### Octonions and quantum physics

Peter Woit reports in "This Week's Hype" string model hype about classical number fields, in particular the possible role of octonions. It would be nice to write a comment and tell how elegantly classical number fields appear in TGD framework and make dual descriptions in terms of 8-D Minkowski space (sub-space of complexified octonions) and M

^{4}× CP

_{2}unique. Unfortunately, Peter Woit wathces over his territory so jealously against invasion of anything which stinks like a good idea that it does not bother to take the risk of getting biten. Therefore John Baez - who as a Name is allowed to make intelligent comments- must continue to live in the illusion that no-one does anything to understand the role of octonions in physics.

The non-associativity of octonions is the basic problem if one attempts to build octonionic quantum mechanics. Nothing like this is tried in TGD. Instead, classical number fields appear at the level of classical physics (see this). Space-time surfaces as classical correlates of quantum physics are conjectured to decompose to associative (/quaternionic/Minkowskia)n and co-associative (/co-quaternionic/Euclidian) regions so that the weakness of octonionic quantum mechanics would turn into a strength making classical physics completely unique purely number theoretical. More precisely, the induced spinor structure for 8-D imbedding space has a special representation in terms of octonionic gamma matrices and the induced gamma matrices (not strictly speaking matrices anymore) are conjectured to span a quaternionic or co-quaternionic subspace of octonions over complex numbers at each point of the preferred extremal of Kähler action.

**Addition**: Also Motl has comments about octonions. The usual flood of insults and extremely arrogant super-stringy attitude towards anyone who does not regard superstrings as the laws of Moses for physics and dares to ask whether some aspects of super-strings might be part of a more successful physical theory. John Baez was the target of the aggression at this time. Maybe it is high time to Lubos to realize that the glamour of Harward does not last forever: we also remember that the exit of Lubos from Harward was not graceful. Some real output would be desperately needed if Lubos wants to keep his position as a blog authority and we have been waiting for years. My comment about the role of classical number fields in physics of course goes un-noticed: Lubos reads nothing which he has decided to represent crackpot theory. In any case, Lubos does a valuable work: he teaches us to tolerate people behaving like complete idiots. Learning this is after all the only manner to build a better world;-).

## 13 Comments:

Quote of the day

March 1, 2011

“Science cannot be stopped. Man will gather knowledge no matter what the consequences — and we cannot predict what they will be. Science will go on — whether we are pessimistic, or are optimistic, as I am. I know that great, interesting, and valuable discoveries can be made and will be made… But I know also that still more interesting discoveries will be made that I have not the imagination to describe — and I am awaiting them, full of curiosity and enthusiasm.”

Linus Pauling

c/o Marco Frasca

I have commented a few times on his blog, but it has always been deleted. It is funny, when very stupid things can be there. Kea comment, so you should also be qualified.

Trevlig valborg. Skriv nångång.

Matti

I found it hard to search some of your terms like Kahler action. But that does no matter.

Of course octonions apply to all of this (and beyond that at least to 16 space of which I am not quite sure that is what you mean by hyper-octonion or some sort of complex duplications.

I do not see (as of yesterday) the idea of the primes as a concept so restricted but I do see the math forms you are adept at rather cumbersome and misleading in our less rigid ideas of hyperspace. I am not sure of the dynamics but certainly we can expand 4 into 8 and that is a condition we seem to want to explain (compactification is the germ of a good idea here) The use of Feynman diagrams and the group notation loses information unnecessarily. Classical and other differences are irrelevant as on a higher level these ideas are transitive over all systems including spinning.

I will take this as our differences in how we see finite or continuous things- in general I think the quantum terms misleading here for such a reach of your generalization.

Hopefully we can speak again in details when some of this gets sorted out better. I will be taking a break soon.

The PeSla

Matti,

I see Lubos too today had some comments on octonions.

"idiosyncratic bullshit" is what he referred to for Baez.

One can claim an other does not understand a theory (string theory) but where is Lubos showing his work?

The numeric properties of these various spaces- apparently many want to keep it in the old physics framework- seems to me to be done more with practical considerations than with deep theory.

The radius of nine units to a square of 8 units as the ancient approximation to pi comes to mind as engineering, not magic for the ancient Egyptians- but theory may be hidden under all this that is not as numerological as the string ideas. There is nothing magical about ten dimensions.

And for all its apparatus, the idea of powers or integration over series, or thinking of calculus from this side of things in three space now a breeze- our common language shared common errors.

i to the i for example, as if acceleration was the key to all things comes out a real number- in fact, 4n + 1 can make many of these real numbers- your strength is the practical seeing of this.

I for one found Baez to make a lot of sense, and perhaps in ways even he does not realize yet.

Well,we keep on for some reason, play with roots and all, surely you have moments to question the project and the outcome- I have- I mean such growing wisdom for me in a sense comes too late. Like St. Augustine, loving Sophia too late.

I our abandonment at least we can sense that in the end all that we are capable of seeing now in the math and physics turns our so simple after all.

As always we are punished for our discovery of fire...

The PeSla

I have been wondering what is the magic of Lubos. Why we take him so seriously?

He was kicked out from Harward. He has not published anything for years. He hasn't proposed a single original idea in his blog. He has been repeating the same 15 year old propaganda about string theory and string theory is dead for all practical purposes. His latest comments about indications for new particles have been completely uncritical wishful thinking. And finally, the brilliant Lubos is unable to understand any argument which does not repeat what he has already said: usually this is not regarded as a sign of superior intelligence.

Why? Is the brutal secret of the success that Lubos insults people: is this the sole reason for why we read his blog? Just as we are looking for reality TV in which people are teasing each other? Why we love Stalinoids?

I think on the contrary that it is important that we do NOT TOLERATE that behaviour.

We don't tolerate a child behaving like that either.

The reason Hitler grew so strong was exactly because he was tolerated. There are plenty of creatures in this world creeping for such beasts. He gets support, you just have to look at his blog, weak people that scare to look at the world in other ways. They are 'locked in' in old thinking, but the world change, and always will change. Life is not rigid. You know that :) It is your hope.

I have been told there are others caring for that Lubos will not grow too big, but I don't know. He is compared to Nige. At least he is good in ridiculing himself. Not even the Cern people look so very much on what he says. There is something very wrong with him. Sorry Lubos.

E8 is a part of the heterotic strings too, so octonions should be interesting.

http://photos-b.ak.fbcdn.net/hphotos-ak-snc6/224925_218465664831739_100000049225675_874647_6343951_s.jpg

Without his court maybe Lubos isn't that big?

Matti,

I looked again and decided that the octonions do have a place in the dynamics of things. Is this something that you explored before to reach the conclusion they do not apply?

See this post of March 3:

Division Algebra over Relativistic Fields (Ottonians)

The PeSla

As I have explained in posting, one can imagine many manners for bringing in octonions to quantum physics. One possibility is to replace complex numbers with quaternions or octonions in the basic formalism. This leads to problems as was found long time ago.

In TGD framework one could imagine also quaternionic space-time and octonionic imbedding space. One could consider quaternionic and octonionic variants of complex analyticity be replacing functions of z with functions of h or o with real Laurent coefficients. This does not work either. These approaches could be call romantic;-)

%%%%%%

Division algebras can appear also in a more refined manner via their automorphism algebras respecting the basic algebraic structure.

a) In TGD framework one can consider replacing ordinary 8-D gamma matrices identifiable as tangent space vectors of 8-D space with their octonionic variants. This replaces SO(7,1) as tangent space group of M^8 with G_2 which is automorphism group of octonions identified as unit vectors in tangent space of M^8. This selects preferred time direction and G_2 as subgroup of SO(7). The interpretation is in terms of selection of preferred quantization axes and one does not loose Poincare invariance.

b) In M-theory one has 4+7-D spacetime and G_2 would be associated with 7 compactified dimensions (replacing the 6 compactified dimensions of Calabi-Yau in superstring models). I think this is basically the manner in which octonions emerge in M-theory and in many respects similar to the manner how they emerge in TGD.

c) In TGD framework I assume just the octonionic representations of the imbedding space gamma matrices to define /associative quaternionic space-time surfaces as space-time surfaces with the property that one can assign to each point of this kind of surface a quaternionic and associative subspace of octonionic gamma matrices. Also co-associative/co-quaternionic tangent spaces are possible.

If the action defining the space-time surface were 4-volume, the quaternionic subspace would be tangent space of space-time surface. 4-volume is however unphysical choice. For Kahler action the quaternionic subspace it is not tangent space. Also 2-D string world sheets and partonic 2-surfaces are an essential element of TGD and they could correspond to hyper-complex and complex 2-surfaces with the property that one can assign to their points commutative or co-commutative 2-D subspace of octonions.

d) Again I want to emphasize the principles involved rather than technical details. What is essential is that non-associativity and commutativity which defined the basic problems of quaternionic and octonionic approaches are turned to a strength. (Co-)Associativity can be taken as classical dynamical principle for space-time surfaces and (co)commutativity gives string world sheets and partonic 2-surfaces as sub-manifolds of space-time surfaces.

Note that at quantum level conformal field theories postulate that correlation functions satisfy associativity and this more or less fixes the situation since it leads to so called fusion rules.

Hi Matti,

you certainly have given a good presentation both in how physics is done and for some areas of your new theories.

I looked up fusion rules, a sparse article in wiki really, thinking perhaps that was what I woke up and saw this morning, but it was not I am talking about other things that apply in other areas that will not accept certain decompositions and irreducible groups as a fundamental idea.

I posted today not thinking my decomp over relativistic one could have a sequel- in the for of an outline of ideas to which I may expand upon later- in short I used your format from your pages and now see the efficiency of it.

It is quite a burden really though things must have names to pin these ideas in the language of assigning a name to them for there are way too many names to explore. Not that we should not give accurate credit, but the legal credit at the end of movies takes up way too much space and time.

I do like your original ideas as approach to things and hope that, if it matters, I can find some links between our systems that we can make more breakthroughs. It is hard not to see where you are in agreement with say Lubos on some issues but I am trying. Keep up the work, I like the last posts on the flux tubes and dark matter- but from my view although it does not change anything- these are descriptions not fundamentally different save the current physics will not consider the implications of your wider ideas which to me does not make sense on their part.

The PeSla

In this connection I should perhaps mention my post Luboš Motl calls Baez "an irrational numerologist".

To Jason: the claim of Lubos about John Baez is just incredibly silly.

To Pesla: I agree with Lubos about the fundamental role of conformal invariance and super-symmetry but experiments are demonstrating that their usual realizations are wrong.

*Conformal symmetry for light-like 3 surfaces is what physics requires: this fixes uniquely space-time dimension to four: If Witten would state this fact publicly, it would be accepted everywhere within five minutes.

*Supersymmetry with right handed neutrino and antineutrino replaces supersymmetry in TGD and allows to get rid of unphysical R-parity symmetry. As a matter fact super-symmetry in TGD is even larger since all fermion oscillator operators act as super-symmetries but it is badly broken.

I have found it completely impossible to communicate my view about supersymmetry to Lubos. He just refuses to read written text and has decided that I hate supersymmetry.

M-theory and TGD are diametrical opposites of each other in terms of conceptual economy.

*TGD is obtained from general relativity by reducing the number of degrees of freedom: space-time becomes a surface which poses enormous constraints and among other things one gets rid of the basic problems of GRT related to cosmological constant.

*M-theory in turn implies inflation in the number of degrees of freedom. First of all it doubles the gravity: gravity from strings in M^10 is fine but world is not 2-D. Therefore on must introduce second gravity by making M^10 dynamical by spontaneous compactification. As if this were not enough, one introduces also branes so that no one knows whether our space-time corresponds to brane or compactified target space or compactified brane! The outcome is landscape which brings to my mind the gigantic inflation of Germany during second world war: tons (I mean thousands of kilograms) of money to by a piece of bread!

I share also the belief in holography but again in minimal rather than inflated form.

*Holography in TGD follows from general coordinate invariance in TGD framework and means that basic objects are almost 2-D so that one obtains holography almost as we usually understand it.

*In AdS-CFT approach you try to describe nuclear physics and super-conductivity in terms of 10-D black holes. I would be really surprised if this turns out to be more than a fashion lasting decade or two. It is too far from the reality and one loses totally the power of physical intuition.

"*TGD is obtained from general relativity by reducing the number of degrees of freedom: space-time becomes a surface which poses enormous constraints and among other things one gets rid of the basic problems of GRT related to cosmological constant. "

This was the reason Einstein made his GR, to get rid of the time-sheets, by assuming one iniert time (speed of light). Movements in relation to it would change the time (and gravity?) At c time is 0?

This makes your approach a bit circular? I think you must build GR instead?

Matti,

Thanks for the informative replies on comments in your last few posts.

Today I found similarities in our general approaches in which I have mentioned TGD so you might want to correct me where I may misunderstand it. Look under:

Canonical Identification and Hyperquasics.

Oddly enough 10D is involved here and it could possibly be seen as black holes- in the coordinate notation. But even this would be but a start to this new hyperphysics. I feel like Klein in relation to Sopheus Lie to you in founding a new level of theory.

The PeSla

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