Sunday, March 04, 2007

Subject: Re: My Cal Tech M Theory Talk - Draft 3 March 16-17 2007
Date: March 5, 2007 3:12:09 PM PST

This is a more popular version. CIT version will be edited down.
On Mar 4, 2007, at 5:13 PM, Jack Sarfatti wrote:

I challenge Witten's M Theory with the Destiny M Theory! ;-)
On Mar 3, 2007, at 6:36 PM, Jack Sarfatti wrote:

Actually I will not have all this intro-discussion in the Cal Tech talk, which I think is 10 minutes and all those guys know about local gauge invariance and something about spontaneous symmetry breaking from inflation cosmology.

1. The principle of local gauge invariance together with spontaneous breakdown of vacuum/ground state symmetry is the most successful battle-tested technique in physics today.

Localizing a rigid global symmetry of the initial action of some source field (e.g. lepton and quark spinors) is a deep expression of the generalized relativity principle of no action without direct reaction,i.e., no absolute arenas in the sense of Rovelli's discussion of Leibniz vs Newton in his "Quantum Gravity" on-line book.

2. What is local gauge invariance?

Start with the nonlocal Lagrange method used by Feynman in his path integral amplitude formulation of micro-quantum theory in contrast to the fixed time Hamiltonian wave function method. All physical systems are controlled by their "classical dynamical action S." S is an integral over a finite region of space-time, indeed in some cases it can include the entire history of the universe from Alpha Point inflation to hot big bang to us to the dark energy deSitter "thermal future horizon" Omega Point worth 10^122 Bekenstein BITS of "entropy." Indeed, it may be that this future world hologram screen sends advanced waves back from the future to the initial Planck area scaled seeds that inflated to our own "pocket universe" in the megaverse on the populated cosmic landscape (Lenny Susskind) of eternal chaotic inflation.

Self-Creating Pocket Universe
The colored dashes are advanced waves from the future dark energy deSitter horizon of huge area to the tiny area seeds of inflation in the false vacuum of the Higgs potential.

Tiny area early seed universe (white ball on top of the hill) in unstable false vacuum pre-inflation.

The white golf ball is the inflation seed proto-universe poised unstably in the false vacuum. A random quantum fluctuation sends it rolling down the viscous molasses slope causing the tiny proto-universe to inflate by at least 10^60.
Much larger area-entropy by 10^60 early universe post-inflation.
Damping of ball's Higgs motion up and down slope provides heat for hot Big Bang.
Random motion around the rim is Goldstone phase noise.

The jiggling Higgs motion up and down the slope is, via A. Linde's viscosity, transformed into the tremendous heat of the big bang. What happens next is described vividly by Steven Weinberg in "The First Three Minutes."

The actual potential may have a rim that is not S1 as pictured, but S8 that we cannot visualize directly. S8 gives curvature + torsion with the 6D Gennady Shipov "oriented point" as the proto Calabi-Yau space giving different positions on Susskind's cosmic landscape. With signal nonlocality violating the no-cloning-a-quantum theorem we can detect the entire cosmic landscape of parallel pocket universes in principle here-now because linearity, unitarity & Born probability all break down in the "More is different" emergence of the smooth c-number geometrodynamic macro-quantum field. The local nonlinear non-unitary Landau-Ginburg equation (for emergent complexity inherent in the post-inflation vacuum order parameters) replaces the nonlocal linear unitary Schrodinger equation for the large-scale structure of the string theory megaverse made Popper testable through signal nonlocality as in telepathic remote viewing used allegedly succesfully by the US military intelligence.

Facts come from unexpected corners. The true skeptic ignores facts like unexplained UFOS and alleged floating stargate portals at the Bigelow Utah Ranch at his peril. Note that multi-millionaire Robert Bigelow has a personal satellite orbiting Earth and he has funded serious UFO research using retired military intelligence personnel and PhD physicists.

This in a nutshell is the Stanford Duet, lyric of A. Linde & L. Susskind.

You can also wear the wire mesh on your head to gather orgone energy! :-)

Symmetry is a core concept of physics.

Symmetry is the stillness in the movement.

The fixed point.

The Center of the Cyclone.

Symmetry is the set of invariants that do not change relative to a "group" of transformations of frames of reference, i.e. observers looking at the same objective reality processes from different perspectives.

Global symmetry is "rigid" "absolute" it means that exactly the same changes are made over the entire universe. Localizing the symmetry is the Triumph of Our Freedom of The Will. Note I am listening to Maestro Furioso, Arturo Toscanni, overture Tristan & Isolde (1865).

All local observers are free to do as they wilt! This induces the compensating gauge potentials also called the connection fields for parallel transport of tensor and spinor structures along the paths of the destiny matrix (world lines or "timelines" if you like).

Examples of the technique.

Standard model of leptons, quarks, gauge force bosons of electro-weak (beta-radioactive) and strong sub-nuclear forces of the solar inferno.

We have three globally rigid internal symmetry groups of extra dimensions.

The single-parameter group U(1) is generated by the electric charge operating rigidly, the same phase shift over the entire universe of the lepton and quark spinor fields. Spinors are a special kind of "qubit" of the world quantum computer having to do with invariant properties of light in Einstein's 1905 special theory of relativity. Localizing this rigid U(1) "unitary symmetry group" gives the compensating gauge potential called the "vector potential" 1-form. Its Cartan exterior differential is

F(EM) = dA(EM)

is the Maxwell field 2-form that is the curvature of the connection 1-form in the internal space. You can think of it as a tiny unit circle at each point of space and time. Indeed, as a tiny clock with only one hand.
Above is global rigid gauge or phase invariance of the source fields, i.e., same clock hand position shift everywhere-when.
The effect of local gauging. ;-) (Salvador Dali)

The Triumph of Freedom of the Will, is that you can locally set the hand of the clock anyway you like on your transient timeline from birth to death. Get the picture? The quantum of the A(EM) 1-form compensating field is the photon.

We now have a larger dynamical global action than we started with. It is invariant under this large group of localized U(1) transformations in which all of you Angels, Humans & Demons in the The Great Chain of Being and Becoming are free to move the one hand on your local clocks willy nilly as the spirit moves you. ;-)

The next group is SU(2) with 3 weak charges generating it operating on both quarks and leptons, corresponding to three angles of rotation in internal space. You might try to think of this in analogy with U(1) as a tiny unit 3-D spherical surface embedded in a 4 real dimensional space explicated out of 2 complex dimensions. (However, see below.) There are now 3 Yang-Mills connection field 1-forms A^a(Weak), a = 1,2,3 whose quanta when combined with A(EM) give the photon, two charged weak currents and one neutral weak current.

But now

F(Weak)^a = dA^a(Weak) + Cbc^aA^b/\A^c

The weak bosons are charged and self-interact. This is unlike the photon that does not carry electric charge but connects electric charges.

Cbc^a are structure constants of the closed Lie algebra of commutators of the charges of the internal symmetry Yang-Mills Lie group.

The general rule for SU(N) is N^2 - 1 "charge" generators of the continuous Lie group that form a Lie algebra whose "products" are "commutators."

This is not the whole story. We also have "chirality". The universe is not mirror symmetric. Left-handed leptons and quark spinors behave very differently from right-handed leptons and quarks.

Furthermore here we need spontaneous breakdown of symmetry, i.e. Higgs mechanism to give the weak gauge bosons a mass ~ 100 Gev. The nucleon (proton & neutron mass ~ 1 Gev, electron mass ~ 1/2000 of that roughly).

Spontaneous symmetry breaking is the emergence of new orders of complexity of matter, what P.W. Anderson calls "More is different." It's important in the condensed matter physics of metals, ferromagnets, lasers, superfluids, superconductors, 2D anyon physics of the fraction quantum Hall effect, and all sorts of nano-tech phenomena and applications like LCD & plasma screens for HDTV.

In fact the theory of the origin of inertia (rest masses) of Haisch and Puthoff et-al is wrong in the view of ALL elementary particle physicists who believe in this standard model Higgs-Goldstone mechanism that is battle-tested though it does have a lot of fudge factors - nevertheless, it explains very accurately and makes correct precise predictions that the Haisch-Puthoff theory cannot even formulate. Note that looking for the actual Higgs quanta on-mass-shell is not directly relevant to the Higgs vacuum condensate which is a macro-quantum coherent Glauber (possibly squeezed) state of virtual off-mass-shell Higgs intensity and Goldstone phase quanta.

Next we have SU(3) in three complex dimensions. N^2 - 1 = 9 - 1 = 8 strong charges that operate on the quarks, but not the leptons. You can think of an abstract 8D unit spherical surface embedded in a 9 real-D internal space. How that maps to space of 3 complex dimensions is not obvious until you think of matrices.

SU(3) consists of 3x3 matrices with complex matrix elements and one constraint (unit determinant). So you have 8 independent complex matrix elements (each one like a little U(1) S1 unit circle). Similarly, SU(2) consists of 2x2 complex matrices hence 3 little unit U(1) circles. You can also try to think of these as "tori"

S1xS1xS1 3-torus, also S2xS1 as well as S3.

In any case we now have 8 connection 1-forms for the strong sub-nuclear force


a = 1,2,3, ... 8

The scheme is similar to the above weak fields.

Now finally we come to gravity and torsion fields!

All of the above symmetries are internal symmetries. Also they are not universal. Leptons do not have strong charges for example.

Einstein's special relativity is universal - all fields "carry" special relativity charges of total energy, total linear momentum, total rotational (angular momentum) and Boosts between inertial observers moving uniformly relative to each other.

The number of 4D space-time charges is

1 + 3 + 3 + 3 = 10

This is the RIGID 10-parameter Poincare group of 1905 special relativity.

Einstein did not think this way in 1905 nor in 1915 because Emmy Nother did her famous theorem about all this in 1915 the same time of Einstein's "Kampf" to get general relativity. We are looking backward from the modern POV.

Take the 1 + 3 of energy and linear momentum, that's the 4-parameter translation group T4. Localize it for all non-gravity field actions. The compensating gauge potentials are the curved pieces A^a of the Einstein-Cartan tetrad 1-forms e^a

e^a = I^a + A^a

a = 1,2,3,4

A^a is the intrinsic objective WARP "gravity field" (Rovelli's book on Quantum Gravity).

I^a is the curvilinear (accelerated frame) tetrad of globally flat special relativity.

In this 1915 limit, the torsion field is zero, there is only curvature.

This means

T^a = de^a + W(T4)^ab/\e^b = 0 = vanishing torsion field 2-form

W(T4)^a^b is the non-dynamical curvature-only piece of the spin connection to parallel transport spinors. Einstein's Levi-Civita connection is related to it in a complex way that is too much detail for now.

The curvature field of gravity is the 2-form

R^a^b = dW^a^b + W^ac/\W^cb

Note the analogy to the Yang-Mills fields

F^a = dA^a + C^abcA^b/\A^c

A^a is not the direct potential in Einstein's 1915 theory, it determines W^a^b with the constraints of zero torsion and something called metricity.

Einstein's key local invariant is the differential squared line element

ds^2 = e^aea = (Flat Metric)abe^ae^b

= (Curvilinear Metric)uvdx^udx^v

The next step is to locallize the 3 + 3 Lorentz group to get the torsion field spin connection 1-form S^a^b

Then we derive A^a and S^a^b

Where the non-vanishing torsion field 2-form is

T^a = S^ab/\e^b

Finally we get A^a & S^a^b from the coherent vacuum Goldstone phases of the post-inflation Higgs field controlling both dark energy and dark matter.

That's the idea that A^a & S^a^b emerge like the superflow 1-form field in liquid helium 4 at low temperature.

Imagine two sets of 4 Cartan scalar 0-forms that I will call "Goldstone phases."

Theta^a & Phi^a

a = 0,1,2,3

I define the GCT scalar local invariant non-closed 1-form M matrix

M^a^b = (Theta)^a/\d(Phi)^b - d(Theta)^a/\(Phi)^b

I define the localized 4-parameter translation subgroup T4 intrinsic curvature piece of the Einstein-Cartan tetrads as the diagonal

A(T4)^a = M^a^a = (Theta)^a/\d(Phi)^a - d(Theta)^a/\(Phi)^a

e^a = I^a + A(T4)^a

I^a is the globally flat set of tetrad 1-form fields when T4 is globally rigid.

My M-Theory equation

A(T4)^a = M^a^a = (Theta)^a/\d(Phi)^a - d(Theta)^a/\(Phi)^a

was motivated by the much simpler superfluid helium velocity field equation

v = (h/m)dTheta

v is the velocity 1-from in Galilean relativity 3D space.

(h/m) is the quantum of circulation-vorticity.

Theta is the single Goldstone phase of the helium 4 ground state order parameter.

The non-trivial first order homotopy gives vortex core string stable topological defects.

I need a dimensionless order parameter. The obvious choice is the number of Bekenstein BITs (or rather its inverse square root). That is

e^a = I^a + (Lp*^2/\zpf)^1/2A^a

Where /\zpf is the scale-dependent local dark energy/matter density.

Lp*^2 = hG*/c^3

G* is the renormalization group flowing scale-dependent gravity coupling.

Note there is no gravity when

/\zpf = 0

h = 0

c -> infinity

(Lp*^2/\zpf)^1/2 is the 4D SUPERSOLID analog to SUPERFLUID HELIUM h/m

The curved A^a(T4) with the non-vanishing 2-form

F(T4)^a = dA(T4)^a = 2d(Theta)^a/\d(Phi)^a

With vanishing 3-form

dF(T4)^a = d^2A(T4)^a = 0

Note the Dirac substratum Maxwellian field structure

d*F(T4)^a = d*dA(T4)^a = J(T4)^a source current density

dJ(T4)^a = 0

local conservation of substratum current density.

The above is the substratum for 1915 GR i.e. curvature without torsion

T(T4)^a) = de^a + S(T4)^ac/\e^a = 0

S(T4)^ac are the curvature-only zero torsion non-dynamical spin connection 1-forms determined by metricity plus zero torsion from keeping the 6-parameter Lorentz subgroup SO(1,3) globally rigid.

The Riemann-Christoffel curvature 2-form is

R(T4)^a^b = dS(T4)^a^b + S(T4)^ac/\S(T4)^c^b

The Einstein-Hilbert action density with cosmological constant /\zpf is the 0-form local frame-invariant scalar under GCTs and LLTs.

&S(E-H)/&x^4 = *[R(T4)^a^b/\e^c/\e^d + /\zpfe^a/\e^b/\e^c/\e^d]

* is the Hodge dual i.e. contract with completely antisymmetric tensor in 4D
* = {abcd}

Next to get the dynamically independent torsion field localize SO(1,3).

T^a(1,3) ~ S^(1,3)/\e^a =/= 0

The new spin connection 1-form to define the extended curvature 2-form is therefore

S^a^b(10) = S(T4)^a^b + S^(1,3)^a^b

where, in terms of the 8 0-form Goldstone phases, we take the antisymmetrized part of the matrix M^a^b

S^a^b(1,3) = M^[a,b] = - S^b^a

The additional 6 angular degrees of freedom of Gennady Shipov's "oriented point" lumped parameter description of the extended M-matrix object is a proto Calabi-Yau space

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