The Fine Structure Constant As Fractal Construct?, A "Physio-theoretical" Exploration

A CLEAN THREAD TO BEGIN ANEW...

A continuation of...
Euler’s Identity And The Fine Structure Constant Go Golden?
http://forum.physorg.com/index.php?showtopic=18660

Constructive feedback in an exploratory, constructive and imaginative vein welcome and desired.

Best,
Raphie Frank

In honor of... The Weave & The Darn
http://raphie.wordpress.com/2007/05/09/the...iness-artivism/

May we one day tie it all together in an exceptionally simple theory of everything
(see... http://forum.physorg.com/index.php?showtopic=19183&st=0).

Oh, and Happy Thanksgiving!

==============================================
ALPHA - The FINE STRUCTURE CONSTANT
Towards a Fractal Interpretation of the Fine Structure Constant

Incorporating Self Duality and Euler's Identity modified for the (diffeomorphic?) transcendental plane.

(a collaborative work in progress, if only because of the feedback I have already received...)
==============================================

A== A conceptual foray into the implicate by an aspiring "cognitive physicist" with, prior to late 2006, little to no advanced knowledge of math or physics save College Calculus (1986) and High School Physics (1985). Retained knowledge as of April 2006: the formula of a circle. (Well, just about...)

See... A New Member Request for Feedback (March 7, 2007)
http://forum.physorg.com/index.php?showtopic=13694

B == Explorations in "Contextual" Education and "Tantextual" Learning in the hopes of developing educational methods by which to teach artists and the gifted and even possibly the autistic? ("Kolo Math" i.e. "Circle Math" under development)

==============================================

A FEW GUIDING HYPOTHESES/ASSUMPTIONS REGARDING THE BELOW "NUMEROLOGICALLY" DERIVED "PHYSIO-THEORETICAL" APPROXIMATIONS FOR ALPHA:

1) In order to bridge the very large with the very small, one must incorporate the "progression" (i.e. evolution).

2) Dimensionless Constants, by definition, must have dimensionless Equivalents

3) All truly "Fundamental" Constants are dimensionless by definition. They only seem to be not so RELATIVE to our "somewhat" arbitrarily chosen units of measurement, but...

4) IF the Laws of physics apply to ALL things in the known Universe, including human patterns of perception and organization on all levels from the individual psyche to the world collective, and including a progressive component THROUGH TIME, then such laws apply also to the development and evolution of our units of measure. In theory, then, such measurements approach, but never reach some optimal "mean" (golden or otherwise).

5) Pure mathematics alone can be used to describe the workings and underlying structure of the Cosmos, which does not exclude the need for Empirical experimentation and verification, as there are infinite possible mathematical structures from which to choose, not all of which can accurately describe at least THIS Universe.

6) Phi, the Golden Ratio, represents the Universal Constant of progression through space/time in a resistanceless environment. Viswanath's Constant, on the other hand, represents a state of maximum entropy/equlibrium. ( About Viswanath's Constant for the uninitiated: http://en.wikipedia.org/wiki/Viswanath's_constant )

==============================================

ALPHA: BASIC DEFINITION
The fine-structure constant or Sommerfeld fine-structure constant, usually denoted , is the fundamental physical constant characterizing the strength of the electromagnetic interaction. It is a dimensionless quantity, and thus its numerical value is independent of the system of units used.

http://en.wikipedia.org/wiki/Fine-structure_constant

==============================================

A FEW PRELIMINARY NUMBER "PHYSIO-THEORETICAL" NOTES

a) The first three digits of @^-1, 1, 3, 7 correspond with I, II, III in base two binary, suggestive of some sort of binary progression

The first three digits of @^-1 correspond, additionally, with the first three Mersenne numbers (2^1 -1), (2^2 -1), (2^3 -1), in increasing numerical order (read from left to right), not unrelated tangentially to the Mersenne Prime hierarchical approach of H. Pierre Noyes.
See: A Short Introduction to Bit-String Physics http://adsabs.harvard.edu/abs/1997hep.th....7020N )

c) These three digits, furthermore, are conjoined with a secondary base 10 progression. (i.e. 1 * 100, 3 * 10, 7 * 1) INVERSELY related to the Mersenne number progression. As the Mersenne numbers increase the powers of 10 decrease. In a metaphorical sense, one can think in terms of "waves" in an ocean. Even as the tide comes in, the tide also goes out.

d) 7 is the first cyclic number, numerically suggestive of a point of "harmonic equilibrium"or the "cresting" of a "three-step" wave.
See... http://en.wikipedia.org/wiki/Cyclic_number

e) a-d, taken together, suggest a "break down" of clear order, and the introduction of "interference" patterns subsequent to the first harmonic 7. It is at this point where some sort of fractal string "overlay" may come into play.


============================================================

CONJECTURE #1 - TRANSCENDENTAL CONGRUENCE OF PI & PHI
e^(i*pi) == e^((i*phi)^2)
in as-yet TBD extra-dimensional projective space

============================================================

CONJECTURE #2 - MODIFIED EULER'S IDENTITY
e^(i*pi) + 1 = 0 == e^(i*phi)^2 + I' = 10*@

============================================================

(HIGHLY EXPLORATORY) CONJECTURE #3 - ALPHA(Numeric) FRACTAL STRINGS
I' = a/10^5 + b/10^8

where...
a = 1+ sqrt 3

a few (of many) other equivalencies...
----------------------------
= 2*(cos 30 degrees + sin 30 degrees)
= -tan 105 degrees - 1
= 2*(e^(i*pi/6) + e^(i*pi/3))
(last one a complex # equivalent, dispensing with imaginary component...)

and where...

b = hypothesized "fractal string" component of the fine structure constant, beginning with the harmonic 7 mentioned above in the introductory notes. Thus, if going by the CoDATA value of @^-1, then...

b = 7.03599910810831

Combined together, then...

I' = (1 + sqrt 3 + (7.03599910810831*10^-3))/10^5

============================================================

(HIGHLY EXPLORATORY) CONJECTURE #4 - SELF DUALITY

b = @^-1 - 130

SELF-DUALITY: BASIC DEFINITION
A geometric proposition is said to be self-dual when application of the duality principle of projective geometry results in a proposition equivalent to the original. Desargues' theorem is an example of a self-dual proposition.
http://mathworld.wolfram.com/Self-Dual.html

In other words, the conjecture is that whatever the measured valued of alpha ultimately turns out to be, then b less 130 will be exactly equivalent. If true, then one need only balance the equation to arrive at a value for alpha.

============================================================

SO WHAT DO WE HAVE SO FAR?


e^(i*phi)^2 + I' = 10*@

e^(i*phi)^2 + a/10^5 + b/10^8 = 10*@

.1*e^(i*phi)^2 + a/10^6 + b/10^9 = @

.1*e^(i*phi)^2 + (1 + sqrt 3 + (7.03599910810831*10^-3))/10^6 = @

==========================================

COMPARISONS - DIFFERENT VALUES OF ALPHA


Let
@ = empirically measured value for alpha
@' = exploratory value for alpha

CASE #1
CO-DATA 2006 VALUE FOR ALPHA
--------------------------------------------------
@ = 0.0072973525680±0.0000000000240
--> @^-1 = 137.03599910810831
@' = .1*e^(i*phi)^2 + (1 + sqrt 3 + 0.00703599910810831)/10^6 ~= 0.007297352573393 27264 ~= 1/137.0359990068 2877044

"SELF -DUAL" ACCURACY
@ = 0.0072973525680 vs. @' = 0.0072973525 733
accurate to 10 DIGITS

CASE #2
G. Gabrielse,D. Hanneke,T. Kinoshita,M. Nio,and B. Odom*
http://hussle.harvard.edu/~gabrielse/gabri...ureConstant.pdf
(see Erratum at end of paper)
--------------------------------------------------
@ = 0.0072973525701±0.0000000000051
--> @^-1 = 137.0359990686727049
@' = .1*e^(i*phi)^2 + (1 + sqrt 3 + 0.00703599906867270)/10^6 ~= 0.007297352573393 23274 ~= 1/137.0359990068 2953782

"SELF -DUAL" ACCURACY
@ = 0.0072973525701 vs. @' = 0.00729735257 33
accurate to 11 DIGITS

CASE #3

DICRETE "BIT STRING" VERSION
using as a starting point common empirically verified digits of alpha
--------------------------------------------------
@'' = 0.0072973525737(6) ± ???
--> @''^-1 = 137.035999
(.1 * (e^((i * phi)^2))) + (1 + sqrt 3 + 0.007035999) / (10^6) ~= 0.007297352573393 16422 ~= 1/137.0359990068 308168

"SELF -DUAL" ACCURACY
@'' = 0.007297352573 7 vs. @' = 0.007297352573 3
accurate to 12 DIGITS

(where @'' signifies a non-empirically derived alpha)


COMPARISON
====================

Co-DATA Value for Alpha
@ ~= 0.0072973525 6 80

G. Gabrielse,D. Hanneke,T. Kinoshita,M. Nio,and B. Odom*
@ ~= 0.0072973525 7 01

Raphie Frank "numerologically" derived value
@'~= 0.0072973525 7 33

James Gilson "numerologically" derived value
@'~= 0.0072973525 3 18

http://en.wikipedia.org/wiki/Fine-structure_constant


CONCLUSION?

Well, seems we've got Gilson beat anyway...

See...
James G. Gilson, Relativity, Stochastic Schrödinger Quantum Wave Mechanics,
Fine Structure Constant
http://www.maths.qmul.ac.uk/~jgg/

NOTE TO SELF :: LEARN HOW TO BALANCE AN EQUATION... Hmmm...

This post has been edited by Raphie Frank on Nov 22 2007, 04:59 PM

A not unrelated paper...

=============================================

On the Coupling Constants, Geometric Probability and Complex Domains
by Carlos Castro Perelman
Volume 2 PROGRESS IN PHYSICS April, 2006

excerpt...
A typical objection to the possibility of being able to derive the values of the coupling constants, from pure thought alone, is that there are an infinite number of possible analytical expressions that accurately reproduce the values of the couplings within the experimental error bounds. However, this is not our case because once the gauge groups U(1), SU(2), SU(3) are known there are unique expressions stemming from Geometric Probability which furnish the values of the couplings. Another objection is that it is a meaningless task to try to derive these couplings because these are not constants per se but vary with respect to the energy scale. The running of the coupling constants is an artifact of the perturbative Renormalization Group program. We will see that the values of the couplings derived from Geometric Probability are precisely those values that correspond to the natural physical scales associated with the EM, Weak and Strong forces.

Another objection is that physical measurements of irrational numbers are impossible because there are always experimental limitations which rule out the possibility of actually measuring the infinite number of digits of an irrational number. This experimental constraint does not exclude the possibility of deriving exact expressions based on ? as we shall see...


Download Paper in PDF format
http://www.ptep-online.com/index_files/2006/PP-05-09.PDF

=============================================

Critically speaking, that term "pure thought alone" always bothers me. Without related Experience, the concept is meaningless. The issue, then, becomes "what kind of experience"?

frank-who is castro perelman?
you is saying that the superstrings is intrinsically relationed with number theory?
how? and the clifford algebra,what affinities has?

Given that you've admitted to not having mathematical knowledge above a child in highschool, why are you attempting to talk about things like:

• Diffeomorphisms
• Gauge groups
• Projective spaces
• Self Duality

Do you just skim scientific papers for words and phrases you think sound impressive, with the intention to use them in posts full of nonsensical drivel? Didn't we have a short conversation about this kind of misguided behaviour yesterday?

Just as I had the same conversation with Ivars, Mott, Farsight, NeoNo.1, StevenA, Precursor, Zephir and all the other cranks.

It's a common theme. Lies in order to cover ignorance. Ironically, in some cases (like basic algebra or Newton's laws of motion) cranks spend more time making excuses about why they don't have to know such things than it takes to learn such things! People prefer putting in a load of effort to dodge a small amount of effort working!

This post has been edited by AlphaNumeric on Nov 24 2007, 07:09 PM

This is called experimentation and attempt at innovation, Euler (which is rarely recognized as such at the time). And we have been over this quite indeed and you apparently did NOT read the introduction, stating the purpose of this thread.

AS FOR THESE TERMS
Diffeomorphisms
Gauge groups
Projective spaces
Self Duality

Feel free to tell me I don't know the math, but PLEASE do not tell me I do not understand the concepts. And, by the way, if I LINK to something using a term, this does NOT mean I presume to know everything contained within the link, particularly where math and physics is involved.

As for the email I sent you, that you publicly called "inane," feel free to share it with Alphanumeric because he has suddenly gone quite suspicious on me. I did not say much more than that my father was tenured at 31 at Princeton (Economics) and that if you believed intelligence an inherited trait, then you might surmise that I am no dummy, since you have attacked my intelligence and one can not defend oneself on that account, especially publicly, without sounding like a dumba** I will add to that, that my mother was the first woman to drop out of Princeton because she was in the first class of female graduate students there, and she left to marry my father when he went off to teach in Africa...

So... feel free to call my mother a Grad school drop-out... as you insult my intelligence repeatedly based on a thoroughly limited perspective. I said that high school students in terms of EQUATIONS & FORMULAS might be ahead of me mathematically, not in terms of understanding of concepts which is far more important. So happens, my mother became a lawyer later... and I am the only one in my nuclear or extended family WITHOUT an advanced degree; and there is a reason for that and if you study up on the gifted you may learn a thing or two.

I also asked you, basically, to not be a part of the problem regarding censorship, which you are being 100% at the moment. And right here is a link to me PUBLICLY asking you as much with respect to me personally...

http://forum.physorg.com/index.php?showtop...ndpost&p=285421

Schooling-wise, I did not go the academic route, frankly, because I knew I would have to deal with people like you, because in all honesty, you are more than a little close-minded and more than a little outright mean to people. I can take it now, but I couldn't then, and know that others can't. People QUITE LITERALLY die from the type of words you call HUMOUR, as you will see if you go and read the Laissez Faire Libel thread.

http://forum.physorg.com/index.php?showtop...ndpost&p=285450

WHO stands up for those who can't stand up for themselves, for those who think outsude the box in VISUAL, GEOMETRIC manner, Euler? Alphanumeric? You? Certainly not, it would seem. You will BOTH likely attack me now, if only to save face. OR others will come along and attack me, which actually would provide me with a wonderful little case study in mobbing behavior for if/when I go back to grad school in Sociology, problem being that I may have missed the GRE deadline for this year and will have to ask for an extension or wait a year.

As for Carlos Castro Perelman, feel free to email Nobel Laureate Brian Josephson director of the mind/matter Unification project at Cavendish laboratories at Cambridge with Carlos Castro in the subject title and let me add: BOTH of you would have attacked Ramanujan -- who viewed numbers as equations from the mind of God -- at the time if he did not have Hardy there to tell others he was a genius. It was only because others validated him that you, Alphanumeric, perhaps refer to him with awe and respect and we have yet, in my opinion, only begun to understand his work.

If you would like to "check up" on who I am, feel free to contact my old partner Brian Reisinger at swandivedigital, or Michelle Thomas Maran at the Markle Foundation or Jen Tattenbaum of the Shubert Organization or Ida Dupont, a Professor of Criminology at Pace University here in NYC who is my oldest friend in the world. They can all vouch for my lack of "crank-hood" and critical analytic skills, if not the latent mathematical abilities I never realized I had that do NOT require a high school education but "DATA-POINTS" of experience from which to "draw" connections.

I might add, Alphanumeric, I have treated you only with respect and am rather shocked. If you wish to insult me, do it to my FACE with your name out in the open, because I expect much from you. I am easy to find. Or tell me where you are and who you are and maybe the next time I am in London, I will buy you a beer and you can go off on me in person.

Kindest Regards,
Raphie Frank
917-202-2610

100 Metropolitan Ave. #6
Brooklyn, NY, 11211
USA

P.S. Again, apologies if overly self-defensive.

This post has been edited by Raphie Frank on Nov 25 2007, 03:01 AM

mott.carl

Dr. Carlos Castro Perelman is a physicist who has worked extensively with number theory, which YES, is deeply related to the natural order of things as any reasonable survey would make clear, and Lisi's Exceptionally Simple Theory of Everything will make explicit if it gains any traction.

As for Dr. Carlos Castro Perelman, he has explored the fine structure constant, has been working on a proof for the Riemann hypothesis, and in December will have a paper coming that will deal with Grand Unification from a Clifford Space perspective. It is not at all unrelated to Lisi's work.

Best,
Raphie

Ok, fair enough, I wont attack you and become your college project. But let me ask you one thing about what you just said.

What exactly is that supposed to mean? Did you actually read the related article, or are you just using it to score some kind of point? Who, exactly, called what happened in that article "humor"? And let me be perfectly clear that what happened to that innocent girl should be a crime. But trying to compare what has been said in the context of this forum to what happened to her is just stupid.

Are you sure you arent a drama major?(I couldnt help myself)

Kindest Regards,
Occidental

</edit> Previous text posted to wrong thread.

Dear Occidental,

You just gained my immediate respect! I was a Dramatic WRITING major in school, as well as a Psychology major. As for the former, the major did not exist so I had to create it. It was a blending of Drama, Film, English, Art History (Architecture) and Psychology, as well as a Contemporary Press class in journalism by Richard Severo, who I hope is still writing for the New York Times, although he may well be retired at this point.

Related Quote -
The reasonable man adapts himself to the world, but the unreasonable man tries to adapt the world to him--therefore, all progress depends upon the unreasonable man.
-- Samuel Butler

As for acting, I get along quite well with actors, but suffered from severe stage fright as a youth. I didn't like to put myself in front of others which is not unrelated to some of the recent discussion upon this thread.

============
CONTEXTUAL LINK
============

Fear Survey
http://boojummy.blogs.friendster.com/snipe...ear_survey.html

Best,
Raphie


P.S. Edit to previous post. The text should have read...

"... from a Clifford Algebra / Chern Simon perspective. It is not at all unrelated to Lisi's work."

P.P.S. I don't need to understand the maths (as much as I would love and hope to!) to understand the relevancy. In private communications, Nobel Laureate Dr. Brian Josephson spoke (i.e wrote) highly of Dr. Carlos Castro Perelman's work. As I said, feel free to contact him for verification purposes, obviously in as brief manner as possible, since he is a busy man. His information is publicly available.

Brian Josephson's Home Page
http://www.tcm.phy.cam.ac.uk/~bdj10/

This post has been edited by Raphie Frank on Nov 25 2007, 04:40 AM

Thats cool. Have you ever heard of these folks?
cure-fear.com
They have a program that they say works in just one hour.

raphie-thank you very much for your reply
raphie,what the PHYSICAL relations between pi,e,and i for the biquaternions of clifford? would the duality that correspond the existence of spacetimes,through the couplements of opposed rotation twistors?
why the rotational invariance is breakdown in three dimensional spaces? the "spaces" to a nonassociative and noncommutative geometry,that connect space and time,in spacetime curved geometries in 4-dimensional manifolds?then the quaternions would explain the conection of space and time in spacetimes,in geometrical purely space,with one auto-operator that produce interaction in itself,changing the geometrical topological configurations to a physical configurations,where the particles or pseudo particles are generated by mathematical asymmetry,that generate discontinuty fields,or "holes",being that the symmetry groups( as of lie),generate singularity,when its automorphysmisms
form discrete groups,in infinite dimension spaces,as the of hilbert.

the fractal structures construct the continuos and linear structures seen in the non-turbulence configurations of the physical universe? how the mathematical worlds
generate the physical worlds?

My maths are not up to the task of answering those those questions mott.carl, but they seem like great questions.

But hopefully someone else who comes along will be able to provide some insight.

Best,
Raphie

P.S. Thank you for getting this back on topic.

This post has been edited by Raphie Frank on Nov 25 2007, 10:44 AM

=====================================================
From an October 31 email from Carlos Castro Perleman. (Published by permission)
=====================================================

Dear Raphie :

A book I recommend by M. R. Schroeder (Springer Verlag) is :

Number Theory in Science and Communication with applications in Cryptography, Physics, Biology, Digital Information and Computing.

Chapter 5 is devoted to the Fibonacci and Lucas numbers.

Some important relations that you need to know (in case you didn't know them ) are :

( 1 + phi )^n = F_{n+1} + F_n phi .

phi^n = ( 1 + phi )^{ -n } =

( - 1 )^n F_{ n -1} + ( -1)^{ n+1} F_n phi.

where my phi convention is = 0.618.... and F_n, F_{n-1}, F_{n + 1} are 3 consecutive Fibonacci numbers.

These relations combined with the two Bernoulli relations

F_n =

( 5 )^{ -1/2 } [ ( 1 + phi )^n - ( - phi )^n ]

and

F_n = i^{ n -1} [ sin ( n z ) / sin z ] .

where

z = (pi / 2 ) + i ln ( 1 + phi )

will be helpful. Especially the very last relationships due to its cyclic naure might be the most helpful to you.

Best wishes

Carlos

This post has been edited by Raphie Frank on Nov 25 2007, 10:54 AM

Except it isn't cyclic. Just because you're taking the sin of somethign doesn't mean it's cyclic, because you're taking the sin of a complex number.

Let nz = nx+i.ny = n(pi / 2 ) + i n*ln ( 1 + phi )

sin(nx+i.ny) = sin(nx).cos(i.ny)+cos(nx).sin(iny) = sin(nx).cosh(ny)+i.cos(nx).sinh(ny)

That is clearly not periodic because if I increase n->n+4, the sin(nx) and cos(nx) don't change but the cosh(ny) and sinh(ny) more certainly do.

He's reshuffled the expression to make it superficially look periodicy when it quite clearly isn't. The left hand side, F_n, is not periodic so you cannot express it as a periodic function, that's nonsense.

Thank you for this feedback, Alphanumeric.