gill1109 wrote:Gordon Watson wrote:.
Abstract: In a nutshell, this is Bell's theorem: No locally causal theory can produce the predictions of quantum mechanics. Against this, and bound by the axioms of locality, completeness, true realism, and free choice: we refute Bell's theorem and his related inequality. We also reveal his error. It follows that Einstein and locality prevail: the physical world is locally causal. We thus advance Einstein's quest to make quantum mechanics intelligible in a classical way.
I have a draft, titled as above, in discussion at
https://www.academia.edu/s/9feada3a8d?, and available via the same link.
NB: There is a typo in eqn (20). The first expression should read:
E(AB)[1+ E(AC)] ≤ .......
Thus far, the main Bell-supporters there appear to be Andrew Laidlaw, Richard Gill, Justo Pastor Lambare.**
I'd welcome advice, critical and other comments, etc, in this forum. (The discussion space at Academia.edu is mainly restricted to text; LaTex is not available.)
** I am about to release a new version soon, with replies to critics. I'll bring that here too.
Thanks; Gordon
Dear Gordon
As I said a few times over at Academia.edu,
https://www.academia.edu/s/9feada3a8d, your paper does *not* show there is a locally causal theory that produces the predictions of quantum mechanics. You *assume* the predictions of quantum mechanics in formulas (5) and (6). You say that you are using Malus' law from high school physics but that is a law about intensities of light, thought of as a continuous variable. You have no theory of a local and causal nature which predicts (5) and (6).
It is however a relief that your paper is fairly short and transparent.
Your logic in section 4 (concerning Bell's inequality) is faulty. You say that you have your own inequality "WI" which has a different bound than Bell's. So what? It's true that 2 is smaller than 3. It is also true that 2 is smaller than 4. Neither of those true statements implies that the other is false.
I have proven (well: I think so, and the referees of the mathematical journals where I published these results agreed) mathematical theorems that give a bound on the probability that Bell's inequality could be violated (by chance) by a certain amount, by a local realistic physics. Someone filled in particular choices of number of trials, amount of violation, and found that my bound was larger than 1. He said this showed my theorem was wrong. No, it was not wrong. It's obviously true that that probability is not larger than 1, so it is therefore also true that it is not larger than, say, 1.2. The theorem did not lie. A correctly proven mathematical theorem is a tautology. But my theorem only became *interesting* when the number of trials was taken to be somewhat larger -- when the numerical bound on the probability in question got very, very small indeed.
Richard
Thanks Richard
gill1109 wrote:You *assume* the predictions of quantum mechanics in formulas (5) and (6). You say that you are using Malus' law from high school physics but that is a law about intensities of light, thought of as a continuous variable. You have no theory of a local and causal nature which predicts (5) and (6).
Not true. (i) We need only consider (5); (6) is a true consequence. (ii) I say that I used Malus' Law as
one heuristic, among many; which, under my equivalence relations, held beyond my wildest expectation.
* (iii) Focussing just on (5), as I've explained: the LHS is a consequence of the locally causal interactions in (3)-(4). (iv) Squared trig-functions came into play when I explained the correlations in Mermin (1988); the ones he found mysterious, to the point of "impossibility" and "guaranteed failure".
gill1109 wrote:Your logic in section 4 (concerning Bell's inequality) is faulty. You say that you have your own inequality "WI" which has a different bound than Bell's. So what? It's true that 2 is smaller than 3. It is also true that 2 is smaller than 4. Neither of those true statements implies that the other is false.
WI, as I say, has the same LHS as BI (Bell's 1964 inequality). And I provide an example in (25), wherein BI has an upper bound of
against WI's 0.
So the point you miss is this: It is UNSURPRISING that experiments exceed Bell's upper-bound of
, when the true upper bound is 0. Or, of equal importance: It is UNSURPRISING that QM exceeds Bell's upper-bound of
. Thus, to the extent that BI provides false upper-bounds, to that extent BI is false.
As it must be given the high-school math in (18)-(24)!
Richard, further, against your false claims about my locally causal theory: In (1) I provide a schematic that is, in many ways, better than an experiment. For it allows us to infer differently. That difference, as I see it (and I do not recall seeing it elsewhere), is that (1) includes the post-polariser particles
, etc:
the outputs of wholly local interactions. Please note: there is nothing in (5) that requires you to ignore (1)-(4)!
* especially when I later learned that Aspect (2002) had discussed the Malus connection.
Thanks again; Gordon