Reciprocal System Forums

General Discussion :: RE: Lepton mass relationships

davelook — Sat, 03 Jan 2009 20:37:09 GMT

Author: davelook
Posted: Sat Jan 03, 2009 1:37 pm (GMT -7)

Hi Doug,

12.7323954 degrees = 2/9 radians

General Discussion :: RE: Lepton mass relationships

davelook — Sat, 03 Jan 2009 20:17:48 GMT

Author: davelook
Posted: Sat Jan 03, 2009 1:17 pm (GMT -7)

From http://adsabs.harvard.edu/abs/2008arXiv0801.1580L

Quote:

We present a new measurement of the Newtonian gravitational constant G based on cold-atom interferometry. Freely falling samples of laser-cooled rubidium atoms are used in a gravity gradiometer to probe the field generated by nearby source masses. In addition to its potential sensitivity, this method is intriguing as gravity is explored by a quantum system. We report a value of G=6.667×10-11m3kg-1s-2, estimating a statistical uncertainty of ±0.011×10-11m3kg-1s-2 and a systematic uncertainty of ±0.003×10-11m3kg-1s-2

Substituting the above value for G into the equations above, you get 128.5149524.

...and from http://prola.aps.org/abstract/PRL/v78/i3/p424_1

Quote:

We report the first purely electroweak measurement of the strengthening of the electromagnetic coupling, αQED with increasing momentum transfer Q2, by comparing the process e+e-→μ+μ- with the process e+e-→e+e-μ+μ-. The data were accumulated at an average center-of-mass energy sqrt[s] = 57.77 GeV using the TOPAZ detector at the TRISTAN e+e- collider. We measure αQED-1(Q2) to change from its known value of αQED-1≅137.0 at Q2 = 0 to 128.5±1.8(stat)±0.7(syst) at Q2 = (57.77 GeV/c)2. This result agrees with electroweak predictions.

Also, Fig. 2a of http://arxiv.org/pdf/hep-ph/0605002v2 shows that alpha "bottoms out" at about 128.3

General Discussion :: RE: Lepton mass relationships

Douglas Bundy — Sat, 03 Jan 2009 16:53:07 GMT

Author: Douglas Bundy
Posted: Sat Jan 03, 2009 9:53 am (GMT -7)

Hi Dave,

This is really good stuff, but I can't get the value 12.732395... for some reason. Can you help this tonto out?

The thing that intrigues me most is Foot's observation that, if we "define theta as the angle between this vector [from the origin to the point (m_e^1/2, m_u^1/2, m_r^1/2 )] and the symmetric vector (the symmetric vector is the one which passes through the origin and the point (1,1,1)), then Koide’s mass relation is equivalent to the statement that theta = pi/4."

I'm not sure, but I think this maps the masses plotted on Larson's 2x2x2 cube, to the geometry of the unit sphere, if the vector from the origin to one of the vertices of the cube is 2^1/2, which it will be in the unit cube. Essentially, this transforms the values of the vector from the cube's coordinates, corresponding to the outer sphere (containing the cube), to the cube's coordinates, corresponding to the inner sphere (contained by the cube).

Since the inner sphere corresponds to the real sphere (radius = 1), while the outer sphere corresponds to the imaginary sphere (radius = 2^1/2), it seems to imply a connection between complex and real numbers, but more specifically, between complex numbers and integers, because, while pi makes the 1D, 2D and 3D values of the real sphere irrational, its radius, which after all is the generator of these values, is the unit integer 1.

Among other things, this means that Koide's formula is telling us that our mathematics should be scalar, not vectorial. What a concept!

Doug

General Discussion :: RE: Lepton mass relationships

davelook — Sat, 03 Jan 2009 00:29:25 GMT

Author: davelook
Posted: Fri Jan 02, 2009 5:29 pm (GMT -7)

From http://www.sciencenews.org/pages/pdfs/data/1997/151-06/15106-12.pdf

Quote:

From their data, the researchers obtained a value of the fine structure constant, a number
that characterizes the inherent strength of the electromagnetic force. As expected theoretically,
the newly obtained value of 1/128.5 is significantly larger than the 1/137 observed for a fully
screened electron.
“Ours is a clean measurement of the electromagnetic effect,” Koltick says. In higher-energy
experiments at other accelerators, the effect is swamped by additional factors, including the
strong force, which holds neutrons and protons together in an atomic nucleus and binds
quarks into protons and neutrons. Those factors make it difficult to distinguish the relative
contributions of the nuclear and electromagnetic forces.

General Discussion :: RE: Lepton mass relationships

davelook — Fri, 02 Jan 2009 03:25:57 GMT

Author: davelook
Posted: Thu Jan 01, 2009 8:25 pm (GMT -7)

I should mention the relationship that started me looking into the lepton mass relationships. I wanted to compare the gravitation and charge forces of the electron, ignoring the space² denominator of the force equations so that we are comparing the time portion only.

Using 2006 CODATA values, you have Gm_e² = 5.538373819(E-071), and ke² = 2.307077127(E-028).
Since mass/gravity is a 3D effect, take the cube root of Gm_e² to reduce it to it's 1D equivalent: (Gm_e²)^1/3=3.811776444(E-024).

So (Gm_e²)^1/3 / ke² = 16522.10236.

Now, since the force equations start by SQUARING the mass/charge to compute the interaction, and according to Larson it's only an apparent motion with each mass/charge moving independently, to get a real comparison we need to compare the square roots of each: 16522.10236^1/2 = 128.5383303

I found the following quote from NBM applicable here... http://library.rstheory.org/books/nbm/12.html

Quote:

On the basis of the theoretical considerations discussed in the preceding paragraphs, there are 4 possible orientations of each of the two two-dimensional rotations of the atoms, and 8 possible orientations of the one-dimensional rotations, making a total of 4 × 4 × 8 = 128 different positions that a unit displacement of the scalar translational motion of the atom (the inward scalar effect of the rotation) can take in three-dimensional time. In addition, each of the rotating systems of the atom has an initial unit of vibrational displacement with three possible orientations, one in each dimension. For the two-dimensional basic rotation this means nine possible positions, of which two are occupied. Thus, for each of the 128 possible rotational positions there is an additional 2/9 vibrational position which any given displacement unit may occupy. The inter-regional ratio is then 128 (1 + 2/9) = 156.44.

The part about "...(1 + 2/9)... ...an additional 2/9..." is why I included it in the post above, where it is actually added to the complex cube roots of unity.

Another interesting thing to keep in mind is that if you have 2 lines starting at the origin, one going to (1_x, 1_y, 1_z), and another going to (.040349908_x, .5802119201_y, 2.3794381716_z), the angle between them is exactly 45^o. See http://arxiv.org/pdf/hep-ph/9402242v1

Now, this might be nothing, but 128.5383303/3=42.846, and m_p/m_e=1836.15267247, and sqrt 1836.15267247=42.85035

General Discussion :: RE: Lepton mass relationships

JS — Mon, 29 Dec 2008 20:29:46 GMT

Author: JS
Subject: Lepton mass relationships
Posted: Mon Dec 29, 2008 1:29 pm (GMT -7)

A google ad pointing to http://www.tau.ac.il/~elicomay/ came up while reading this. Interesting.

On Mon, Dec 29, 2008 at 12:47 PM, davelook <davelook@yahoo.com (davelook@yahoo.com)> wrote:

Quote:

If you take the cube roots of unity, which are located at 120, 240, and 360 degrees, and you simply ADD 2/9 radians to each (as Larson sort of did in BPM), you get the relations between the electron, muon, and tau leptons to a high accuracy:

1+(sqrt(2)*cos(120+12.732395...))=0.040349908219... (electron)
1+(sqrt(2)*cos(240+12.732395...))=0.580211920147... (muon)
1+(sqrt(2)*cos(360+12.732395...))=2.379438171633... (tau)

(tau/electron)2= 3477.4728371... (2006 CODATA 3477.4
(muon/electron)2= 206.77031597... (2006 CODATA 206.7682823)
(tau/muon)2= 16.81804673... (2006 CODATA 16.8183)

see http://carlbrannen.wordpress.com/2008/02/13/koide-formulas-and-qubit-qutrit-mubs/

--
"The best way to destroy the capitalist system is to debauch the currency." � Vladimir Lenin
_________________
"My mission is vague. I am here to appreciate the situation."
- from the film Lawrence of Arabia

General Discussion :: Lepton mass relationships

davelook — Mon, 29 Dec 2008 17:47:55 GMT

Author: davelook
Subject: Lepton mass relationships
Posted: Mon Dec 29, 2008 10:47 am (GMT -7)

If you take the cube roots of unity, which are located at 120, 240, and 360 degrees, and you simply ADD 2/9 radians to each (as Larson sort of did in BPM), you get the relations between the electron, muon, and tau leptons to a high accuracy:

1+(2^.5 x cos(120+12.732395...))=0.040349908219... (electron)
1+(2^.5 x cos(240+12.732395...))=0.580211920147... (muon)
1+(2^.5 x cos(360+12.732395...))=2.379438171633... (tau)

(tau/electron)²= 3477.4728371... (2006 CODATA 3477.48)
(muon/electron)²= 206.77031597... (2006 CODATA 206.7682823)
(tau/muon)²= 16.81804673... (2006 CODATA 16.8183)

Also, if you add electron, muon, tau, it comes out to 3 exactly.

see http://carlbrannen.wordpress.com/2008/02/13/koide-formulas-and-qubit-qutrit-mubs/

General Discussion :: RE: RStheory main site updates

bperet — Sat, 27 Dec 2008 04:02:14 GMT

Author: bperet
Subject: Beyond Space and Time now available in library
Posted: Fri Dec 26, 2008 9:02 pm (GMT -7)

Beyond Space and Time is now available in the RStheory library, thanks to Bob Tucek (original publisher) supplying me with the HTML source for the book. I have converted it to the latest XHTML standard, and it has been added to the RStheory search engine. 364 pages.

Enjoy!
_________________
Dr. Bruce Peret
ISUS Secretary, Webmaster, Accountant, Librarian, Editor