Angular Momentum, Mass, andMagnetic Dipole Moment

This view of the GUT monopole raises the possibility that it may catalyze the decay of the proton ...". ]...

SU(5) GUT Monopole formation ends and the Inflationary X-Boson Higgs mechanism eliminates the relic Monopoles.

  • According to The Early Universe, by Kolb and Turner (1994 paperback edition, Adddison-Wesley, page 526): "... the full symmetry of the GUT cannot be manifest; if it were the proton would decay in 10^(-24) sec. The gauge group ... must be spontaneously broken to [ SU(3) x SU(2) x U(1) ]. For SU(5), this is accomplished by ... masses of the order of the unification scale for the twelve X ... gauge bosons. ...[
                    X color charges              X electric charges       3 3 3 X X          red red                        -4/3 -1/33 3 3 X X        green green                      -4/3 -1/33 3 3 X X         blue blue                       -4/3 -1/3X X X 2 2  antired antigreen antiblue          +4/3 +4/3 +4/3X X X 2 2  antired antigreen antiblue          +1/3 +1/3 +1/3

    ]... Thus, ... at energies below 10^14 GeV or so the processes mediated by X ... boson exchange can be treated as a four-fermion interaction with strength ... [proportional to 1 / M^2 ] ... where M = 3 x 10^14 GeV is the unification scale. ... these new ... interactions are extremely weak at energies below 10^14 GeV. ... the proton lifetime must be ...[about]... 10^31 yr. ...".  

  • In The Early Universe (paperback edition Addison-Wesley 1994) Kolb and Turner say (at p. 526): "... SU(5) GUT ...[has]... at the very least one complex 5-dimensional Higgs. The 5-dimensional Higgs contains
    • the usual doublet Higgs required for W-Boson SSB ...[which]... must acquire a mass of order of a few 100 GeV and
    • a color triplet Higgs ... which can also mediate B,L [baryon,lepton] violation. The triplet component must acquire a mass comparable to ... M = 3 x 10^14 GeV ... to guarantee the proton's longevity, ...".


After the Inflation Era, Our Universe begins its current phase ofexpansion

controlled by Gravity according to a MacDowell-Mansouri Mechanismbased on the Conformal Group Spin(2,4) = SU(2,2) with 15generators:

According to gr-qc/9809061 by R. Aldrovandi and J. G. Peireira:"... By the process of Inonu-Wigner group contraction taking thelimit R -> 0, ...[where R is the de Sitter pseudo-radius,the] ... de Sitter group... [ whether of metric ...(-1,+1,+1,+1,-1) or (-1,+1,+1,+1,+1) , is]... contracted to thegroup Q, formed by a semi-direct product between Lorentz and specialconformal transformation groups, and ... de Sitterspace...[is]... reduced to the cone-space N, which is a spacewith vanishing Riemann and Ricci curvature tensors. As the scalarcurvature of the de Sitter space goes to infinity in this limit, wecan say that N is a spacetime gravitationally related to an infinitecosmological constant.".

If the 2+4 = 6-dimensional spacetime on which the fullConformal Group Spin(2,4) acts linearly is viewed in terms of anelastic Aether, its rigidity would correspond to the VEV of theX-Boson Higgs Condensate on the order of 10^14 GeV. Since theaction of the Conformal Group Spin(2,4) = SU(2,2) is nonlinear on4-dimensional physical spacetime, the 4-dimensional elastic Aethercan, within the Conformal Expanding Domain of Our Universe, bedeformed by Special Conformal and Dilation transformations withoutthe restrictions of X-Higgs VEV rigidity on the order of 10^14GeV.

The Aldrovandi-Peireira paper shows that

the 10 Generators (4 Special Conformal and 6 Lorentz)describe Our Universe expanding due to Dark Energy (also known,somewhat inaccurately as it is variable, a cosmologicalconstant).

 What about the other Generators?

The 4 Translation Generators describe spacetime,singularities of which are black holes, and Primordial Black Holesafter the End of the Inflation Era make up the Dark Matter of OurUniverse that organizes the Large Scale Structure of GalaxyFormation.

The 1 Scalar Dilation Generator corresponds to the Scalar Higgsof the W-Bosons, with VEV 250 GeV, that gives mass to Ordinary Matterin Our Universe.

Those 15 Conformal Group Spin(2,4) = SU(2,2) Generators indicatethat the basic tree-level ratio Dark Energy : Dark Matter : OrdinaryMatter is 10 : 4 : 1 = 67 : 27 : 6 . After taking into account thehistory of Our Universe to the Present Time, that ratio is calculatedto be, as of Now, consistent with observations including WMAP:

Dark Energy : Dark Matter : Ordinary Matter = 75.3 : 20.2: 4.5

After conventional expansion of our universe begins, some regionsof our Universe become Gravitationally Bound Domains (such as, forexample, Galaxies) in which the 4 Conformal GraviPhoton generatorsare frozen out, forming domains within our Universe like IceBergs inan Ocean of Water. Within each Gravitationally Bound Domain,spacetime (regarded as Aether) is incompressible with a rigidity onthe order of the W-Boson Higgs VEV = 250 GeV.

On a large scale (billions of light years), the GravitationallyBound Domains are roughly traced out by Galaxies and Clusters ofGalaxies

so the the white dots would be the Gravitationally Bound Domains(like rigid pennies on an expanding balloon, or rigid raisins in anexpanding cake) and the black background would be the ConformalExpanding Domain of Our Universe.

When the Gravitationally Bound Domains begin to form as GalaxyCluster Structures in the early stages of the current phase ofexpansion of Our Universe, according to a 6 December 2006 caption toESO PR Photo 45/06

"... Spatial, three-dimensional distribution of galaxies in aslice of the Universe as it was 7 billion years ago, based on theVVDS study: brighter areas represent the regions of the Universe withmost galaxies. Astonishingly, the galaxy distribution - the'building blocks' of the large scale structure - takes the shapeof a helix at this primordial epoch. ...". Such a helicalstructure suggests that helical magnetic fields might be involved ingalaxy formation. Further, Battaner et al, in in astro-ph/9801276,astro-ph/9802009, and astro-ph/9911423, suggest that the simplestnetwork pattern for distribution of superclusters of galaxies that iscompatible with magnetic field constraints

is made up of octahedra contacting at their vertexes, which isrelated to a tiling of 3-dim space by cuboctahedra and octahedra, andalso to the heptaverton of Arthur Young and octonionic structures ofOnar Aam.


Within each Gravitationally Bound Domains there can exist Islandsof Conformal Expansion in which all 15 generators of ConformalSpin(2,4) = SU(2,2) remain effective,

like Puddles of Water (red) on an IceBerg (blue) floating in anOcean of Water (red), so the overall structure of Our Universe interms of Gravitationally Bound Domains (pennies, raisins, IceBergs)and Conformal Expanding Domains (balloon, cake, water) is quitecomplicated.

To get some feeling for this structure, begin by consideringClusters of Galaxies to be the largest Gravitationally Bound Domainsand then looking at the next level down in sixe, Galaxies. AsHartmann and Miller say in their book Cycles of Fire (WorkmanPublishing 1987)


Going down one more level in size, to Stars and Stellar Systemslike Our Solar System, Hartmann and Miller describe

"... a star just formed ...[in]... its disk-shaped cocoonnebula some of which is being blown out in bipolar jets ... near adark molecular cloud ... embedded in a ... nebular region ... Thedust in the cocoon reddens the star's light ...".

Kohji Tomisaka of Niigata University says in astro-ph/9911166:"... the star formation process ... angular momentum transfer in thecontraction of a rotating magnetized cloud is studied withaxisymmetric MHD simulations. Owing to the large dynamic rangecovered by the nested-grid method, the structure of the cloud in therange from 10 AU to 0.1 pc is explored. First, the cloud experiencesa run-away collapse, and a disk forms perpendicularly to the magneticfield, in which the central density increases greatly in a finitetime-scale. In this phase, the specific angular momentum j of thedisk decreases to about 1/3 of the initial cloud. After the centraldensity of the disk exceeds about 10^10 cm ^(-3) , the infall on tothe central object develops. In this accretion stage, the rotationmotion and thus the toroidal magnetic field drive the outflow. Theangular momentum of the central object is transferred efficiently bythe out\flow as well as the effect of the magnetic stress. ... theseeding region (origin of the outflow) ... expands radially outward.This outflow is driven by the gradient of the magnetic pressure ofthe toroidal magnetic fields ... which are made by the rotationmotion ... The magnetic fields exert torque on the outflowing gas toincrease its angular momentum. On the other hand, they exert torqueon the disk to decrease the angular momentum ... [in about 7000years] ... the outflow expands and reaches ... [about 4AU] ... The angular momentum distribution at that time ... hasbeen reduced to ... a factor of 10 ^(-4) from the initial value (i.e.from 10^20 cm^2 s ^(-1) to 10^16 cm^2 s ^(-1)). ... the couplingbetween gas and magnetic fields ... becomes stronger as long as weconsider the seeding region, indicating that the mechanism of angularmomentum transfer works also in the later stage of the evolution[after 7000 years]. ...".

If you look closely at the central star in the star-formationimage above, you might see Birkeland Current Loops (image web page) that look up close like SolarCoronal Loops (image from web page).


Up close, Birkeland Current Loops are seen to have braidedfilament structure (Cygnus Loop image from


The scale of Birkeland Current Loops extends beyond Stellar toGalactic (images, SOHO of Sun and NRAO of Fornax A webpage, which said as to NGC "... a tiny butenergy-dense plasmoid at the center of the galaxy ... Fornax A ...discharges energy along oppositely-directed Birkeland filaments(invisible in this image) into the radio lobes. Diffuse currents loopback from the lobes to the spiral arms, where their increasingdensity triggers star formation as they return to the centralplasmoid. ..." ...).


The scale also extends down to Planetary, as is seen in theJupiter-Io system (image from Anthony Peratt's book Physics of thePlasma Universe (Springer-Verlag 1992)).

The scale may also extend down to Asteroidal. According toa 17 September 1994 article by Jeff Hecht in the New Scientist: "...inclusions ... in chondrules ... in chondrites, the commonestmeteorites ...[were]... heated ... to about 2000 kelvin atthe birth of the solar system, 4.6 billion years ago....[possibly by]... Lightning ... and ... magnetic discharges... laser tests ... to model the intense visible and infrared lightexpected near electric or magnetic discharges ... produced darkstructures ... remarkably similar to .... inclusions found inchondrules ...".

As can be seen from the image below (adapted from some of theabove images and also An Introduction to Modern Astrophysics, byCarroll and Osterlie (Addison-Wesley 1996), Solar System Evolution,by Stuart Ross Taylor (Cambridge 1992), and B. V. Vasiliev's papersastro-ph/0002048 and astro-ph/0002171), Angular Momentum, MagneticDipole Moment, and Mass are systematically related or Stars andStellar Systems and their components.




Angular Momentum J and Magnetic Dipole Moment P are related by aconstant that is on the order of unity ( J = P ) (natural units) dueto Gravity-Induced Electric Polarization of matter.

As to the relationship between Angular Momentum J and Mass (which,due to the Angular Momentum - Magnetic Dipole Moment relationship,implies a relationship between Magnetic Dipole Moment and Mass),Jack Sarfatti's paperwessonI.PDFdescribes a 1981 paper by Paul Wesson in which Wesson plotted totalangular momentum J against mass M for the solar system, double stars,star clusters, spriral galaxies, the Coma cluster, and the localsupercluster in which Wesson found that Angular Momentum J and Mass Mare related by a constant p such that

J = p M^2 and

J/M = p M.

Wesson's observations indicate approximately, that

p = 10^(-16) g^(-1) cm^2 sec^(-1) (cgs units) and

p = 1 / alpha_EM = 137 (natural units G = hbar = c =1).

For Elementary Specific Angular Momentum J/M = hbar, in naturalunits where hbar = 1 and the unit of mass is the Planck massMplanck:

M = (J/M) / p = alpha_EM, which gives

M = Mplanck / 137

which is roughly the mass of an SU(5) Magnetic Monopole.

Wesson's observations are consistent with a Compton Radius VortesKerr-Newman Black Hole related to the Wesson Force. The equation (inunits with G = c = hbar = 1) for a Kerr-Newman Black Hole withcoincident outer and inner event horizons and with Q = 1

meaning that the Black Hole Core has UNIT amplitude to absorb or emit a gauge boson, in accord with Feynman's statement in his book QED (Princeton 1988): "... e - the amplitude for a real electron to emit or absorb a real photon. It is a simple number that has been experimentally determined to be close to -0.0854... the inverse of its square: about 137.03... has been a mystery ... all good theoretical physicists put this number up on their wall ..."

is Q^2 + (J/M)^2 = 1 + (J/M)^2 = M^2. Dividing through by M^2, youget

J^2/M^4 = (J/M^2)^2 = 1 - (1/M)^2

For the Wesson force for which J = p_wesson M^2 with p_wesson = 1/ alpha_EM

J = sqrt(1 - (1/M)^2) M^2 = p_wesson M^2 = 137 M^2

so that 1 - (1/M)^2 = 137^2 and 1/M = sqrt(1 -137^2) = 137 i = 137exp(pi/2)

Then the magnitude | 1 / Mwesson | = 137 which (since the unitsare natural units with G = c = hbar = 1) implies that

Mwesson = Mplanck / 137 = 10^19 / 137 = 7.3 x 10^16GeV

which is consistent with Wesson's observation that

Mwesson = 7.3 x 10^16 GeV = Mmonopole


The Linear Angular Momentum, Magnetic Dipole Moment, and MassRelationships hold in Gravitationally Bound Domains, which arecharacterized by

Energy Below about 250 GeV = VEV of W-BosonHiggs where:

Although the Wesson angular momentum / mass relationship covers avery wide range of mass scales (at least from Asteroids to Stars andStellar Systems), it is not Universal. Some other angular momentum /mass relationships are:

The differences may be that the Wesson relationship involves acombination of ElectroMagnetic and Gravity forces duringCollapse/Formation, while, for the others, the forces involvedare:


Can a laboratory-scale experiment extend the Wesson-typerelationship between Angular Momentum J and Magnetic Dipole Moment Pto sub-asteroid laboratory mass scales ?

Saul-Paul Sirag, in his 3 November 2000 paper Vigier III: "Gravitational Magnetism: an Update", says:
"... The most straightforward test ... would be to measure directly the magnetic field of a rotating neutral body (which is not also a ferromagnetic substance). Blackett ... suggested that a 1-meter bronze sphere spun at 100 Hz would do nicely, except that this is the maximum safe speed, and there are severe problems in nulling out extraneous magnetic fields. With modern SQUIDs and mu-metal shielded rooms, such an experiment can be attempted. Exactly such an experimental design ... was described at the SQUID '85 conference in Berlin. However, the results of this experiment have not been published. ...".


What about MicroScale Connections between AngularMomentum and Electromagnetism ?

The MicroScale Particle Physics proportionality between Q and Mobviously does not extend far into the MacroScale, since Asteroids,Planets, and Stars do not have large net Electric Charges.

The Kerr-Newman Black Hole structure of a Compton Radius Vortexhas the property that the square of the electric charge Q plays thesame role as the square of J/M (specific angular momentum, or angularmomentum over mass) in that their sum, relative to the square of themass, determines whether the outer and inner event horizons are

Jack Sarfatti relates Compton Radius Vortex structure ofElementary Particles to the formula of Saul-Paul Sirag (based onearlier work of Blackett and Schuster, and perhaps Pauli) in his 1979Nature paper Gravitational Magnetism (vol. 278 pp. 535-538, 5 April1979), in which Saul-Paul Sirag says: "The gravi-magnetic hypothesisproposes that a rotating mass, measured in gravitational units, hasthe same magnetic effect as that of a rotating charge, measured inelectrical units. The respective force constants determine thisrelationship

G^(1/2) M = k^(1/2) Q

where G is the gravitational constant, M is mass, k is the Coulombconstant, and Q is electric charge. ... Thus the ratio of magneticmoment P to angular momentum J for a sphere of mass M, density factorf, radius r, angular velocity w, and magnetic field B is (in SI units[with magnetic permeability muo of the vacuum]):

P / J = ( (5/4) 4 pi B / muo ) ( r / f w M ) = G^(1/2) / 2k^(1/2)

... A priori, we should expect a correlation between P and J. ...The surprise is that this correlation ratio, P/J, should turn out tobe close to P = ( G^(1/2) /2 k^(1/2) ) J. ... The gravi-magnetichypothesis (stated in [ Log = log_10] form) predicts a P/J of-10.37. The mean P/J of the data points plotted in Fig. 1 is -11.13with a standard deviation of 0.42. ... Therefore, for a given valueof the angular momentum J, the gravi-magnetic hypothesis overstatesthe magnetic dipole moment P by a factor of 10^(-10.37 - (-11.13)) =10^0.76 = 5.75. Saul-Paul Sirag says: "... the deviation from thegravi-magnetic hypothesis line is fairly systematic. ... deviations... may well be due to electrical-magnetic effects. ... [ P / J =G^(1/2) / 2 k^(1/2) ] predicts a surface field about three timesgreater than that measured at the surface of the Earth. ... the Earthis not a uniformly dense sphere ... At the Earth's surface ... [( (5/4) 4 pi B / muo ) ( r / f w M ) = G^(1/2) / 2 k^(1/2) ]predicts a B of 2.1 x 10^(-4) T. That is not, however, a great dealmore than the 1.4 x 10^(-4) T that [the equation] predictsfor the surface of the Earth's core. ... this core magnetismpredicted by the gravi-magnetic equation is greater than the magneticfield of 6 x 10^(-5) T measured at the Earth's surface. ... This iswhat we expect if we suppose that gravitational magnetism is modifiedby an electrical-magnetic effect stronger at the Earth's surface thanin the interior. ...".

 B. G. Sidharth, in physics/9908004, says: "... We firstobserve that as is known an assembly of Fermions below the Fermitemperature occupies each and every single particle level, and thisexplains the fact that it behaves like a distribution of Bosonicphonons: The Fermions do not enjoy their normal degrees of freedom.... [there is a] Bosonization or semionic effect. ... Let usnow consider an assembly of N electrons. As is known, if N+ is theaverage number of particles with spin up, the magnetisation per unitvolume is given by

M = mu ( 2 N+ - N ) / V

where mu is the electron magnetic moment. At low temperatures, inthe usual theory, N+ = N / 2, so that the magnetisation ... is verysmall.

On the other hand, for Bose-Einstein statistics we would have, N+= N. With the above semionic statistics we have,

N+ = b N, 1/2 < b < 1,

If N is very large, this makes an enormous difference ... Let ususe ... the case of Neutron stars. In this case, as is well known, wehave an assembly of degenerate electrons at temperatures about 10^7K, whereas the Fermi temperature is about 10^11 K ... So the aboveconsiderations apply. In the case of a Neutron star we know that thenumber density of the degenerate electrons, n = 10^31 per c.c. So ...remembering that mu = 10^(-20) G (Gauss), the magnetic field near thePulsar is about 10^11 G < 10^8 Tesla, as required. Some WhiteDwarfs also have magnetic fields. If the White Dwarf has an interiorof the dimensions of a Neutron star, with a similar magnetic field,then remembering that the radius of a White Dwarf is about 10^3 timesthat of a Neutron star, its magnetic field would be 10^(-6) timesthat of the neutron star, which is known to be the case. It is quiteremarkable that the above mechanism can also explain the magnetism ofthe earth. As is known the earth has a solid core of radius of about1200 kilometers and temperature about 6000 K. This core is made upalmost entirely of Iron (90%) and Nickel (10%). It can easily becalculated that the number of particles N = 10^48 , and that theFermi temperature is about 10^5 K. In this case we can easily verify... that the magnetic field near the earth's surface is about 1 G,which is indeed the case. It may be mentioned that the anomalousBosonic behaviour ... would imply a sensitivity to external magneticinfluences which could lead to effects like magnetic flips orreversals. ... Remembering that the core density of Jupiter is of thesame order as that of the earth, while the core volume is about 10^4times that of the earth, we have in this case, N = 10^52 , so thatthe magnetization ... is about 10^4 times the earth's magnetism, asrequired. ....".

According to a 23 March 2006 ESA news web page: "... MartinTajmar, ARC Seibersdorf Research GmbH, Austria; Clovis de Matos,ESA-HQ, Paris; and colleagues have measured ... a gravitomagneticfield ... generate[d] ...[by]... a moving mass... Their experiment involves a ring of superconducting materialrotating up to 6 500 times a minute. Superconductors are specialmaterials that lose all electrical resistance at a certaintemperature. Spinning superconductors produce a weak magnetic field,the so-called London moment. The new experiment tests a conjecture byTajmar and de Matos that explains the difference betweenhigh-precision mass measurements of Cooper-pairs (the currentcarriers in superconductors) and their prediction via quantum theory.They have discovered that this anomaly could be explained by theappearance of a gravitomagnetic field in the spinning superconductor(This effect has been named the Gravitomagnetic London Moment byanalogy with its magnetic counterpart). ... Although just 100millionths of the acceleration due to the Earth's gravitationalfield, ...[ gr-qc/0603033 says "... the peaks ... "only" 100micro g ... are 30 orders of magnitude higher than what generalrelativity predicts classically ..."]... The electromagneticproperties of superconductors are explained in quantum theory byassuming that force-carrying particles, known as photons, gain mass.By allowing force-carrying gravitational particles, known as thegravitons, to become heavier, they found that the unexpectedly largegravitomagnetic force could be modelled. ... The papers can beaccessed on-line at the Los Alamos pre-print server using thereferences: gr-qc/0603033 and gr-qc/0603032. ...".



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