Calculating Fred Diether's r_0 term

[Bryan Sanctuary]

Dear all,

I will try to guide Fred through the calculation step by step that led me to find r_0 is not zero.  

Start by assuming

and then we have

I will go on when Fred agrees,

Bryan

[Fred Diether]

Nope.  You are still not paying attention.  That is an un-necessary step.  You are still completely clueless.

Local Quantum Mechanical Prediction of the Singlet State Using Geometric Algebra

https://www.scirp.org/journal/paperinformation?paperid=147271

Bell was wrong big time.

[Bryan Sanctuary]

Fred

I really am listening and trying to help, (and ignoring your insults), since I want to show you. So bear with me, and tell me if you agree with that and I will go on.  Put aside your animosities, and do some simple vector algebra. Tell me when we objectively disagree.  I think it will be productive.

You put s_1 = -s_2 =s which I plugged into r_0.  Do you agree and if not, tell me? 

You said "That is an un-necessary step."  how? and what should I use?

Bryan

Bryan

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[Fred Diether]

What are you missing in the overall calculation?

[Bryan Sanctuary]

Fred,

Having published a paper, it is incumbent on you to defend it, and you are refusing to do that.  I believe I am missing nothing, but you most certainly are missing a great deal.  I just found that Joy made an error in arXiv 2202.05615v1 in Eq 20.  Joy has a minus sign error, This equation 

is incorrect. The last term is not negative, but positive.  This is a critical error that you just copied from Joy without checking, so I  corrected your equation and write

I do not think you are capable of agreeing with me on this, so I copied Joy he must defend his work.

Once this is agreed to, I can continue to show the term does not average to zero.  

By the way, Fred, what is the meaning of the little bar over the zero?

Bryan

To view this discussion visit https://groups.google.com/d/msgid/Bell_quantum_foundations/05728053-6969-4451-aa3c-37207ea86d74n%40googlegroups.com.

[Fred Diether]

Ok, for the benefit of lurkers here is the last part of the calculation,

Apparently, you don't understand mu_a and mu_b nor the limits.  Also you should study Appendix B so you can correct your errors.  It's a null vector; r_0 ends up a null vector.

Local Quantum Mechanical Prediction of the Singlet State Using Geometric Algebra

https://www.scirp.org/journal/paperinformation?paperid=147271

Bell was wrong big time.

[Bryan Sanctuary]

Fred, ( and Joy)

The little arrow above the zero is  two errors: it is not null and it is not a vector. I will expand my derivation and we can discuss it,  If you will not discuss it, fine, but that makes you an intellectual coward,  so I urge you to engage (civilly if you are capable.)   If you and Joy cannot defend the work, I will just publish it without your input. 

,
Joy's equation, that you pasted  is wrong,  arXiv 2202.05615v1 

The last term should be positive.   Joy should respond  because it seems this error permeates all his EPR work, thereby invalidating it. 

Fred should know that copying and pasting other peoples' work always requires checking first, and he did not.  He needs to eat humble pie. 

Bryan

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[Fred Diether]

I see BS is still completely clueless and doesn't want to pay attention so I will ignore him for now.  If anyone else has questions, I would be happy to answer them.

[Fred Diether]

Oh, I forgot this,

Local Quantum Mechanical Prediction of the Singlet State Using Geometric Algebra

https://www.scirp.org/journal/paperinformation?paperid=147271

Bell was wrong big time.

[Austin Fearnley]

Hi  Fred

I will make more comments when I am ready.  Will take a little time and close reading of your paper.

I mentioned my comments on Joy's one-page paper in
https://ben6993.wordpress.com/commentary-on-joy-christians-model-of-correlation-a-b-in-his-one-page-paper/

As far as Bryan's comments go, I noted hearsay years ago that some critics claimed that there was a sign error somewhere.  Not sure without more reading but if a particular term is tending to zero then it should not matter if the term is + or -.

Bryan is also pointing out, I think, that your correlation should be a scalar and yet has a non-scalar term in it.  Again, I long ago commented that I was not too concerned about that as the non-scalar term tended to zero.  In Joy's paper that or a similar term only tended to zero because the trivector sign was cancelling out + with - in approx equal numbers in the summation over particle pairs.  Not sure yet if your paper uses both +1 and -1 trivector signs.  And if both signs are not used it will be interesting to see how you enforce tending to zero.

The tending of s1 to mu_a at the S_G device is a vipers' nest. Collapse of the wave function etc.   I need to see how s1 --> mu_a  gives appropriate +1 readings and -1 readings for A.

All for now

[Fred Diether]

Not a viper's nest at all;  quite simple actually.

Here are the definitions of mu_a and mu_b.  What this means for the limits is that s_1 --> +/- a and s_2 --> +/- b.  Of course the plus or minus is determined by sign of the dot product.  But as far as r_0 goes, the sign doesn't matter since all the cross products will be zero whether plus or minus upon taking the limits thus making r_0 a null vector.  In Mathematica language, {0,0,0}.  There is nothing "tending to zero" here since a null vector is in fact zero.  That just leaves the scalar, -a.b.

Do you now see how we get +/- 1 at A and B or do you need more explanation?

Local Quantum Mechanical Prediction of the Singlet State Using Geometric Algebra

https://www.scirp.org/journal/paperinformation?paperid=147271

Bell was wrong big time.

[Bryan Sanctuary]

Dear All and Joy,

I attach a short pdf that explains the error in Fred and Joy's work.  In deference to Joy, I will not submit this before giving him an opportunity  to respond, so we might discuss.  I will not respond to Fred unless he is civil and engages objectively.

Regards,

Bryan

To view this discussion visit https://groups.google.com/d/msgid/Bell_quantum_foundations/af261069-cb63-4827-88b4-48f913153f33n%40googlegroups.com.

[Austin Fearnley]

Hi Fred

Thanks for your feedback.  I need time to read your paper in detail.  I don't need any more clarification at this point.

I note that Bryan wants your cross product terms not to cancel to zero.  I assume Bryan's model needs his terms (if any) not to cancel to zero as they are essential parts of his model. Joy's cross product terms did cancel to zero IMO, but only approximately.  For an individual pair of particles the contribution of cross product terms in my commentary
https://ben6993.wordpress.com/commentary-on-joy-christians-model-of-correlation-a-b-in-his-one-page-paper/

was evaluated with dummy data for one pair of particles and its contribution to the correlation calculation was:

= – e1 e1 e2 e2 /sqrt2  + e1 e1 e2 e3 /sqrt2   =  – 1/sqrt2 + e2e3 /sqrt2  = – 1/sqrt2  – e1/sqrt2.  This is in a left-handed framework where (-e1) e2 e3 = -1.
You can make your own mind up if  the cross product t erm   e2e3/sqrt2  = – e1/sqrt2 is a vector or a bivector.

In the long run, the cross product terms average to zero but only because both signs of trivector are used in the calculation for successive pairs of particles.

I will get back to you when I can.

[Bryan Sanctuary]

Dear Austin,

No, I did not need the terms not to cancel. I am not coniving nor promoting my approach.   It has nothing to do with philosophy or framework.  It is a one page of undergrad vector analysis that shows that Fred's null vector is a non null bivector.  It is only math.  Fred is wrong unless he finds my error.  His error came from Joy.  It is very short and concise which I paste below.  I hope you can spend 5 minutes, which is all it takes.

Fred has published a paper and it is incumbent upon him to defend it.  He must find an objective error in the page below.  If neither he nor Joy can, then Fred's paper and at least a dozen of Joy's contain a fatal error.  Fred prefers insults, but it is his responsibility to find an objective error.

I appreciate your comments and point of view.

Bryan

Fred, where is the objective error?

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[Fred Diether]

Austin, the model is a lot different now-a-days from the old one you are describing.  Improved quite a bit.  Any questions please feel free to ask.

BS is really acting weird.  I just explained how r_0 is a null vector and it seems he completely ignored the explanation.  I guess it just proves how completely clueless he is.

Local Quantum Mechanical Prediction of the Singlet State Using Geometric Algebra

https://www.scirp.org/journal/paperinformation?paperid=147271

Bell was wrong big time.

[Austin Fearnley]

Hi Bryan

I did not mean to cause offence and I know that you are sincere in your writing about models.

In seeing a recent post I was struck by a difference in your's and Joy's models based on the treatment of the cross product.
IMO Joy's cross products were approximately zero but only because different trivector values were being used in the one calculation.
Some time ago geometric algebra experts were said to only allow one sign of trivector in an entire calculation.  I am not an expert in GA, of course.
If only one trivector sign is used in a calculation then the cross product term will in general be non-zero.

I have not yet looked in detail at Fred's calculations for his model, and it will take me more than five minutes.  I will need to make my mind up about whether or not Fred's cross products tend to approx zero, although they are not strictly scalars.  

I did look up algebra of Cl(2,2) and noted that there were four vectors and three trivectors etc and quite different from Cl(3,1).

All for now.  

Best wishes

[Bryan Sanctuary]

Hi Austin,

 I do not believe that Fred or Joy actually did the calculation.  They made the assumption it was a vector that averages to zero (well not quite, Fred just copied Joy).  But that r_0 is a bivector and does not average to zero .  I will show you 

so the bivector contribution is clearly visible.  Just looking at r_0 in the form Fred states, you can see it is a grade 2 multivector and not a vector, if you know GA.  I know that GA is not current, but I am convinced that it will replace QFT.  (If you know someone with good GA background, send him/her the r_0 expression and ask them what r_0  is as a multivector).  If you want I can send you the evaluation of the bivector term. 

I believe Joy has good ideas, but unless he finds an error in my one page, his dozen papers all start out right with quaternions, but he throws it all away by setting r_0 to 0.

Clifford algebra (2,2) is two times and two spatial components.  The two times are regular time i \gamma^0 and internal rotation,  i\gamma^2.  It is the same that Penrose uses in Twistor theory.  The point is, that (2,2) bifurcates into two sectors in the Dirac equation:  the Body FF Cl(1,2) and the Lab FF, the three sphere S^3.  So that is where Joy and I agree since the rotation is a quaternion.  That is, a bivector has two distinct sectors: BFF of even parity (a 2d disc, or a plane and a plane is a bivector)  and LFF of odd parity (a quaternion).  It is the duality of spin, like position and momentum.

I hope this helps.  You are not offending me in any way, and I am pleased to have your comments and responses.

Bryan

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[Fred Diether]

Austin,

Did you understand the explanation that I gave why r_0 ends up being a null vector in my calculation? 

It seems that BS doesn't understand it though I now suspect he has lost his mind.  That could explain why he still remains completely clueless about these matters.

Local Quantum Mechanical Prediction of the Singlet State Using Geometric Algebra

https://www.scirp.org/journal/paperinformation?paperid=147271

Bell was wrong big time.

[Austin Fearnley]

Hi Bryan

I give an extract far below from my commentary on Joy's one page paper.  I am not yet ready to comment in detail on Fred's paper to you or to Fred.

When lambda=1 for a pair of particles, their contribution to the AB term is – 1/sqrt2  + e1/sqrt2.  
When lambda=-1 for a pair of particles, their contribution to the AB term is – 1/sqrt2  - e1/sqrt2.  
You can see that the     + e1/sqrt2  and   - e1/sqrt2 terms cancel in the summation across these two pairs of particles.
As the sign of lambda depends on the overal trivector being used in the calculation, an issue at the time of the publication was whether one could legitimately use two trivector signs in one calculation.  After two such pairs, the calculation would be (-1/sqrt2  + e1/sqrt2  – 1/sqrt2  - e1/sqrt2 )/2 = – 1/sqrt2  = -0.707
It is not up to me to say if using alternating (or random allocation of) lambda signs is a legitimate usage within one experiment.

If one insists on using only one trivector sign per experiment, then there will not be a cancellation to zero.
If one only counted n pairs where lambda=1, their contribution to the AB term is n*(– 1/sqrt2  + e1/sqrt2)/n =  – 1/sqrt2  + e1/sqrt2.  

Testing my memory here, as I did not mention it in my commentary paper, I was very surprised that these two terms were the only terms appearing in the calculation!  But then
I realised that this was because of the other aspect of the sum, which is that s1-> +/-a and s2-> +/-b so the orientation attribute of s1 and s2 drops out of the scene leaving behind only the sign, which then was attached to a and b.  So there are only two different terms in the sum.



EXTRACT
----
"From here onward these comments agree that 𝓔 (a,b) = – a.b and this will be shown using a practical example.  But the earlier reservations concerning the values of A and B undermine this finding.

As a practical example, this calculation will be executed using vector a = (0,0,1) and vector b = (0,1,1)/sqrt 2.

When λ = +1, then (Laλ) (Lbλ) = (e1^e2) (e1^[{e2-e3}/sqrt2]) = + e1 e2 e1 e2 /sqrt2 – e1 e2 e1 e3 /sqrt2 = – e1 e1 e2 e2 /sqrt2  + e2 e1 e1 e3 /sqrt2

= – 1/sqrt2 + e2e3 /sqrt2  = – 1/sqrt2  + e1/sqrt2.  This is in a right-handed framework where e1 e2 e3 = +1.

This calculation could have been performed using (Da)(Db) in place of (Laλ)(Lbλ), with the same result.

 

When λ = -1, then (Laλ) = ( – Da) and as (Da) is a right-handed bivector then (- Da) is a left-handed bivector.  So here we use (Laλ) and (Lbλ) or (- Da) and (-Db) in left-handed bases with λ = – 1.

then (Laλ) (Lbλ) = ((-e1)^e2) ((-e1)^[{e2-e3}/sqrt2]) = + (-e1) e2 (-e1) e2 /sqrt2 – (-e1) e2 (-e1) e3 /sqrt2 =  e1 e2 e1 e2 /sqrt2  – e1 e2 e1 e3 /sqrt2

= – e1 e1 e2 e2 /sqrt2  + e1 e1 e2 e3 /sqrt2   =  – 1/sqrt2 + e2e3 /sqrt2  = – 1/sqrt2  – e1/sqrt2.  This is in a left-handed framework where (-e1) e2 e3 = -1.

In the long run, sum AB averages to – 1/sqrt 2.  Which for this example is – cos 45 degrees where 45 degrees is the angle between vectors a and b.  This is the desired correlation which exceeds in absolute magnitude the  0.5 limit set by Bell’s Inequality.
------

I am very interested in you saying that there are two 'time' vectors in Cl(2,2) as I have moved on in my own post-Bell work to reality having more than one time dimension.  I will write about that another time.

[Austin Fearnley]

Hi Fred

I need more time to think about your model.  If you are using two trivector signs in one experiment then you can probably cancel out (approximately) the cross terms.

But if not, then I would be interested to see how it is managed.

[Bryan Sanctuary]

Fred,

You expect me to read your paper again to show me I am wrong when there lies your error!!  I have shown your paper to be fatally flawed and blew a dozen papers of Joy's out of the water, unless you can find an error in the attached one page of undergad vector algebra.  Please indicate the exact line and equation where the error occurs and justify it. You are unable to act as a scientist and incapable of civil exchanges.  Send the attachment to your blogger friend Ben for his opinion.  He seems to know what he is talking about.

r_0 is not a vector and it is not null as I showed in detail.  You, well Joy actually, made a pure mathematical error with a yes or no answer: is the average < r_0>  zero or not?  If you say zero, you MUST prove it, because you have zero credibility, and for me, you rhetoric is not enough.

My conclusion is you are now flummoxed and getting a bit scared because you made such a fool of yourself: first by arguing against CHSH. Then again after I have shown your paper is fatally flawed.     I used this word sparingly, but Fred is fucked. 

I will likely submit it after Christmas unless you or Joy respond, which means you should write half a page to show me wrong. But you cannot.

Bryan

To view this discussion visit https://groups.google.com/d/msgid/Bell_quantum_foundations/14a03294-1d4f-416b-b6a9-ad092cedf614n%40googlegroups.com.

[Fred Diether]

Austin, it sounds like you didn't even read my explanation for r_0 ending up as a null vector.  Do you want me to post it again?  We are not using two trivector signs.  Joy stopped doing the model that way a long time ago.

Local Quantum Mechanical Prediction of the Singlet State Using Geometric Algebra

https://www.scirp.org/journal/paperinformation?paperid=147271

Bell was wrong big time.

[Austin Fearnley]

Hi Fred

Yes, please re-post the r0 information that you think I need.  I did continually say that I needed time to consider your model.  But Bryan is putting time limits on your response so I will get down to the ro issue asap.

My commentary on Joy's model was seven years ago and I have not worked with geometric algebra since then.    The job was relatively easy because of biases in the model with respect to lack of variability in 'variables' which I assume you have amended in your model.  I did not even need to specify s1 and s2 values. However, my commentary on your model will be harder to make as there will be more complexity to investigate.  I will need specify s1 and s2 values for at least four particle pairs and see what happens, while keeping a = (0,0,1) and b = (0,1,1)/sqrt2.

I do not use Mathematica software so I cannot comment on your computer program syntax.  I do not use geometric algebra software so I am on my own with paper and pen.  Despite my maths/stats background I do not trust myself (or anyone else) with complicated algebra. I am 76 years old and have gradually lost patience/interest/enjoyment with using my Excel VB software. But I am OK with using paper and pen.  It is essential for me to be able to use concrete examples to believe the formulae.  Everyone should do that to avoid becoming lost in maths, IMO.

Austin
(aka ben or ben6993)

[Fred Diether]

Here's a repost...

Not a viper's nest at all;  quite simple actually.

Here are the definitions of mu_a and mu_b.  What this means for the limits is that s_1 --> +/- a and s_2 --> +/- b.  Of course the plus or minus is determined by sign of the dot product.  But as far as r_0 goes, the sign doesn't matter since all the cross products will be zero whether plus or minus upon taking the limits thus making r_0 a null vector.  In Mathematica language, {0,0,0}.  There is nothing "tending to zero" here since a null vector is in fact zero.  That just leaves the scalar, -a.b.

Do you now see how we get +/- 1 at A and B or do you need more explanation?  If you don't understand something, just ask.

This also demonstrates that BS's paper about r_0 is a bunch of junk just like his papers.  I think my work here is done.

Local Quantum Mechanical Prediction of the Singlet State Using Geometric Algebra

https://www.scirp.org/journal/paperinformation?paperid=147271

Bell was wrong big time.

[Bryan Sanctuary]

Dear Fred 

Nonsense and clueless.

Bryan

To view this discussion visit https://groups.google.com/d/msgid/Bell_quantum_foundations/53ad0ed4-82a4-4ac4-9835-c9713e2c6cb4n%40googlegroups.com.

[Austin Fearnley]

Hi Fred


It is a vipers' nest.

I see what you are doing but I am not sure how it fits into the formal maths equations.
Also I am beginning to appreciate why Joy originally worried that his  model was not transferable to a computer.

The term (a x s1) x (s2 x b) is the issue, I think.
At the beginning or at the production of the particle pair, s1= -s2. And that does not give a null term for anyone applying the calculation using s1=-s2.

Yet by the time of the simultaneous measurements of A and B, the states have progressed to: s1 = +/- a  while s2 = +/- b.  Where a does not equal +/-b.
The term (a x s1) x (s2 x b) becomes  (a x a) x (b x b) = null   because a x a = zero.
which is the null that you wish to use.

I understand and agree that the measuring device slowly or maybe instantly converts s1 into +/-a. But that destroys the equation s1=-s2.
I am not sure how to convert this into the maths.  It needs a more expert user of GA than me to break down the steps where s1=-s2 transitions to s1=+/-a and to explain how .
(a x s1) x (s2 x b) becomes  (a x a) x (b x b) = null

Best wishes

[Fred Diether]

OK let's put it all together and maybe clueless BS will understand this very simple math.  Here is the last part of the calculation.  Please see the paper for the whole product calculation.

Here are the definitions of mu_a and mu_b.  What this means for the limits is that s_1 --> +/- a and s_2 --> +/- b.  Of course the plus or minus is determined by sign of the dot product.  But as far as r_0 goes, the sign doesn't matter since all the cross products will be zero whether plus or minus upon taking the limits thus making r_0 a null vector.  In Mathematica language, {0,0,0}.  There is nothing "tending to zero" here since a null vector is in fact zero.  That just leaves the scalar, -a.b.

So that gives for r_0 upon taking the limits,

r_0 = I_3{(+/-1)(0,0,0) + (+/-1)(0,0,0) - (0,0,0) x (0,0,0)} = {0,0,0}

I can only imagine that BS never finished high school if he doesn't understand it.

Local Quantum Mechanical Prediction of the Singlet State Using Geometric Algebra

https://www.scirp.org/journal/paperinformation?paperid=147271

Bell was wrong big time.

[Austin Fearnley]

Hi Fred

A difficulty in following the paper is the sudden jump from s1 = -s2  to s1 = +/-a  within your equation 25.

I suggest you keep s1 and s2 in equations 18 and 19 where you need them to explain values of A and B measurements.
But after that, you do not need s1 = -s2 any more so is it possible to ditch s1 and s2 and replace them by +/-a and +/-b in equations 20 to 25?
And so give a slower introduction to the switch.  

It is concerning that you build a framework of maths based on s1=-s2 but make no mention that this maths framework also applies to s1=+/-a.

[Fred Diether]

Austin, it is all about taking the limits for the "sudden jump".  That is when detection happens and r_0 becomes a null vector.

Local Quantum Mechanical Prediction of the Singlet State Using Geometric Algebra

https://www.scirp.org/journal/paperinformation?paperid=147271

Bell was wrong big time.

[Bryan Sanctuary]

Dear Jarek 

I request you eject Fred Dieher from the group since he violates the terms of Google Groups.  See email example below. There many more.  It is not just me, he denigrates, it is almost everyone whose work he calls junk, nonesense, and question their competence. His behavior is unacceptable.

Please review Fred's emails and please apply google group rules of conduct and eject him.

I will leave the group in the New Year

Bryan

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[Austin Fearnley]

Hi Fred

I have downloaded some GA software but can't get it to work yet.


A definition of ab is a.b + a X b
where a X b is not in general a null term.

That means your equations leading up to eqn 26 must be doing something out of the norm.

I have looked to see if setting s1 = +/-a in the earlier equations would lead away from the norm, and yet those equations appear to treat s1 and s2 independently and should hold in general.  So far so good.

Next I have looked at the transition from eqn 20 to eqn 21.
Eqn 20 uses A(ak,s1k) which seems fine.
Eqn 21 uses {a s1} which does not clearly a transition in the logic?  BTW what are the curly brackets.  Just normal brackets?
A(ak,s1k) uses an s1k value appropriate to particle pair labelled k.
AFAIK s1k does not necessarily equal s1m for all k and m.
So, removing the k index is not straightforward in going from eqn 20 to 21 as it seems it could be losing the correct sign of A for some particles?

That is as far as I have gone this morning.

[Fred Diether]

LOL!  I successfully shoot down BS's claim about my r_0 and now he wants me off the group.  He really is a clueless jerk.

I only call out what I see people posting as clueless nonsense.  If you can't take it, get out!  Don't respond.

And... I don't think Jarek is owner of this group.  :-)

Local Quantum Mechanical Prediction of the Singlet State Using Geometric Algebra

https://www.scirp.org/journal/paperinformation?paperid=147271

Bell was wrong big time.

[Mark Hadley]

Fred

Neither your behaviour or competence are appropriate for this group.

I am not calling in anyone to ban you. I'll just ignore your messages.

I strongly encourage everyone to ignore your work and posts because you lack basic competence and don't have the maturity to engage in a constructive dialogue.

Mark

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[Alexandre de Castro]

I see no reason to remove anyone from the group. I have presented arguments challenging the work of one of the most influential authors of physics textbooks (Sakurai), yet I never expected unanimous agreement. Individuals have their own reasons for endorsing one position or another. What is regarded as scientific today may not necessarily be viewed the same way tomorrow. Regrettably, science is not always guided solely by rigorous methodology; it is also shaped by underlying assumptions and beliefs. This group is unmoderated, and members are fully responsible for the content of their comments.

Alexandre

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[Fred Diether]

Since Gill and Larsson appear to be gone, Mark is now the chief clueless nonsense maker for the group.

You keep saying you will ignore my posts, yet you don't.  LOL!

Local Quantum Mechanical Prediction of the Singlet State Using Geometric Algebra

https://www.scirp.org/journal/paperinformation?paperid=147271

Bell was wrong big time.

[Fred Diether]

Austin, what was the GA software you downloaded?  Maybe I can help.  Plus, I can do full GA math in Mathematica with the Clifford package addition.

Yes, the interaction product of two vectors is a scalar dot product and a vector cross product.  Do you know what the interaction product is in geometric algebra?

The equations 21 to 23 are geometric algebra.  You need to see Appendix B for proof of equation 24.

You must have missed this in the text, "In advancing the AB product calculation, the k indices are omitted subsequent to the initial step."

Equation 21 is from 18 and 19.  The curly brackets are just brackets.

On Saturday, December 20, 2025 at 5:07:27 AM UTC-8 ben...@hotmail.com wrote:

Hi Fred

[Austin Fearnley]

Hi Fred


I was just playing with the script page in Eigenmath 137-1
> Cl(3)
> a=e3
> b=0.707e2 + 0.707e3
> gp(a,b)-->


and getting output
> ? Cl(3)
stop:syntax error

I found the calculator here despite my computer saying the site was  not secure
http://beyhfr.free.fr/EVA/
-----------------
There is a page of usage guidance:
EVALGEBRA is a symbolic calculator working with Clifford numbers.  
 
The Clifford algebra is generated by vectors of real space Rn together with an associative, bilinear, vector product wich satisfies the basic axiom that the square of a vector is a scalar :
                                                                                  a a =  |a|²            
This allows the theory and properties of the algebra to be built up in an intuitive, geometric way.
 
Clifford algebra is usefull in physics. It provides a more compact and intuitive description of classical and quantum mechanics, electromagnetic theory and relativity. Also usefull for computer vision, robotics, etc ...
new site at evalgebra.org
 
The main objective of the application is to providie a simple tool to make easy calculations with Clifford numbers with possibility to change, add, improve functions, writing own scripts.
 
Some EVA command examples :
 
define basis               e0,e1,e2,e3,e12,e13,e23,e123      (dimension 3)
e0=1                         scalar unit  
e1, e2, e3                  unit orthogonal verctors
e12, e13, e23             unit bivectors : eij = ei ^ ej
e123                         pseudoscalar : e1 ^ e2 ^ e3
>  Cl(3)
 
define 3D vectors                 a=(3,2,-1), b=(3,0,-5)                
> a=3e1+2e2-e3
>  b=3e1-5e3
 
geometric product  a b
>  gp(a,b)  --> 14e0-6e12-12e13-10e23
 
inner product         a.b
>  inp(a,b)  --> 14e0 or 14    (e0 is scalar 1, 14e0=14)
 
outer product        a^b
>  outp(a,b) -->  -6e12-12e13-10e23
 
define multivector              B=(3,1,-5,0,1,1,0,0)  :
>  B=3e0+e1-5e2+e12+2e13
 
grade projection :
scalar part  :  grade 0
>  grade(B,0) :  3e0
vector part  :  grade 1                          
>  grade(B,1)  :  e1-5e2
bivector part  :  grade 2                          
>  grade(B,2)  :  e12+2e13
pseudoscalar part  : grade 3  (upper grade for cl(3))                    
>  grade(B,3) :  0
 
involutions  :                    
reversal                              
>  rev(B)        :  3e0+e1-5e2-e12-2e13
grade involution                    
>  invol(B)      :  3e0-e1+5e2+e12+2e13
clifford conjugation                
>  cj(B)         :  3e0-e1+5e2+e12+2e13
 
inverse 1/B                                                  
>  inverse(B)
 
dual B                                                          
>  dual(B)
 
magnitude  |B|                                              
>  magnitude(B)
 
normalize  B/|B|                                            
>  normalize(B)
 
math functions :
exp1, log1, sqrt1, pow1, sin1, cos1, tan1, sinh1, cosh1, tanh1
asin1, acos1, atan1, asinh1, acosh1, atanh1
 
Mastering EVA syntaxis need only few hours practice.
 

script control instructions :
 
do( expression1, expression2,..., last_expression)   return last_expression
test( predicate1, do(...), predicate2, do(...),..., do(...))
for(k,1,n, do(...))
sum(k,1,n,do(...))
product(k,1,n,do(...))
if only one expression, do(...) not necessary.
 
A tutorial on Eigenmath is  here.
 
If you are interested on quantum computig, you may find an introduction here and there.
 
EVAlgebra suppport Cl(p,q) with p+q < 4, number of basis vectors, p positive squares and q negative squares  .
 
Installing  EVA:
 
1. download EVAlgebra  at  source forge            
 
2. have a look at evalgebra.org for exemples
-----------

============

Yes, I am familiar with the wedge product as I wrote in my commentary on Joy's one page paper:

"First, in the practical example above, the detector axes, vectors a and b, have been chosen so that they both lie in the plane of (e2, e3).  The wedge product a^b points in the direction e1 for a right handed basis and it points in the direction of -e1 for a left-handed basis. These clearly cancel. "

------

Thanks for the clarifications.  I will look at eqn 21 again but will insert the k indices which you have omitted for brevity of notation.

[Fred Diether]

Is the program Eigenmath or EVAlgebra?  My security software blocked the links so I'm not going hassle with it.  But it looks like a decent GA program.  I have a GA program called GAviewer that I could email you if you have Windows operating system.  It gives visual output along with the calculations.

Yeah, equation 21 is just the A and B geometric product from 18 and 19 as I said.  The main heavy calculation is going from 23 to 24 which is in Appendix B.

[Fred Diether]

Actually, here is a link for GAViewer downloads for Linux and Mac also,

https://geometricalgebra.org/gaviewer_download.html

It is a fun program and excellent for learning GA.  But I don't use it anymore after I learned how to do GA in Mathematica which is much more powerful.

Local Quantum Mechanical Prediction of the Singlet State Using Geometric Algebra

https://www.scirp.org/journal/paperinformation?paperid=147271

Bell was wrong big time.

[Austin Fearnley]

Hi Fred

Thanks.  I have run your  linked file and had a look at GAviewer. Will play with it later.


Austin

[Fred Diether]

You're welcome.  Have fun with it.  Any question about it feel free to ask.

Local Quantum Mechanical Prediction of the Singlet State Using Geometric Algebra

https://www.scirp.org/journal/paperinformation?paperid=147271

Bell was wrong big time.

On Sunday, December 21, 2025 at 6:37:48 AM UTC-8 ben...@hotmail.com wrote:

Hi Fred

[Fred Diether]

I forgot to mention that scripts can be run in GAViewer also.  If anyone is interested, I will post a sample script.

Local Quantum Mechanical Prediction of the Singlet State Using Geometric Algebra

https://www.scirp.org/journal/paperinformation?paperid=147271

Bell was wrong big time.

[Austin Fearnley]

I have been thinking about  the issue for a few days.  I note your paper referenced [6] a paper by Jay Yablon and I have been reading that this morning.
https://jayryablon.wordpress.com/wp-content/uploads/2019/10/lrhvcqm-1.1.pdf

As usual with Jay's papers, it is a very interesting read as his writings are more like thriller novels than dry academic papers.  And his paper covered the issues that were in my mind. However, the formulae are as tricky as ever though his explanations are clear.

On page 7 Jay writes:
 "the detection of an “up” versus a “down” result depends only on the spin component in the plane" defined by the two magnet orientations. "
That seems to me to indicate that measurements A and B are not independent as they depend on the plane in which vectors a and b jointly lie.

In eqn 18 and 19 of your paper, A and B are derived as signs of dot products.  There are scalars in geometric algebra and are +/-1 in value.  If you were to multiply A and B for an individual particle pair at this stage you would get +/1 because GA scalars multiply the same as scalars in ordinary algebra. When you proceed to eqn 20 you treat A and B as vectors again despite knowing that they are or will become scalars.  However you need to treat A and B as vectors so as to arrive at ab = a.b + a^b because as Jay mentions, the detection values depend on knowing the joint plane of vectors a and b.

On page 10 onwards of Jay's paper, he introduces the term h which seems to me to play the role of the trivector as alternating values of h (that is +/-1) cause a^b to cancel to zero.  This maybe applies only to Joy's early model rather than yours, though I do understand this method of cancelling to zero.

Your eqns 20 to 25 have a sum Σ over particle pairs and s1->a in the same formulae.  The limit of s1->a occurs for an incoming particle to Alice's detector and is separate from and prior to the sum over particles.  I like Jay's treatment of a sudden snap to +/-a at measurement rather than a slow conversion of s1 to a. That is because I am suspicious of 'weak' measurements which are implied by a slow transition.

In the limit of sum Σ over particle pairs, no variable changes its value mid-formulae.  This is standard usage of sum Σ for calculating a limit over n terms.  A variable is a variable is the same variable throughout.

I need more time to work on your Appendices and Jay's very useful paper.  My own puzzle is that S^3 is not R^3.  The latter is (three dimensional) flatland.  I suspect you would get more acceptance if there was no claim that S^3 is the current view of reality.  It may be the correct view of reality, but flatland is surely the common or old time classical view of reality as meant by 'local realism'?

Best wishes.

[Bryan Sanctuary]

Dear Austin,

I agree that Jay's analysis is interesting. A few years ago, I pointed out to Jay that he was using the geometric product of Pauli matrices incorrectly.  He had thought the two Pauli matrices referred to the two distinct spins, like one for Alice and one for Bob.  He quickly recognized his error when I pointed it out and he was a gentleman about it.  That stopped his development, and what you have, I think, is where he left it, I have not looked. I tell  you this so you're aware that, unless he corrected the error, it might still exist, and may mislead you.

Jay appeared to appreciate the correction, and responded professionally. We became FB friends and I am still in contact with him.  

So perhaps keep this in mind.

Bryan

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[Fred Diether]

Yeah Austin, Jay Yablon did some really good work in that paper and was inspiration for my paper.  Mainly, he did a neat matrix calculation for the solution of equation (5) in my paper.  Which was inspiration for my calculations in Appendix A.  Unfortunately, Jay's proof that quantum mechanics is local for EPR-Bohm didn't work out.

The vectors a and b don't lie in the same plane since they are separated.  The planes they lie in can be parallel but they don't have to be. So, A and B are indeed independent.

A and B in my paper are multi-vectors until the limits are taken.  Then they are scalars.  I never arrive at ab = a.b + a^b.  Not sure why you even mention that.  My prediction is via the product of A and B multi-vectors.

And I am not sure where you are getting this "slow conversion" from of the limits?  Yes, you do need to study Appendix B.

In my viewpoint, the elementary particles are 3-sphere objects.  Since our reality is built up from elementary particles, it probably is S^3 overall.

[Fred Diether]

Austin, I forgot to address this,

"In the limit of sum Σ over particle pairs, no variable changes its value mid-formulae.  This is standard usage of sum Σ for calculating a limit over n terms.  A variable is a variable is the same variable throughout."

Are you talking about the averaging limit here?  I'm not sure why you are talking about "variable changes".  The number of trials, n, is not going change its value.  The other limits for detection are taken before averaging where applicable.

And Jay's "h" is referring to the uncertainty principle.

Local Quantum Mechanical Prediction of the Singlet State Using Geometric Algebra

https://www.scirp.org/journal/paperinformation?paperid=147271

Bell was wrong big time.

[Austin Fearnley]

Hi Fred

1. You made a few points and I will reply below.
2. I will summarise what I meant by ab=a.b + a^b and how the paper revolves about that equation.
3. Then I will mention Jay again

1.  "In the limit of sum Σ over particle pairs, no variable changes its value mid-formulae.  This is standard usage of sum Σ for calculating a limit over n terms.  A variable is a variable is the same variable throughout."

Are you talking about the averaging limit here?  I'm not sure why you are talking about "variable changes".  The number of trials, n, is not going change its value.  The other limits for detection are taken before averaging where applicable.

I was merely saying that the sum Σ limit is a standard maths approach.  (So I agree with what you write.)
whereas the limit of s1->a is changing the value of s1 though I didn't mention that s1 as I wanted to come back to that.

"And Jay's "h" is referring to the uncertainty principle."  

In Joy's model, the alternating trivector sign (which GA users at the time said was inadmissible, though I did not quibble) caused the sum over a^b terms to tend to zero, approx.  Jay somewhere in his paper writes that tendency to zero in his paper is caused by the h term. I need to look more carefully at that.


2.  Back to the nest of vipers.
I agree that s1=-s2 at the beginning of the time of flight of each particle pair
And I agree that at the instant of detection (although it may be more associated with the particle vector at and after detection?) s1 = +/-a and s2 = +/-b.
I am fairly sure that everyone here knows the importance of ab = a.b + a^b to the paper, probably more so than me.

At the beginning of the time of flight, (s1)(s2) = (s1).(s2) + (s1)^(s2) though this isn't one of your explicit equations.
If I assume s1 and s2 to be unit vectors then (s1)(s2) = -1
although you might say I am using flatland algebra.

(s1)^(s2) = 0 because the parallelogram between the two vectors has zero area.

At the instant of detection we have s1 = +/-a and s2 = +/-b
and (s1)(s2) = (s1).(s2) + (s1)^(s2)
becomes ab = a.b + a^b
and as a general rule a^b does not equal zero despite (s1)^(s2) being zero.  

I believe this is why some people are suspicious of the results.  s1^s2 =0  but a^b is not generally zero.


At the point of detection in QM there is wave collapse where, I have often read, the maths of the collapse is outside of QM equations.
So QM equations (unless an expert corrects me) would not be able to take you smoothly from s1 = -s2 through to s1 = +/-a and s2 = +/-b.

Yet your paper is using GA to take us from s1 = -s2 through to s1 = +/-a and s2 = +/-b.

So it seems like a magician is pulling a rabit out of a hat to obtain a^b = 0.

3. Jay Yablon

When I started to read your paper I did not realise what contribution Jay had made.

I have carefully read over many weeks and years a lot of Jay's papers, and even commented on them (probably on your website).  Some feedback may have even helped Jay.  But it is very much a teacher-student relationship and I have learned much from studying Jay's papers on many different topics.  So this has stopped me dead.  I intend to read your and Jay's papers slowly and if any magician can pull a rabbit out of a hat, it is Jay.  However, I am very, very suspicious of the result.  I won't be able to come to a conclusion anywhere near Bryan's New Year deadline.  

There is also Bellism to consider. I am not an antiBellist, and I never cared to study the Theorem carefully. However, I have never obtained a correlation of 0.707 using local realism in a computer simulation. My own model implies a lack of realism.  I am not sure that S^3 is current realism as it is surely not R^3 flatland.  My own thought, rather than relying on Bell, is that using integer projections as measurements gives 0.5 whereas real valued measurements (though not allowed) in flatland would give you 0.707 for theta = 45 degrees.

Best wishes
Austin

[Fred Diether]

Austin, a quick reply here; I will respond to the rest tomorrow.

My paper does not revolve around  ab=a.b + a^b.  If you mean uv = u.v + u^v as general notation, then OK.  I do (a s_1) = a.s_1 + a^s_1 and (s_2 b) = s_2.b + s_2^b.

No where do I ever have a^b!

[Austin Fearnley]

Thanks Fred

I am OK with changing to  uv = u.v + u^v as general notation.  This is what I really meant.
Also I need time to follow Jay's paper, so I should not yet talk of your particular equations.
Instead I am referring to the problem in physics as I see it.  Call it a straw man if you like.

uv = u.v + u^v       has u^v = 0 when u=s1 and v=s2.  So the wedge term drops out as zero.  This is the situation in flight, giving (s1)(s2) = -1.
uv = u.v + u^v       has u^v = not equal 0 when u=a and v=b.  So the wedge term does not drop out as zero.  This is the situation at the instant of detection(?)

The issue, rather than your paper, does revolve about finding ab = a.b with a zero wedge term.
I look forward to finding out how the maths in the paper does this ... as it seems to be impossible because of mathematically handling wave collapse.

Best wishes

Austin

[Bryan Sanctuary]

Dear All,

  I’ve submitted a brief paper to the Journal of Quantum Information Science analyzing Diether’s EPR derivation.
It shows that his Equations (20)–(27) are algebraically flawed, discard a non-zero bivector contribution, and therefore do not assail Bell’s result or produce the −cosθ correlation without introducing non-locality.  

Happy New Year to you all, and best wishes,

Bryan

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[Fred Diether]

LOL!  All it proves is that you, BS, are a clueless jerk.  How does it feel to be a traitor?

You are just jealous that Dr. Christian has a model that actually works to disprove Bell and all you have is a pile of junk that just proves how clueless you are.

[Fred Diether]

Austin, you are missing a big part of the calculation.  It is not u = a nor v = b.

It is (a s_1) = a.s_1 + a^s_1 and (s_2 b) = s_2.b + s_2^b.  Then it is,

(a.s_1 + a^s_1)(s_2.b + s_2^b) = -a.b + r_0

See Appendix B.  Then in the calculation when the detection limits are taken, r_0 equals a null vector.  There is never an a^b wedge term.

Local Quantum Mechanical Prediction of the Singlet State Using Geometric Algebra

https://www.scirp.org/journal/paperinformation?paperid=147271

Bell was wrong big time.

[anton vrba]

Hi Alexandre, wishing you the best for 2026

Please the group has attained spam status, how many more times are you tolerating Fred to spam us with his:

Local Quantum Mechanical Prediction of the Singlet State Using Geometric Algebra

https://www.scirp.org/journal/paperinformation?paperid=147271

Bell was wrong big time.

together with some stupid, derogatory text, nothing scientific or defending his work on a scientific basis. 

It leaves us no option to be equally reply derogatory to Fred, why should we not reply in his language even though it is unfit for a scientific forum. 

You already lost respected members, which makes this group uninteresting as no meaningful dialogue is possible. 

The ball is in your court to bring this group back to a meaningful forum, or loose all your original intentions.

Regards

Anton

[Fred Diether]

OK Austin, I am going to continue to address your comments from below.  Got distracted by some freakin' nonsense from Bell fanatics.

For your number 2, at after creation and at detection there is no (s1)(s2).  They are separated at that point.  (s1)(s2) only exists at the time of pair creation.

You say, "Yet your paper is using GA to take us from s1 = -s2 through to s1 = +/-a and s2 = +/-b."  That is false.  It is not due to GA, it is merely detection that changes s1 and s2.

For number 3, yes please study Jay and my papers.  Hopefully someday you will understand the actual physics and realize the Bell inequalities are broken physics.  I can explain that to you more if you wish.

Happy New Year!

[Fred Diether]

Thanks Anton for posting my link again.  Now..., what have you contributed to the group?  You contributed a bunch of freakin' nonsense from a chatbot that anyone with any intelligence knows that they make mistakes.  That is spam to me!  You want to make this group better?  Leave it and take your freakin' Bell fanatic nonsense with you.

And I do believe Alexandre has already addressed this.  But you weren't paying attention.

[Richard Gill]

Dear all, this is addressed to Bryan Sanctuary’s first post in a thread on Fred Diether’s paper 

Local Quantum Mechanical Prediction of the Singlet State Using Geometric Algebra

First a remark on terminology. You can’t start by *assuming* s_1 = s and s_2 = -s. You can however *rename* them both separately, however you like.  s_1 and s_2 are dummy variables. They appear in limits as s_1 (and s_2) converge to certain limits. Differentblimit expressions.

They are supposed to converge to mu_a and mu_b. But these are illegally defined in terms of s_1 and a, and s_2 and b, respectively. The initial definitions are illegal. Recall, we are told mu_a = sign(s_1.a) a. The sign of s_1.a, as s_1 varies but a is fixed, where both are real 3d vectors of length 1, is constant on two complementary half spheres. So the limit of s_1 as s_1 converges to mu_a reads: “the limit as s_1 converges to +a or to -a”. Those are two different limits. The two results are different. The choice is not made.

Conclusion: the initial definitions of Fred Diether’s paper https://www.scirp.org/journal/paperinformation?paperid=147271 do not define anything. A(a, s) and B(b, s) are not well defined. They are actually not defined at all. The paper does not obtain the quantum mechanical prediction of -a.b for the singlet state using Bell’s approach. 

 
for the singlet spin state employing local measurement functions following Bell’s approach.

Richard

On Monday, December 15, 2025 at 6:22:56 PM UTC+1 bryancs...@gmail.com wrote:

Dear all,

I will try to guide Fred through the calculation step by step that led me to find r_0 is not zero.  

Start by assuming

and then we have

I will go on when Fred agrees,

Bryan

[Richard Gill]

Dear all

I’d like to point out the real error in “Local Quantum Mechanical Prediction of the Singlet State Using Geometric Algebra” by Fred Diether. It’s right at the beginning, before any calculations are done, and I think Bryan Sanctuary and others missed it.

It’s in the basic definitions of the paper. They turn out not to be definitions at all. The author has not come up with functions A(a, s), B(b,s) with the usual properties. The problem is a problem of mathematics, not of physics. It appears that the author is probably unaware of the mathematical definition of the limit operation. (Cauchy’s famous epsilon-delta definition).

The arguments a, b, s etc stand for unit vectors. I’ll write mu(a) instead of mu_a; but actually it should be written mu(a, s).

We are given:

A(a, s) = lim_{s -> mu(a)} [s a]

mu(a) = sign(a . s) a

But mu(a) is actually a function of s as well as of a, since sign(a.s) equals +/-1 depending on which hemisphere s lies in relative to a. So mu(a) = +/-a depending on the location of s relative to a.

For s in the Northern hemisphere relative to the North Pole a, s converging to mu(a) means s converges to +a; for s in the Southern hemisphere it means s converges to -a.

s cannot converge to +a and to -a at the same time, unless we identify +a with -a.

The basic definitions in the paper include the implicit assumption +1 = -1.

Richard

Sent from my iPad

On 8 Jan 2026, at 18:23, Fred Diether <fredi...@gmail.com> wrote:

Well Alexandre, you were wrong.  This group is moderated as Gill deleted my reply to him.  Which is silly because the posts in the group get sent out in email.  So, not actually deleted.

On Thursday, January 8, 2026 at 8:05:24 AM UTC-8 Fred Diether wrote:

That is the short list of basic rules.  I will post the long list later.

As for Google's basic rules for groups, you can always click on the Report button.  Too bad there isn't a Google rule for those that post nonsense.  Add that to the list above.  LOL!

Local Quantum Mechanical Prediction of the Singlet State Using Geometric Algebra

https://www.scirp.org/journal/paperinformation?paperid=147271

[Fred Diether]

This post did not appear on the group.  At least I can't find it.  Alexandre must be moderating all posts now.

s1 does not go to +a and -a at the same time.  You must have had some kind of brain fart here.  LOL!

And it is mu_a to differentiate it from mu_b.  It is really obvious what they are functions of.

[Richard Gill]

Dear Fred

The brain fart was yours. You define A via limits as s converges to +a and to -a. A nonsensical definition enables a nonsensical result. I will take a look next at your Mathematica code. What does Mathematica do when you ask it to do the impossible?

I get the impression you don’t know the Cauchy definition of limit (often called the epsilon-delta definition).

mu_a is obviously a function of a and of s. Sign(a.s) depends on a and on s.

Richard

[Bryan Sanctuary]

Hi Richard,

True, I had not thought of the beginning, just their use as limits in Diether's calculation.  I think  I understand your point: are you saying that the problem arises because the “limit” s \to \mu(a) is not a limit at all, since the limit result depends on s? You say one cannot define a limit where the point being approached depends on the point doing the approaching?  If so, that makes sense, and is cute when you think like that.. So you say Joy's A(a,s) and B(b,s) are not limits, and Diether's equation 20 to 27 must fail because the starting definitions cannot have \pm 1 limits as stated? They give a sort of blur being \pm 1 at the same instant?  Please correct my view.  

Then, can you tell us what the actual result would be using your interpretation of A and B, rather than using them as limits as Diether and Joy do?

Thanks

Bryan

[Austin Fearnley]

Hi Richard

I now see what you mean. I did not immediately.
I am familiar with using sign (s1.a) to determine the outcome of measurement A.
In 2017 I obtained an abs correlation of (only) 0.499454164 using one million pairs of particles in a simulation for theta = 45 degrees using this method.
This treated s1 as a fixed vector not a variable, and used ordinary algebra, not geometric algebra.
If one allows s1 to become a variable vector, as it must be if it tends to another value, then one can no longer be certain of the outcome of measurement A.
However, there are restrictions on the variation of the value of s1 as it is trapped in the magnetic fields of the detector.
Forget Stern Gerlach detectors here and think of a detector only registering a click or not a click.  If a fixed s1 would have registered a click, could the detector magnet easily change s1 so that it did not register a click.  If so, in this way I can see that s1 is guided to either +a or -a. Though I know nothing of how easily this reversal could take place.

Austin

[Richard Gill]

Hi Bryan

The short answer is that nobody with first year university maths for STEM would ever write lim_{s \to mu(a,s)}.

Perhaps however the author really meant  lim_{ (s - mu(a,s)) \to 0}.

But this doesn’t make sense either because s can’t be close to both +a and -a at the same time.

Anyway, looks more to me like subterfuge. The author used the mu_a, mu_b notation in order to mislead.

They certainly mislead themselves.

In case of doubt, one must check the epsilon delta definition.

lim_{s \to t} f(s) = y if and only if for all eps > 0 there exists delta > 0 such that whenever the distance between s and t is smaller than delta, then the distance between f(s) and y is less than epsilon.

If in advance you don’t know y and you are working in a complete metric space you can use Cauchy’s criterion lim_{s \to t} f(s) exists and is unique if and only there exists delta > 0 such that whenever the distance between s and s’ are both smaller than delta, then the distance between f(s) and f(s’) is less than epsilon.

Is this sort of thing part of a standard STEM education?

Richard

PS I suspect that there could be some gaps (or loss of memory) in Bryan’s basic math education as well as in Fred’s - cf. the confusion about whether you can add correlations or take convex combinations of them. Go back to basics! The textbooks you learnt university level exact sciences math from.

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On 9 Jan 2026, at 10:50, Bryan Sanctuary <bryancs...@gmail.com> wrote:



[Bryan Sanctuary]

Hi Richard,

Well I agree with you that my math has gaps, and you have the definite advantage there of course,  but I do see your point about the limits. I think your analysis means that in Joy's papers that everything beyond the starting equation,  <(a.\sigma )(b.sigma)> is incorrect. Do you agree?  If not, where should we start? This is the first time I have seen the limit discussion in critics' responses. I  think that you have now shown the start is wrong, and I showed that using them as intended limits leads to the incorrect result in agreement with you. Both ways indicate the projection method of Christian fails.  

I do hope we can close the Diether paper issue.   I think we have both shown that Diether's use of Joy's erroneous approach led to, well, nonsense. Doing that critique of Diether was, however, a useful exercise for me and it seems to have withstood objections.  With Diether gone, we can move away to other topics. 

But you then jump to add average, and so, I ask, how do you explain the two channel calculation I did in my analysis of Diether, that is "2.4 Correct EPR correlation" where the isotropic average gives the sum of the two?  the 1/3 a.b and the 2/3 a.b?  I agree that within one convex set you must average, but between dual convex sets, you must add, (the Minkowski sum).  If you average the two channels you cannot get the correct cos\theta.  So what is wrong with that 2.4 section where adding gives the observed correlation, and averaging does not?

It seems like things might have settled down.  I look forward to more academic discussions, but for now I feel like I need a reprieve from all this, but glad we, as a group, prevailed over Diether, and he has gone. 

Bryan

[Richard Gill]

Dear Austin

The idea that taking a mathematical limit of a mathematical expression as mathematical variable “s” converges to mathematical variable “a” has anything to do with a particle with spin moving to be close to a device set to some direction is just nuts. It is seeing mathematical formulas as a physical picture of stuff happening in space and time. It’s child-like. 

Richard

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On 10 Jan 2026, at 06:15, Austin Fearnley <ben...@hotmail.com> wrote:

Hi Richard

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[Richard Gill]

Actually there is one intriguing thing. Diether verified his computations with Mathematica. He therefore asked Mathematica to do something meaningless, but Mathematica didn’t notice and just carried out the same wrong formal calculations.

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On 10 Jan 2026, at 06:15, Austin Fearnley <ben...@hotmail.com> wrote:

Hi Richard

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[Richard Gill]

Dear Austin, I think you need to understand the concept of “dummy variable”. As do Fred Diether and Joy Christian.

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On 10 Jan 2026, at 06:15, Austin Fearnley <ben...@hotmail.com> wrote:

Hi Richard

--

[Fred Diether]

Oh dear, Richard has once again failed basic calculus.

In[1]:= Limit[x, x -> a]

Out[1]= a

That is read as the limit of x as x goes to a.  The answer is a.  So simple.  What are you going to say now?

[Richard Gill]

Dear Fred

Ask Mathematica sensible question, it’ll give you a sensible answer.

On the other hand, …

Fred, if you’d like a Zoom conversation I’d be happy to sort out your misunderstandings at the blackboard.

Richard

PS Mathematica uses simple substitution rules which usually work. It does not actually calculate a mathematical limit using the Cauchy definition or the Cauchy criterium. It does not do a numerical investigation, when it thinks the user doesn’t want that.

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On 11 Jan 2026, at 01:45, Fred Diether <fredi...@gmail.com> wrote:

Oh dear, Richard has once again failed basic calculus.

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[Fred Diether]

Here is the proof,

Local Quantum Mechanical Prediction of the Singlet State Using Geometric Algebra

https://www.scirp.org/journal/paperinformation?paperid=147271

Bell was wrong big time.

[Richard Gill]

Fred, what’s happened is you’ve actually found is what looks to me to be a bug in Mathematica.

Mathematica has failed basic calculus. Please show us the Mathematica code you wrote, in its context.

This needs to be reported.

There were two instances of the dummy variable “s” in the “…” in your “limit as s converges to …” expression. Mathematica prefers to do formal substitution to numerical calculation. Probably that would have made a huge difference in this case. It’s very amusing, actually.

A cautionary tale for those teaching calculus 101 for STEM, ie for students capable of understanding formal mathematical proofs and definitions.

Richard

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On 12 Jan 2026, at 21:19, Fred Diether <fredi...@gmail.com> wrote:

Here is the proof,

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[Fred Diether]

Oops, let's fix the image for the proof,

Here is another way of looking at the problem,

In[2]:= Simplify[Limit[x, x -> Sign[(s1 . a)] a]]

Out[2]= a Sign[s1 . a]

The answer is +a or -a.  Not both at the same time.

[Richard Gill]

Fred, You take the limit of [a s1] as s1 converges to mu_a. But mu_a = sign(a . s1) a). It depends on “a” and on “s1”. You probably got Mathematica badly confused.

Please recite to yourself the epsilon delta definition of limit and think carefully about “scope”. In “lim_{s1 to …}[…]” the variable s1 is a so-called dummy variable. Merely a placeholder. It can be renamed in an arbitrary way, as long as that doesn’t interfere with other variable names. But there is another s1 hiding in the formulas, in the definition of mu_a. Are they the same s1 or different ones?

[Austin Fearnley]

Hi Richard


I like to visualise the physics within equations. Equations without the physics aren't important to me.  And this is a foundations forum so the old QM mantra of "shut up and calculate" should not be welcomed.

Fred writes at just above initial eqn. 20 that " the k indices are omitted subsequent to the initial step".
Mu does not appear until eqn. 21 and mu ought to have been tagged by s (or by k) in eqn. 21 and k not dropped until eqn. 22.

A suggestion:  in an earlier thread you commented on a circle being split into four arcs.  That has suggested to me that the single term in eqn. 21 could be split into four distinct parts and four outcomes summed at the end.

Part 1.  s1-> +a and s2-> +b
Part 2.  s1-> +a and s2-> -b
Part 3.  s1-> -a and s2-> +b
Part 4.  s1-> -a and s2-> -b

These four parts would segregate the k particle labels into 4 non-overlapping groups.
That should overcome your point about limits?  It might look awkward or bulky in equations but would be simple to program.

It is a concern that Fred writes in comments that s1 is not really tending to +a or -a but that there is a sudden jump to +/-a.  Presumably that jump is at the instant of measurement or click.  That makes s1 and s2 fixed vectors.  I have long ago run a simulation with fixed vectors and the output correlation does not reach a QM  level.  I do not see how geometric algebra fixes that.  If s1 and s2 were to be variable vectors, one could not separate out the equation into four parts as there would be no formula to say which part was associated with which particle (k).

This says nothing about correctness of the paper but I think evades your objection about limits?

[Richard Gill]

Fred, these exercises are irrelevant.

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On 15 Jan 2026, at 10:59, Fred Diether <fredi...@gmail.com> wrote:

Oops, let's fix the image for the proof,

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<limit-proof.png>

[Richard Gill]

Austin, Fred is quite simply writing down a formula which Mathematica should have known was illegal.

Fred does not known the concept of free vs. bound variable. I hope you do.

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To view this discussion visit https://groups.google.com/d/msgid/Bell_quantum_foundations/542f21c2-74c1-4af4-801b-f217a027265fn%40googlegroups.com.

[Fred Diether]

Richard, you need to stop with your nonsense.  We know it is nonsense because you keep blaming it on Mathematica when Mathematica has nothing to do with my analytical calculation.

[Richard Gill]

Seems that many people here do not understand the basic rules of mathematics, logic, and computer science concerning bound and free variables.

I hope this note will be useful.

[Richard Gill]

The analytical calculation you did is wrong.

Sent from my iPhone

On 16 Jan 2026, at 16:41, Fred Diether <fredi...@gmail.com> wrote:

Richard, you need to stop with your nonsense.  We know it is nonsense because you keep blaming it on Mathematica when Mathematica has nothing to do with my analytical calculation.

To view this discussion visit https://groups.google.com/d/msgid/Bell_quantum_foundations/337f506d-ba80-4673-a1c1-5a15a2eacfd8n%40googlegroups.com.

[Bryan Sanctuary]

Fred,

All you must do is say, ok, I will use Bell's 64 equation 1.  Then Richard has no argument and your 20 to 27 follow from Bell's limit.  The error is in what I found, not Richard's limit ruse.  That is his methods, obfuscate and deflect.  He should put his argument in Chat GPT to see his errors.

Bryan

On Fri, Jan 16, 2026 at 5:08 PM Richard Gill <gill...@gmail.com> wrote:

Seems that many people here do not understand the basic rules of mathematics, logic, and computer science concerning bound and free variables.

I hope this note will be useful.

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[Fred Diether]

Richard, my analytical calculation is 100 percent correct.  I will post it step by step tomorrow.

BS, r_0 is a null vector after the limits are taken.   We can do that step by step also.  You guys are going to look really foolish.

[Richard Gill]

Fred, that’s excellent. I will be looking out for problems with bound vs. free variables. You might want to rethink your notation.

Wikipedia: https://en.wikipedia.org/wiki/Free_variables_and_bound_variables

In mathematics, and in other disciplines involving formal languages, including mathematical logic and computer science, a variable may be said to be either free or bound. Some older books use the terms real variable and apparent variable for free variable and bound variable, respectively. A free variable is a notation (symbol) that specifies places in an expression where substitution may take place and is not a parameter of this or any container expression. The idea is related to a placeholder (a symbol that will later be replaced by some value), or a wildcard character that stands for an unspecified symbol.

In computer programming, the term free variable refers to variables used in a function that are neither local variables nor parameters of that function. The term non-local variable is often a synonym in this context.

An instance of a variable symbol is bound, in contrast, if the value of that variable symbol has been bound to a specific value or range of values in the domain of discourse or universe. This may be achieved through the use of logical quantifiers, variable-binding operators, or an explicit statement of allowed values for the variable (such as, "...where n {\displaystyle n} is a positive integer".) A variable symbol overall is bound if at least one occurrence of it is bound.[1] Since the same variable symbol may appear in multiple places in an expression, some occurrences of the variable symbol may be free while others are bound,[1]: 78  hence "free" and "bound" are at first defined for occurrences and then generalized over all occurrences of said variable symbol in the expression. However it is done, the variable ceases to be an independent variable on which the value of the expression depends, whether that value be a truth value or the numerical result of a calculation, or, more generally, an element of an image set of a function.

[1]  Quine, Willard Van Orman (1982). Mathematical Logic (Revised ed.). Harvard University Press. pp. 142–143. ISBN 978-0674554511.

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On 17 Jan 2026, at 03:11, Fred Diether <fredi...@gmail.com> wrote:

Richard, my analytical calculation is 100 percent correct.  I will post it step by step tomorrow.

To view this discussion visit https://groups.google.com/d/msgid/Bell_quantum_foundations/690e7c90-7699-4a9a-ada2-6fbe31122414n%40googlegroups.com.

[Fred Diether]

I decided not to do it.  I want to see what you submit to the journal first.  It will be real easy to shoot that down. 

Ok, you can resume more nonsense now.  LOL!

[Richard Gill]

I took a look at your Mathematica code, Fred. It does not implement the definitions in your paper at all. It is a correct textbook QM calculation of the singlet correlation.

Your paper is a hoax. The model which your paper defines, generously interpreting your math by taking the “s” hidden in the definition of mu_a to be a free variable, is actually Bell’s example LHV, which has the famous triangle wave as correlation function.

The Mathematica calculations in your paper (see the link given in your paper to your own archived Notebook) do not follow your model definitions at all.

Sent from my iPad

On 17 Jan 2026, at 17:46, Fred Diether <fredi...@gmail.com> wrote:

I decided not to do it.  I want to see what you submit to the journal first.  It will be real easy to shoot that down. 

To view this discussion visit https://groups.google.com/d/msgid/Bell_quantum_foundations/e23b0557-ad8f-4596-ba5e-bd3c756166edn%40googlegroups.com.

[Fred Diether]

What is the title of my paper?  That might give you a clue.

[Richard Gill]

Indeed Fred, the title “Local Quantum Mechanical Prediction of the Singlet State Using Geometric Algebra” proves my point. The title of the paper misrepresents the content. Moreover, the word “local” should be deleted.

Had the whole paper been no more than a correct “Quantum Mechanical Prediction of the Singlet State Using Geometric Algebra” there would have been no point in publishing it, it’s been done many times before.

The abstract of the paper contains falsehoods. Sentence 1, 3 and 4 are all lies.

Abstract:

"We deduce the quantum mechanical prediction of − a . b for the singlet spin

state employing local measurement functions following Bell’s approach. This

result represents the quantum mechanical expectation value for the joint meas-

urement of spin projections in the singlet state. And is equal to the negative

cosine of the angle between vectors a and b . Our derivation is corroborated

through a computational simulation conducted in the Mathematica program-

ming environment using geometric algebra."

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On 17 Jan 2026, at 20:57, Fred Diether <fredi...@gmail.com> wrote:

What is the title of my paper?  That might give you a clue.

To view this discussion visit https://groups.google.com/d/msgid/Bell_quantum_foundations/fe55281c-c8e5-4b98-a586-1495682342d4n%40googlegroups.com.

[Fred Diether]

We can only hope that some day you will learn physics.

[Richard Gill]

I’m going to stick to mathematics, Fred.

Sent from my iPad

On 17 Jan 2026, at 22:08, Fred Diether <fredi...@gmail.com> wrote:

We can only hope that some day you will learn physics.

To view this discussion visit https://groups.google.com/d/msgid/Bell_quantum_foundations/d87864f9-d4dc-49c7-a66e-42196e367a63n%40googlegroups.com.

[Richard Gill]

Austin, splitting equations into parts and reducing sophisticated mathematical expressions to child-like pictures is exactly why both Fred Diether and Bryan Sanctuary come up with so much non-sense. Using equations to visualise physics is fine, but if you can’t actually *read* the equations (they may say subtle things in a very condensed technical notation) you will likely go astray. I think they have both missed (or just forgotten) the basic mathematical grounding which should have become second-nature in a scientist’s further career.

Richard

[Richard Gill]

Bryan, Bell’s 1964 equation (1) is A(a, lambda) = +/-1, B(b, lambda) = +/-1. My argument would be to duplicate the rest of Bell’s paper.

Bell’s justification is Einstein "But on one supposition we should, in my opinion, absolutely hold fast: the real factual situation of the system S2 is independent of what is done with the system S1 , which is spatially separated from the former."

Interestingly, he does later in the paper touch on the case of multiple channels:

The example considered above has the advantage that it requires little imagination to envisage the measurements involved actually being made. In a more formal way, assuming [7] that any Hermitian operator with a complete set of eigenstates is an "observable", the result is easily extended to other systems.
If the two systems have state spaces of dimensionality greater than 2 we can always consider two dimensional subspaces and define, in their direct product, operators d1 and d2 formally analogous to those used above and which are zero for states outside the product subspace. Then for at least one quantum mechanical state, the "singlet" state in the combined subspaces, the statistical predictions of quantum mechanics are incompatible with separable predetermination.

[7] P. A. M. DIRAC, The Principles of Quantum Mechanics (3rd Ed.) p. 37. The Clarendon Press, Oxford (1947).

[Fred Diether]

OK pal, it is your funeral.  LOL!

You will never know how Nature actually works.

[Richard Gill]

Nobody will ever know how Nature actually works.

Right now I am more than ever interested in how people work. 

“Apart from hydrogen, the most common thing in the universe is stupidity.”

On 18 Jan 2026, at 17:49, Fred Diether <fredi...@gmail.com> wrote:

OK pal, it is your funeral.  LOL!

To view this discussion visit https://groups.google.com/d/msgid/Bell_quantum_foundations/dd94a51f-05fa-4858-beb7-f68e4a643815n%40googlegroups.com.

[Fred Diether]

Yeah, but if you actually knew enough physics, you would see my calculations are 100 percent correct. 

One can do stuff in mathematics that can't be done in physics.  So, math is probably about one half fantasies.

[Richard Gill]

Dear Fred

You are wonderful!

Richard

Sent from my iPad

On 19 Jan 2026, at 23:59, Fred Diether <fredi...@gmail.com> wrote:

Yeah, but if you actually knew enough physics, you would see my calculations are 100 percent correct. 

To view this discussion visit https://groups.google.com/d/msgid/Bell_quantum_foundations/61751d3d-10e0-4dfa-82b4-22509eae6815n%40googlegroups.com.

[Fred Diether]

Here is an updated Mathematica simulation PDF to go with the paper.

https://drive.google.com/file/d/1afLIztWia47OA3H0MS8X4pT14dmdjutz/view?usp=sharing

The product calculation is averaged now and it also now has the correct product calculation.

Local Quantum Mechanical Prediction of the Singlet State Using Geometric Algebra

https://www.scirp.org/journal/paperinformation?paperid=147271

Bell was wrong big time.

[Richard Gill]

Dear Fred

I’m not a Mathematica wizard and I can’t afford to buy it.

Can you rewrite it in R or Python?

Better still, simply create a file with say 10,000 counterfactual values of A(a1, lambda), A(a2, lambda), B(b1, lambda) and B(b2, lambda). So that would be a 10,000 x 4 spreadsheet of numbers +/-1.

Then anyone can pick 10,000 pairs of settings a, b taking values 1 and 2, completely at random, compute four experimental correlations, and calculate S.

Sent from my iPhone

On 22 Jan 2026, at 03:37, Fred Diether <fredi...@gmail.com> wrote:

Here is an updated Mathematica simulation PDF to go with the paper.

To view this discussion visit https://groups.google.com/d/msgid/Bell_quantum_foundations/62935a7e-3c21-45dc-a8a0-5b780f54e512n%40googlegroups.com.

[Richard Gill]

PS of course, anyone can also compute the four correlations of interest for all 10,000 ai, bj pairs.

As you probably realise, those correlations should not differ much from correlations based on a random sample of about 2,500 pairs.

Sent from my iPad

On 22 Jan 2026, at 08:12, Richard Gill <gill...@gmail.com> wrote:

Dear Fred

[Fred Diether]

Richard, you can have a chatbot rewrite my simulation in R yourself.  Try Google Gemini or Apple must have a good chatbot.  I don't have R Studio installed anymore.  But maybe I will do it if I get bored enough.

The simulation does the local QM prediction via the product calculation.  The same way as regular QM predictions.  

On Wednesday, January 21, 2026 at 11:12:53 PM UTC-8 Richard Gill wrote:

Dear Fred

I’m not a Mathematica wizard and I can’t afford to buy it.

Can you rewrite it in R or Python?

Better still, simply create a file with say 10,000 counterfactual values of A(a1, lambda), A(a2, lambda), B(b1, lambda) and B(b2, lambda). So that would be a 10,000 x 4 spreadsheet of numbers +/-1.

Then anyone can pick 10,000 pairs of settings a, b taking values 1 and 2, completely at random, compute four experimental correlations, and calculate S.

Sent from my iPhone

On 22 Jan 2026, at 03:37, Fred Diether <fredi...@gmail.com> wrote:

Here is an updated Mathematica simulation PDF to go with the paper.

[Richard Gill]

Yes, but we need to see a product calculation for well-defined +/-1 valued measurement outcomes, defined locally. 

I’m not going to do your work for you.

Sent from my iPad

On 22 Jan 2026, at 16:22, Fred Diether <fredi...@gmail.com> wrote:

Richard, you can have a chatbot rewrite my simulation in R yourself.  Try Google Gemini or Apple must have a good chatbot.  I don't have R Studio installed anymore.  But maybe I will do it if I get bored enough.

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[Fred Diether]

We don't need to see that since quantum mechanics can't do it.  My work is done.  

Local Quantum Mechanical Prediction of the Singlet State Using Geometric Algebra

https://www.scirp.org/journal/paperinformation?paperid=147271

Bell was wrong big time.

https://drive.google.com/file/d/1afLIztWia47OA3H0MS8X4pT14dmdjutz/view?usp=sharing

[John Reed]

I have Mathematica, and I am investigating Fred's program.  I'll let you know what I find.

John

To view this discussion visit https://groups.google.com/d/msgid/Bell_quantum_foundations/dfe2f168-3c82-492b-b264-be83dd975f56n%40googlegroups.com.