Time counts. by Thomas Howard Ray

'lo Mr. Ray,

you absolutely certain you didn't peek just a little at the WMAP data first?

way big grin.

lovely.

:-)

matt k.

Matthew:

Do you mean, did I adjust my numbers to match WMAP? No, but

I recognized the WMAP data when I saw it, as the keystone

that upheld the theory.

The result (eqn. 5) from my ICCS 2006 paper

[link:home.comcast.net/~thomasray1209/site/] that led to

the value, was derived as the zeroth term of a conjectured

well ordered sequence of hyperspheres. The 2006 paper aimed

to demonstrate organic continuation of analysis with

physics, so the term didn't just happen to fit--the theory

predicted it.

The data that I did adjust, though, are the conjectured

n-dimension kissing numbers. I knew that I had the right

topology for d=4, as demonstrated in my proposed

InterJournal article (included in the link to my web site,

above). I knew that only congruence subgroup mod 12

would work.

As you may know, however, the n-dimensional kissing number

problem remains unsolved--and I had to "peek" at current

research into the boundaries of these numbers. I found

that I was within all lower bounds. I conjectured new

precise (non-lattice) upper bounds for dimensions 5, 7 and

10. When I added these terms up to Order 10 in my "big O"

notation, I expected the sum to be >23 4, of the time

metric, which is necessary to ensure energy exchange at

the boundaries of n-dimension kissing spheres. Eventually,

I remembered my result (eqn 5) from the ICCS 2006 paper,

for which I had not yet imagined a physical application.

In retrospect, I should have seen immediately that the term

applied to the zeroth sphere (the 2-sphere underlying

manifold) of my big-O order. Hindsight being better than

no sight, when I plugged the value into the zeroth term of

my big-O sequence, I was again amazed that that zero, plus

an additional fraction of 1, gave exactly the observed

percentage of atomic matter in our 3-dimensional universe.

And I was gratified to see that the growth of that

percentage to a maximum 0.5 was renormalized to unity in

d=4. If you follow the discussion section of my ICCS 2006

paper, you understand why this has to be true:

Briefly, sqrt 1 divided by 2 equals sqrt 1/4. The Riemann

Hypothesis follows for every positive n subsituted for 1,

in an n-dimensional complex space, without limit (infinite

dimension Hilbert space).

Tom

Good grief. Why did the link I tried to insert span

almost the whole length of my post? Sorry--I will never

understand this computer stuff, it seems.

Tom

Hi Tom,

re:

--------------------------------------

Do you mean, did I adjust my numbers to match WMAP? No, but

I recognized the WMAP data when I saw it, as the keystone

that upheld the theory.

--------------------------------------

my comment was intended as a humorous jest, by no means as a serious accusation.

no, i hadn't suspected you had manipulated your calculations.

very nice.

:-)

matt kolasinski

Wow, excellent work! I concur with your treatment of time. It must be complex-valued in agreement with a harmonic universe. Furthermore, we often do not see this, because in any instant, as you observe, time assumes a single value, and simply hops along by "beats" of dissonant entropic decay. Furthermore, these steps are too small for us to notice- only the beats of larger energy-wavelengths are obvious at our scale. Wonderful insight.

I see you too have a full appreciation for the "imaginary" or "irreal" numbers as Blumschein (another entrant) put it. Bravo.

Thanks, Ryan!

I know that you know by now that Blumschein doesn't assign physical meaning to complex analysis.

It is uplifting to hear from someone who actually understands and appreciates the gist of my argument. As a computer scientist, I suggest you might also like my ICCS 2007 paper, "Time, change and self-organization."

All best,

Tom

Tom,

I really appreciate your encouragement. And you are right- I certainly need to read further into the details of Blumschein's paper, and admittedly your paper too.

I tend to screen for fundamentals first. Next I will read again for the more complicated texture which emerges (it takes more time/energy to ponder and digest). And your paper is rich with mathematics and actual (WMAP) data. What fun!

Tom,

I gave your paper a first read through, I must confess I am scratching my head a bit over some of it. By cardinal points is this the same as a cardinal series? The sphere packing stuff looks right. The 24-cell is the minimal sphere packing for the R^4, yet to tessellate a curved spacetime with a constant curvature you have to go to the 120-cell, where things get really fun. It is worth noting that from the 24-cell you can derive the 26-dimensional bosonic string, which I indicate in my paper here Time as a Scaling Principle.

This approach is interesting IMO, for it connects aspects of string theory with loop quantum variables.

I will read more closely before the 15th.

cheers,

L. C.

Lawrence,

Thank you for your reading and detailed response. Much appreciated.

Yes, I know this summation of cardinal points is more than a bit off the wall. You can find me commenting on the construction in David Finkelstein's forum here.

By cardinal points, I mean spatial coordinate points. The 3 ordinary dimensions, and the 10 non-redundant points of the Riemann tensor metric. The construction first appeared in my ICCS 2006 paper, tied to my argument for continuation of physical space with analytical space (and hence continuation of the time metric in hyperspace). I got to this point, actually, by trying to derive a physics of counting, an analytic (vice axiomatic) derivation of the real integers.

I thought you might like the sphere packing treatment. I appreciate that the 24 cell plus time produces a 26 dimensional bosonic string. My aim was to get that same numerical result plus inertia. Because 24 is also the kissing number in 4 dimensions, my holy cow moment (although I don't think I actually said "cow") came when I was playing around with Sophie Germain primes and discovered a very strange and beautiful geometric order in a pure number context--which fit right into the n-dimension kissing number problem. I don't want to impose on your time, although I do think you might appreciate this derivation--it's in my proposed InterJournal article, which is the long version of this FQXI essay. Just click in almost any spot in the post in this forum that I messed up, and you'll get to my web page, with address links.

I think we've got a lot to talk about. This stuff may just be "crazy enough"(Who said that?--Gell-Mann?).

All best,

Tom

Hi,

The bosonic string comes about because the 24-cell is a root space representation for B_4, D_4 and a Weyl group F_4, where for the F_4 there is a 52 dimensional irrep, here given in the ADE notation of groups. From the F_4 comes the 26 dimensional string. This is of course the string "101" theory, but it is important and unfortunately often ignored.

The theory of 4-dimensional sphere packing was proven by Musim back in 2002, and the 3-d Kepler problem solved (God and I can drum up his name) 10 years ago. Eckles has an emperical demonstration of the 8 dimensional case, which is where the E_8 Gossett polytope exists in. This is a computer derivation with illustrates how E_8 tessellated 8 dimensions to very small error bars. BTW, Eckles wrote the "7th Brandenburg concerto," which JS Bach never completed for Friedrick of Preussia.

Keep plugging on the number theory. I have found this brushes up to Merssene primes. Also the nonassociative structures require some type of graph theory, combinatorics and potentially a number theoretic representation. A general matrix theory or representation of nonassociative field theory is not possible.

Lawrence B. Crowell

Thanks, Lawrence. I need more group theory.

Oleg Musin proved k=24 kissing number for dimension 4. I thought it was 2004, though. Thomas Hales proved the Kepler sphere packing conjecture.

Thanks for that infomration about Eckles. I did not know that--but I love the Brandenburg concertos, and I'll be sure to look it up.

Thanks for the encouragement. As you know, there's often a lot of chasing up dead end trails in number theory and combinatorics.

All best,

Tom

Tom Hales, that's the name. I don't know why I couldn't remember it. Mathematically I have looked at this largely according to group theory, which leads into the sporadic groups. The sporadic group of primary interest is the Leech lattice L_{24} of 196560 elements.

Physically these groups are error correction codes, which does connect with your Bekenstein reference. A black hole is the perfect von Neumann quantum computer, and in one dimensions the black hole is an information channel. I think quantum bits are preserved and quantum gravity is a sort of encryption system which transmits the information back out in a form which appears random in a coarsed grained setting, such as Hawking radiation. There are a number of other physical aspects to this I have been exploring, such as the 120-cell tessellation of the AdS spacetime, which is what my paper #370 discusses.

I like playing Bach, though Schweitzer I never was. My music playing days are pretty much over, since I broke a lot of bones in my right hand. Eckles' rendition of what Bach's 7th Brandenburg Concerto might have been was played on NPR's "Performance Today" a couple of years ago. The problem is that the baroque period is long over, and modern renditions simply sound too formulaic. It would be hard to write a "Beethoven's 6th Piano Concerto" and make it sould right.

Hold on to your hat, for this stuff ultimately gets into some really strange territory. The automorphism group of the Leech lattice is the Fischer-Greiss group, sometimes called the "Monster." This is the final sporadic group, and beyond that is unknown mathematics. At this stage we probably don't need to go anywhere near that territory.

There is an interesting set of relationships here. The 240-cell, or octahedrochoron, has 24 elements. This can be deformed into the 120 cell by a "rule of fives" which are pentagonal Stasheff associators, and this leads to the E_8 and octonions. Each vertex of the 24-cell is assigned a pentagon. Further the 24-cell is a root space that is the "span" of the 24-dimensional space of the Leech lattice of automorphisms. This is a triality of E_8's. Then the automorphism over that is the monster.

Beyond this we might run out of mathematics. If so then maybe this tells us that on the Planck scale states are purely self-referential and physics dissolves into a Godelian sort of chaos.

Cheers,

Lawrence B. Crowell

Lawrence, perhaps our neurons really are wired similarly. At least, though you've sent me back to the books, I grok the implied relation among time, quantum information and group theory. I concur in your 2nd paragraph above, and I think those facts are reflected in both your and my research in parallel ways.

I do know about the monster, but in no depth.

Trying hard to stay on topic here, speaking of the Leech lattice, the extreme symmetry that produces 196,560 non zero vectors nearest to zero and at minimum distance 2 from each other, reminds me of Jorge Luis Borges' Library of Babel on which I commented in Paul Halpern's forum, as a metaphor for the labyrinth of time.

In reference to your last paragraph above, I connect this R^24 sphere packing to the order 1 (big O_N=1, radius 1)in which the 4-dimensional term is informed by the zeroth 3-dimensional) member of the well ordered set of n-dimensional hyperspheres. This suggests that proportion and recursion are just as native to the real physical world as to the line of real positive integers. As Chaitin said and with which I agree, "Perhaps mathematics and physics are not so different as most people think." This holds promise of a completely algebraically based physical theory once we've got first principles right (I accept that scale invariance is one of those principles; least action is another), and drags the time dependence and randomness of quantum mechanics right along with it. Chaitin's research into the randomness of arithmetic is a milestone; it produces that "Godelian sort of chaos" you describe.

All best,

Tom

PS: I'm sorry about your hand. Even though I am no more than a hack guitar picker, I am often frustrated by the arthritis in my fingers caused, I suspect, by breaking at least 4 or 5 of my fingers playing baseball and softball. I hope to find that piece you mentioned on a podcast.

The development of associator dependent mathematics comes from a Finsler geometry. The a fibre pi:E ---> M is usually considered as a horizontal construction. Yet consider X = x ct, or as X = gam(x - ct), where in special relativity gam = 1/sqrt{1 - (v/c)^2). This defines a vertical portion of the bundle on a vector space orthogonal to the horizonal space. The braid system for a quantum group (xy)---(yx) with a noncommutative geometry exist on the horizontal bundle. For s and y corresponding to different quaterionic sectors (triplets etc) the vertical bumdle determines products of the form xy x(cgt) y(cg't') (cgt)(cg't'), (g = gamma) which mix quantum group basis elements by associators. The four product (gt)(g't') obeys the "rule of fives" or the Stasheff associator or pentagon. So two elements of the 24-cell plus its dual, which is a self duality, assigns pairs of elements of the 48 vertex system with the pentagon, or the 120 vertex system of the 600 cell, equivalently its dual the 120-cell.

Nonassociative QM is not unitary, but it preserve Q-bits. On a coarse grained level it leads to the Bogoliubov transformations of states, which appears to be the origin of thermodynamics. This is of course the connection between time and dS/dt >= 0, the second law of thermodynamics.

In some ways the hardest part of this is to come up with the physical principles behind this. It appears natural to think that physics should transcend into more generalized algebrao-geometric systems. Yet in the end this is required by the physics, more than anything else.

Dear Thomas Ray,

Please find attached something concerning which I would like you to take issue.Attachment #1: 6_Microsoft_Word__How_do_negative_and_imaginary.pdf

Eckard, I thought we'd already been through this. I haven't changed my mind. In any case, my model _must_ yield to complex analysis, because the the two-dimensional plane of complex numbers is the surface on which past events are holographically projected. See, e.g., references to Maldacena holography, & Bekenstein-Mayo black hole information channel.

Tom

These polytope structures define quaternions, Hurwitz quaternions on the 24-cell and icosians on the 120-cell, which are a basis for quantization. The hierarchy of structures R, C, Q, O (reals, complex, quaternions, octonions) are determined by the Hopf fibration and the Cayley numbers N = 2^n, n = 0, 1, 2, 3 for R, C, Q, O. Quantum mechanics is complex valued or higher, and in order to identify connections between gravity and quantum theory one has to extend beyond the real numbers.

Lawrence B. Crowell

Tom and Lawrence,

My criticism is not against your use of complex numbers or even quaternions. My intention is to point out possible mistakes and their serious consequences. For the latter look into the attached 2nd part.

Eckard BlumscheinAttachment #1: 6_Microsoft_Word__How_do_part_2.pdf

Eckard, I guess I understand your argument a little better now.

However, I think you make an unecessary assumption that past and future (events) must be symmetric in order to make accurate physical meaning of analysis using complex terms. The mathematical model is static--it doesn't care about the order of events, only that the physics of the event corresponds to an observed outcome. I often quote Hadamard and Painleve: "The shortest path between two truths in the real domain passes through the complex domain." When the two truths concern two different points in time--past and future in your context--the one truth symmetric about the complex plane axis is everywhere an honest recording of an observed instant of a real measurement. "All real functions are continuous," as supported by Dedekind, Weierstass, Brouwer, Weyl, et al.

All best,

Tom