## Bell's theorem refuted: Einstein and locality prevail

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

### Bell's theorem refuted: Einstein and locality prevail

.
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
.
Gordon Watson

Posts: 403
Joined: Wed Apr 30, 2014 4:39 am

### Re: Bell's theorem refuted: Einstein and locality prevail

Took a look over there Gordon. Sorry, looks like a bunch of nonsense to me. Besides, we already have two different ways of blowing Gill's theory out of the water and has leaky sides that are blown out. Bell's theory was gone a long time ago.
.
FrediFizzx
Independent Physics Researcher

Posts: 2905
Joined: Tue Mar 19, 2013 7:12 pm
Location: N. California, USA

### Re: Bell's theorem refuted: Einstein and locality prevail

Gordon Watson wrote:.NB: There is a typo in eqn (20). The first expression should read: E(AB)[1+ E(AC)] ≤ .......

The article at https://vixra.org/pdf/2109.0171v1.pdf has the same typo.
Mikko

Posts: 163
Joined: Mon Feb 17, 2014 2:53 am

### Re: Bell's theorem refuted: Einstein and locality prevail

FrediFizzx wrote:Took a look over there Gordon. Sorry, looks like a bunch of nonsense to me. Besides, we already have two different ways of blowing Gill's theory out of the water and has leaky sides that are blown out. Bell's theory was gone a long time ago.
.

Thanks Fred, quick straight-forward response much appreciated.

Did you note that my derivation of the QM results* endorses what you and Joy call "Bell's implicit assumption of the additivity of expectation values in the proof of his theorem." **

Though Bell erred, as I show in §5, I suspect that means that I also endorse von Neumann's approach?

Thanks again; Gordon

* And thus in accord with the experimental results.
** See my eqn (11).
.
Gordon Watson

Posts: 403
Joined: Wed Apr 30, 2014 4:39 am

### Re: Bell's theorem refuted: Einstein and locality prevail

Mikko wrote:
Gordon Watson wrote:.NB: There is a typo in eqn (20). The first expression should read: E(AB)[1+ E(AC)] ≤ .......

The article at https://vixra.org/pdf/2109.0171v1.pdf has the same typo.

Thanks Mikko,

I'll welcome your pinpointing any other mistakes or errors in the newer version, available as above!

All the best; Gordon
.
Gordon Watson

Posts: 403
Joined: Wed Apr 30, 2014 4:39 am

### Re: Bell's theorem refuted: Einstein and locality prevail

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
gill1109
Mathematical Statistician

Posts: 2812
Joined: Tue Feb 04, 2014 10:39 pm
Location: Leiden

### Re: Bell's theorem refuted: Einstein and locality prevail

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 $-\frac{\sqrt{2}}{2}$ against WI's 0. So the point you miss is this: It is UNSURPRISING that experiments exceed Bell's upper-bound of $-\frac{\sqrt{2}}{2}$, when the true upper bound is 0. Or, of equal importance: It is UNSURPRISING that QM exceeds Bell's upper-bound of $-\frac{\sqrt{2}}{2}$. 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 $_{p}(a^{+}),\:_{p}(b^{+})$, 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
Gordon Watson

Posts: 403
Joined: Wed Apr 30, 2014 4:39 am

### Re: Bell's theorem refuted: Einstein and locality prevail

Gordon Watson wrote:
gill1109 wrote: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.

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 $-\frac{\sqrt{2}}{2}$ against WI's 0. So the point you miss is this: It is UNSURPRISING that experiments exceed Bell's upper-bound of $-\frac{\sqrt{2}}{2}$, when the true upper bound is 0. Or, of equal importance: It is UNSURPRISING that QM exceeds Bell's upper-bound of $-\frac{\sqrt{2}}{2}$. 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 $_{p}(a^{+}),\:_{p}(b^{+})$, 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.

Gordon, a heap of heuristics is not a mathematical proof. Just *saying* that something is locally realistic doesn't make it so. You use schoolboy math but you apparently do not acknowledge basic logic. You've seen some formulas before and you can quote them. I do hope that as an engineer, you don't design bridges in that way. I think you are confused by the meaning of words like "or" and "and".

I once had a student who came to me after a lecture and asked me about the "less than or equals" symbol. Did it mean: less than *or* equals, or less than *and* equals? He was not dumb. He did come from another culture (his family came from North Africa, Islamic; languages French and Arabic and Berber). I explained as well as I could. Later, he did well in the exams.

You wrote "There is nothing in (5) that requires you to ignore (1)-(4)". I don't ignore them. You are making claims which contradict well known mathematical results. The onus on you is to come up with a water-tight argument. But in fact, you have no argument at all. The whole paper just says: "it is so because I say so". At least, that's my present opinion. Maybe you have better luck communicating to someone else. As far as I can see you only get support from people like you who want Bell's theorem to be false. But they do not adopt your arguments. They could write their own paper citing your self-publications and submit their own work to a refereed journal. If anyone came up with a watertight disproof of Bell's theorem all the journals in the world would be fighting to have the honour of publishing it.
gill1109
Mathematical Statistician

Posts: 2812
Joined: Tue Feb 04, 2014 10:39 pm
Location: Leiden

### Re: Bell's theorem refuted: Einstein and locality prevail

gill1109 wrote:
Gordon Watson wrote:
gill1109 wrote: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.

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 $-\frac{\sqrt{2}}{2}$ against WI's 0. So the point you miss is this: It is UNSURPRISING that experiments exceed Bell's upper-bound of $-\frac{\sqrt{2}}{2}$, when the true upper bound is 0. Or, of equal importance: It is UNSURPRISING that QM exceeds Bell's upper-bound of $-\frac{\sqrt{2}}{2}$. 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 $_{p}(a^{+}),\:_{p}(b^{+})$, 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.

Gordon, a heap of heuristics is not a mathematical proof. Just *saying* that something is locally realistic doesn't make it so. You use schoolboy math but you apparently do not acknowledge basic logic. You've seen some formulas before and you can quote them. I do hope that as an engineer, you don't design bridges in that way. I think you are confused by the meaning of words like "or" and "and".

I once had a student who came to me after a lecture and asked me about the "less than or equals" symbol. Did it mean: less than *or* equals, or less than *and* equals? He was not dumb. He did come from another culture (his family came from North Africa, Islamic; languages French and Arabic and Berber). I explained as well as I could. Later, he did well in the exams.

You wrote "There is nothing in (5) that requires you to ignore (1)-(4)". I don't ignore them. You are making claims which contradict well known mathematical results. The onus on you is to come up with a water-tight argument. But in fact, you have no argument at all. The whole paper just says: "it is so because I say so". At least, that's my present opinion. Maybe you have better luck communicating to someone else. As far as I can see you only get support from people like you who want Bell's theorem to be false. But they do not adopt your arguments. They could write their own paper citing your self-publications and submit their own work to a refereed journal. If anyone came up with a watertight disproof of Bell's theorem all the journals in the world would be fighting to have the honour of publishing it.

Thanks Richard,

Since I'll be putting you forward as a Referee, I suggest we save everyone a lot of time and address the following here.

1. My article is intended to be watertight, so please show me the major claims that contradict well-known math facts. This will allow us to quickly cut to the chase.

2. You really need at least one from each section. §3: Bell's theorem refuted. §4: Bell's inequality refuted. §5: Bell's error identified and explained.

4. To be clear. A heuristic enables one to discover or learn something for oneself; like proceeding to a solution by trial and error or by rules that are only loosely defined. In my case, they delivered a proof, consistent with locality and QM and experiment, that waits to be seriously challenged.

Thanks again; Gordon
.
Gordon Watson

Posts: 403
Joined: Wed Apr 30, 2014 4:39 am

### Re: Bell's theorem refuted: Einstein and locality prevail

Gordon Watson wrote:
gill1109 wrote:Gordon, a heap of heuristics is not a mathematical proof. Just *saying* that something is locally realistic doesn't make it so. You use schoolboy math but you apparently do not acknowledge basic logic. You've seen some formulas before and you can quote them. I do hope that as an engineer, you don't design bridges in that way. I think you are confused by the meaning of words like "or" and "and".

I once had a student who came to me after a lecture and asked me about the "less than or equals" symbol. Did it mean: less than *or* equals, or less than *and* equals? He was not dumb. He did come from another culture (his family came from North Africa, Islamic; languages French and Arabic and Berber). I explained as well as I could. Later, he did well in the exams.

You wrote "There is nothing in (5) that requires you to ignore (1)-(4)". I don't ignore them. You are making claims which contradict well known mathematical results. The onus on you is to come up with a water-tight argument. But in fact, you have no argument at all. The whole paper just says: "it is so because I say so". At least, that's my present opinion. Maybe you have better luck communicating to someone else. As far as I can see you only get support from people like you who want Bell's theorem to be false. But they do not adopt your arguments. They could write their own paper citing your self-publications and submit their own work to a refereed journal. If anyone came up with a watertight disproof of Bell's theorem all the journals in the world would be fighting to have the honour of publishing it.

Thanks Richard,

Since I'll be putting you forward as a Referee, I suggest we save everyone a lot of time and address the following here.

1. My article is intended to be watertight, so please show me the major claims that contradict well-known math facts. This will allow us to quickly cut to the chase.

2. You really need at least one from each section. §3: Bell's theorem refuted. §4: Bell's inequality refuted. §5: Bell's error identified and explained.

4. To be clear. A heuristic enables one to discover or learn something for oneself; like proceeding to a solution by trial and error or by rules that are only loosely defined. In my case, they delivered a proof, consistent with locality and QM and experiment, that waits to be seriously challenged.

Thanks again; Gordon

Dear Gordon, please do put forward my name as a referee. I would be delighted to explain to my peers what I have failed to explain to you.

Sorry, but I just don't see any point in *my* trying yet again to explain anything to you. I have already done what you ask in points 1, 2, and 3. Regarding heuristics, point 4, the problem is that your heuristics did *not* deliver any proof. Sure, they gave you ideas. Everybody works that way.

Your "proof" has been seriously challenged, and not just by me, but by numerous others. The problem seems to me that you do not have any conception of ordinary logical reasoning.

If you want to prove to the world you are right, then learn computer programming, or hire a computer programmer, and show by a computer simulation that you are right. If you really are right, you'll also win the Nobel prize and undying fame; and all quantum physics textbooks will be rewritten.

I hope you'll get some *interesting* responses from others on this forum.
gill1109
Mathematical Statistician

Posts: 2812
Joined: Tue Feb 04, 2014 10:39 pm
Location: Leiden

### Re: Bell's theorem refuted: Einstein and locality prevail

gill1109 wrote:The problem seems to me that you do not have any conception of ordinary logical reasoning.

When mysterian arguments fail, insults must suffice.
local

Posts: 295
Joined: Mon Aug 05, 2019 1:19 pm

### Re: Bell's theorem refuted: Einstein and locality prevail

local wrote:
gill1109 wrote:The problem seems to me that you do not have any conception of ordinary logical reasoning.

When mysterian arguments fail, insults must suffice.

Hi local, in this case, I must agree with Richard. I tried to make sense of Gordon's arguments but they are not rigorous at all. It is good that somebody tells him so.
He does not understand that to refute the theorem a concrete counterexample/model is needed like the one Joy claims he has. Whether Joy geometric algebra models really accomplish that is another discussion. Personally do not have an opinion about those models because I do not know GA.
I suppose that a computational model can also serve as a counterexample, however, I think a concrete mathematical model would be less controversial.
Justo

Posts: 83
Joined: Fri Aug 20, 2021 8:20 am

### Re: Bell's theorem refuted: Einstein and locality prevail

There's a difference between pointing out a flaw or lacuna in an argument and telling someone they have no conception of logic. The latter is Gill's modus operandi and that is one of the reasons he is reviled here.

I'm with you on the GA stuff. I don't have the expertise to make a judgement on it. I also agree that Gordon could greatly further his cause with a simulation. Several people have offered to help him with that, but he does not produce adequate specifications, which you too have noted.
local

Posts: 295
Joined: Mon Aug 05, 2019 1:19 pm

### Re: Bell's theorem refuted: Einstein and locality prevail

gill1109 wrote:
Gordon Watson wrote:
gill1109 wrote: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.

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 $-\frac{\sqrt{2}}{2}$ against WI's 0. So the point you miss is this: It is UNSURPRISING that experiments exceed Bell's upper-bound of $-\frac{\sqrt{2}}{2}$, when the true upper bound is 0. Or, of equal importance: It is UNSURPRISING that QM exceeds Bell's upper-bound of $-\frac{\sqrt{2}}{2}$. 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 $_{p}(a^{+}),\:_{p}(b^{+})$, 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.

Gordon, a heap of heuristics is not a mathematical proof. Just *saying* that something is locally realistic doesn't make it so. You use schoolboy math but you apparently do not acknowledge basic logic. You've seen some formulas before and you can quote them. I do hope that as an engineer, you don't design bridges in that way. I think you are confused by the meaning of words like "or" and "and".

I once had a student who came to me after a lecture and asked me about the "less than or equals" symbol. Did it mean: less than *or* equals, or less than *and* equals? He was not dumb. He did come from another culture (his family came from North Africa, Islamic; languages French and Arabic and Berber). I explained as well as I could. Later, he did well in the exams.

You wrote "There is nothing in (5) that requires you to ignore (1)-(4)". I don't ignore them. You are making claims which contradict well known mathematical results. The onus on you is to come up with a water-tight argument. But in fact, you have no argument at all. The whole paper just says: "it is so because I say so". At least, that's my present opinion. Maybe you have better luck communicating to someone else. As far as I can see you only get support from people like you who want Bell's theorem to be false. But they do not adopt your arguments. They could write their own paper citing your self-publications and submit their own work to a refereed journal. If anyone came up with a watertight disproof of Bell's theorem all the journals in the world would be fighting to have the honour of publishing it. [Emphasis added, GW.]

Dear Richard,

Thanks for the gillibluster: extreme verbosity with much avoidance and next-to-zero meaningful content.

Since all my paragraphs and relations are identified by a number:

1. Please identify where my schoolboy math does not acknowledge basic logic.

3. Please show where I am confused by the meaning of words like "or" and "and".

4. The only point of difference that I am aware of is WRT my eqn (5): you see it as a nonlocal relation, whereas I show that it a conditional probability over clearly local (and spacelike separated) results!

So Richard, in happily putting you forward as an adversarial referee, I'll be listing the above (and more) as some of the features the editors may expect from you.

You could here, of course, save some busy people much wasted effort if you would state you case in mathematical terms. At this stage in our discussion, it will be an honest representation when I tell editors that, beyond #4, I have no clue as to what you objections refer to! I might also send them: Against Gill, "Watson's locality proof via tunable sources."

Time you got serious; Gordon
.
Gordon Watson

Posts: 403
Joined: Wed Apr 30, 2014 4:39 am

### Re: Bell's theorem refuted: Einstein and locality prevail

Gordon Watson wrote: Thanks for the gillibluster: extreme verbosity with much avoidance and next-to-zero meaningful content.

Feigned erudition to cover for intellectual bullying.

Gordon, do you have a link to the latest version of the paper that does not require an account at academia.edu? Thank you.
local

Posts: 295
Joined: Mon Aug 05, 2019 1:19 pm

### Re: Bell's theorem refuted: Einstein and locality prevail

local wrote:
Gordon Watson wrote: Thanks for the gillibluster: extreme verbosity with much avoidance and next-to-zero meaningful content.

Feigned erudition to cover for intellectual bullying.

Gordon, do you have a link to the latest version of the paper that does not require an account at academia.edu? Thank you.

HOWEVER, as far as I know, AND BETTER: you only need register FOR FREE to see and PARTICIPATE in the whole discussion, including much squabbling among Bellians Gill, Laidlaw, Lambare, Jackson.

I'd welcome your input there as well as here. Also, so far as I know, I've answered every Bellian objection there.

All the best, HTH; Gordon
.
Gordon Watson

Posts: 403
Joined: Wed Apr 30, 2014 4:39 am

### Re: Bell's theorem refuted: Einstein and locality prevail

gill1109 wrote:
Gordon Watson wrote:
gill1109 wrote:Gordon, a heap of heuristics is not a mathematical proof. Just *saying* that something is locally realistic doesn't make it so. You use schoolboy math but you apparently do not acknowledge basic logic. You've seen some formulas before and you can quote them. I do hope that as an engineer, you don't design bridges in that way. I think you are confused by the meaning of words like "or" and "and".

I once had a student who came to me after a lecture and asked me about the "less than or equals" symbol. Did it mean: less than *or* equals, or less than *and* equals? He was not dumb. He did come from another culture (his family came from North Africa, Islamic; languages French and Arabic and Berber). I explained as well as I could. Later, he did well in the exams.

You wrote "There is nothing in (5) that requires you to ignore (1)-(4)". I don't ignore them. You are making claims which contradict well known mathematical results. The onus on you is to come up with a water-tight argument. But in fact, you have no argument at all. The whole paper just says: "it is so because I say so". At least, that's my present opinion. Maybe you have better luck communicating to someone else. As far as I can see you only get support from people like you who want Bell's theorem to be false. But they do not adopt your arguments. They could write their own paper citing your self-publications and submit their own work to a refereed journal. If anyone came up with a watertight disproof of Bell's theorem all the journals in the world would be fighting to have the honour of publishing it.

Thanks Richard,

Since I'll be putting you forward as a Referee, I suggest we save everyone a lot of time and address the following here.

1. My article is intended to be watertight, so please show me the major claims that contradict well-known math facts. This will allow us to quickly cut to the chase.

2. You really need at least one from each section. §3: Bell's theorem refuted. §4: Bell's inequality refuted. §5: Bell's error identified and explained.

4. To be clear. A heuristic enables one to discover or learn something for oneself; like proceeding to a solution by trial and error or by rules that are only loosely defined. In my case, they delivered a proof, consistent with locality and QM and experiment, that waits to be seriously challenged.

Thanks again; Gordon

Dear Gordon, please do put forward my name as a referee. I would be delighted to explain to my peers what I have failed to explain to you.

Sorry, but I just don't see any point in *my* trying yet again to explain anything to you. I have already done what you ask in points 1, 2, and 3. Regarding heuristics, point 4, the problem is that your heuristics did *not* deliver any proof. Sure, they gave you ideas. Everybody works that way.

Your "proof" has been seriously challenged, and not just by me, but by numerous others. The problem seems to me that you do not have any conception of ordinary logical reasoning.

If you want to prove to the world you are right, then learn computer programming, or hire a computer programmer, and show by a computer simulation that you are right. If you really are right, you'll also win the Nobel prize and undying fame; and all quantum physics textbooks will be rewritten.

I hope you'll get some *interesting* responses from others on this forum.

Dear Richard,
You will obviously need to explain things more clearly to an editor, so why not try openly here? I know of no better site for such discussion. Can you point me to one? I'm happy to take you on in any forum that is as accommodating as Fred's! (NB: from his early comments, it looks like he and you are on the same side here. Quite an accomplishment for one with no conception of ordinary logical reasoning ... but then again ... maybe it's a love-hate triangle.)

I will tell any editor that this draft has NOT been validly challenged; FULL STOP: neither by you, nor others. Your explanation (with others) of, or your claim for a "nonlocal" mechanism in EPR-Bohm experiments is surely demolished by my conditional probabilities over local-caused spacelike-separated results? (NB: at no stage do my results depart from local causality, nor from OQT's or experimental results.)

As for computer programming, I'd rather deal here with real experiments at the moment. If I'm wrong here then I'm wrong everywhere.

PS: Closing an escape route for you, please do NOT refer me to your papers. In this draft we are dealing with little more than high school math and elementary logic, so there's no escape for any of us!

HTH; Gordon
.
Gordon Watson

Posts: 403
Joined: Wed Apr 30, 2014 4:39 am

### Re: Bell's theorem refuted: Einstein and locality prevail

local wrote:There's a difference between pointing out a flaw or lacuna in an argument and telling someone they have no conception of logic. The latter is Gill's modus operandi and that is one of the reasons he is reviled here.

I'm with you on the GA stuff. I don't have the expertise to make a judgement on it. I also agree that Gordon could greatly further his cause with a simulation. Several people have offered to help him with that, but he does not produce adequate specifications, which you too have noted.

Thanks local,
My current focus on real experiments convinces me that the boundary conditions on realistic simulations are flawed. But let's get the HS math sorted first.
All the best; Gordon
.
Gordon Watson

Posts: 403
Joined: Wed Apr 30, 2014 4:39 am

### Re: Bell's theorem refuted: Einstein and locality prevail

Justo wrote:
local wrote:
gill1109 wrote:The problem seems to me that you do not have any conception of ordinary logical reasoning.

When mysterian arguments fail, insults must suffice.

Hi local, in this case, I must agree with Richard. I tried to make sense of Gordon's arguments but they are not rigorous at all. It is good that somebody tells him so.
He does not understand that to refute the theorem a concrete counterexample/model is needed like the one Joy claims he has. Whether Joy geometric algebra models really accomplish that is another discussion. Personally do not have an opinion about those models because I do not know GA.
I suppose that a computational model can also serve as a counterexample, however, I think a concrete mathematical model would be less controversial.

Dear Justo,
As I recall, you made some objections to my theory at Academia.edu, BUT you withdrew them after I'd responded. Against you, I claim rigour, so show me where I lapse or depart. PS: Every paragraph, and every equation is numbered: so what is your problem? Please show me: where am I NOT rigorous?
Thanks; Gordon
.
Gordon Watson

Posts: 403
Joined: Wed Apr 30, 2014 4:39 am

### Re: Bell's theorem refuted: Einstein and locality prevail

Justo wrote: ... He does not understand that to refute the theorem a concrete counterexample/model is needed like the one Joy claims he has. Whether Joy geometric algebra models really accomplish that is another discussion. Personally do not have an opinion about those models because I do not know GA.
I suppose that a computational model can also serve as a counterexample, however, I think a concrete mathematical model would be less controversial.

Justo, that is a lame copout that you don't know GA. What about quaternions? Don't know those either? If not, then you have no business being in these discussions.
.
FrediFizzx
Independent Physics Researcher

Posts: 2905
Joined: Tue Mar 19, 2013 7:12 pm
Location: N. California, USA

Next