if you give us the opportunity, we try to explain the reasons why Enzo Bonacci should have the priority on tridimensional time theory.

WE belong to the “maths’ friend circle”, people around the world who desire to support our shy friend Enzo Bonacci to get the notoriety he deserves. If he gets famous you will know our identities as well.

ENZO BONACCI is the greatest mind we know, able to speak ten languages, to play chess with different people toghether, consultant for strategic defense in the past (now convinced pacifist) and for several boards today, indefatigable teacher and writer. His greatest defect (in this imageaholic society) is shiness. That’s why he needs friends. After years striving, the Italian Scientific Community has decided to accept his theories about Relativity. You only know two parts of a trilogy of Relativity revision because the consequences in terms of energy sources will be huge and he fears military applications.

GEORGE SPARLING is a former Phd pupil of Roger Penrose, the first physicist to whom Enzo Bonacci sent his publications. The coincidence of his claiming for a new esadimensional theory some months after, seemed rather strange to our eyes, but in the meantime Enzo and George have become friends because their works could merge without collision and they are both reasonable people.

RAYMOND CRITCHLEY is the real father of esadimensionality (1978) but in different terms from Bonacci and Sparling.

DANNY ROSS LUNSFORD is a brilliant researcher whose work enforces the esadimensional theory in a way different from both Bonacci’s diode-photodiode ideal experiments or Sparling’s spinorial calculations, but somehow close to Critchley’s trace anomaly explanation.

INDIRECT PROOFS: like the ones provided by Critchley, Sparling and Lunsford are marvellous analytic essays, but according to our opinion less important than the direct measures by Enzo Bonacci. He actually measured time in different positions, having the courage to call the extra-dimensions “time” and not in exotic ways as Critchley’s “integrated dimensions”, Lunsford’s “coordinatized matter” or Sparling’s “time-like dimensions”.

TRIDIMENSIONAL TIME is an expression you couldn’t find on research engines until 2006 January, when Enzo Bonacci published on-line his work reaching soon ranks of 100000 people visiting his site! By the way, copyright about his works (especially the plans for matter-antimatter and gravity engines) were registered some years before… He just delayed the publications frightened of possible weapons until the time he realized that oil-wars were frightening as well.

FAIR PLAY has always characterized Enzo Bonacci who is going to quote ALL past essays in the long way to the esadimensionality (From Kerr esasolutions of black holes to Sparling esaXitransform) in an official way so that all the people who have worked about this problem could have their deserved place in physics and it will be the Community to judge their contributions. We invite all the other pioneers in esadimensional field to do the same.

Thank you all for your kind attention.

MFC

]]>Did you tell him about operads, then?

Nope, I didn’t get a chance to get there. The non-compact exceptional groups and their relations with S-theory and some mysterious three time extension ate most of the time up. I didn’t get to talk to him very long because his friends were taking him to dinner.

]]>Did you tell him about operads, then?

]]>As to more times, Paul Bird has written about 4-time physics in 16-dim in:

arxiv.org/abs/physics/0103004v2

and

arxiv.org/abs/physics/0604225

Years ago, I had a brief e-mail correspondence with Itzhak Bars.

Back in 1999 (before the arXiv went to Cornell and I was blacklisted) I wrote hep-th/9908205 in which I suggested physics in

“… 6 spacetime dimensions with local Conformal symmetry of the Conformal Group C(1,3) = Spin(2,4) = SU(2,2) …”.

In February 2000, I wrote to Itzhak Bars asking him what he thought about “… decompos[ing] a 10-dimensional spacetime into

a 6-dimensional physical/conformal spacetime

plus

a 4-dimensional compactified internal symmetry space …”.

and

Itzhak Bars replied (also in Febraury 2000), saying in part:

“… Six dimensions is not essential …”.

Then, in August 2000, Bars wrote hep-th/0008164 saying:

“… The Standard Model of particle physics can be regarded as a gauge fixed form of a 2T theory in 4+2 dimensions. …”.

Now, the web page of Itzhak Bars says:

“… Amazingly, the best understood fundamental theory in Physics, the Standard Model of Particles and Forces (SM) in 3+1 dimensions, is reproduced as one of the “shadows” of a parent field theory in 4+2 dimensions. But even more amazing is that this emergent SM has better features than the ordinary SM in 1T-physics. …

The permitted motions in 4+2 phase space are highly symmetrical, as they are constrained by a Sp(2,R) gauge symmetry that makes momentum and position indistinguishable at any instant. ….”.

The symplectic structure of Sp(2) gives the momentum-position duality, and

the isomorphism Sp(2) = Spin(2,3) gives the inclusions

Lorentz Spin(1,3) inside Spin(2,3) inside Conformal Spin(2,4)

so that the Sp(2) = Spin(2,3) momentum-position duality fits naturally.

Something that Itzhak Bars does not (AFAIK) yet do is to get gravity by a version of the MacDowell-Mansouri mechanism (described by Mohapatra in section 14.6 of his book Unification and Supersymmetry (2nd edition, Springer-Verlag 1992)) which also uses the inclusions

Lorentz Spin(1,3) inside Spin(2,3) inside Conformal Spin(2,4)

in which the Spin(2,3) = Sp(2) is used as the antideSitter group.

I have worked on that approach, and it gives a prediction of the Dark Energy :Dark Matter : Ordinary Matter ratio of 75.3 : 20.2 : 4.5

where

Dark Energy comes from the special conformal generators of the Conformal Group Spin(2,4)

and

Dark Matter is primordial black holes.

In short summary, I think that the work of Itzhak Bars is very interesting,

and

I am happy to see advances in the physics of 4+2 conformal spacetime

but

I am not sure about his objections to the 4-time physics of Paul Bird.

For instance, there might be some dualities among branes etc that could be used as Itzhak Bars uses Sp(2) symplectic duality.

Tony Smith

]]>The two-time physics talk by Itzhak Bars was quite enjoyable. The content of the talk consisted of the SO(4,2) compactification of S-theory. Some related slides can be found online here.

About halfway through the talk, Bars noted that adding more than two extra time dimensions is troublesome. When I asked about this later, he clarified this point, stating that one might indeed be able add more time dimensions as long as one can find a clever way to get rid of the ghosts (negative norm states). Bars said he is only able to do this in the two-time framework by invoking a position-momentum symmetry. For a three-time theory, such as an SO(11,3) supergravity, he said one would need to find a new symmetry to eliminate the ghosts.

]]>E6(-26) where

g(0) = so(1,9)+R, dim(g(-1))=16

E7(-25) where

g(0) = so(2,10)+R, dim(g(-1))=32 and dim(g(-2))=1

E8(-24) where

g(0) = so(3,11)+R, dim(g(-1))=64 and dim(g(-2))=14

The 3-time E8 structure can also give a 4-time structure if you just look at it in terms of even and odd grades.

Consider the even part g(ev) of the 3-time grading E8(-24) where

g(0) = so(3,11)+R, dim(g(-1))=64 and dim(g(-2))=14

g(ev) = g(-2) + g(0) + g(2)

so that

dim(g(ev)) = 14 + 91+1 + 14 = 120 = dim (so(4,12))

and we have

g = E8(-24)

g(ev) = so(4,12) which has a 4-time signature with the odd graded part g(-1) being 64-dimensional.

See Table 8 of Soji Kaneyuki’s chapter entitled Graded Lie Algebras, Related Geometric Structures, and Pseudo-hermitian Symmetric Spaces,

as Part II of the book Analysis and Geometry on Complex Homogeneous Domains,

by Jacques Faraut, Soji Kaneyuki, Adam Koranyi, Qi-keng Lu, and Guy Roos (Birkhauser 2000).

Therefore, the 1-time, 2-time, 3-time, and 4-time structures might look like:

E6(-26) where

g(0) = so(1,9)+R, dim(g(-1))=16

E7(-25) where

g(0) = so(2,10)+R, dim(g(-1))=32 and dim(g(-2))=1

E8(-24) where

g(0) = so(3,11)+R, dim(g(-1))=64 and dim(g(-2))=14

E8(-24) where

g(ev) = so(4,12), dim(g(-1))=64

Tony Smith

]]>“… S-theory’s algebraic structure looks very similar to the 5-grading forE7(-25) where

g(0) = so(2,10)+R, dim(g(-1))=32 and dim(g(-2))=1.

I’ve been wondering if there is some three-time theory with structure similar to the 5-grading of E8(-24) with

g(0) = so(3,11)+R, dim(g(-1))=64 and dim(g(-2))=14

…”.

I have not looked into that (thanks very much for mentioning the idea), but it is very suggestive to think that the following gradings might correspond respectively to 1-time, 2-time, and 3-time:

E6(-26) where

g(0) = so(1,9)+R, dim(g(-1))=16

E7(-25) where

g(0) = so(2,10)+R, dim(g(-1))=32 and dim(g(-2))=1

E8(-24) where

g(0) = so(3,11)+R, dim(g(-1))=64 and dim(g(-2))=14

Maybe Itzhak Bars might comment on that in his UCLA talk tomorrow?

If he does, could you (kneemo) post a comment here saying what he said?

Tony Smith

]]>I had years ago very useful discussions with Tony. In particular, I learned a lot about octonions and quaternions from Tony and started seriously to consider the possibility that dimension 4 and 8 might really relate to them somehow although the metric signatures seemed to be an obstacle.

]]>S-theory’s algebraic structure looks very similar to the 5-grading for E7(-25) where g(0)=so(2,10)+R, dim(g(-1))=32 and dim(g(-2))=1. I’ve been wondering if there is some three-time theory with structure similar to the 5-grading of E8(-24) with g(0)=so(3,11)+R, dim(g(-1))=64 and dim(g(-2))=14. Perhaps there would be a related SO(3,11) covariant supergravity in this case. Have you looked into this any?

]]>