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CATEGORY: The Nature of Time Essay Contest (2008) [back]
TOPIC: Constants of Nature, Dynamics of Time by Michael A. Sherbon [refresh]
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Michael A. Sherbon wrote on Nov. 6, 2008 @ 11:14 GMT
Essay Abstract

An archetypal model for the constants of nature is found from the ancient geometry of the the Cosmological Circle and is related to Plato's cosmology,with its dynamics and harmonics of time cycles. The inverse fine-structure constant and the proton-electron mass ratio are calculated, connecting fundamental mathematical constants of geometry with the latest theoretical and experimental values of these physical constants. Continuing in the tradition of George Gamow's suggestion, "Since the works of Sir Arthur Eddington, it has become customary to discuss from time to time the numerical relations between various fundamental constants of nature. Although until today such discussions have not led to any practical results - that is, to any valuable road signs toward further development of the theory of the still unclear fundamental facts in physics - it may be of some interest to survey the present status of this `clairvoyant' branch of science."

Author Bio

Michael A. Sherbon is a graduate of Case Western Reserve University interested in the history of science and philosophy.

Download Essay PDF File

Doug wrote on Nov. 24, 2008 @ 18:13 GMT
Great essay, Michael! Thanks so mcuh for the extensive references.

Michael Sherbon wrote on Nov. 24, 2008 @ 18:55 GMT
You're welcome Doug! And hope you enjoy the references too, some of the best kept secrets of nature :-)

Michael Sherbon wrote on Dec. 3, 2008 @ 20:33 GMT
New experimental results for the fine-structure constant,

our calculation remains within these error bars:

Combination of Bloch Oscillations with a Ramsey-Bordé Interferometer: New Determination of the Fine Structure Constant

Malo Cadoret,1 Estefania de Mirandes,1 Pierre Cladé,1 Saïda Guellati-Khélifa,2 Catherine Schwob,1 François Nez,1 Lucile Julien,1 and François Biraben1

Phys. Rev. Lett. 101, 230801 (2008)

(Received 19 June 2008; published 3 December 2008)

We report a new experimental scheme which combines atom interferometry with Bloch oscillations to provide a new measurement of the ratio h/mRb. By using Bloch oscillations, we impart to the atoms up to 1600 recoil momenta and thus we improve the accuracy on the recoil velocity measurement. The deduced value of h/mRb leads to a new determination of the fine structure constant alpha-1=137.035 999 45 (62) with a relative uncertainty of 4.6×10-9. The comparison of this result with the value deduced from the measurement of the electron anomaly provides the most stringent test of QED.

Michael Sherbon wrote on Dec. 7, 2008 @ 00:51 GMT
Typo! Deepest apologies to Marcus Cohen at New Mexico State University for the spelling error!

Lawrence B. Crowell wrote on Dec. 12, 2008 @ 23:20 GMT
I found your paper to be curious. My paper #370 explores how time is a scaling principle or provides a renormalization group. The fine structure constant is of course the zero energy value, where as you probe smaller regions around a charged particle it renormalizes to smaller values than alpha =~ 1/137. I don't know how this links with how you are thinking, but maybe there are connections.

Lawrence B. Crowell

Michael Sherbon wrote on Dec. 13, 2008 @ 21:20 GMT
Amazing, you must be somewhat "clairvoyant" too Lawrence B. Crowell! Your response is appreciated, I've been studying Feigenbaum's first constant in connection with the fine-structure constant (n-dimensional hyperspheres and pi). Quoting your note from your essay page...

Time as a Universal Scaling Principle by Lawrence B. Crowell

"I also do think that scaling or renormalization group physics is crucial. To be honest I think that numbers such as the fine structure constant may be determined in the way that Feigenbaum's number is --- or for that matter pi. The alternative is an ambiguity in how the physical vacuum is reached..."

And a clue from some ancient correspondence:

In the Orphic tradition, from the wholeness of Time (the Cosmological Circle) emerge Ether and Chaos, which interact to form the Cosmic Egg of creation. This is usually shown with a great serpent (the Ether) spiraling around the Egg.

See Manly P. Hall, "Lectures on Ancient Philosophy."

How the fine-structure constant derivation here connects with your "how time is a scaling principle" remains as we shall say in a twist on Jens Koeplinger's phrase, "mathematics yet to be 'comprehended'" (ps. in regard to your question about sedenions in the notes to Jens essay, Charles Muses also worked with the Leech lattice). Another possibly important clue from ancient philosophy is simply "harmonic proportion" (from your essay, "The conformal structure means this renormalization group exhibits a fractal or self-similar structure.").

Quoting a portion of another note on your essay page:

"The bigger picture than this involves the Leech lattice /_{24}, which contains 3 E_8's in a Theta function construction... The crux here is that the hyperbolic space is tiled by polytopes with pentagonal symmetry." (The Ether, Quintessence, or "fifth element" was traditionally associated with the pentad)

Thanks, Michael Sherbon

Lawrence B. Crowell wrote on Dec. 14, 2008 @ 16:19 GMT
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.

If there is any connection with what I am doing then your analysis involves the E --> 0 end of the renormalization group. The trajectories leaving the boundary with v =~ c and on the great hyperbolic curves reach it again at v = 0 as time ---> oo. Of course on the boundary the time rates increase enormously, opposite to the slowing down of a clock near a black hole, and so an observer in the AdS could see the particle reach infinity (oo) in a finite time. So this is how the scaling principle works. At E = 0 the coupling constants are at the physical zero energy limit, where alpha = e^2/hbar-c ~ 1/137.


Lawrence B. Crowell

Anonymous wrote on Dec. 28, 2008 @ 22:01 GMT
Something more to consider, Lawrence, when thinking about a "universal scaling principle."

"The Fine-Structure Constant as a Universal Scaling Factor"

by Malcom H. Mac Gregor

Nuovo Cimento Letters 1, 759-764 (1971)

"This paper describes the universal manner in which the fine structure constant alpha = e^2/hslash*c = 1/137 occurs as a scaling factor in particle masses, particle lifetimes, and stellar densities. The periodicity of metastable elementary particle lifetimes in powers of alpha is displayed, and a phenomenological relationship is deduced between the mass of the muon and the gravitational constant G. This is the first paper by the present author in which the work of Y. Nambu was encountered and included as a reference." (The Power of Alpha)

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Michael Sherbon wrote on Dec. 29, 2008 @ 22:00 GMT
Speaking of alpha and powers of alpha,

"...the electron and its coupling constant alpha generate not only the photon, but also the spectrum of leptons and hadrons. Thus the domain of the fine structure constant alpha seems phenomenologically to be larger than currently believed." p.72 "The Power of Alpha" by M. H. Mac Gregor

(2/3)Muon-electron mass ratio ~ 1/alpha ...from Mac Gregor.

Classical electron radius r(e) = alpha^3 / 4pi(Rydberg constant).

We noted alpha^3, pi, and 1.8 in our essay. 1.8 = 9/5.

((9/5 + (alpha^3 x pi^1/3))^-1 - 3/9 = 0.2222220466 ~ 2/9 radians.

From Carl Brannnen's alternative formulation of density matrices...

"The symmetry breaking between the electron and muon families is by a rotation by the mysterious angle delta."

"To get an exact proportionality, to current measurement error, one replaces 2/9 with ..., 0.22222204717(29)."

From Marni Sheppeard, "the phase angle determining the charged lepton mass matrix, which is 0.22222204717 to within experimental precision: notably close to 2/9.... Since phases usually involve factors of pi...."

Michael Sherbon wrote on Dec. 30, 2008 @ 21:25 GMT
Speaking again of icosahedral symmetry and time as a universal scaling principle, also the domain of alpha from Mac Gregor's "elementary particle lifetimes in powers of alpha."

We began with these papers:

Lisa L. Everett, Alexander J. Stuart

"Icosahedral (A5) Family Symmetry and the Golden Ratio Prediction for Solar Neutrino Mixing"(2008) arXiv:0812.1057v2 [hep-ph]

Yuji Kajiyama, Martti Raidal, Alessandro Strumia

"The golden ratio prediction for the solar neutrino mixing"

Phys. Rev. D76:117301,(2007) arXiv:0705.4559v2 [hep-ph]

Then we noticed the solar neutrino mixing angle, theta12.

tan^2 (theta12) = 0.45 = 1.8/4

and also relevant here, (2 x 1.62)^1/2 = 1.8

1.62 is the phi harmonic of the golden ratio.

Or from the exact phi value as the golden ratio,

sin (theta12) ~ 1/(2phi)^1/2

Lawrence B. Crowell wrote on Dec. 31, 2008 @ 13:49 GMT
The A5 icosahdral symmetry is the permutathdral group for sporadic groups and E_8. Also the underlying homotopy group describes a nonassociative algebra.

The 24-cell is the minimal sphere packing for four dimensions. The 24-cell (tetrahedachoron) has 24 vertices and 96 edgelinks, where the 24-cell is self dual. So consider the 48-cell given by this cell plus its dual. A reassignment of...

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Lawrence B. Crowell wrote on Dec. 31, 2008 @ 14:50 GMT
I cross posted the message above on my site. I will then continue sinly here. As I see it the values of gauge coupling constants are determined by a renormalization group of running parameterizations. I do think this system is determined by tessellations of polytopes. The system of boosts from cell to cell "maps" fields to the conformal boundary. It would be interesting to know if the endpoints, say when energy E ---> 0 whether the conformal boundary of a space tessellated with 120-cells will have an icosahedral group system. The boundary of the 120-cell are octahedra, which should I think map these as the tessellation of the boundary. This would then potentially set the endpoint (zero energy) value of constants according to the tessellation of the conformal boundary.

With the fine structure constant alpha = e^2/hbar-c, we have that the charge is e = sqrt(4pi eps c^2), where eps is the dielectric constant. Clearly if we try to rescale the speed of light the fine structure constant does not change. After all the speed of light is a parameter which gives the projectivization of spacetime, or blow up of a point. This is of course the light cone. The Planck unit of action is a similar number which defines a projective structure in geometric quantization. In Planck units one can convince yourselves that any change in either hbar or c leaves everything invariant. So in the change in the fine structure constant at high energy, such as at the TeV domain alpha ~ 1/128 involves the dielectric constant of the vacuum, and not either hbar or c.


L. C.

Michael Sherbon wrote on Dec. 31, 2008 @ 18:41 GMT
Thanks again Lawrence, somehow you've been giving me clues

to help with what I have been studying. I was thinking about octahedra yesterday, and it stayed with me, even had a dream with the "big geometry screen", then you even provide pictures! So lots more to consider! :-)

Posted this to Marni Sheppeard's essay page yesterday:

Seems the idea of changing constants is more fashionable than the constants themselves. Anyway, about alpha, "New optical clock promises increased accuracy" -

"...the improved accuracy of the optical clock has led the researchers at NIST to look at whether the fine-structure constant, which governs how light and electrons interact, has actually been changing over time. By measuring the ratio of clock frequencies for aluminium and mercury the researchers at NIST have concluded that the fine structure constant is not changing to within 1.6 x 10-17 per year. Indeed, they believe they have met the required precision to say that it is not changing at all. “This measurement of the ratio of aluminium and mercury clock frequencies is the most accurate known physical constant,” says Rosenband."

Lawrence B. Crowell wrote on Dec. 31, 2008 @ 22:16 GMT
If the fine structure constant does not vary by one part in 10^17} in a year, this means that through the entire period of the universe since the CMB "end of opaqueness" that the constant has not changed by any more than on part in 10^7. This appears reflected in measurements of atomic spectra from distant galaxies. So I suspect that it is an absolute number at zero energy. Of course once you probe into short distances within the Compton wavelength of a charged particle, such as the electron, vacuum polarizations renormalize this value to larger numbers. At EW unification alpha ~ 1/128 or so.

Lawrence B. Crowell

Michael Sherbon wrote on Jan. 1, 2009 @ 20:42 GMT
Hi Lawrence, Now that we're at the beginning of a new year, time for some reflection. Actually, and briefly, it was the mystery of the running value of alpha that helped with the first formulation for alpha. I was studying an analog harmonic mapping of energy density which was determined in part by the Fibonacci sequence. The lower limit of one portion of a quadrispiral mapping, a Fibonacci number, and the golden ratio; were central to calculating the value for alpha.

Marni D. Sheppeard wrote on Jan. 7, 2009 @ 03:28 GMT
Thanks for the interesting comments, Michael. I will now take a look at your essay!

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