two separate sources) to begin with if we do not believe the source imparts shared hidden properties to the particle pairs?
Answer to question 1: just as is the case with classical correlation, one can (according to conventional QM theory) create quantum entanglement from nothing by post-selection.
...
Therefore the answer to question 2 is: we don't need a single source, if our experiments involve post-selection.
PS I found Michel's recent posts somewhat offensive and I don't want to be provoked into ad hominem attacks as a defence against ad hominem attacks. In order to de-escalate (cf. Putin saying the Ukraine referenda should be postponed) I made his posts temporarily invisible. Someone had better let me know if he says something I should respond to.
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