QFT: The cross-section for graviton scatter, scaled by Feynman’s rules from the weak interaction

Article finished at 2am on 30 Nov. (7.3 MB PDF file, 63 pages, downloadable here.) Also hosted at http://rxiv.org/abs/1111.0111, the General Science Journal, and (with some extra material) as the brief mail-order paperback book,

*Quantum Gravity and the Standard Model,*ISBN 978-1-4709-9745-8, which is being listed on Amazon for those who want to help ensure a warmer global future (by turning trees into paper). High-quality book cover PDF (featuring yours truly on the back) is linked here.

Dr Tommaso Dorigo comments on his post Higgs Expectations:

"... in order to really prove that our understanding of electroweak symmetry breaking is flawed and that there is no Higgs boson we would need a much, much more solid evidence than a mere "95% exclusion". I would not be satisfied with anything less than a 99.9% exclusion (over three sigma) across the full mass range.

But I do not honestly believe that we will ever get into such a situation. I do believe, in fact, that the particle is there, and that it will be found very soon! So stay tuned and place your bets if you haven't already. Time is running short.

We avoid the usual electroweak symmetry breaking problem, by changing electromagnetism from U(1) to a massless SU(2) gauge theory (which works out correctly, yielding Maxwell's equations from the Yang-Mills, because charged massless vector bosons can't propagate asymmetrically), so that SU(2) becomes a complete electroweak theory. (This is fine for the weak bosons, while the apparent discrepancy between weak isospin charges and fractional quark electric charges disappears with a vacuum polarization model, which predicts that 1/3 or 2/3 of the electric charge energy of quarks is present as strong colour charge.) U(1) is not abandoned altogether; it is dark energy, which also predicts gravity. The mass of SU(2) weak bosons is then produced by the Glashow-Weinberg mixing of U(1) gravity with SU(2) electromagnetism. Instead of a electroweak symmetry being broken to yield Nambu-Goldstone "Higgs" bosons, the weak interaction emerges from a simple mixing of SU(2) electromagnetism with U(1) gravity. I'll try to get a briefer paper done, ready to replace the Higgs boson.

**Update (7 December 2011):**

http://www.science20.com/quantum_diaries_survivor/alejandro_rivero_fermion_mass_coincidences_and_other_fun_ideas-85187?nocache=1

"Then Koide went some steps beyond and considered quarks and leptons with substructure, so that lepton mass quotients could predict the Cabibbo angle too, even if this is a mixing between quarks."

{(sqrt(M_e)+sqrt(M_mu)+sqrt(M_tau))^2} /( M_e + M_mu +M_tau) = 2/3

The key factor of 2/3 in the Koide relationship is the fractional electric charge of the up/charm/truth quarks, which arises from a mixing effect. It's the 2/3 electric charge of up/charm/truth quarks that's so interesting. The -1/3 charge of the down/strange/bottom quarks is very easily predicted by analysis of vacuum polarization for the case of the omega minus baryon (Fig. 31 in http://rxiv.org/pdf/1111.0111v1.pdf). It appears that the square root of the product of two very different masses gives rise to an intermediate mass (see http://nige.wordpress.com/2009/08/26/koide-formula-seen-from-a-different-perspective/ for the simple maths) that the Koide relationship implies a bootstrap model of fundamental particles (akin to the bootstrap concept Geoffrey Chew was trying to develop to explain the S-matrix in the 1960s before quarks were discovered). The square root of the product of the masses of a neutrino and a massive weak boson may give an electron mass, for instance. This seems to be the deeper significance of the Koide formula, from my perspective for what it's worth. All fundamental particles are connected by various offshell field quanta exchanges, so their "charges" are dependent on other charges around them. This means that the ordinary approach of analysis fails, because of the reductionist fallacy. If your mathematical model of rope is the same for 100 one-foot lengths as for a single 100 foot length, it leads to customer complaints when you automatically send a sailor the former, not the latter. It's no good patiently explaining to the sailor that mathematically they are identical, and the universe is mathematical. If the Koide formula is correct, then it points to an extension of the square root nature of the Dirac equation. Dirac made the error of ignoring Maxwell's 1861 paper on magnetic force mechanisms: the chiral handedness of magnetism (the magnetic field curls left-handed around the direction of propagation of an electron) is explained in Maxwell's theory by the spin of "field quanta" (Maxwell had gear cogs, but in QFT it's just the spin angular momentum of field quanta). Maxwell's theory makes EM an SU(2) Yang-Mills theory, throwing a different light on the Dirac's spinor. It just so happens that the Yang-Mills equations automatically reduce to Maxwell's if the field quanta are massless, because of the infinite self-inductance of electrically charged field quanta, so SU(2) Maxwellian electromagnetism in practice looks indistinguishable from Abelian U(1), explaining the delusions in modern physics.

The very interesting results Alejandro Rivero gives are from equation 4 on page 3 of his paper http://www.vixra.org/abs/1111.0062, which solves the Koide formula by writing one mass in terms of the two lepton other generation masses. Koide's formula also implies (my 2009 post):

Me + Mm + Mt = 4 * [(Me * Mm)^1/2 + (Me * Mt)^1/2 + (Mm * Mt)^1/2]

where Me = electron mass, Mm = muon mass, Mt = tauon mass. I.e., the simple sum of lepton masses equals four times the sum of square roots of the products of all combinations of the masses, making it seem that if Koide's formula is physically meaningful, then Geoffrey Chew's bootstrap theory of particle democracy must apply to masses (gravitational charge) in 4-d. At high energy, early in the universe, tauons, muons and electrons were all represented and we only see an excess of electrons today because the other generations have decayed, although some of the other masses may actually exist as dark matter, and thus still undergoes the interaction of graviton exchange, which determines the Koide mass spectrum today (this dark matter is analogous to right-handed neutrinos). The basic physics of the Koide formula seems to be the Chew bootstrap applied to gravitation (Chew applied it to the strong force, pre-QCD):

"By the end of the 1950s, [Geoffrey] Chew was calling this [analytic development of Heisenberg’s empirical scattering or S-matrix] the bootstrap philosophy. Because of analyticity,

*each particle’s interactions with all others would somehow determine its own basic properties and ... the whole theory would somehow ‘pull itself up by its own bootstraps’*.” - Peter Woit, Not Even Wrong, Jonathan Cape, London, 2006, p148. (Emphasis added.)

The S-matrix went out when the SM was developed (although S-matrix results were used to help determine the Feynman rules), but at some stage a Chew-type bootstrap mechanism for Koide's mass formula may be needed to further develop a physical understanding for the underlying theory of mass mixing, leading to a full theory of mixing angles for both gravitation (mass) and weak SU(2) interactions of leptons and quarks.

There are pedagogy and presentation problems: "Darwin's theory of evolution is disproved because Lamarke had an evolution theory before Darwin, which was wrong." (Joseph McCarthy's "guilt by false association", applies to LeSage's gravity mechanism. If one person gets something wrong, nobody else is ever allowed to correct the errors in it. Darwin was only able to proceed by pretending that Lamarke hadn't existed. Science is not a logical system where errors get corrected. It's a political process whereby theories are pre-judged in their incorrect nascent state, then dismissed for ever when found incorrect. If someone else later corrects all the errors, that person is wrong by being "associated", much like friends of people who turned out to have been student communist party members were guilty of being Stalin's friends, in McCarthy's eyes. This story is of course usually turned around to a very different conclusion: the fact that McCarthy was wrong in shooting everyone who had ever heard of Marx was used to try to "defend" Stalin's evil, a kind of one upmanship or reversal of McCarthy's trick. Anyone criticising Stalin was then compared to McCarthy, and their message unheeded. Science is more political than normal politics, because it pretends that there is no political element and uses this deception to "disprove" the need for democratic debate, etc. Science is the worst sort of politics, the sort which pretends it's always justified by good intentions, no matter the consequences, exactly like Stalinism and Nazism, but Godwin help you if you say it.)