The Foundations of Quantum Mechanics

**(c) Robert Neil Boyd**

[R. N. Boyd]:

The problem with the concept of mind-matter unification is that matter and mind are *NOT* unified. Mind is a coherent holographic *energetic structure* which lives in a Clifford space (named after the Clifford algebra).

It is **NOT** a quantum-based phenomenon. The quantum aspects of consciousness are only *secondary effects* of the holographic N-dimensional energetic of consciousness, on the material world.

The mind-matter unification concept is a red herring, a distraction from the facts of the matter. Disinformation. "Mind" *is not contiguous* with the physical form. This has been verified instrumentally. See for example: http://www.zynet.co.uk/imprint/Tucson/4.htm#Physical

Also see reference materials by Pribram and Talbot. For example, "The Holographic Universe" by Talbot.

Note the fact that the intention, attention, and emotional conditions of the operators of symplectic E/M transmission facilities *directly* alter the radiation pattern of the symplectic antenna. This is *not* a quantum phenomenon, but the variations in the symplectic E/M radiations *result* in a divergence in the quantum field.

[Arkadiusz Jadzcyk]: What is Clifford space?

[R. N. Boyd]:

I consider [Clifford Space] to be similar to a quaternionic space, with several graded orders of infinite dimensions, rather in the manner of the graded Clifford algebra.

And, as you know, the quaternions are one of the Clifford algebras.

Related to this, Tony Smith says: "...looking at the 8-real-dimensional SpaceTime as a 2-Quaternionic-dimensional space (with Fueter's Quaternioinic analyticity and Quaternionic Cauchy-Riemann equations as described, for example, in On the Role of Division, Jordan and Related Algebras in Particle Physics, by Feza Gursey and Chia-Hsiung Tze (World 1996)) or by looking at the 8-real-dimensional SpaceTime as a 1-Octonionic-dimensional space; and, according to YGGDRASIL (journal of paraphysics whose name is "... the "world tree" in Norse mythology. It is also known as the "tree of knowledge," the "tree of the universe" and the "the tree of fate." ..."), the idea of looking at the imaginary part of an 8-real-dimensional SpaceTime was used by Elizabeth Rauscher in 1977 and Puthoff, Targ and Edwin May in 1979."

Also, at http://www.valdostamuseum.org/hamsmith/clfpq2.html#13vs31

"Since Cl(3,1) and Cl(1,3) provide two Clifford Paths to the D4-D5-E6-E7-E8 VoDou Physics Model,

Which Signature is more Physically Realistic ?

John Baez, on the usenet group sci.physics.research, said:

Note that Spin(-+++) = Spin(+---) = SL(2,C), so that you can't use the Spin group to tell which is the right one, so look at the Clifford algebra from which the Spin group is derived. The Clifford algebras of candidate physical spacetimes are:

(+---) = Cl(3,1) = M(4,R) the 4x4 real matrix algebra

Cl(-+++) = Cl(1,3) = M(2,Q) the 2x2 quaternionic matrix algebra.

Both of them are Clifford algebras with a real 4-dim vector space, and graded structure

The grade-0 1 is the scalar space (like Higgs boson).

The grade-1 4 is the vector space (like spacetime).

The grade-2 6 is the bivector space (like gauge bosons).

Since all these spaces are real, the bosons in both of them are real.

However, the fermions should correspond to half-spinors, with the fermion particles being +half-spinors and the fermion antiparticles being mirror image -half-spinors.

For Cl(+---) = Cl(3,1), the full spinor space (minimal ideal of the Clifford algebra) is 1x4 real column of the 4x4 real matrix and each half-spinor space is 1x2 real column, so a fermion half-spinor would be real.

For Cl(-+++) = Cl(1,3), the full spinor space (minimal ideal of the Clifford algebra) is 1x2 quaternionic column of the 2x2 quaternionic matrix and each half-spinor space is 1x1 quaternion column, or, in other words, a fermion is a quaternion.

Therefore, if "... fermions are quaternionic and bosons are real ..." then

Also see: http://www.valdostamuseum.org/hamsmith/clfpq2.html#physicspaths

and http://www.valdostamuseum.org/hamsmith/clfpq2.html#clifstructure

and http://www.valdostamuseum.org/hamsmith/Lie.html#spin8clif

Also, I'm certain that you know that any Lie algebra can be constructed from the Clifford algebra, as can the Kac-Moody algebra, etc. These algebras can also be used to define spaces, manifolds, etc., as Saul-Paul Sirag and Tony Smith have done.

Also, I'm sure you are aware of the quaternionic quantum theories which have been developed there in Australia, and at the Institute for Advanced Research in Austin, Texas.

In summary, since there is extant literature on quaternionic manifolds and spaces, and since the quaternions are one of the Clifford algebras, it does not seem to me to be much of a stretch to generate a Clifford space or a Clifford manifold.

Once again, apparently I was among the first to consider the concept, but a Clifford space does not seem at all unreasonable.

[Arkadiusz Jadzcyk]:

I know that Clifford space is similar to a quaternionic space. However, I do not understand "graded orders of infinite dimensions." I know what is a graded algebra. It may have grades within grades. OK. I know what it would mean to have each grade infinite dimensional. I do not know where quaternions would fit.

Also, What do you mean by "graded Clifford algebra?" Clifford algebra is naturally Z2 graded - it has even and odd part. Do you mean this?

Then it can be also graded 0,1,2,...,n - (scalars, vectors, bivectors,3-vectors,...,n-vectors) which is not its natural grade, but which comes when you identify Clifford algebra with Grassman algebra. Do you mean this?

Or you can have some BIG algebra, which is graded, and whose grades are Clifford algebras. Do you mean this?

Canonical anticommutation relations used for quantum Fermion fields are nothing but infinite dimensional Clifford algebra and its representation by operators in infinite dimensional Hilbert space. Do you mean this?

And what is its relation to mind? Why Fermions rather than Bosons? Or Anyons?

Questions, questions, questions,.....

[R. N. Boyd]:

"Graded Clifford Algebra" is related to consciousness by the symplectic E/M, the even part.

Regarding your statement, "Then it can be also graded 0,1,2,...,n - (scalars, vectors, bivectors,3-vectors,...,n-vectors) which is not its natural grade, but which comes when you identify Clifford algebra with Grassman algebra."

This is what I had in mind. This is an extension from the quaternionic descriptions of Karl Pribram, which I suggested to him in 1995. The reason for the extension is that there are infinities of realities and kinds of consciousnesses in those various realities, which can be describable by such structures, applied to consciousness in terms of vector spaces. Unfortunately, these are only basic and partial descriptions.

Many energetic behaviors and operations of the various forms of consciousness must then be accomplished by some suitable detailed description which is appropriate to that particular reality.

This is why I was interested in an N-dimensional gauge theory, for example. Because I am seeking the skeins which underlie all the different realities, so that themes of relational behaviors can be developed and used to understand and describe other realities. And to better understand ours.

The inflation theories of A.D. Linde started in this direction of descriptions of multiple realities with various sets of physical laws, which imply various forms of consciousness within those realities. But his inflationary scheme has only a few flavors of realities, which is not true to fact. In fact there are infinities of variety.

Tony Smith developed a description of consciousness based of the periodicities of the Cl(8) Clifford algebra, from my suggestion that consciousness could be modeled in terms of the Clifford algebras. While this description corresponds quite well with consciousness as we know it, this description does not appear to me to be sufficient in an N-dimensional way. I was hoping to stretch Tony to be able to see these aspects, but he has some internal reluctance, apparently.

I am hoping that your N-dimensional Kaluza-Klein theory will go farther in these directions. It appears to me that this approach may be sufficiently rich to describe the infinite varieties of energetic behaviors and variations of consciousness which inhabit these various realities.

I sincerely hope you will try. Such modeling will bring your work immortality, because it will live on and find application here, and in other worlds, long after you have gone on to occupy some other reality(ies).

Regarding your statement, "Or you can have some BIG algebra, which is graded, and whose grades are Clifford algebras. Do you mean this?"

This doesn't seem like it. But it could be. I am leaning more and more to your infinite dimensional Kaluza-Klein theories, just because I really like the foliations and variations that are possible. Instinctively, these descriptions are true to fact.

Is there perhaps some combination of these approaches of Clifford space and Kaluza-Klein space that can work? Or perhaps the K-K descriptions alone are adequate?

I don't know exactly how far you've progressed in this direction, although I do know that you have made some major breakthroughs, and succeeded in many of your goals, regarding the non-compactified infinite dimensional Kaluza-Klein theory. I can see, from where I am, that it works. What you have done so far is valid. But I can only get impressions. Not details, unfortunately...

Regarding your description, "Canonical anticommutation relations used for quantum Fermion fields are nothing but infinite dimensional Clifford algebra and its representation by operators in infinite dimensional Hilbert space." --

This sort of description could easily apply very accurately in a description of consciousness, where we live.

However, the issue of descriptions of various consciousnesses in the other universes, with variations in physical laws and differing dimensionalities does not appear to be sufficiently covered by such an approach.

I'm glad you are taking the time to examine these things very deeply with me here. I have some very strong instinctive drives to explore in these directions. I have a strong instinct that your Kaluza-Klein studies will bear fruit in these directions.

Regarding your question, "And what is its relation to mind? Why Fermions rather than Bosons? Or Anyons?" --

There is a view that electrons are multidimensional entities, with links into various realities other than this one.

Questions are good, because they lead us to finding out. I don't think we'll ever run out of questions though...

I reckon the only way to deal with these questions is to put them into the context of some general theme, such as interdimensional consciousness, and then resolve for that particular issue, answering one question at a time in that theme. I have an instinct that N-dimensional physics will find real uses in this world, and in other universes. It's rather odd to me, when compared to the "average person" that I contemplate these things, but I experience such explorations as being exceedingly important and exceedingly interesting.

It's times like these, that I wish I had more math tools.