My Talk at AGACSE 2021 in Honor of David Hestenes

[Austin Fearnley]

OK. Forget my reservation.

In looking only at the first and last terms in that line of formulae for A(a, lambda), I discounted s1. So the formula is not true for all vectors a, for all particles with hidden variable lambda, but only when s1 for a particle tends to vector a.
So that is not odd.

Sorry.

[gill1109]

OK. Forget my reservation.

In looking only at the first and last terms in that line of formulae for A(a, lambda), I discounted s1. So the formula is not true for all vectors a, for all particles with hidden variable lambda, but only when s1 for a particle tends to vector a.
So that is not odd.

Sorry.

s1 is a dummy variable! It can’t “belong” to a particle. It belongs to a mathematical expression with a clear mathematical definition in which the envisaged physical application or interpretation is irrelevant.

As Joy said today: “I’m not a mathematician! I don’t care about mathematics! I’m a physicist!”.

[Joy Christian]

s1 is a dummy variable! It can’t “belong” to a particle.

s1 is not a dummy variable. It is a vector direction about which the spin bivector heading towards Alice is spinning. As such, it is subject to the conservation law of spin angular momentum.
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[Joy Christian]

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I have posted the slides for my talk at Academia.Edu and Research Gate, with the following DOI: http://dx.doi.org/10.13140/RG.2.2.21753.39529
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[gill1109]

s1 is a dummy variable! It can’t “belong” to a particle.

s1 is not a dummy variable. It is a vector direction about which the spin bivector heading towards Alice is spinning. As such, it is subject to the conservation law of spin angular momentum.

Right. I forgot. You don’t do mathematics. You do physics.

I find this a fascinating idea, that physics is independent of mathematics. You write formulas which could pass for mathematical formulas, but they were never intended to be read as such. It’s just an unfortunate coincidence that they mean something different as mathematics than what they mean as physics.

BTW, who was the Brno participant who had recently verified your work by another computer simulation? It’s interesting to see how what look like mathematical formulas, but which aren’t mathematics, can be implemented in computer code.

This problem also explains a lot of flatlanders’ problems with Fred’s latest programs.

[Joy Christian]

s1 is a dummy variable! It can’t “belong” to a particle.

s1 is not a dummy variable. It is a vector direction about which the spin bivector heading towards Alice is spinning. As such, it is subject to the conservation law of spin angular momentum.

Right. I forgot. You don’t do mathematics. You do physics.

I find this a fascinating idea, that physics is independent of mathematics. You write formulas which could pass for mathematical formulas, but they were never intended to be read as such. It’s just an unfortunate coincidence that they mean something different as mathematics than what they mean as physics.

BTW, who was the Brno participant who had recently verified your work by another computer simulation? It’s interesting to see how what look like mathematical formulas, but which aren’t mathematics, can be implemented in computer code.

This problem also explains a lot of flatlanders’ problems with Fred’s latest programs.

Is the delta function invented by Dirac mathematics? Is the renormalization process of cancelling infinities for which 't Hooft won a Nobel Prize mathematics?

Physicists don't care about mathematics. They use it when it is convenient to do so. When it does not exist, they invent their own mathematics as Dirac and 't Hooft did.

I am not permitted to name the person who did the Maple code for my Socks paper.
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[gill1109]

s1 is a dummy variable! It can’t “belong” to a particle.

s1 is not a dummy variable. It is a vector direction about which the spin bivector heading towards Alice is spinning. As such, it is subject to the conservation law of spin angular momentum.

Right. I forgot. You don’t do mathematics. You do physics.

I find this a fascinating idea, that physics is independent of mathematics. You write formulas which could pass for mathematical formulas, but they were never intended to be read as such. It’s just an unfortunate coincidence that they mean something different as mathematics than what they mean as physics.

BTW, who was the Brno participant who had recently verified your work by another computer simulation? It’s interesting to see how what look like mathematical formulas, but which aren’t mathematics, can be implemented in computer code.

This problem also explains a lot of flatlanders’ problems with Fred’s latest programs.

Is the delta function invented by Dirac mathematics? Is the renormalization process of cancelling infinities for which 't Hooft won a Nobel Prize mathematics?

Physicists don't care about mathematics. They use it when it is convenient to do so. When it does not exist, they invent their own mathematics as Dirac and 't Hooft did.

I am not permitted to name the person who did the Maple code for my Socks paper.
.

Of course, great physicists have again and again invented new mathematics, and this has been great for mathematicians.

So we just have to wait 100 years for physicists to get accustomed to your mathematics, and when they have massively decided that they need to use it, at last the mathematicians will wake up and start trying to formalise it. Another 100 years, perhaps.

[gill1109]

Very exciting talk by Anthony Lasenby just now at AGACSE! Working in Cl(1, 3)(R), which he calls the STA (Space-Time Algebra), he has shown that you can define a product and a norm *in fairly simple terms using the given GA structure* which convert this 8-dimensional space into ... wait for it ... a normed division algebra! ie ... the octonions!

It was pointed out in the discussion that you could also do this with Cl(3, 1)(R) which also has some further attractive advantages. For instance: it contains *two* copies of (a representation of) SU(3), not just one, and this enables some of the things that Anthony has been doing to be re-done in a nicer way. More symmetries. The Cl(1, 3)(R) approach suffers from some kind of built in chirality. Handedness. The Cl(3, 1)(R) approach gives full symmetry.

BTW, Chris Doran says we should be moving from Python to Julia.

[Joy Christian]

Very exciting talk by Anthony Lasenby just now at AGACSE! Working in Cl(1, 3)(R), which he calls the STA (Space-Time Algebra), he has shown that you can define a product and a norm *in fairly simple terms using the given GA structure* which convert this 8-dimensional space into ... wait for it ... a normed division algebra! ie ... the octonions!

It was pointed out in the discussion that you could also do this with Cl(3, 1)(R) which also has some further attractive advantages. For instance: it contains *two* copies of (a representation of) SU(3), not just one, and this enables some of the things that Anthony has been doing to be re-done in a nicer way. More symmetries. The Cl(1, 3)(R) approach suffers from some kind of built in chirality. Handedness. The Cl(3, 1)(R) approach gives full symmetry.

Lounesto has shown all that and more twenty years ago in his extensive studies linking the four of the five normed division algebras with various Clifford algebras. The fifth, the even subalgebra of the algebra Cl(4,0), is already a Clifford algebra.

See Lounesto's paper here: Advances in Applied Clifford Algebras, Vol. 11 No. 2, 191--213 (2001). What Lasenby presented is nothing new. It is all well known for at least twenty years.
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[gill1109]

Very exciting talk by Anthony Lasenby just now at AGACSE! Working in Cl(1, 3)(R), which he calls the STA (Space-Time Algebra), he has shown that you can define a product and a norm *in fairly simple terms using the given GA structure* which convert this 8-dimensional space into ... wait for it ... a normed division algebra! ie ... the octonions!

It was pointed out in the discussion that you could also do this with Cl(3, 1)(R) which also has some further attractive advantages. For instance: it contains *two* copies of (a representation of) SU(3), not just one, and this enables some of the things that Anthony has been doing to be re-done in a nicer way. More symmetries. The Cl(1, 3)(R) approach suffers from some kind of built in chirality. Handedness. The Cl(3, 1)(R) approach gives full symmetry.

Lounesto has shown all that and more twenty years ago in his extensive studies linking the four of the five normed division algebras with various Clifford algebras. The fifth, the even subalgebra of the algebra Cl(4,0), is already a Clifford algebra.

See Lounesto's paper here: Advances in Applied Clifford Algebras, Vol. 11 No. 2, 191--213 (2001). What Lasenby presented is nothing new. It is all well known for at least twenty years.
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Thanks, I will check that out. Lasenby knows the literature very well and did mention errors in earlier published work. He will be publishing a paper soon on his present understanding of these things.

You say "five division algebras". But there are only four division algebras. (According to modern definitions thereof)

PS I checked Lounseto's paper. I did not notice the connection with Cl(3, 1) or with Cl(1, 3).

Of course, you can start with any real algebra based on an 8-dimensional vector space (ie, you have a multiplication on top of R^8 as a real vector space with the usual compatibility conditions) and then define a multiplication and a norm making it a division algebra, in terms of some chosen basis. It's a different matter to start with Cl(1, 3) and a particular basis of Cl(1, 3) and define a new multiplication and a new norm in simple terms of the existing Clifford algebra structure such that you now also have the octonions superimposed [url]in a very harmonious way[/url] on the GA.

I am sure that Anthony knows Lounesto's work, and if he says that he is presenting something very new in his talk, then as a serious mathematician he certainly means what he says.

[Joy Christian]

I will be presenting my work on understanding quantum correlations at the upcoming conference AGACSE 2021 in Honor of Prof. David Hestenes, the creator of Geometric Algebra. The opening talk will be by Prof. Hestenes himself, on "Maxwell-Dirac QED" [using Geometric Algebra]: http://agacse2021.fme.vutbr.cz/main.php. My talk is number 13 in the list of talks: http://agacse2021.fme.vutbr.cz/participants.php. It is tentatively scheduled to take place on Tuesday, the 7th of September, 2021. The title and abstract of my talk are as follows:

Title: "Quantum correlations are weaved by the spinors of the Euclidean primitives"
Abstract: I will review my approach to local-realistically underpinning the origins and strengths of quantum correlations using geometric algebra. My approach turns out to be related to the “1d up approach” to conformal geometric algebra advocated by Prof. Anthony Lasenby in a different context. The framework I have proposed is based on an interplay between the quaternionic 3-sphere and an octonion-like 7-sphere. It circumvents Bell’s theorem by allowing a locally causal underpinning of quantum correlations, without requiring backward causation, superdeterminism, or any other conspiracy loophole. After reviewing my approach, I will respond to its partial critique by Prof. Lasenby.

…
The papers associated with all of the talks will be published in the proceedings of the conference, possibly in a Royal Society journal.

Selected papers will appear in a certain Wiley journal “Mathematical Methods in the Applied Sciences”, all others in a journal of the University of Brno, “Mathematics for Applications”.

Selected contributions will be invited for publication in the special volume of Mathematical Methods in the Applied Sciences. https://onlinelibrary.wiley.com/journal/10991476This has been already confirmed by the publisher. Only contributions presented at the conference will be considered for publication. Also at least one author per paper has to pay the conference fee. Generally, the contributions will be published as a special issue of Mathematics for Applications http://ma.fme.vutbr.cz/. However, the standard peer review procedure will apply.

I have now received an invitation from the organizers to submit a paper for the proceedings in MMAS by the 30th of December 2021. The proceedings may be published by March 2022.
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[Joy Christian]

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I already have an extensive response to Lasenby's critique of my work written up previously:

https://www.researchgate.net/publicatio ... _Mechanics

I will be expanding on this with my response to some additional points raised by Lasenby at the GA conference. He will regret that he followed the lead of Gill and made some of the same mistakes Gill has been making for many years. Lasenby had a near-perfect record so far as both a mathematician and a physicist. His critique of my work has put a blemish on this record.
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