Time and the Multiverse

Dear Lawrence,

I don't recall H12?

K12 is the Coxeter-Todd lattice (Conway & Sloane, 3rd Ed., pp. 127-129). I originally called my "lattice" E12 (12x(2*28+1)) because I based it on an extrapoloation of the mathematical formulation of G2 (2x(2*3+1)), F4 (4x(2*6+1)), and E8 (8x(2*15+1)). E6 (6x(2*6+1)) didn't exactly fit the pattern (instead of (6x(2*10+1))) . I later called it K12' because it has significant similarities to Coxeter-Todd (K12' is 8/9th's as large as K12, so they both share a "pentality" and "triality" symmetry). K12' also had the same order as some of the shallow holes in the Leech lattice (Conway & Sloane, 3rd Ed., pp. 517-520). Last year, you observed the similarities between K12' and E8xH4. I like E8xH4 because it specifically states the underlying symmetries of an 8-D Hyperspace E8 multiplied into a 4-D Spacetime H4.

Have Fun and Enjoy the 4th!

Right, I just used the wrong letter, H instead of K. I just needed a momentary reminder of what this structure is presumed to be.

Cheers LC

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We have not been right when thought we have found the "whole thing". Nothing authorizes us to think our backyard-Universe is - that time - the whole. As long as we know, cosmic fabric has no starting point and that IS his exact nature: energized matter. Our Universe can be a very diminutive particle of an true infinite tissue.

Once the cosmos have not an start, time can not have start eighter. So, time is just a measure of movement of eternally energized matter.

Dear Wilton,

I once thought that our Universe was everything that there is. After having found scale invariance in my TOE models, I'm now convinced that our Universe is only a fractal fragment of Cantor dust.

http://en.wikipedia.org/wiki/Cantor_set

Have Fun!

Dear Wilton,

Are you Brazilian? If so, I can cross-post:

http://pt.wikipedia.org/wiki/Conjunto_de_Cantor

Have Fun!

Ray,

All of us were educated to think that our neighborhood-universe were all that existed. Perhaps we live badly together with the idea of an infinite cosmic fabric because we (unconsciously)desperately need the sensation of womb-like protective boundaries.

Unfortunately, ee have never found any boundaries and I am afraid we will never...

Yes, I am from Brazil. Thanks for your attention and Wikipedia address!

Cheers,

For a bacteria, glued to a sand grain, deep one meter in a large beach, dreaming about understanding the entire coast is as foul as we trying to understand the entire cosmos.

But we are something more intelligent...

:)

Yes Noel

the only time is now

yours amrit

http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=PHESEM000023000002000330000001&idtype=cvips&gifs=yes&ref=no

Wilton,

Bacteria or prokaryotes are not that dumb. In point of fact they really run this planet in a network that is a sort of biochemical internet. Eukaryotes are assemblies of prokaryotes, such as the mitochondria with their own DNA, and they evolved in some molecular biological response to the increased role of RNA (sRNA etc) in molecular pathways. We might see eukaryotes as assemblies of prokaryotes that increase the energy flow through in the planetary eco-system, primarily for the benefit of prokaryotes. For every somatic cell in our bodies there are 10 prokaryotic cells --- we are walking micro-ecosystems of prokaryotes.

On the other hand prokaryotes are not conscious, and I doubt there is any consciousness in this prokaryotic planet-net. So we have a transient advantage in that sense. In the end Homo sapiens is a very brief blip on the unfolding evolutionary tapestry of life.

As for the discussion of time, or ideas that time does not exist, it might be worthwhile to consider the opposite perspective. Maybe time, or some quantum process of elementary events that define time, is truly fundamental. If so then everything else emerges as a consistency condition. For instance, if there exists a discrete hyperbolic group system which defines time, then a non-signaling requirement that prevents some violation of that group (eg backwards time looping) requires the existence or emergence of unitary or modular transformations in a space. So not only might space emerge this way, but the gauge fields and their potentials that generate unitary transformations emerge as well.

Food for thought

Cheers LC

Nourishing food for thought, indeed.

In every context I can think of, Nature informs us that her redundance of simple elements self-organize into novel forms. As you point out, the overwhelming proponderance of single celled organisms and their constituents leads to higher forms that can be described as corporations of cooperating cells.

Likwise, out into the cosmos, we find that over 99% of matter is in its two simplest forms, the remainder of elements created in the crucible of star furnaces and scattered by exploding stars to self organize into the novel life that we know.

So it is only natural to push back a little further, to ask what happens when we consider evolution from space and time alone.

Tom

Tom,

With all this talk about time not existing, maybe the opposite view should be at least entertained. Maybe time is some elementary quantum effect, upon which all else emerges.

Cheers LC

Dear Lawrence,

I was reading Constantinos' papers yesterday, and although I think he simply rederived some existing Hamiltonian and/or Lagrangian mathematics and physics, his papers do bring an emphasis back to action.

The Planck unit is the minimum change in action. If space (and its conjugate variables momentum) are "REAL" enough to cause changes in action, and if time (and its conjugate variable energy) is "REAL" enough to cause changes in action, then time must be as "REAL" as space, momentum and energy.

I'm getting tired of this no-time-trend. Perhaps we can describe geometrical gravity with space curvature, but I think it is a joke to try to use relativity to describe black holes and the quantum gravity that most likely exists there. In one of my models, a time-like dimension prevents the collapse of the black hole "singularity". Without that time-like dimension, we might all collapse into a super black hole singularity, instead the "singularity" is effectively truncated.

What do you think of AdS_5~CFT_3?

Have Fun!

The point of AdS_n ~ CFT is that the boundary of AdS_n, a space E_{n-1}, is equivalent to the CFT on a sphere S^n. The result is a holographic principle, where the boundary or horizon of a spacetime holds all the information in that spacetime. In this case it is this hyperbolic space AdS_n with a group O(n-1, 2). There are some subtle issues of the conformal completion on a patch of the AdS, and the boundary space E_n is this conformal completion. This is found with a discrete group on the O(n-1,2) that acts properly on AdS and then on the E_n it acts as a discrete conformal group.

The nature of time is rather odd, for it does not really have a conjugate variable relationship with energy. All that we do have is the Fourier transform result, which in quantum theory is the uncertainty principle. However, from a physical perspective the idea that "if energy exists then so must time" is not half off the mark. I suppose Constantino posted a website for these, but I don't have that.

Cheers LC

Ah, yes, Lawrence. I think there is going to be a great deal of research in the near future devoted to the proposition that time is causal.

After all, when we routinely calculate quantum effects by conjugate variables, and t = 1, can we be far from where it all began? I don't think so. Once we have negative space of 2 dimensions, a modulus squared implies to me that action has bootstrapped itself from imaginary to real. Self organization on the complex plane seems quite logical to me, given the algebraic completeness of C*.

Tom

It is possible to look at this in some ladder or hierarchy. Goyal illustrates how a noncommutative logic leads to complex arithmetic for quantum mechanics. So there is in that mathematics a noncommutative structure which permits any observer to see only half the degrees of freedom for a system. We might consider the prospect there is a deeper level, where Goyal abandons the noncommutative logic. This would then imply some noncommutative mathematics, or quaternionic representation of observables. So this next level might then be a C* noncommutatve geometry. Here the metric variables of are such that [x, y] =! 0, or they do not close up under a parallel translation, even in spacetime that might be classically flat. There is some quantum uncertainty which prevents one from a parallel translation of this sort with complete closure. We might then be tempted to go one level deeper where things are nonassociative. At this deeper level we might be at some pre-geometric structure that connects our spacetime cosmology with other cosmologies in the grand super-geometry or superspace of all cosmologies (multiverse). The restriction to associative might then restrict any spacetime cosmology to have a unique direction in time.

Cheers LC

It seems that some people takes themselves to the navel of the world if I can say.

These people, vains, are vary easy to pick.

In fact, you can see their words which do not change their strategies and superiority.

They brag about their super ideas(which are winds in fatc) that are not.

The meanders of their confusions reveal their limitations.

Like frustrateds of system by lack of recognition.

They use small techniques for pseudoscientifics or ignorant public.Like ....you know them .

Respect can be won only by skills, by a generality,by the sincere desire of universal quest ..... but never in these games,irrelevants to the rational scientific community.

Me at my age and with my theory ,I can lost my time here on FQXi before the creation of My INTERNATIONAL HUMANISTIC SCIENCES CENTER but for someones , frankly.......ahahah jalous.

Let's be serious a little and PLEASE THE SCIENTIFIC COMMUNAITY....WHERE ARE THE LIMITS AND RATIONALS .....WE CAN4T TEACH THAT AT UNIVERSITIES? IT4S NOT POSSIBLE.

Ps sometimes people take the choice to not answer, not because they think they are superiors, or they try to pass a kind of comportment of wisdom and rationality.......no no dear Friends...they fear in fact, this technic is ok for several but not with me ....

How would they understand, touch their souls, enjoy the secrets of eternity ,...... without a love for their quests.

The generality of this question,which is always in my mind, is a wave oscillating among the stars of evolution.

Some researchs, works are not that....The dimensions of our Universe, tell it like you want, God, the entity, the eternity, the equation, the cause, the entropy, the all, the whole,the unknown.......are in 3D.....this God deosn't play at dices, please respect the uniqueness....and its laws, its aim....its plan.

Regards

Steve

Dear Lawrence,

You have been working with a 27-D SO(3)-like three-octonian Jordan transform. What about a 28-D SO(4)-like six-quaternion Jordan transform? I relate a Quaternion to an H4, and an Octonian to an E8, but E8~H4xH4.

Perhaps we can't see half (or three-quarters?) of the degrees of freedom. In my models, these relate to my unseen dimensions, Supersymmetry, and scale invariance.

Have Fun!

Ray,

This extension to 28 dimensions from the 27 dimensional J^3(O) would be an F-theoretic extension. The three E_8's are related by the g_2, which decomposes into su(3)+3+3-bar. The J^3(O) is the hermitian part of the exceptional algebra, and the anti-Hermitian is 38 dimensional. These together form the 45 dimensional complex exceptional algebra. Think of this as a "real plus imaginary" construction. This extends to the 78 dimensional exceptional algebra that is E_6 quaterionic valued. Then of course there is the 256 dimensional octonionic exceptional algebra --- E_8 valued octonions. All of these can be extended to the F-theory.

The Weyl group for E_8 includes a matrix of two H_4's. The H_4 is the 120 or 600 cell which tessellates a hyperbolic space, such as the O(3,1) in AdS_5. There are other ways to see this construction. The stabilizer F_4 has a B_4 ~ so(9) realization, which is the boundary of a 10 dimensional spacetime. The infinite momentum gauge on J^3(O) reduces this to an SO(16) and E_8xE_8 in 10 dimensional superspace. So the 26 dimensional bosonic string contains this duality between 16 and 10 dimensions. The so(9) is then a "boundary" on the 10 dimensions. The F_4 and g_2 are the centralizers of E_8, g_2 the automorphism. The transformations of g_2 then leave the irreps of F_4 invariant. One of the irreps of F_4 is D_4 ~ so(8). This is contained in the so(16), 120 + 8, and the 120 is the icosian of quaternions or 120/600 cell in the Gosett polytope.

The problem of course is there are a vast number of irreps for this. Yet there does appear to be AdS content here.

The half degrees of freedom stem from the complete sets of commuting operators in quantum mechanics. You can access either position or momentum, but not both simultaneously. As a result you have information of only half of what corresponds to the classical phase space.

Cheers LC

Dear Lawrence,

Yes - It does look F-theoretic. That's why I was studying that Heckman paper. I'm just a stuborn Particle Physicist who keeps running into more String Theory than I bargained for. I am convinced that G2 x G2 implies imaginary time (the simplest way that we can have four mutually perpendicular basis vectors in one 2-D plane?), and if that is the primary difference between M-Theory and F-Theory, then I'm forced to study F-Theory. As a result, I don't think that the event horizon is a simple 2-D spherical surface - I think it is effectively 4-D (2-D surface x real/imaginary). This probably starts sounding more like some of Tom's ideas.

Certainly, QM limits us to position OR momentum, but not both simultaneously, so we have lost half of our dgf's. But what about SUSY? Are SUSY partners much heavier than anything we have explored to date, or does QM also limit our observation of SUSY (such that we only observe a quarter of the implied dgf's)?

Have Fun!