Arcadian Functor

occasional meanderings in physics' brave new world

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Marni D. Sheppeard

Tuesday, March 18, 2008

The Dirac Code

Thanks to Carl Brannen for links to slides by physicist Peter Rowlands. I thought the name was familiar: had I met him at a conference a few years ago? If so, it was odd that I could not recall somebody working on a nilpotent operator theory related to Brannen's measurement algebra. Ah! That's it! He has also been banned by the arxiv server, without explanation, despite being a qualified physicist and author of a book on the foundations of physics.

Do any of the blacklisted physicists not have an interest in this approach to unification?


Anonymous Anonymous said...

Dr Rowlands states on the arxiv freedom site:

"... Some of the material has already appeared in refereed publications. It didn't violate any known physical laws or principles.

"However, it was novel and original in its approach, which, of course, is the whole reason for doing research in the first place.

"The arXiv is not a journal with specific stated policies for inclusion. It claims to represent the whole of physics, and it does not say anywhere that it will refuse to publish papers that fall outside the narrow interests of its moderators. This covert censorship is even more insidious in the light of arXiv's pretended policy of being open."

I think that this is a clear statement of what is wrong with arXiv. It's not a problem that it refuses to publish, it's a problem that it claims to be an automated science preprint server, yet censors off - in an arbitrarily way - preprints.

March 19, 2008 2:24 AM  
Anonymous Anonymous said...

correction to last sentence:

It's not a problem that it refuses to publish, it's a problem that it claims to be an automated science preprint server, yet censors off - in an arbitrary way - preprints.

What arxiv needs to do is to publicise the fact that it will not host papers that don't look mainstream in approach, unless they are by friends of arXiv moderators. Then there would be no deception over it's policies. We'd all be clear that it's just a social networking forum for mainstream or friends of mainstream people, rather than a strictly open, scientific prepreint server based on ethical, transparent principles.

March 19, 2008 4:15 AM  
Blogger Kea said...

I think you are right, anonymous. If it was just another social forum, why would we mind? After all, we have plenty of places to post papers on the web for anybody to download, so the arxiv really isn't very important.

March 19, 2008 8:55 AM  
Blogger Alejandro Rivero said...

But Clifford algebra is a mainstream topic. It is a prerequisite for Bott periodicity and all such stuff.

March 21, 2008 12:53 AM  
Blogger Kea said...

Hi arivero. Clearly, it depends what you are doing with Clifford algebra. Saying that string theory is wrong, and associating with the wrong people, tends to get you banned by the arxiv. You seem to have survived quite well so far, but that might be because they just haven't noticed everything.

March 21, 2008 9:58 AM  
Blogger Yoyo said...

I had a brief look at the slides but they don't make much sense to me. For example, on slide 30

- he claims that $A$ is a multiple of an element of his algebra. But $A$ is supposed to be a spinor - how can it be an algebra element? Sure, it's possible to use a left-ideal of the Clifford algebra as a spinor space but that doesn't appear to be what he's doing.

- he claims $A$ and hence $\psi$ are `nilpotent`, but what does this mean for spinors? This again suggests that he's thinking of $\psi$ as being an element in his algebra (where 'nilpotent' might mean something), but then he goes on to claim that this 'must have been true even before we made the substitution of algebraic operators for matrices'. Well, no, in the original equation $\psi$ really is a spinor and being 'nilpotent' has no meaning that I'm aware of.

March 21, 2008 11:38 PM  
Blogger Kea said...

Philip, I don't think A is supposed to be a spinor. Whether or not his algebra is completely well-defined or not, I'm not sure. Personally, I prefer Carl's more well developed formalism, not to mention the airy-fairy stuff.

March 22, 2008 7:27 PM  
Blogger Yoyo said...

I think $A$ has to be a spinor - Rowland's written his plane-wave solution on slide 29 as $\psi = A exp(-iEt - p \cdot r)$ - the exponential part is a scalar and the $A$ stands in for what would normally be a basis spinor.

I think the algebra is defined ok, it appears to be the tensor product of the quaternions and biquaternions. It would be nice if this were made clearer in the slides. It's bigger than needed though - it has real dimension 32 instead of the 16 dimensions of the Clifford algebra $Cl(3,1)$ generated by the $\gamma$ matrices.

March 22, 2008 8:16 PM  
Blogger CarlBrannen said...

In the non Geometric algebra world, a spinor is a vector of complex numbers. The geometric algebra community does an equivalent thing by using stuff in the ideals of the Clifford algebra.

To get started at understanding this, note that if you took, say, a Pauli 2x1 spinor and expanded it out to be a 2x2 matrix by putting the spinor in the first column of the matrix and zeros in the second column, you'd have an object that would satisfy all the equations that your spinor satisfied. The only difference is that it would be carrying around a column of zeroes.

This concept is called "square spinors" or something similar and you can learn more about them in mathematical books on Clifford algebras and spinors.

A good reference is Lectures on Clifford (Geometric) Algebras and Applications by Rafal Ablamowicz and Garret Sobczyk. Look in the index under "spinor, as square matrix, page 18." You don't have to buy the book, just go to Amazon and look in the index to see the reference.

And by the way, this reminds me of the analysis that people give Lisi's work. Only people who are quite ignorant of geometric algebra and Clifford algebra can claim that it is nonsense to add scalars to vectors.

I do not mean to compare Philip's polite commentary with the stuff that Lisi put up with.

And Rowland's stuff is not "airy" as compared to mine. My stuff is built on a foundation that is in complete disagreement with special relativity. I hide the disagreement by sticking to internal states.

Rowland (and Lisi too) tried to make their stuff compatible with special relativity and ended up with very messy things. Rather than face the wrath, I hid in the finite version of the theory. And that reminds me, I'm going to write a series of posts taking relativity apart, piece by piece.

March 24, 2008 5:57 PM  
Blogger CarlBrannen said...

I guess I should add that a nifty way of getting a square spinor out of a spinor is to take your spinor ket, and right multiply it by the bra spinor for spin up. That will make a density matrix with zero in the right column and your spinor ket in the left column. Or you can use spin down to get switch the columns. Or you can use any arbitrary spinor.

You can also do the same thing to convert a bra spinor into a matrix. If you use the same fixed spinor to do this (say spin up), then you will have mapped the spinor arithmetic, including the inner product, into matrices.

This whole thing is a central idea to the density matrix formalism. I should write up a blog post.

March 24, 2008 6:02 PM  

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