Video Article: Through a Glass Darkly

Haven't watched the video yet but...String theory seems to require *11* dimensions, with *7* extra spatial dimensions for a unified description, otherwise it reduces to separate effective theories for varying energy limits.

Does this mean the octonion description can never completely explain or describe reality for the whole energy spectrum? Wouldn't it therefore need to derive a 6 dimensional compactification that string theory has until now not been capable of producing, when "collapsing" the bulk structure to a single octonion 4D spacetime?

There is a relationship between 10 and 11 dimensional string theory. String theory is written in the infinite momentum frame. In 4-dim spacetime this is where one uses E^2 = p^2 m^2 and break up p^2 = p_x^2 p_y^2 p_z^2 with p_z huge. In other words the system is boosted enormously. This is called the light cone or infinite momentum frame. We then have

E = sqrt{ p_x^2 p_y^2 p_z^2 m^2} = p_z sqrt{1 (p_x^2 p_y^2)/p_z^2 m^2/p_z^2}

This means the physically relevant Hamiltonian is H' = (p_x^2 p_y^2)/p_z^2 m^2/p_z^2, where for p_z huge this acts a bit like an inertia and dilates the transverse momenta p_x^2 p_y^2 to small values, such (p_x^2 p_y^2)/p_z^2 so the large p_z acts as a Lorentz factor or equivalently a large mass term. The longitudinal modes along p_z are then factored out. Strings are then described in a Newtonian fashion in one dimension less. This connects to Susskind's holographic principle, where those transverse modes are on the stretched horizon of a black hole as seen by a stationary observer away from the black hole.

In 11 dimensions the 10 dimensional theory can be derived by putting the physics on a highly boosted frame. Similarly in 10 dimensions the theory can be boosted to recover a 9 dimensional theory. The infinite momentum frame in 10 dimensions connects to the 24-cell, which has a number of representations. The full representation is the F_4 group with 1154 Hurwitz quaternions. The other is the B_4, which is the 16 cell plus an 8-cell, and the other is D_4 which is three 8-cells. The more general automorphism is then F_4. The quotient between the 52 dimensional F_4 and the 36 dimensional so(9) ~ B_4 defines the short exact sequence

F_4/B_4:1 --> spin(9) --> F_{52\16} --> OP^2 --> 1,

where F_{52\16} means F_4 restricted to 36 dimensions, which are the kernel of the map to the 16 dimensional Moufang or Cayley plane OP^2. The occurrence of 36 and 9 is no accident, and this is equivalent to the structure used to prove the KS theorem. To add another ingredient into this mix I reference , which illustrates how the Kochen-Specker result is an aspect of the 24-cell.

The infinite momentum frame in 11 dimensions recovers 10 dimensional theory, which has SO(16) physics in 10 dimensions. This theory in its fullest representation is the Jordan matrix algebra in 27 dimensions reduced to 26 dimensions by a constraint on the diagonal scalar terms. The F_4 is the automorphism of the Jordan matrix algebra and the centralizer with G_2 of the octonion group E_8. The work by Drey and Manogue illustrates how the F_4 matrix diagonalizes the Jordan algebra. The use of infinite momentum frames indicates there is a holographic interpretation of these results. The Calabi-Yau compactification in 10 dimensions, curling up 6 dimensions, is then the "holographic plate" which projects out compactified dimensions in 7 dimensions within the fuller 11 dimensional theory.

Cheers LC

is there a new paper out - particularly about muons and taus ?

I was just looking in Kevin McCrimmon's book 'A Taste of Jordan Algebras' - page 4 he says that the 'lone exceptional algebra H3(K) was too tiny to provide a home for quantum mechanics.' I guess that applies to Jordan's approach.

Frankly, I think Octonions blow up the idea that spacetime is as fundamental as quanta, but that quanta are consistent with space and time. To put it crudely, complex quaternions define the structure of space, and complex octonions define the structure of matter - ie particles. Physics seems to demand treating spin as a degree of freedom, thus an electron would be treated as a pair of octonionic oscillators.

It may be that quantum mechanics and relativity are categorically equivalent in the language of octonions.

LC

Still the same article for the publicity of false extrapolations and works.

BE RATIONAL PLEASE DEAR EXTRADIMENSIONALISTS. Sciences must be deterministic.

Quaternions and octonions are just mathematical tools, and when you use tools, so you must use them correctly.

Sincerely and honestly and pragamtically and spherically.

Regards

Steve. First of all, it is debatable whether quaternions and octonions are "just tools" or even just human inventions. One can certainly use quaternions as tools, as Hamilton did to re-invent Newtonian physics from scratch - that is one heck of a tool. Further, without that "tool" Pauli would not have been able to deal with Spin, without which atoms make no sense. Further,

Perhaps there is a philosophical issue of whether mathematical structure should accommodate or define. Since Clifford algebra can accommodate any number of dimensions it can not explain why space is three dimensional. The default position in physics is to accommodate - but then you lose the ability to say that things have to be as they are. But then nobody is quite sure exactly how they are anyway, and much that seems definitive turns out to be wrong. Of course one might accommodate so much that it makes no sense why the world has any particular structure, and that might be wrong too.

Consider the Wiki page on Spacetime:

The question in the wiki page is why the Minkowski signature is "privileged" and as usual one looks at the other possibilities, as did Synge in 'Special Relativity' p 17. Perhaps one says Privileged because experiment agrees with Minkowski. But if the world makes algebraic sense we should expand the search space to include Octonions and observe that complex quaternions are even subalgebras of complex octonions, and thus are Lorentz operators, which makes the signature of complex octonions +--- or -+++ (or some variant). I argue that the Minkowski signature is privileged because Complex Octonions are privileged, at least if one accepts that alternativity restricts the algebras to consider. Dixon does not - using OxHxC, which is not alternative, but is like SU(3)xSU(2)xU(1). [G.M. Dixon 'Division Algebras ... and the Algebraic Design of Physics']. One feature indicating Complex octonions are priviliged is that one is not running thru signatures, but rather has a pair of opposite signatures, which happen to be Minkowski, so it is not put in by hand, or chosen to agree with experiment. The wiki page would appear to be missing something here. So Complex Octonions appear to Define rather than merely Accommodate spacetime, as would be the case with Clifford Algebra. In fact Clifford has +--- in a different algebra from -+++.

To push the case that Complex Octonions are 'really privileged' one would hope to see quanta defined as well as spacetime structure, but one might say the parentheses allow us to define duality oscillators, like the photon, and generalize to all quanta. Perhaps this is what is missing from the Standard Model.

Anyway, this is rather unlike Tegmark's Platonistic view, and no mention of anything Anthropic is needed. Minkowski doesn't just agree with experiment, it also 'makes algebraic sense' in a surprising Octonionic sort of way.

As to 10d etc, which Dixon, and a number of others espouse, if the LHC finds supersymmetric boson-fermion pairing, then experiment would invalidate the alternativity assumption above, and Complex Octonions would be only 'partly privileged'.

Hi Joel,

I can not accept an ocean of confusions and irrationalities(considering the article of course).The real probelm is simple you know Joel. In fact, some universities continue their bad habits. The strings are interesting I agree for the computing. But the people confounds this computing and the possible reversibility with a pure irreversibility of this Times.

The conclusions are bizare. The symmetries imply bizare particules. Or extradimenions. In fact all these extrapolations are just very subjective and irrational. The algebras of pierre paul Jacques are not the probelm , but the utilization and the conclusions, yes. Physics need determinismù and rationalism. We can extrapolate but we must respect several universal foundamentals, like the time constant, c,the 3D,...it is essential. Clifford and Minkowski 's works are not the probelm, but some people interpet them with decoherences. The dimenions are in 3D at all scales. See the Planck lenght and our others calculations like gauge.

The probelm is not philosophical. The probelm is technical. Pauli , Hamilton, Rieman, Poincarré,Clausius,...and friends are not the probelm. But the interpretation,false of their works , yes.

The aim is not to superimpose a serie of works or ideas, or to add several names. The aim is simply to search the truths with a pure deterministic road.

The quaternions and octonions are not realistic and rational. There still the computing is confound. I beleive sincrely Joel that the probelm is more that you can imagine. Always this monney and these investments. The financial markets are bizare Joel ! You understand you why the higgs are searched at the LHC or why it exists Labs which try to create a micro BH. Or why it exists experiments to travel in the times. Or why people can invest to so many stupidities??? What a world Joel.

In conclusion,These geometrical algebras are not foundamental and their predictions are not rational. So why investments to these works without real meaning. It is just a lost of time and a lost of monney. But it is just my opinion of course.

I think that USA must rethink its financial markets,

Regards

The problem comes from the string theorists and extradimensionalists. Now they are going to invent falses convergences.

I beleive simply that it is the end of strings and extradimensions.

These methods are just mathematical plays without a real respect of our foundamentals !

It is surprising that it is a fashion from USA ! Sometimes the competitions imply stupid conclusions!

More recent take on $T = C\otimes H \otimes O$, if interested. Cheers.

"Division Algebras, Lattices, Physics, Windmill Tilting".

Interesting to see how the strategists can insist on the false roads.

In fact the strings theorists fear to be less listened just due to my revolutionary theory.

In fact they confound the computing and the realistic universal sphere in 3D.

The rest is vain.

MIT you know , be rational and less in the subjectivities and less in the business of copycats.

PicoPhysics standard model is different. It considers only one particle type called UCO (Photon of mainstream physics) constitutes all matter in the universe. It may be mass-particles, fields, dark-matter or Radiations.

Based on single postulates Space contains Energy (Knergy) it has explaination for importance of number 3 in physics and establishes three dimensions of space from unary law 'Space contains Knergy'. It views universe at 5-Dimensional reality. Please review and comment on my essay 5-Dimensional Universe by Vijay Mohan Gupta at http://fqxi.org/community/forum/topic/1326

Your comments and rating will be appreciated.