gill1109 wrote:Nobody is doing that. There is (1) a substitution of theoretical mean values by empirically observed averages.
And there is (2) a "fair sampling" assumption, aka no-conspiracy, or freedom.
So (1), statistical error has to be allowed for
(2) we need to assume that the particle pairs on the basis of which one particular sample correlation was observed, are a random sample from all particle pairs. Or at least, a representative sample from all the particle pairs. Taking a random sample is a good way to guarantee that.
gill1109 wrote:Is Theorem 1 a true theorem, yes or no? (That's in Section 2).
You'll need to refresh your memory concerning the Hoeffding inequalities which are used in the proof of Theorem 1 (in the appendix). You can find them on wikipedia.
Rosinger wrote: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.
...
Once again, and quite regrettably as far as many in the physics com-
munity are concerned, it cannot be overemphasized that the inequal-
ities in section 5, as much as those in the present section, are purely
mathematical, and as such, they have absolutely no need for any kind
of so called "physical" considerations in their proofs.
Therefore, let us repeat once more that it is one of the major merits of
DRHM to have pointed out so clearly the essential and so far hardly
known fact that the inequalities in section 5, as well as those in this
section, simply cannot be violated either by classical, or by quantum
physics. And they cannot be violated, precisely due to the fact that
they only depend on mathematics, and of course, logic.
Since I intend to stay polite on this forum, I won't say what I think about everything else you have just written.
gill1109 wrote:De Raedt has known my work for a long time. We have discussed both of our works with one another. We fully agree on all substantial points. Similarly, Giullaume Adenier has known my work for at least 15 years. We have discussed his and my ideas together. We are in full agreement.
John Bell’s inequalities have already been considered by Boole in 1862. Boole established a one-to-one correspondence between experimental outcomes and mathematical abstractions of his probability theory. His abstractions are two-valued functions that permit the logical operations AND, OR and NOT and are the elements of an algebra. Violation of the inequalities indicated to Boole an inconsistency of definition of the abstractions and/or the necessity to revise the algebra. It is demonstrated in this paper, that a violation of Bell’s inequality by Einstein-Podolsky-Rosen type of experiments can be explained by Boole’s ideas. Violations of Bell’s inequality also call for a revision of the mathematical abstractions and corresponding algebra. It will be shown that this particular view of Bell’s inequalities points toward an incompleteness of quantum mechanics, rather than to any superluminal propagation or influences at a distance.
Data produced by laboratory Einstein-Podolsky-Rosen-Bohm (EPRB) experiments is tested against the hypothesis that the statistics of this data is given by quantum theory of this thought experiment. Statistical evidence is presented that the experimental data, while violating Bell inequalities, does not support this hypothesis.
The examples (counterexamples) with the patient-investigations and the relation of these examples to EPR experiments prove, at least in the opinion of these authors, that neither realism nor Einstein locality need be abandoned because of a violation of Bell’s inequalities.
...
As shown elsewhere18, the validity of the fair sampling can actually be questioned on the basis of experimental data.
...
In the meantime, analysis shows that it indeed is still possible to ascribe properties to objects independently of observation, and contrary to David Mermin’s statement2, I would thus argue that Einstein’s attacks against the metaphysical underpinning of quantum theory are still valid today, and do not contradict nature itself.
gill1109 wrote:The fact of a local hidden variables theory ensures that we have counterfactual definiteness.
Mikko wrote:gill1109 wrote:The fact of a local hidden variables theory ensures that we have counterfactual definiteness.
Seems right if determinism and factual definetess are assumed, but can it be proven? Or does it depend on some other assumption that we naively make without noticing? Anyway, if factual definiteness is not assumed, counterfactual definiteness seems unlikely. With non-determinism it is less clear as any particular subsystem (such as a measurement) can be modelled as deterministic with random input from environment or a probabilistic or otherwise indeterministic subsystem.
gill1109 wrote:I don't know what you mean by "an otherwise indeterministic subsystem".
Mikko wrote:gill1109 wrote:I don't know what you mean by "an otherwise indeterministic subsystem".
There are theories that allow alternative possibilities without assigning any probabilities. I don't know any that would be interesting for physics but they can be useful, e.g., for safety analyses.
Any non-deterministic system can be converted to a deterministic one. But what do probabilities mean in a deterministic world? The probabilities of quantum mechanics quite obviously do mean something.
gill1109 wrote: The big question is, is there a fundamental difference between the QM probabilities and the classical ones? Einstein was sure that the answer would be no. John Bell dashed that hope (at least, that is the present concensus view).
FrediFizzx wrote:gill1109 wrote: The big question is, is there a fundamental difference between the QM probabilities and the classical ones? Einstein was sure that the answer would be no. John Bell dashed that hope (at least, that is the present concensus view).
QM probabilities are non-linear; most classical probabilies are linear. But that is wrong now since Joy has shown us that the predictions of QM can be accomplished in a local realistic classical way. So Einstein was right after all. But... there is still the situation of Lucien Hardy's fifth axiom, "Continuous reversibility" as the difference between quantum and classical.
FrediFizzx wrote:But I think you really could make a better attempt at a full understanding of the math. How come it all looks just fine to me and I understand it perfectly well? Personally, I like best a combination of the Geometric Algebra version with version 2.0. Having that e_0 original vector helps the understanding of the GA model. So how does that relate to the Pearle version? See... I'm trying to drive the discussion somewhat back on topic.
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