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More on the Higgs-Goldstone origin of gravity and inertia



 
 
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Old August 23rd 05 posted to sci.physics.relativity,sci.physics.particle,sci.astro,sci.math,sci.physics
Jack Sarfatti
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Posts: 2,218
Default More on the Higgs-Goldstone origin of gravity and inertia


"Still haven't found Higgs after 20 years, so I don't think it exists.
The LHC is coming on line in short time, so I think this will be the
definitive end of the line for a Higgs boson search. If it isn't found
in the LHC, then quantum field theorists will be forced to confront
other models for inertia and mass that have nothing to do with the
Standard Model formulation." Eric Davis


What Eric Davis wrote above is wrong. He does not understand the Higgs
mechanism origin of inertia at all! It does not depend at all on the
finding of a real Higgs particle on-mass-shell. The Higgs-Goldstone
origin of inertia is strictly a virtual quantum effect inside the
coherent vacuum with order parameter phi. See for example the recent
SLAC Summer School Lectures

http://www-conf.slac.stanford.edu/ss...s1/default.htm

http://www-conf.slac.stanford.edu/ss...s2/default.htm

especially

http://www-conf.slac.stanford.edu/ss...age_10_jpg.htm

For the Yukawa coupling formulae for the inertia of the quarks and
leptons. This only depends on the charge neutral component magnitude of
the order parameter |phi| = v. Eric simply is speaking off the top of
his head. The mass of the Higgs is in the small vibrations around v! It
has nothing to do directly with the equilibrium value v about which the
small vibrations occur.



Consider a harmonic oscillator for the small linear Higgs vibrations up
the slope of the trough.

d^2(x - v)/dt^2 + f^2(x - v) = 0

For small linear oscillations around the "equilibrium" v from SSB in the
vacuum probably from the SU(2)hypercharge group.

The potential is

U = (k/2)(x - v)^2 = (k/2)(x^2 + v^2 - 2vx)

dU/dx = k(x - v)

d^2U/dx^2|(x=v) = k 0 (for stability, i.e. Goldstone phase rigidity)

That is, k is the curvature at the bottom of the well. There is no
necessary connection of k to v because v is determined from

dU/dx = 0

The choice of first and second derivatives is contingent. There is an
additional f parameter.


The mass m of the on-mass shell Higgs here is from

f^2 = k/m

It is essentially independent of v!

The Yukawa coupling for the inertia of the quarks and leptons in the
standard model does not at all depend on the actual rest mass of the
on-mass-shell Higgs particle.

Where does v come from? It comes from the entirely different equation (I
do U(1) SSB for math simplicity in a toy model)

V(psi) = a|psi|^2 + b|psi|^4

dV/d|psi| = 0

2a|psi| + 4b|psi|^3 = 0

a + 2b|psi|^2 = 0

i.e.

a + 2bv^2 = 0

v^2 = - a/2b 0 is SSB

Note the Yukawa coupling formula for the inertia of the quarks and the
leptons in

http://www-conf.slac.stanford.edu/ss...age_10_jpg.htm

has fermion inertia ~ v

The boson inertia is in

http://www-conf.slac.stanford.edu/ss...age_09_jpg.htm



Eric Davis has raised a RED HERRING based on his ignorance of the
standard model.


Therefore at the trough of the Mexican Hat order parameter potential

http://www-conf.slac.stanford.edu/ss...age_07_jpg.htm


http://www-conf.slac.stanford.edu/ss...age_08_jpg.htm

Think of x as the order parameter

U ~ (k/2)(x - v)^2

Note that a = k/2 ~ d^2U/d|phi|^2 at the equilibrium trough x = v

v ~ -(d^2U/dx^2)/2b

mass of the Higgs is

m = k/f^2 = 2(d^2U/dx^2)/f^2

But f is a free parameter coming from the coefficient of

(dx/dt)^2

in the inhomogeneous part of the Hamiltonian density i.e. COHERENCE
LENGTH of the order parameter has no necessary connection to the shape
of the Mexican Hat Potential for vacuum SSB. The mass of the Higgs
depends on this coherence length in addition to the curvature at the
bottom of the Mexican Hat SSB vacuum ODLRO potential.

H = M(dx/dt)^2 + (k/2)(x - v)^2

This M is NOT m the mass of the Higgs.

And in the field theory case, that we need to use, the kinetic energy
density Landau-Ginzburg term is like

nuv(phi,u)(phi*^,v) + a|phi|^2 + b|phi|^4

nuv is the flat metric tensor, , is the flat partial derivative

for the pre -- post inflation vacuum phase transition creating our
universe in the multiverse.

B = Lpd(argphi)

gives the emergent guv(curved spacetime).

This is the Decoding of The Cipher of Genesis.

Eric Davis's remark (and James Woodward's) about the Higgs mechanism not
being the origin of both gravity and inertia is like the Haisch ZPF and
the Puthoff PV models "not even wrong."






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