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/
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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
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============

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.