Herman Weyl's great paper of 1929 on gauge theory

"I am as dissatisfied as you are with distant parallelism and your
proposal to let the tetrads rotate independently at different space-time
points is a true solution." Pauli to Weyl (1929).

"IT FROM BIT" John Archibald Wheeler

e.g. Goldstone phases are macro-quantum BIT fields of physical information.

v(superfluid Helium 4) = (h/m)dTheta 1-form O(2) symmetry

A^a(warped tetrad) = M^a^a = dPhi^a/\Theta^a - Phi^a/\dTheta^a 1-form
O(9) symmetry - gravitation

F^a = dA^a = -2dPhi^a/\dTheta^a 2-form

S^a^b = M^[a,b] - spin connection 1-form

A^a & S^a^b form the noncompact Poincare group Lie Algebra

On the conversion of Weyl's 1918 aborted scale factor on the uncharged
metric IT field to a quantum phase factor on the electrically charged
BIT pilot field:

"One can summarize Einstein's objection to Weyl's (1918) theory as the
statement that, according to atomic spectroscopy, there is no
Bohm-Aharonov effect for gravitation." p. 85.

Metricity in GR is like unitarity in QM, i.e. inner products are
invariants of the evolution i.e. parallel transport whether in spacetime
or Hilbert space. Nonmetricity, therefore, is like "collapse of the
state" in von Neumann quantum measurement theory.

On May 22, 2007, at 7:42 PM, Jack Sarfatti wrote:

Weyl in 1918 made the mistake of applying the gauge principle to
Einstein's 2nd rank symmetric metric tensor. What he actually found was
a non-metricity vector field in which the magnitudes of vectors parallel
transported along world lines depends on the world line. This would be a
memory - a hysteresis non-integrability anholonomy not observed in the
electromagnetic world where the spectral lines of atoms in the stars are
recognizably the same once the gravity red shifts are subtracted out.
Einstein pointed this out to Weyl back then. Slowly (Fock, Schrodinger,
London ...) it was recognized that this path dependent electrodynamic
(Bohm-Aharonov) non-integrability applied to the deBroglie pilot quantum
waves not to the Einstein geometrodynamical field.

What Weyl really did in 1918 was to find the non-metricity piece of the
connection beyond Einstein's 1916 metric connection. Later Cartan found
the torsion field antisymmetric piece to the possible connection fields
for parallel transport.

i.e.

Connection = Einstein metric connection + non-metricity vector field
connection + antisymmetric (con) torsion

metric connection ~ disclination rotation defects in vectors around
closed self-generated infinitesimal parallelograms

(con) torsion connection ~ dislocation defects in which the basic
self-generated parallelograms has a gap to 2nd order of smallness (e.g.
Penrose "The Road to Reality").

Weyl's 1918 non-metricity vector field means that the lengths of vectors
are different around the closed loops i.e. disastrous multi-valuedness -
a kind of Riemann surface fiber? In any case Weyl's 1918 vector field is
not the EM 4-potential A 1-form but is some alien kind of
geometrodynamic field whose flux field tensor 2-form F = dA is zero in
our ordinary spacetime without topological defects giving non-vanishing
deRham integrals of F through 2D surfaces even when A is closed. 1D
string line defects involve surfaces with boundaries whose non-bounding
loop integrals of A are quantized "winding numbers" (1st nontrivial
homotopy) when the A -form derives from a single coherent Goldstone
phase of two real Higgs fields. If there are three real Higgs fields
with two independent Goldstone phases then A is not a closed 1-form the
non-bounding 2D surface is closed without boundary and we have interior
point "monopole defects" with quantized radial fluxes given by "wrapping
numbers" (2nd non-trivial homotopy). What would be the physical effects
of these non-metricity fluxes? Are they in the interior of the leptons
and quarks as Bohm hidden variables that appear as points as the
scattering probe magnification increases because of extreme
micro-warping. The effective geometrodynamic coupling constant
renormalization group flow is to larger values at the 1 fermi scale - it
can then get smaller in both UV and IR directions with peaks between
10^-13 - 10^-16 cm.

L.O'R wrote (Ch 5):"(Hermann Weyl) had always been convinced that there
was a close analogy between gravitation and electromagnetism ... in 1929
he was able to formulate the analogies ... by means of the tetrad
formalism ... Weyl's formulation was complete and went beyond all
previous ideas in proposing that electromagnetism be derived from the
gauge principle ... that ... has turned out to be a powerful principle
for deriving the nuclear interactions and to be the common principle
underlying all the known fundamental interactions. ... the six sections
of the paper ... two-component spinor theory in Minkowski space ...
parity ("chirality" screw helical mirror reflection symmetry now known
violated by quarks and leptons, but not known in 1929 of course) and
time reversal invariance ... tetrads (AKA vierbeins) ... spinor theory
in curved spaces ... Noether conservation laws ... spin connection ...
invariant action ... (local) energy-momentum conservation laws from
invariance with respect to both general coordinate transformations and
Lorentz transformations of the tetrad (Noether's theorem) ... He then
recast gravitational theory in the tetrad formalism with a view to
exhibiting the analogies between it and electromagnetism. In the final
section, he came to what he considered the most fundamental part of the
paper, namely, the derivation of electromagnetic theory from the gauge
principle."

All of fundamental theoretical physics today depends on only two
battle-tested grand organizing ideas, and that includes the extra
dimensions of string theory bye the bye, Witten need look no further IMHO.

I. The gauge principle

"AKA" here means "also known as" in a rough qualitative sense with minor
differences of detail

II. "More is different" AKA "hidden symmetry" AKA "spontaneous breakdown
of symmetry" AKA "ODLRO" AKS "macro-quantum coherence" AKA
"Bose-Einstein condensation" AKA "macroscopic eigenvalues of correlation
functions" AKA "collapse of phase space volume" AKA effective order
parameters including nonlocal topological order of 2D Anyons in FQHE
(Fractional Hall effect) as well as the more familiar local order of the
Landau-Ginzburg phenomenology with the O(N) Mexican Hat effective low
energy potentials for macroscopic phase transitions from quantum to
misnamed "classical."

to be continued.

On May 20, 2007, at 1:43 PM, Jack Sarfatti wrote:

Commentary 1 (Draft 2 expanded)

This is a very useful little book by Lochlainn O' Raifaeartaigh in
Dublin published by Princeton 1997. It has seminal papers by Weyl,
Klein, Fock, Schrodinger, London & Pauli in English from the original
German.

The two great battle-tested principles of basic theoretical physics are

1. The local gauge principle, i.e. "relativity" in the most general
sense of no action without reaction, no passive absolute Newtonian
arenas, Leibniz's relationism of Bohm's "dialogue" not monologue.

2. The spontaneous breaking (or "hiding" Sidney Coleman, Erice Lectures
1970's) of continuous symmetries in the ground state of real on mass
shell quanta and also in the vacuum of virtual zero point quanta. AKA
"More is different" (P.W. Anderson) "Emergent complexity." "ODLRO"
(Onsager & Oliver Penrose), "Goldstone theorem" "Macroquantum states",
"Glauber coherent & squeezed states" et-al. The idea of "hidden
symmetry" is that whilst the dynamical classical action in the Feynman
path integral alternative to second quantization is invariant under the
symmetry group G, the vacuum (ground state) is not. One familiar example
is a ferromagnet near absolute zero with a Galilean relativity 3-vector
order parameter "magnetization" in a coherent domain. This is three real
"Higgs fields" with two continuous 2pi periodic "Goldstone phases"
defining the S2 vacuum manifold of minima in the Landau-Ginzburg
effective quartic renormalizable interaction Higgs-type field
Lagrangian. Non-trivial 2nd order homotopy would give point "monopole"
defects not actually observed in real ferromagnetic phases. What is
observed are wall domain defects with a S0 vacuum manifold without any
continuous Goldstone phase at all corresponding to another broken
symmetry from three real Higgs fields to only one effective Higgs field
that vanishes on the domain wall. That is S3 broken to S1 - curious.

Emergence of "The Nine"

My original parsimonious theory explains the origin of gravity &
inertia, torsion (i.e. emergent "tetrad" local observer/detector frames
and "spinor" connections as macroquantum coherent "surface" world
hologram Goldstone phase modulations from an "M-Matrix" of non-closed
1-forms made from two Lorentz 4-vectors of eight 0-form continuous
periodic Goldstone phases Theta^b & Phi^a from nine post-inflation real
Higgs scalar vacuum ODLRO fields.

a,b = 0,1,2,3 are Lorentz group indices

M^a^b = Phi^a/\dTheta^b - dPhi^a/\Theta^b

dM^a^b = 2dPhi^a/\dTheta^b

A^a = M^a^a (diagonal elements of the Matrix)

Einstein-Cartan tetrad 1-forms are e^a = I^a + @A^a are spin 1
Yang-Mills type Lorentz group VECTOR renormalizable quantum translation
group T4 localized gauge fields.

@ = (Lp^2/\zpf)^1/3 dimensionless "world hologram" self-gravity coupling

I^a are the global Minkowski tetrad frames that we have when either

G - 0 gravity coupling switched off

h - 0 quantum action switched off

c - infinity, i.e. no causal retardation and/or advanced retro-causation

/\zpf - 0

i.e. no gravity when supersymmetry is perfect! /\zpf in the IR limit is
Lenny Susskind's cosmic landscape parameter ~ (area of future deSitter
horizon of pocket Hubble bubble universe in the "megaverse" of eternal
chaotic inflation.

Supersymmetry is square root of T4, i.e. anticommutator of
supersymmetries is T4.

"Spinor" connection 1-forms are (gets dynamical degrees of freedom when
total 10-parameter Poincare group P10 = T4*O(1,3) is locally gauged
(Utiyama, Kibble et-al 1961)

S^a^b = - S^b^a = M^[a,b]

Torsion field 2-forms are

T^a = de^a + S^ace^c

Curvature field 2-forms are

R^a^b = dS^a^b + S^acS^cb

Einstein-Hilbert (E-H) "classical" Lagrangian density is the 0-form

L(E-H) ~ {a,b,c,d}R^a^b/\e^c/\e^d

ds^2 = guvdx^udx^v = e^aea = I^aIa + @(I^aAa + A^aIa) + @^2A^aAa

Quantum noise corrections in second quantized formalism with
macro-quantum vacuum |0 condensate ODLRO is

A^a = 0|A^a|0 + &A^a

&A^a is the quantum excitation spin 1 tetrad vector field annihilation
operator

Note that R^a^b is quadratic in A^a and its gradients, therefore L(E-H)
has up to quartic terms in the tetrads consistent with renormalization.

Note that

F^a = dA^a = dM^a^a = dPhi^a/\dTheta^a =/= 0

We have "Maxwell" equations

dF^a = 0

d*F^a = *J^a (warped tetrad current density)

d*J^a = 0 (local conservation of warped tetrad current density)

The Einstein geometrodynamic field ds^2 = e^aea is quadratic in the
tetrads, therefore obviously made from entangled Einstein-Rosen-Podolsky
(1935) pairs of spin 1 tetrad quanta, hence we have quantum
geometrodynamic corrections of spin 2 tensor gravitions, spin 1 vector
gravi-photons and spin 0 scalar gravitons.

3x3 = 5 + 3 + 1

i.e.

1 + 1 = 2, 1, 0

for the irreducible spin/angular momentum representations of O(3)
subgroup of O(1,3).

This does not affect the macro-quantum c-number ODLRO sector of the
theory in most cases.

Dark energy and dark matter are both very simply virtual quanta inside
the total physical vacuum of positive and negative zero point
fluctuation energy density respectively.

Einstein showed that for an isotropic Ricci source in 3+1 spacetime, the
space-time bending power of the source is

(G/c^2)(energy density of source)(1 + 3w)

Lorentz invariance and general coordinate invariance imply

w = -1

for isotropic ZPF distributions of all quantum fields of all spins.

Bosons have positive ZPF energy density

Fermions have negative ZPF energy density.

Non-isotropic boundary conditions e.g. Casimir effect will shift the ZPF
w, but as long as w - 1/3 i.e. quintessent field region then

positive ZPF energy density - antigravity universal repulsion blue
shift (dark energy)

negative ZPF energy density - gravity universal attraction red shift
(clumping dark matter) - this is indistinguishable from w = 0
conventional CDM for distant observers looking at gravity lensing for
example.

Note when w - 1 that is "phantom energy" BIG RIP

I predict that the LHC will NOT find dark matter particles on mass shell
as a matter of basic principle. Looking for dark matter inside the LHC
is like looking for the motion of the Earth through the mechanical
Victorian aether with a Michelson-Morley interferometer. Null results
then and in the future I do declare. All of this is only based on 1 & 2
above. The book is mostly about the early history of 1 and how it
affected C.N. Yang as a graduate student. Robert Shaw's little-known
important independent work is also discussed.

"The role of geometry in physics has always been central. But ... it was
passive, providing only the stage on which physics took place ... the
theory of special relativity in 1905, when it became clear that space
and time were not independent ... But the most profound and astonishing
entry of geometry into physics came with Einstein's theory of
gravitation in 1916, which showed that gravitation was nothing but the
curvature of four-dimensional space. ... George Bernard Shaw ... wrote
'Asked to explain why planets did not move in straight lines and run
straight out of the universe, Einstein replied that they do not do so
because space is not rectilinear but curvilinear.' ... due almost
entirely to the genius of Einstein, geometry graduated from being the
stage on which the drama of physics took place to being a major player
in the drama.

There remained however the electromagnetic and nuclear forces, and the
geometrization of gravity raised the question as to whether these other
fundamental forces were 'true' forces operating in curved space of
gravitational theory or whether they also were part of the geometry.
This question has still not been fully answered. ... these forces and
gravitation have a common geometrical structure. This is ... the gauge
structure."

to be continued

Jack Sarfatti

"If we knew what it was we were doing, it would not be called research,
would it?"
- Albert Einstein
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