Sci.Physics.Foundations

I stumbled across this possibly interesting website that Chantal Roth is involved with.

https://elastic-universe.org/

It has some simulations of 1/2 spin that are very good. However, I was intrigued by their Quaternion Quantum Mechanics that I am trying to make sense of.
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FrediFizzx wrote: ↑Wed Sep 27, 2023 10:28 am I stumbled across this possibly interesting website that Chantal Roth is involved with.

https://elastic-universe.org/

It has some simulations of 1/2 spin that are very good. However, I was intrigued by their Quaternion Quantum Mechanics that I am trying to make sense of.

Still working on figuring out their QQM. But the interaction between two physical vectors is a quaternion. However, the vectors can be quaternions also. Hmm....
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It looks very interesting. I was wondering why they used quaternions instead of geometric algebra. Perhaps their initial interest is to show equivalence to QM. But I think they will make their work clearer by using geometric algebra directly.

Chantal has an interesting wave approach but she concedes in one of her videos that it does not explain the Bell results.

Cohl Furey has further related elementary particles to octonion maths. A Quanta article (link below) gives links to a number of her videos. I have followed some and they are interesting in the same way that Lisi Garrett's use of the Exceptional E8 group related to fundamental particles.
https://www.quantamagazine.org/the-octo ... s-20180720

I have a retrocausal model explaining the Bell result (how the inequalities are bypassed rather than broken). It is really the converse of Joy's one-page model. Time for space. Instead of the analogy of dancers skating spatially backwards in the opposite half of the sphere, the dancers are skating backwards in time.

Austin Fearnley

Well, the EPR-Bohm product calculation prediction for classical mechanics does also work with the 3D vectors as quaternions.





Yep, Bell was wrong in this case also!

Now, wondering if this will work with Pauli matrices.
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minkwe wrote: ↑Tue Oct 03, 2023 7:45 am It looks very interesting. I was wondering why they used quaternions instead of geometric algebra. Perhaps their initial interest is to show equivalence to QM. But I think they will make their work clearer by using geometric algebra directly.

A quaternion is a nice package for the sum of a scalar and a vector. With GA it is multi-vectors. And the name; GA Quantum Mechanics or Quaternion Quantum Mechanics.
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ben6993 wrote: ↑Tue Oct 03, 2023 2:56 pm Chantal has an interesting wave approach but she concedes in one of her videos that it does not explain the Bell results.

Cohl Furey has further related elementary particles to octonion maths. A Quanta article (link below) gives links to a number of her videos. I have followed some and they are interesting in the same way that Lisi Garrett's use of the Exceptional E8 group related to fundamental particles.
https://www.quantamagazine.org/the-octo ... s-20180720

I have a retrocausal model explaining the Bell result (how the inequalities are bypassed rather than broken). It is really the converse of Joy's one-page model. Time for space. Instead of the analogy of dancers skating spatially backwards in the opposite half of the sphere, the dancers are skating backwards in time.

What do you mean exactly by "Bell results"?

More about Cohl Furey's work,

https://www.sciencedirect.com/science/a ... via%3Dihub

Do you have a link for your model?
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I do not have a formal, mathematical, retrocausal model but you can look at my most recent four papers here if you have not already seen them:
https://vixra.org/author/austin_j_fearnley

I did suggest my idea in a casual post many years ago to Joy but he did not like it. And I do not expect anyone to like it now. Take Joy's one-page model. In it, a pair of particles is generated in a trivector orientation taken at random. Say +1, and the next pair from -1 etc. The overall calculation uses a mix of trivector values which drew criticism from GA users who said you have to choose one or the other for a single calculation.

In my model, a pair of particles goes into both trivectors. One into +1 and the other into -1. At the pair creation, the particles are spatially close but are travelling in opposite time directions. This implies that the sign of the trivector determines the arrow (not a vector) of time for that particle. GA users will like this even less than for Joy's model as the calculation mixes up the trivectors even more. Note, particle and antiparticle are travelling in opposite time directions. This applies to photons too, which I have explained using my preon model.

I don't see the value for me in writing up the model more formally.

I am interested in octonions as they bring together three independent trivector orientations. I suspect that they could be used to describe three, co-existing time dimensions for red, green and blue branes of QCD. I do not get too excited by the maths as group theory merely describes rather than causes. The three generations in the paper you showed is a red herring IMO.

Here is a link to Furey's lectures on octonions. I have followed five or six of them.
https://www.youtube.com/channel/UCvsmxU ... ittaeosXMA

Austin Fearnley

ben6993 wrote: ↑Wed Oct 04, 2023 12:02 pm I do not have a formal, mathematical, retrocausal model but you can look at my most recent four papers here if you have not already seen them:
https://vixra.org/author/austin_j_fearnley

I did suggest my idea in a casual post many years ago to Joy but he did not like it. And I do not expect anyone to like it now. Take Joy's one-page model. In it, a pair of particles is generated in a trivector orientation taken at random. Say +1, and the next pair from -1 etc. The overall calculation uses a mix of trivector values which drew criticism from GA users who said you have to choose one or the other for a single calculation.

In my model, a pair of particles goes into both trivectors. One into +1 and the other into -1. At the pair creation, the particles are spatially close but are travelling in opposite time directions. This implies that the sign of the trivector determines the arrow (not a vector) of time for that particle. GA users will like this even less than for Joy's model as the calculation mixes up the trivectors even more. Note, particle and antiparticle are travelling in opposite time directions. This applies to photons too, which I have explained using my preon model.

Joy has a newer improved model that no longer uses the trivector orientation. It is similar to the Mathematica simulation I posted above.
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FrediFizzx wrote: ↑Thu Oct 05, 2023 12:12 pm

ben6993 wrote: ↑Wed Oct 04, 2023 12:02 pm I do not have a formal, mathematical, retrocausal model but you can look at my most recent four papers here if you have not already seen them:
https://vixra.org/author/austin_j_fearnley

I did suggest my idea in a casual post many years ago to Joy but he did not like it. And I do not expect anyone to like it now. Take Joy's one-page model. In it, a pair of particles is generated in a trivector orientation taken at random. Say +1, and the next pair from -1 etc. The overall calculation uses a mix of trivector values which drew criticism from GA users who said you have to choose one or the other for a single calculation.

In my model, a pair of particles goes into both trivectors. One into +1 and the other into -1. At the pair creation, the particles are spatially close but are travelling in opposite time directions. This implies that the sign of the trivector determines the arrow (not a vector) of time for that particle. GA users will like this even less than for Joy's model as the calculation mixes up the trivectors even more. Note, particle and antiparticle are travelling in opposite time directions. This applies to photons too, which I have explained using my preon model.

Joy has a newer improved model that no longer uses the trivector orientation. It is similar to the Mathematica simulation I posted above.
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Yes, that is correct. The paper is under review at a prominent journal. But its preprint is available on arXiv: https://arxiv.org/abs/2204.10288
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Joy Christian wrote: ↑Thu Oct 05, 2023 2:25 pm

FrediFizzx wrote: ↑Thu Oct 05, 2023 12:12 pm

ben6993 wrote: ↑Wed Oct 04, 2023 12:02 pm I do not have a formal, mathematical, retrocausal model but you can look at my most recent four papers here if you have not already seen them:
https://vixra.org/author/austin_j_fearnley

I did suggest my idea in a casual post many years ago to Joy but he did not like it. And I do not expect anyone to like it now. Take Joy's one-page model. In it, a pair of particles is generated in a trivector orientation taken at random. Say +1, and the next pair from -1 etc. The overall calculation uses a mix of trivector values which drew criticism from GA users who said you have to choose one or the other for a single calculation.

In my model, a pair of particles goes into both trivectors. One into +1 and the other into -1. At the pair creation, the particles are spatially close but are travelling in opposite time directions. This implies that the sign of the trivector determines the arrow (not a vector) of time for that particle. GA users will like this even less than for Joy's model as the calculation mixes up the trivectors even more. Note, particle and antiparticle are travelling in opposite time directions. This applies to photons too, which I have explained using my preon model.

Joy has a newer improved model that no longer uses the trivector orientation. It is similar to the Mathematica simulation I posted above.

Yes, that is correct. The paper is under review at a prominent journal. But its preprint is available on arXiv: https://arxiv.org/abs/2204.10288

Oh..., you changed the model again. Well, this way is more simple but I kind of liked that the limits actually got taken the other way. Hmm..., maybe there is a way to do both.
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I posted to let you know that I saw a connection between my retrocausal papers and the one-page model. I did not set out consciously to make my method have such a connection and only saw the connection afterwards. I thought, though, that someone here might be interested in that link.

I am sorry that I am being pointed at a new, long and complicated paper as I do not have the expertise or energy to cope with an ever-moving and complex target. Nevertheless, I have looked at the new arxiv pre-print. Unfortunately, I am not up-to-date with models later than the one-page paper, though I have looked at some of them. I believe it is true that the newer models are meant to be improvements to rather than the discarding of the older models, but no model has been retracted by Joy.

First, page 18 has a typo: even-by-event should be event-by-event.
I like the question and answer section at the end.

The top left of page 14 notes "... if the Mobius-like twists in S3 ...".
That tells me that the S^3 space has trivector issues impicitly even if it could be written as though the trivectors are not playing an explicit role.

Mid right of page 3:
"If, initially (i.e., before the detection process defined by the measurement functions to be specified below), the two unit vectors a and si1 happen to be pointing through the same hemisphere of S2 ֒→ IR3 centered at the origin of si1, then µ1 = sign(a·si1) will be equal to +1,
and if the two unit vectors a and si1 happen to be pointing through the opposing hemispheres of S2
centered at the origin of si1, then µ1 = sign(a · si1) will be equal to −1, provided that a·si1 = 0."

and also the footnote 4 on page 6 seems to define a hidden variable in terms of different orientations which retain the property of 'no cowlicks'. I also note a thread on this website discussing whether there is a hidden variable or not.

It seems to me that trivectors are still important. I agree that it is useful to have hidden variables. I see nothing here to change my opinion of my suggested link.

Austin Fearnley

FrediFizzx wrote: ↑Fri Oct 06, 2023 8:07 am

Joy Christian wrote: ↑Thu Oct 05, 2023 2:25 pm

FrediFizzx wrote: ↑Thu Oct 05, 2023 12:12 pm
Joy has a newer improved model that no longer uses the trivector orientation. It is similar to the Mathematica simulation I posted above.

Yes, that is correct. The paper is under review at a prominent journal. But its preprint is available on arXiv: https://arxiv.org/abs/2204.10288

Oh..., you changed the model again. Well, this way is more simple but I kind of liked that the limits actually got taken the other way. Hmm..., maybe there is a way to do both.

Yes, it works with both ways. I'll post the simulation if anyone is interested.
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FrediFizzx wrote: ↑Sat Oct 07, 2023 1:42 pm

FrediFizzx wrote: ↑Fri Oct 06, 2023 8:07 am

Joy Christian wrote: ↑Thu Oct 05, 2023 2:25 pm
Yes, that is correct. The paper is under review at a prominent journal. But its preprint is available on arXiv: https://arxiv.org/abs/2204.10288

Oh..., you changed the model again. Well, this way is more simple but I kind of liked that the limits actually got taken the other way. Hmm..., maybe there is a way to do both.

Yes, it works with both ways. I'll post the simulation if anyone is interested.

By now we know that there are several different ways to derive the cosine correlations within S^3. So it is not surprising that the simulation works out in this case. But post the simulation anyway, for the record.
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Joy Christian wrote: ↑Sat Oct 07, 2023 2:47 pm

FrediFizzx wrote: ↑Sat Oct 07, 2023 1:42 pm

FrediFizzx wrote: ↑Fri Oct 06, 2023 8:07 am
Oh..., you changed the model again. Well, this way is more simple but I kind of liked that the limits actually got taken the other way. Hmm..., maybe there is a way to do both.

Yes, it works with both ways. I'll post the simulation if anyone is interested.

By now we know that there are several different ways to derive the cosine correlations within S^3. So it is not surprising that the simulation works out in this case. But post the simulation anyway, for the record.

Ok, I just have to figure out what r0 is for BA then I will post it. I know it works anyways because it will be zero when the limits are taken.
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FrediFizzx wrote: ↑Sat Oct 07, 2023 4:56 pm

Joy Christian wrote: ↑Sat Oct 07, 2023 2:47 pm

FrediFizzx wrote: ↑Sat Oct 07, 2023 1:42 pm
Yes, it works with both ways. I'll post the simulation if anyone is interested.

By now we know that there are several different ways to derive the cosine correlations within S^3. So it is not surprising that the simulation works out in this case. But post the simulation anyway, for the record.

Ok, I just have to figure out what r0 is for BA then I will post it. I know it works anyways because it will be zero when the limits are taken.

I think I have this right. Here is a PDF of the Mathematica simulation and the notebook file. I kept the 3D vectors as quaternions in this version. I think the r0 method is better because there is no cross product or bivector residue. It's zero.

sims/Local-S3-prod_calc_1.pdf
sims/Local-S3-prod_calc_1.nb

Enjoy!

Now, we should probably get back on topic with the Elastic Universe.
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