On Oct 30, 2007, at 10:47 AM, Paul Zielinski wrote:

I'm trying to understand tetrads. I'm particularly interested in Rovelli's and others' explanations of the relationship between the Einstein-Cartan tetrad model and the 1916 metric field model for GR.

Good! Remember my basic idea here that seems to be completely original compared to Visser's, Chapline's, Volovik's et-al approaches. The key idea is in superfluid helium

v = (h/m)(dTheta)

v = coherent velocity field (here a closed 1-form in 3D Euclidean space)

Theta = single macro-quantum ground state ODLRO Goldstone phase

PSI = (Higgs Field)e^i(Goldstone Phase)

in this simplest of "More is different" emergence from Sid Coleman's "hidden symmetry" (goes back to Brout-Englert - PW Anderson). PS Robert Brout was one of my tutors at Cornell (in group theory) I saw him again in Brussels when Jagdish Mehra invited me to Prigogine's institute when I was with Abdus Salam in Trieste 1973-4. That's when I suggested

Hadronic Resonance Spin = (1Gev)^-2(Energy)^2 + Jo

as a strong short-range gravity G* - 10^40G(Newton) as a kind of Kerr "black hole" - decay by Hawking radiation. Also wrote about making miniblack holes in accelerators & baby universes in ICTP internal memos 1973-4. Also did a paper on Dirac Eq in curved spacetime David Finkelstein I think published it? - or maybe it was Foundations in Physics? I forget which.

in any case the vorticity vanishes locally:

dv = 0 means irrotational curl-free flow (2-form)

nevertheless first homotopy group is non trivial for stable string (line vortex) quantized circulation defects where the two real Higgs scalars making single-valued complex order parameter vanish, so that THETA is undefined on the string vortex (healing coherence length with string at center - random zero point energy self-trapped inside the core!).

Effective integral of dv on singular area surrounded by closed non-bounding cycle enclosing a stable string defect i.e. circulation integral of v = N(h/m), N = 0, +-1, +-2 .... first homotopy group

OK for the world crystal lattice on 3D spacelike slice we have 2 Goldstone phases THETA & PHI with three real Higgs fields giving stable point "monopole defects" of the EMERGENT GeoMetroDynamic GMD field.

LENGTH 1-FORM is not closed

L = Lp[(dTHETA)(PHI) - (THETA)(dPhi)]

Define closed AREA 2-FORM A

A = LpdL ~ 2Lp^2(dTHETA)/\(dPHI)

dA = 0 is WORLD HOLOGRAPHY of

Volume without volume.

Integral of A over closed surrounding non-bounding 2-surface enclosing N stable elementary GMD monopole point defects is ~ NLp^2 i.e. Bekenstein area quantization from non trivial 2nd homotopy group.

N area quanta (HOLOGRAM) project to N interior volume-without-volume quanta (HOLOGRAM IMAGE)

consistent with Jack Ng's

&L = (Lp^2L)^1/3 = N^1/6Lp

&L is lattice spacing of Kleinert World Crystal Lattice = quantum foam bubble size

L is scale of a null horizon

1-1 map of horizon area bit quanta to volume-without-volume bit quanta = HOLOGRAM PRINCIPLE

OK now to TETRADS

THETA^2 = (THETA)^a(THETA)a

PHI^2 = (PHI)^b(PHI)b

e^a = I^a + @A^a = Einstein-Cartan emergent gravity tetrad field

@ = dimensionless string coupling field - environmentally dependent probability to cut and fuse strings.

I had in one model

@ = N^-1/3

ranges from 0 to 1 like a probability N = 1 is min out to infinity.

ds^2 = guvdx^udx^v = e^aea

A^a = M^a^a

M^a^b = (dTHETA)^a/\(PHI)^b - (THETA)^a/\(dPhi)^b

Spin connection is

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

This requires 9 real Higgs scalars. Stable defects needs one space dimension for each Higgs fields.
This give branes with 6 extra space dimensions (e.g. Shipov's oriented point -> Calabi-Yau).
Basically one HYPERSPACE dimension for each generator in the Lie algebra of the space-time symmetry group - this would be 15D for Conformal Penrose Twistor Group! 10 for Lorentz group.

Supersymmetry is trivial from Penrose map of nth rank Poincare group tensors to 2nth rank spinors.

This becomes TWISTORS for Conformal Group!

Z: "Considering this relationship with reference to both the inertial compensation and Einstein equivalence paradigms could be very illuminating."

I don't think so. "Inertial compensation" is a Newtonian idea making no sense at all in Einstein's GMD theory. It's an inappropriate concept taken out of its proper context. There is no loose string in Einstein's equivalence principle, which in fundamental for is SIMPLY

ds^2 = guv(LNIF)dx^udx^v = e^aea(LIF)

with universal minimal coupling to source matter fields Psi

Du = e^auPa + S^a^bPab

{Pa,Pab} is Lie algebra of Poincare( to Conformal Group)

in a matrix representation in which the source matter field components forms a basis

e.g. 2-component Weyl spinors

4-component Dirac spinors

spin 0 Poincare group scalars

spin 1 Poincare group vectors ...

Pa generate T4 (total momentum 4-vector)


On 10/29/07, Jack Sarfatti wrote:

The problems of interest are:
1. Dark energy
2. Dark matter
3. Multiverse? WAP as explanation for the arbitrary parameters of the standard models of both quarks, leptons & gauge bosons and the precision cosmology of the accelerating universe.
4. Extra dimensions?
5. Practical warp drive & time travel to past seen in UFOs - I take that as established fact for sake of argument at least.

What is the general rule to couple all massless matter source fields to the emergent GeoMetroDynamic field in the unstable pre-inflation "false vacuum" whose percolating bubbles populates the cosmic landscape in eternal chaotic inflation? The moment of inflation to a bubble is a vacuum ODLRO phase transition from micro to MACRO in which the Higgs-Goldstone fields "jell" so to speak converting false vacuum energy to the hot BIG BANG when the dark energy driven initial inflation stops.

http://www.acceleratingfuture.com/michael/blog/images/multiverse.jpg

Let G be RIGID the universal spacetime symmetry group that keeps the dynamical global actions of all massless matter micro-quantum fields invariant in the false vacuum. Its Lie algebra is {Pa,Pi}. For example
G = GL(4,R) (without adhoc branes, extra-dimensions - that sort of creep in later implicit in GR(4,R)) where each real Higgs field acts as an effective extra space dimension in order to keep topological defects stable (non trivial homotopy groups of same order as dimension of the spacetime symmetry Lie algebra).

Then the gauge covariant GDM field partial derivative (excluding internal Yang-Mills for now)

Du = [I^au + A^au(x)]Pa + A^iu(x)Pi

a = 0,1,2,3 & Pa generate RIGID T4

for Dirac spinors the Minkowski tetrads I^au are essentially Dirac gamma matrices

A^ua(x) are the compensating localized T4(x) gauge potentials (conjugate phases to the generators) with the 1916 GR zero torsion field constraint imposed on the tetrads, which are not allowed to have torsion gap dislocation defects in this limit. They still induce curvature disclination defects as in Rovelli's eq. (2.89)

The remaining i = 4 to ? are additional GMD fields, e.g. non-zero torsion field for i = 4,5,6,7,8,9 from localizing Lorentz group. So we have a kind of natural proto Calabi-Yau structure of quasi-extra dimensions here (Shipov's "oriented point").

i = 10,11,12,13 are GMD fields from conformal boosts

i = 15 is the GMD dilaton field.

On Oct 28, 2007, at 11:10 AM, Jack Sarfatti wrote:

Volovik correctly mentions that gravity as a Sakharov emergent macro-quantum field should not be re-quantized. There is a residual q-number part already in ODLRO density matrix theory that are off mass shell zero point fluctuations in the ground state and on mass shell normal fluid excited states at finite temperature.
On Oct 28, 2007, at 9:55 AM, Kay zum Felde wrote:


--- Jack Sarfatti wrote:

quite obviously the tetrads and the spin connections. The metric tensor and the Levi-Civita connection are
derivative composites not suitable for quantum gravity.

"That is a good hint for me to get closer in understanding the general aspects of your theory Jack. For me, this was quite a big puzzle in getting an idea what the challenges are in quantizing gravity. Quantizing the geometry in form of quantizing the metric or the Levi-Cibita connection is indeed quite weird now.

Thanks for explaining

Kay Zum Felde

>

On Oct 27, 2007, at 10:28 PM, Kay zum Felde wrote:
This a paper by G.E. Volovik. I think it is meant as
an overview or summary of some basic aspects of
Volovik’s work. Its title is “Fermi point scenario for
emergent gravity.” It is only 10 pages which makes it
suitable as a compact on hand collection of the
cornerstones of his ideas concerning emergent gravity.
I think this might be his intention.

He underlines the need of emergent gravity theories
being based on vacua composed of chiral left plus
right Weyl fermions. Then Gravity emerges with matter.
He presents the, in his view, 10 basic consequences of
the Fermi point scenario. As I believe, that what
calls Fermi point scenario is a collection of aspects
that yield topologically stable emergence of defects,
e.g. matter, together with gravity.

He presents two distinct appearances of gravity, that
depend the relation of Planck’s energy vs. Lorentz
energy. These are classical hydrodynamics and
Einstein’s General Relativity.

As far as I understood this, he shares, at least in
general, some or many aspects with Jack’s theory.

Kay

http://www.arxiv.org/abs/0709.1258


In a general way yes, but not in detail. I do not use Fermi surface in momentum space. However my false vacuum is Minkowski so that a Fermi surface for virtual massless spin 1/2 Weyl spinors makes some sense. I do not see that Volovik has ODLRO.

Chapline has ODLRO but has many obscure premises. Visser also has an approach. None of them have my precise model getting the tetrads A^a and spin connections S^a^b from the coherent Goldstone vacuum phase 0-forms THETA^a & PHI^b just like the superflow velocity in Helium 4 below Lambda temperature - but more algebraically complicated - not much

A^a = M^a^a

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

M^a^b = dTHETA^a/\PHI^b - THETA^a/\dPHI^b

e^a = I^a + @A^a

@ is the fundamental dimensionless self-gravity coupling

ds^2 = guv(LNIF)dx^udx^v = (Minkowski LIF)abe^ae^b

Locally gauged Poincare group covariant partial derivative on source matter fields is

Du = e^auPa + S^a^bPab on matter source field Psi

Ten generators of Poincare group {Pa,Pab} are in same matrix irrep that source field Psi forms a basis of.

In 1905 SR in a GIF on Dirac spinors

e^a to I^a

I^aPa = i(Dirac Gamma Matrix)u&/&x^u

i.e. free particle Dirac equation in 1905 SR in the GIF is

{I^aPa + mc}Psi = 0 globally flat space-time

EQUIVALENCE PRINCIPLE dictates MINIMAL COUPLING so that Dirac equation for a neutral fermion in curved & torsioned space time is simply for Einstein-Cartan "unified field theory" beyond 1916 GR

{(I^a + @A^a)Pa + S^a^bPab}Psi = 0

The mean (expectation) value of the COM of this fermion moves on a curved & torsioned "autoparallel".
(Ehrenfest's theorem)

Furthermore, even if you could do it, why bother? "Who ordered that?" It's a waste of time. It's not an interesting question. The ball is in your court to prove me wrong here, but I think you are wasting your time.

"It reduces the gravitational field of 1916 GR to an ordinary physical field that has a completely objective definition that can be described entirely in terms of generally covariant quantities, has no intrinsic dependence on any observer's world line, and is thus not fundamentally different, physically speaking, from the electromagnetic field." - Zielnski

You are reinventing the wheel. If it ain't broke don't fix it. You keep garbling different meanings of "gravitational field" as well as garbling Newton's and Einstein's different paradigms.

1861 Maxwell Electromagnetism is a local internal symmetry U1(x) gauge field theory for electrically charged matter field actions.

F = dA

A = compensating U(1) 1-form connection field.

A = Audx^u

It is not a U(1) tensor, A's U(1) transformation has a inhomogeneous term keeping

Pu = pu + (e/c)Au = canonical momentum that is U(1) invariant

where kinetic momentum SR 4-vector

pu = (h/i)&/&x^u

operates on charged source matter fields Psi

F = electromagnetic field 2-form, i.e. curvature in U1(x) fiber space

dF = 0

d*F = *J

d*J = 0

are the EM field equations and local current density conservation laws with EM field action density 0-form

~ *(F/\*F)/4 in 3D + 1

1916 GR Gravity is a UNIVERSAL local spacetime symmetry T4(x) for ALL matter field actions.

ONE EM F 2-form is replaced by TWO 2-forms

curvature R^a^b = dS^a^b + S^ac/\S^cb

torsion T^a = de^a + S^ac/\e^c

forced to zero as adhoc constraint.

Where spin-connection S^a^b is like EM field's A.

S^a^b is not a 6-parameter disclination Lorentz group tensor. Here Lorentz group is like U(1)

However, when you map S^a^b to Levi-Civita {^uvw} - complicated formula in Rovelli Ch 2 then Levi-Civita is like EM A with respect to local T4(x) group.

GR is a lot more complicated.

However

e^a = I^a + @A^a = e^audx^u

ea = Ia + @Aa = e^ua(&/&xu)

is like EM's canonical momentum

P = p + (e/c)A

i.e. more precisely

the local T4(x) covariant partial derivatives on all matter fields are

D^u = ea^uP^a = (I^ua + @A^ua)P^a

P^a is matrix rep of RIGID T4 of the source fields Psi

e.g. 2x2 matrix for Weyl spinor source fields etc.

4x4 for Dirac spinors

the localization is in the "phases" A^ua(x).

This universality is the REAL equivalence principle as minimal T4(x) gauge coupling of tetrads to matter fields.

The U(1) gauge transformations have no direct physical meaning, but the T4(x) do - they connect coincident LIFs with LNIFs!

On Oct 27, 2007, at 12:03 PM, Paul Zielinski wrote:

"OK, fine. But then how does your BEC model explain the relationship between the material sources and the the Higgs-Goldstone fields? Are not material sources sources of your Higgs-Goldstone fields?"

Jack replies:

Very simple. I have written the equations a jillion times. BTW much simpler than George Chapline's vacuum ODLRO theory. I have a more direct motivation from superfluid helium and I don't need supersymmetry, extra dimensions and all the stuff for which there is no evidence - let's see what LHC drags in, if they ever can engineer the magnets properly - like the optics error in the Hubble Space Telescope - multi-million dollar FUBARs. It's hard to find good help these days - the Decline and Fall of Western Science & Civilization and the regression to 7th Century fundamentalist barbarism? ;-)

The pre-inflation unstable false vacuum is essentially the standard model of particle physics, but without the electro-weak Higgs. All quanta have zero rest mass. The moment of inflation creating our pocket universe on a landscape (when you localize GL(4,R) in effect you get additional control parameters that are like extra dimensions. The 4 dimensions of spacetime are from T4 translation group) is the zero temperature quantum phase transition to 8 macroquantum coherent vacuum ODLRO Goldstone phase Cartan 0-forms THETA^a & PHI^b connecting 9 real scalar Higgs fields. You need one "space dimension" for each real Higgs scalar field in order to have STABLE topological defects (i.e. non-trivial homotopy groups larger than the identity (simply connected manifolds). So we now have a physical picture of extra space-dimensions. Supersymmetry generators Q^iA is the "square root" of the translations, something roughly like

[Q^iA,Q^jA] = C^ijPA

PA generates translation group in 9+1 spacetime.

The 3 + 1 space-time emerges from the tetrad 1-forms

A^a = M^a^a

and the spin connection 1-forms

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

where the Witten turned topsy turvy upside-down M-Matrix of non-closed 1-forms is

M^a^b = (dTHETA^a)(PHI^b) - (THETA^a)(dPHI^b)

The world hologram idea is in the use of non-closed 1-forms giving non-zero 2-forms that are essentially the quantized area operators of Loop Quantum Gravity (LQG) giving the Bekenstein BITS ~ Horizon Area/4Lp^2 of "volume without volume" since the 3-forms vanish.

Einstein's 1916 GR is regained from

e^a = I^a + @A^a = Einstein-Cartan tetrad 1-form

@ = dimensionless coupling

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

in no sense are the 2nd & 3rd terms on RHS intrinsically "SMALL" although they can be.

The 1905 Special Relativity pre-inflation false vacuum has

ds^2 = I^aIa

I^a = I^audx^u

I^au = 4x4 identity matrix in GIFs as given by Rovelli Ch2

If you go to GNIFs extending 1905 SR only meant for GIFs (Global Inertial Frames)

then A^a =/= 0 but the curvature disclination GMD field 2-form R^a^b is identically zero, i.e.

R^a^b = dS^a^b + S^ac/\S^cb = 0

also the globally zero torsion gap dislocation GMD field 2-form T^a is identically zero, i.e.

T^a = de^a + S^ac/\e^c = 0

It's impossible to have a RIGID GNIF therefore Newton's idea of uniform static gravity field breaks down in passing from Galilean relativity (Gr) to 1905 SR (Special Relativity) before we even get to 1916 GR (General Relativity).

1916 GR is from localizing only T4 and imposing T^a = 0, which still allows a non-vanishing R^a^b as shown in Rovelli's torsion-free spin connection from the tetrads only in eq. (2.89). Localizing P10 gives an additional T^a =/= 0 and going further to GL(4,R) gives new conformal boost and dilation GMD fields - all relevant to dark energy and dark matter together 96% of our pocket universe in the multiverse of universes next door.

"You've indicated that when these fields collapse you are back in an unstable pre-inflation Minkowski vacuum. So I have to presume that there is a causal connection between your Goldstone phases and the presence and location of matter. What exactly is it?"

As above for the umpteenth time passing over your head. Look to the skies. The Truth is Out There.

"And exactly what is the connection between your Higgs-Goldstone fields and Einstein's frame acceleration fields?"

Elementary Watson:

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

with T^a = 0 in the 1916 GR limit.

Jack Sarfatti wrote:
even if you can do it, it's not important - nothing to be learned - it's futile
On Oct 27, 2007, at 10:57 AM, Paul Zielinski wrote:

Jack Sarfatti wrote:
These two Yahoo Groups now have ~ 600 members world wide.

On Oct 27, 2007, at 2:33 AM, Paul Zielinski wrote:

"I think we can still compare gravitationally deformed geodesics with corresponding flat space geodesics at each spacetime point, as you suggested."

Only in the weak field linearized huv approximation in a non-dynamical Minkowski background which throws away the new physics of GR. You cannot do it in a strong field, e.g. at the horizon of a small black hole where
r ~ rs = 2GM/c^2

"I think I'd prefer to avoid extreme pathological cases like black holes, at least for now. But you have a point that any such model must work for strong fields and not just for weak fields. If the comparison is point-by-point, then we are at most only dealing with infinitesimal neighborhoods and intrinsic curvature should therefore not prevent us from arriving at a covariant description of the gravitational deformation of geodesics resulting
from the presence of material sources. Geometrically, you could think of a flat tangent Minkowski spacetime intersecting with the curved object manifold at each point on the manifold, and local projection of a global Cartesian system projected onto both the curved manifold and the flat tangent manifold. Isn't that basically what happens in the tetrad model when we "solder" a Minkowski spacetime to the abstract tangent vector space at each point using the tetrad one-form? As the object manifold deforms from flat under the action of material sources, you can keep the Cartesian system fixed (fixed
homeomorphic map from the coordinate space R^4 to both the curved and intersecting flat manifolds) while only the metric relationships between the points on the curved manifold change under the deformation. That should zero out the coordinate artifacts that in Einstein's theories are interpreted as frame acceleration fields, leaving an objective residue that we can call the "actual" gravitational field."

No, curvature at horizon ~ rs/r^3 ~ 1/rs^2 -> infinity as rs -> 0

Now you may think this is a paradox - eh?

Because as rs -> 0 that should be flat Minkowski spacetime right?

Not quite because when M falls below 10^-5 gm (assuming G(Newton) at small scale) that's trans-Planckian where quantum gravity takes over.
I don't know about you, but I was talking about Einstein's 1916 theory of gravitation -- how it works, what it does, what it means. Note in my theory what happens is rather boring, when the post-inflation vacuum condensate Higgs-Goldstone fields vanish you are back to pre-inflation false vacuum unstable Minkowski spacetime.

"But how do you relate your Higgs-Goldstone fields to material sources? What is it about matter that its presence results in the appearance of those
Higgs-Goldstone fields?"

BTW on George Chapline's precocious dark star paper - it's brilliant but physically unmotivated. Also his detailed arguments are not clear in their logic and he makes so many premises that one can prove anything. The point is that so far there is no evidence for these premises - same is true for most theoretical physics today of course.

"OK, fair point."

PS George's basic idea is that repulsive dark energy is behind the event horizon (where a phase transition happens) preventing collapse to the classical singularity.

"Right."

I had this idea myself independently qualitatively. Also George working with Laughlin (Nobel fractional quantum Hall effect) has a kind of holography using a 3D analog to 2D anyons (Chern-Simons action), which I think is a fundamentally a correct idea.

"OK. Also, the standard covariant acceleration is fine, since only the sign changes when you use the flat space geodesics as references, as opposed to using the curved space geodesics. Again, the comparison has to be point-by-point, as you suggested."

My point here Paul is that there is no algorithm to implement your quest globally beyond the trite linearization of GR.

"Obviously it also has to work for strong fields -- but I don't think that curvature is a problem for the model I'm proposing. See above. You can intersect a virtual tangent Minkowski reference spacetime with the actual spacetime at each point x and use a fixed Cartesian coordinate chart from R^4 to both manifolds. That allows you to project the effect of the curved metric into a copy Minkowski space at each spacetime point, very much along the lines of the tetrad model ("soldering" one-form)."

Furthermore, even if you could do it, why bother? "Who ordered that?" It's a waste of time. It's not an interesting question. The ball is in your court to prove me wrong here, but I think you are wasting your time.

"It reduces the gravitational field of 1916 GR to an ordinary physical field that has a completely objective definition that can be described entirely in terms of generally covariant quantities, has no intrinsic dependence on any observer's world line, and is thus not fundamentally different, physically speaking, from the electromagnetic field. All that this really requires is dropping all the traditional hocus pocus about "general relativity", and being contented with objective geometrodynamics instead.

Jack Sarfatti wrote:
"accelerative deviation" makes sense only in linearized GR on a non-dynamical flat background - it's weak field and excludes all the "nonlinear" effects of GR that makes it qualitatively different from Newton's theory. Roger Penrose has discussed this at length. You are working on a trite problem.
On Oct 26, 2007, at 4:14 PM, Paul Zielinski wrote:

Jack Sarfatti wrote:

On Oct 26, 2007, at 3:34 PM, Paul Zielinski wrote:

Jack Sarfatti wrote:

On Oct 26, 2007, at 2:54 PM, Paul Zielinski wrote:

Jack Sarfatti wrote:
Bottom Line

"the change in the trajectories of freely falling test particles *with respect to gravity-free inertial trajectories* that is predicted to be observed in the presence of gravitational sources." Zielinski
That's nonsense.

For a given set of initial conditions the 1916 theory predicts a gravity-free trajectory (sources removed), and a gravitational trajectory. Each trajectory is defined as a spacetime geodesic that is defined in a fully covariant manner according to the geodesic equation. These trajectories are clearly not the same . They are two different world lines in spacetime.

Trivially - so what? No way to compare them in general. Apples & Oranges - your idea is background dependent - hence no good in general beyond the trivial linear approximation

guv ~ (Minkowski)uv + huv

huv << (Minkowski)uv

Are you saying that the accelerative deviation of the gravitational geodesic from the corresponding gravity-free geodesic for a given test body has no meaning in Einstein's 1916 theory?

Yes it has no meaning. Show an effective procedure to calculate that.


If there is no precise mathematical description of the accelerative effect of a gravitational field on the trajectories of freely falling test objects in 1916 GR, relative to those in gravity-free spacetime, then I would say the theory must be useless.

.
Freely falling particles in GR are on timelike geodesics, which by definition, have zero 4D covariant acceleration! You could make a point-by-point comparison in the weak curvature limit, but so what? This is a trite issue. Paul, I have lost interest in reading further. Again you are beating a dead horse. The problem in my view is not at all interesting even giving you the benefit of doubt that there is a problem. I am much more interested in looking at Matt Visser's papers - Matt has a good sense of what the important problems are.

"OK. I've made my argument. It's fine with me if you want to set this aside -- at least for now. Without a precise measure of the relative accelerative deviation of gravitationally deformed and gravity-free test particle trajectories, how would you do that?"

All you can do is locally at a single P

(Minkowski LIF)ab = (Tetrad)a^u(Tetrad)b^v(Curvilinear LNIF)uv

this is the deeper meaning of the equivalence principle as the minimal coupling of all matter fields to the GMD field via the tetrads.

"Tetrad shmetrad."

On Oct 26, 2007, at 11:39 AM, Paul Zielinski wrote:

"Your position as I understand it is that in 1916 GR, the choice of a "hovering" reference frame, non-accelerating with respect to the surface of the earth, in which the observed acceleration of test particles near the surface is equal to g (the traditional Newtonian "acceleration due to gravity") is "purely contingent" upon an arbitrary choice of the observer's frame of reference, and thus has no special physical significance in Einstein's 1916 theory. "

That's correct. It has psychological meaning only because we evolved on Earth's surface. It is the amount of non-gravity force we must apply to stand still on a timelike non-geodesic in curved spacetime. That's why we feel heavy. If we were space creatures like in Stapledon's "Star Maker" or Fred Hoyle's "Black Cloud" evolving in a weightless zero-g timelike geodesic environment such a provincial non-Copernican ego-centric requirement would never occur.

"I don't agree with this proposition."

Fine. In any case this is hardly an important question compared to questions about the true nature of the stuff of the world that is 96% something else (i.e. dark energy & dark matter).

I think dark energy/dark matter should lead any rational being to ask some hard question about 1916 GR -- what it means, and why it works within a certain domain of validity.

Yes, but I don't think you have asked a good question.

"Now experimentalists believe that theorists don’t know anything about tools, but that is not true. In my own case, I owned a British sports car for over 20 years (a 1965 Austin-Healey Sprite) and an Italian economy car (a 1974 Fiat 128) for more than 5 years. Anyone who has owned either of those marvels of engineering has had to use tools very often. In my experience, you only need two tools to fix anything: duct tape and WD-40. There are only two rules:
1. If something moves and it shouldn’t, use duct tape.
2. If something doesn’t move and it should, squirt it with WD-40.
The equivalent theoretical tools used for dark energy are the anthropic (or Landscape is you speak string) explanation, and scalar fields (known as quintessence for this purpose)." - Michael Turner
http://arxiv.org/PS_cache/arxiv/pdf/0709/0709.3102v1.pdf

On Oct 27, 2007, at 12:03 PM, Paul Zielinski wrote:

"OK, fine. But then how does your BEC model explain the relationship between the material sources and the the Higgs-Goldstone fields? Are not material sources sources of your Higgs-Goldstone fields?"

Jack replies:

Very simple. I have written the equations a jillion times. BTW much simpler than George Chapline's vacuum ODLRO theory. I have a more direct motivation from superfluid helium and I don't need supersymmetry, extra dimensions and all the stuff for which there is no evidence - let's see what LHC drags in, if they ever can engineer the magnets properly - like the optics error in the Hubble Space Telescope - multi-million dollar FUBARs. It's hard to find good help these days - the Decline and Fall of Western Science & Civilization and the regression to 7th Century fundamentalist barbarism? ;-)

The pre-inflation unstable false vacuum is essentially the standard model of particle physics, but without the electro-weak Higgs. All quanta have zero rest mass. The moment of inflation creating our pocket universe on a landscape (when you localize GL(4,R) in effect you get additional control parameters that are like extra dimensions. The 4 dimensions of spacetime are from T4 translation group) is the zero temperature quantum phase transition to 8 macroquantum coherent vacuum ODLRO Goldstone phase Cartan 0-forms THETA^a & PHI^b connecting 9 real scalar Higgs fields. You need one "space dimension" for each real Higgs scalar field in order to have STABLE topological defects (i.e. non-trivial homotopy groups larger than the identity (simply connected manifolds). So we now have a physical picture of extra space-dimensions. Supersymmetry generators Q^iA is the "square root" of the translations, something roughly like

[Q^iA,Q^jA] = C^ijPA

PA generates translation group in 9+1 spacetime.

The 3 + 1 space-time emerges from the tetrad 1-forms

A^a = M^a^a

and the spin connection 1-forms

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

where the Witten turned topsy turvy upside-down M-Matrix of non-closed 1-forms is

M^a^b = (dTHETA^a)(PHI^b) - (THETA^a)(dPHI^b)

The world hologram idea is in the use of non-closed 1-forms giving non-zero 2-forms that are essentially the quantized area operators of Loop Quantum Gravity (LQG) giving the Bekenstein BITS ~ Horizon Area/4Lp^2 of "volume without volume" since the 3-forms vanish.

Einstein's 1916 GR is regained from

e^a = I^a + @A^a = Einstein-Cartan tetrad 1-form

@ = dimensionless coupling

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

in no sense are the 2nd & 3rd terms on RHS intrinsically "SMALL" although they can be.

The 1905 Special Relativity pre-inflation false vacuum has

ds^2 = I^aIa

I^a = I^audx^u

I^au = 4x4 identity matrix in GIFs as given by Rovelli Ch2

If you go to GNIFs extending 1905 SR only meant for GIFs (Global Inertial Frames)

then A^a =/= 0 but the curvature disclination GMD field 2-form R^a^b is identically zero, i.e.

R^a^b = dS^a^b + S^ac/\S^cb = 0

also the globally zero torsion gap dislocation GMD field 2-form T^a is identically zero, i.e.

T^a = de^a + S^ac/\e^c = 0

It's impossible to have a RIGID GNIF therefore Newton's idea of uniform static gravity field breaks down in passing from Galilean relativity (Gr) to 1905 SR (Special Relativity) before we even get to 1916 GR (General Relativity).

1916 GR is from localizing only T4 and imposing T^a = 0, which still allows a non-vanishing R^a^b as shown in Rovelli's torsion-free spin connection from the tetrads only in eq. (2.89). Localizing P10 gives an additional T^a =/= 0 and going further to GL(4,R) gives new conformal boost and dilation GMD fields - all relevant to dark energy and dark matter together 96% of our pocket universe in the multiverse of universes next door.

"You've indicated that when these fields collapse you are back in an unstable pre-inflation Minkowski vacuum. So I have to presume that there is a causal connection between your Goldstone phases and the presence and location of matter. What exactly is it?"

As above for the umpteenth time passing over your head. Look to the skies. The Truth is Out There.

"And exactly what is the connection between your Higgs-Goldstone fields and Einstein's frame acceleration fields?"

Elementary Watson:

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

with T^a = 0 in the 1916 GR limit.

Jack Sarfatti wrote:
even if you can do it, it's not important - nothing to be learned - it's futile
On Oct 27, 2007, at 10:57 AM, Paul Zielinski wrote:

Jack Sarfatti wrote:
These two Yahoo Groups now have ~ 600 members world wide.

On Oct 27, 2007, at 2:33 AM, Paul Zielinski wrote:

"I think we can still compare gravitationally deformed geodesics with corresponding flat space geodesics at each spacetime point, as you suggested."

Only in the weak field linearized huv approximation in a non-dynamical Minkowski background which throws away the new physics of GR. You cannot do it in a strong field, e.g. at the horizon of a small black hole where
r ~ rs = 2GM/c^2

"I think I'd prefer to avoid extreme pathological cases like black holes, at least for now. But you have a point that any such model must work for strong fields and not just for weak fields. If the comparison is point-by-point, then we are at most only dealing with infinitesimal neighborhoods and intrinsic curvature should therefore not prevent us from arriving at a covariant description of the gravitational deformation of geodesics resulting
from the presence of material sources. Geometrically, you could think of a flat tangent Minkowski spacetime intersecting with the curved object manifold at each point on the manifold, and local projection of a global Cartesian system projected onto both the curved manifold and the flat tangent manifold. Isn't that basically what happens in the tetrad model when we "solder" a Minkowski spacetime to the abstract tangent vector space at each point using the tetrad one-form? As the object manifold deforms from flat under the action of material sources, you can keep the Cartesian system fixed (fixed
homeomorphic map from the coordinate space R^4 to both the curved and intersecting flat manifolds) while only the metric relationships between the points on the curved manifold change under the deformation. That should zero out the coordinate artifacts that in Einstein's theories are interpreted as frame acceleration fields, leaving an objective residue that we can call the "actual" gravitational field."

No, curvature at horizon ~ rs/r^3 ~ 1/rs^2 -> infinity as rs -> 0

Now you may think this is a paradox - eh?

Because as rs -> 0 that should be flat Minkowski spacetime right?

Not quite because when M falls below 10^-5 gm (assuming G(Newton) at small scale) that's trans-Planckian where quantum gravity takes over.
I don't know about you, but I was talking about Einstein's 1916 theory of gravitation -- how it works, what it does, what it means. Note in my theory what happens is rather boring, when the post-inflation vacuum condensate Higgs-Goldstone fields vanish you are back to pre-inflation false vacuum unstable Minkowski spacetime.

"But how do you relate your Higgs-Goldstone fields to material sources? What is it about matter that its presence results in the appearance of those
Higgs-Goldstone fields?"

BTW on George Chapline's precocious dark star paper - it's brilliant but physically unmotivated. Also his detailed arguments are not clear in their logic and he makes so many premises that one can prove anything. The point is that so far there is no evidence for these premises - same is true for most theoretical physics today of course.

"OK, fair point."

PS George's basic idea is that repulsive dark energy is behind the event horizon (where a phase transition happens) preventing collapse to the classical singularity.

"Right."

I had this idea myself independently qualitatively. Also George working with Laughlin (Nobel fractional quantum Hall effect) has a kind of holography using a 3D analog to 2D anyons (Chern-Simons action), which I think is a fundamentally a correct idea.

"OK. Also, the standard covariant acceleration is fine, since only the sign changes when you use the flat space geodesics as references, as opposed to using the curved space geodesics. Again, the comparison has to be point-by-point, as you suggested."

My point here Paul is that there is no algorithm to implement your quest globally beyond the trite linearization of GR.

"Obviously it also has to work for strong fields -- but I don't think that curvature is a problem for the model I'm proposing. See above. You can intersect a virtual tangent Minkowski reference spacetime with the actual spacetime at each point x and use a fixed Cartesian coordinate chart from R^4 to both manifolds. That allows you to project the effect of the curved metric into a copy Minkowski space at each spacetime point, very much along the lines of the tetrad model ("soldering" one-form)."

Furthermore, even if you could do it, why bother? "Who ordered that?" It's a waste of time. It's not an interesting question. The ball is in your court to prove me wrong here, but I think you are wasting your time.

"It reduces the gravitational field of 1916 GR to an ordinary physical field that has a completely objective definition that can be described entirely in terms of generally covariant quantities, has no intrinsic dependence on any observer's world line, and is thus not fundamentally different, physically speaking, from the electromagnetic field. All that this really requires is dropping all the traditional hocus pocus about "general relativity", and being contented with objective geometrodynamics instead.

Jack Sarfatti wrote:
"accelerative deviation" makes sense only in linearized GR on a non-dynamical flat background - it's weak field and excludes all the "nonlinear" effects of GR that makes it qualitatively different from Newton's theory. Roger Penrose has discussed this at length. You are working on a trite problem.
On Oct 26, 2007, at 4:14 PM, Paul Zielinski wrote:

Jack Sarfatti wrote:

On Oct 26, 2007, at 3:34 PM, Paul Zielinski wrote:

Jack Sarfatti wrote:

On Oct 26, 2007, at 2:54 PM, Paul Zielinski wrote:

Jack Sarfatti wrote:
Bottom Line

"the change in the trajectories of freely falling test particles *with respect to gravity-free inertial trajectories* that is predicted to be observed in the presence of gravitational sources." Zielinski
That's nonsense.

For a given set of initial conditions the 1916 theory predicts a gravity-free trajectory (sources removed), and a gravitational trajectory. Each trajectory is defined as a spacetime geodesic that is defined in a fully covariant manner according to the geodesic equation. These trajectories are clearly not the same . They are two different world lines in spacetime.

Trivially - so what? No way to compare them in general. Apples & Oranges - your idea is background dependent - hence no good in general beyond the trivial linear approximation

guv ~ (Minkowski)uv + huv

huv << (Minkowski)uv

Are you saying that the accelerative deviation of the gravitational geodesic from the corresponding gravity-free geodesic for a given test body has no meaning in Einstein's 1916 theory?

Yes it has no meaning. Show an effective procedure to calculate that.


If there is no precise mathematical description of the accelerative effect of a gravitational field on the trajectories of freely falling test objects in 1916 GR, relative to those in gravity-free spacetime, then I would say the theory must be useless.

.
Freely falling particles in GR are on timelike geodesics, which by definition, have zero 4D covariant acceleration! You could make a point-by-point comparison in the weak curvature limit, but so what? This is a trite issue. Paul, I have lost interest in reading further. Again you are beating a dead horse. The problem in my view is not at all interesting even giving you the benefit of doubt that there is a problem. I am much more interested in looking at Matt Visser's papers - Matt has a good sense of what the important problems are.

"OK. I've made my argument. It's fine with me if you want to set this aside -- at least for now. Without a precise measure of the relative accelerative deviation of gravitationally deformed and gravity-free test particle trajectories, how would you do that?"

All you can do is locally at a single P

(Minkowski LIF)ab = (Tetrad)a^u(Tetrad)b^v(Curvilinear LNIF)uv

this is the deeper meaning of the equivalence principle as the minimal coupling of all matter fields to the GMD field via the tetrads.

"Tetrad shmetrad."

On Oct 26, 2007, at 11:39 AM, Paul Zielinski wrote:

"Your position as I understand it is that in 1916 GR, the choice of a "hovering" reference frame, non-accelerating with respect to the surface of the earth, in which the observed acceleration of test particles near the surface is equal to g (the traditional Newtonian "acceleration due to gravity") is "purely contingent" upon an arbitrary choice of the observer's frame of reference, and thus has no special physical significance in Einstein's 1916 theory. "

That's correct. It has psychological meaning only because we evolved on Earth's surface. It is the amount of non-gravity force we must apply to stand still on a timelike non-geodesic in curved spacetime. That's why we feel heavy. If we were space creatures like in Stapledon's "Star Maker" or Fred Hoyle's "Black Cloud" evolving in a weightless zero-g timelike geodesic environment such a provincial non-Copernican ego-centric requirement would never occur.

"I don't agree with this proposition."

Fine. In any case this is hardly an important question compared to questions about the true nature of the stuff of the world that is 96% something else (i.e. dark energy & dark matter).

I think dark energy/dark matter should lead any rational being to ask some hard question about 1916 GR -- what it means, and why it works within a certain domain of validity.

Yes, but I don't think you have asked a good question.

"Now experimentalists believe that theorists don’t know anything about tools, but that is not true. In my own case, I owned a British sports car for over 20 years (a 1965 Austin-Healey Sprite) and an Italian economy car (a 1974 Fiat 128) for more than 5 years. Anyone who has owned either of those marvels of engineering has had to use tools very often. In my experience, you only need two tools to fix anything: duct tape and WD-40. There are only two rules:
1. If something moves and it shouldn’t, use duct tape.
2. If something doesn’t move and it should, squirt it with WD-40.
The equivalent theoretical tools used for dark energy are the anthropic (or Landscape is you speak string) explanation, and scalar fields (known as quintessence for this purpose)." - Michael Turner
http://arxiv.org/PS_cache/arxiv/pdf/0709/0709.3102v1.pdf

On Oct 25, 2007, at 2:04 PM, Jack Sarfatti wrote:

http://www.physorg.com/news112541069.html

Texture defects in 3D space are non-trivial mappings of the 3 sphere S3 with three independent Goldstone phases and four real Higgs scalar fields (Rocky Kolb's "WD40") of third homotopy group.
http://arxiv.org/PS_cache/arxiv/pdf/0709/0709.3102v1.pdf
My theory in 3D space of GMD point defects is S2 of second homotopy group - a sub-case of S3. A GMD texture is a richer defect structure than a GMD field monopole point node of three real Higgs scalars where two world hologram Goldstone phases are undefined (Michael Berry).

The sequence of defects is

domain walls (zero homotopy)

vortex line strings (first homotopy)

point monopoles (second homotopy)

textures (third homotopy)

you can think of these as BRANES

my full theory
http://arxiv.org/abs/gr-qc/0602022
has 8 Goldstone phase 0-forms Theta^I & Phi^Jwith 9 real Higgs - one for each dimension of space (not time).

A^I = M^I^I

M^I^J = (dTheta^I)/\(Phi^J) - (Theta^I)/\(dPhi^J)

e^I = I^I + @A^I is tetrad IT

using Rovelli's notation, where in one of my sub-models

@ = N^-1/3

N = # Bekenstein BITS of the World Hologram

ds^2 = e^IeI(LIF) = guv(LNIF)dx^udx^v

i.e. Equivalence Principle of Einstein - the corner stone of the Temple of Space-Time Physics

You can think of a texture as a projection of a defect in a 4D space down to 3D space.

i.e. 4D + 1 space-time down to 3D+1 space time.

Locally gauging 10-parameter Poincare group naturally leads to this picture.

Remember in my picture mesons are pairs of point defects of second homotopy in the GMD(GeoMetroDynamic) field connected by a string vortex defect of first homotopy.
Nucleons are three GMD monopoles connected by vortex strings. These are Bohm hidden
variables guided by QBIT pilot waves. The IR limit of the vortex string short-range strong
Salam gravity induced by residual dark matter zero point energy per Sakharov 1967 has
and effective "Newtonian" potential energy per unit mass of

V(IR) = c^2/Lp* QUARK CONFINEMENT

Lp* = (Lp^2(Newton)(retro-causal future dark energy de Sitter horizon radius) ~ 1 fermi ~ 1Gev

http://qedcorp.com/APS/desitter.jpg

e.g.

Spin of hadronic resonances ~ (1Gev)^-2(Energy)^2 + zero energy intercept

The UV limit is

V(UV) = c^2r/Lp*^2 ASYMPTOTIC FREEDOM

r = separation of the two GMD point monopoles

Pretty damn simple!

This is like Michael Faraday would have done it. ;-)

"First we polish off some batches of political dispatches ..." Gondoliers G&S
12:45 PM and I am still in pajamas answering e-mails - looks like Nick Herbert has come up with a practical non-local signaling device? Is the "quantum compound" beyond orthodox QM?

On Oct 23, 2007, at 12:35 PM, Paul Zielinski wrote:

Jack Sarfatti wrote:

"equivalence principle" has several meanings.
If you read Norton's paper you will see that Einstein's and Pauli's versions are quite different.

I doubt it. I bet Einstein was fully aware of Pauli's version before Pauli.

Formally it is the tetrad idea as in the Rovelli quotes you sent to Kiehn.

If the principle is restricted to uniform acceleration and static homogeneous fields, then that should be
reflected in the mathematical model.

Wrong. It's obviously not restricted like that. Red Herring. False premise.

"g-force" is always locally indistinguishable from Newton's common sense notion as "weight"! This is independent of local curvature field R^a^b.

Einstein's GR eliminates "gravity force in the inertial frame" as in Newton's picture where

V(gravity) = - c^2rs/r

f(gravity) = - dV(gravity)dr

in the GIF

In Einstein 1916 GR

f(gravity) = - dV(gravity)dr is the "inertial force" in the LNIF (Local Non-Inertial Frame) that you need using a non-gravity force to stand still in the R^a^b =/= 0 curvature field. This is a contingent arbitrary conventional choice. The world line of this "shell observer" is not timelike geodesic in the R^a^B =/= 0 curved spacetime.
See new Wheeler & Taylor "Black Holes" for a high school level discussion of this point e.g. "shell observers" (LNIF).

Now you can be in a rocket ship in flat Minkowski space-time R^a^b = 0 and apply your rocket engine in an arbitrary manner - that will be locally equivalent to being in some dynamical gravity field in some LNIF -it need not be a static uniform field. There can be local gravity waves passing through the LNIF detector for example.

g-force criterion only applies to the Center of Mass (COM) not to relative tidal coordinates. If you are weightless then you know you are on a timelike geodesic and it does not matter what the local curvature R^a^b is. If you feel weight = g-force then you know you are not on a timelike geodesic no matter what local R^a^b is. You can, ALSO, choose to measure R^a^b independently - but that does not violate equivalence principle that only applies to COMs and to a small enough LIF or LNIF whose detector cannot measure the geodesic deviations.


zero g-force LIF <-> non-zero g-forceLNIF at same P local coincidence

a lot of confusion sets in about "gravity force" = "weight" in non-inertial frames that should not be confused with curvature.

Curvature is second order, coordinate metric gradient is first order. Of course these are not the same and
can be varied independently.

Yes, and therefore, when the questions are properly posed the paradox vanishes.

However, all other things being equal, if in GR you vary the curvature R^u_vwl =/= 0 around a source then you also vary the metric gradients g_uv, w, and such variation of the metric gradients has *nothing at all to do with any observer's world line*.

False. When you do that you change the pattern of geodesic world lines both null and timelike.

Basically in those discussions the static hovering frames are tacitly meant as when one writes

g00 = 1 - rs/r = - 1/grr

rs/r < 1

so for example

g ~ c^2rs/r^2

is what you need in an off-geodesic LNIF that stands still, as it were, in the curved spacetime in that simplest of metrics.

Yes, and if as Einstein suggested a uniform frame acceleration field is in essence not different from a static homogeneous field,

That's only a special situation - the underlying idea is general.

What Einstein did in above is to say that a local constant inertial g-force g per unit mass is AS IF one is in a static frame with a Newtonian potential energy per unit mass V = -gz .

In Newton's theory the static frame is Minkowski geodesic GIF, however in Einstein's GMD the same static frame is off-geodesic (in curved spacetime) LNIF where e.g.

g00 = 1 + 2V for a special static LNIF detector

This paradigm shift is oft overlooked in pop informal discussions - even in some text books.

Now

g00 = 1 + 2V

is perfectly general for a non-rotating dynamic source

with

g ~ - (1/2)dg00/dr

V need not be gz

then the definition of the gravitational field is made relative to an observer's world line, i.e., dependent on the observer's frame of reference, and the "weight" then has only contingent meaning. If, on the other hand, the objective physical gravitational field is not the same physically speaking as any frame acceleration field, then the weight assumes absolute objective physical meaning.

Your words here do not mean anything to my way of thinking. g-force is 100% contingent always. You have garbled different meanings of "gravitational field"

R^a^b = "gravitational field 1"

g-force = "gravitational field 2"

"weight" = g-force = 0 in REST LIFs & REST GIFS on timelike geodesics (relative to whatever R^A^B might be) is universally true in both 1905 SR & 1916 GR

g-force =/= 0 in REST LNIFs & REST GNIFS is universally true in both 1905 SR & 1916 GR

In REST FRAMEs the detector measures itself, as it were, in a kind of Godelian self-reference.

R^a^b 's value is completely irrelevant. You can measure it independently from the above.


On Oct 22, 2007, at 6:48 PM, Paul Zielinski wrote:
If Einstein's equivalence principle is the cornerstone, then I think it's important to be clear about what it actually is and what parts of it can still be considered valid in the 1916 theory.

It looks to me that the tetrad model is built around Einstein's version of the principle as presented very clearly by Einstein himself in 1916, and not Pauli's.

Yes.

OK...

Einstein's version, unlike Pauli's, refers to uniform frame acceleration in a Minkowski spacetime.

No, it's more general, i.e. Pauli's. Look what Einstein says informally is not all that he had in mind.

But Einstein was consistent on this to the end of his life. Read Norton.

Maybe one day.

In the 1916 quote Einstein is very clear: a uniformly accelerating frame is physically completely the same in essence as a non-accelerating frame equipped with a static homogeneous gravitational field.

This is garbled. "non-accelerating frame" in Newton's paradigm is an "accelerating frame" in Einstein's paradigm, hence the semantic confusion. A static shell frame in curved space-time is an accelerating off-geodesic LNIF frame! It's acceleration is precisely

g = - c^2rs/r^2

the LNIF needs to accelerate to stand still in curved spacetime. This is counter-intuitive to "common sense".

When we stand still on Earth, we are accelerating relative to the local GMD curvature R^a^b =/= 0 field. That's why we feel weight from the electrical Van der Waals reaction forces in the ground. Bernie Haisch got that part right in his otherwise over simplistic "EM ZPF origin of inertia" model.

If the tetrad model is based on this version, then you need to understand that in order to understand the
meaning of the tetrad model in GR.

Weight as gravity force (Newton's sense) is always an inertial force in a LNIF off-geodesic independent of the local curvature until and unless you contingently arbitrarily specify the static "shell" (Wheeler) frame which does not always exist. All inertial forces pushing test particles off timelike geodesics require non-gravity forces to create them.
True, given Einstein's 1916 version of the equivalence principle.

That's the one. If it ain't broke don't fix it.

However, in addition to this Mickey Mouse stuff

So you agree that the Einstein principle is "Mickey Mouse stuff"?

How about "Alice in Wonderland"!

I made a nice picture of quark forces today all from Sakharov's zero point energy induced gravity that is strong on short scale in 3D space - none of this extra-dimensional nonsense needed for this experimental problem - enough of excess mathematical baggage!

OK. No unseen higher spatial dimensions folded up 10^500 ways? No hypergeometric oregami?

Excess formal baggage. Keep it simple Stupid!, though not simpler than is possible. ;-)

Remember Feynman's "a beautiful theory is murdered by an ugly fact" - see Lee Smolin's "The Trouble With Physics" for examples.

Was he talking about GR? :-)

No, he is talking about superstring/M-theory.

Imagine two point monopole defects connected by a string "vortex" defect". By "defect" I mean Goldstone phase singularities (Michael Berry's term) in the several real Higgs fields of the vacuum. The "cores" of the point defects (the quarks) are spherically symmetric with uniform negative zero point energy density giving the induced Sakharov gravity potential energy per unit mass of

V(monopole quark) = -c^2(r/Lp*)^2

out to the coherence "annealing" length within which the quark force per unit mass is

f(UV) ~ c^2r/Lp*^2 -> 0 as r = distance between two point defects -> 0

this is UV "asymptotic freedom"

In the opposite IR limit of "confinement" assume that the zero point energy density in the line vortex core falls off as 1/Lp*r

This gives

f(IR) ~ c^2/Lp*

similar to the cosmic dark energy repulsion (but of different sign)

g(accelerating universe) ~ cH ~ 1 nanometer/sec^2 - same as Pioneer anomaly, but in opposite direction?

Note the UNIFORM large-scale dark energy density corresponds to /\zpf ~ 1/(Hubble radius)^2

i.e. V(cosmic) ~ c^2r^2/(Hubble)^2

~ c^2r/(Hubble)^2 ~ c^2/(Hubble) on large scale

compare to the IR quark force of similar origin c^2/Lp*

Newton saw the equivalence of the falling apple to the motion of the planets.

Sarfatti saw the equivalence of the quark force to the accelerating universe!

Looks interesting -- but beware of mathematical red herrings!

There is very little math here beyond high school level. It's the physical ideas that are important.

Supersymmetry? Extra dimensions? we don't need no damn supersymmetries and extra dimensions! ;-)

(well maybe we do :-))

?

I mean for example, locally gauging 10-parameter Poincare group gives curvature and torsion GMD fields with an extra 6 dynamical degrees of freedom, i.e.

FOUR tetrads e^a and SIX dynamically independent of tetrads spin connections S^a^b = - S^b^a. The latter SIX form a 6D fiber - Shipov's "oriented point" manifold that sure looks like a primitive Calabi-Yau sort of space.

Now if we locally gauge Penrose's 15 parameter twistor conformal group then there are even more GMD fields that both Tony Smith & Carlos Castro seem to get? This then, according to Castro, gives a new kind of UV/IR duality in which

g(UV Pioneer Anomaly) = cH = c^2/(Hubble radius) ~ 1 nanometer/sec^2 on short UV scale = c^2/R (below)

mod sign (attractive to center of Sun)

i.e. dark matter shell /\zpf = -H/cr

just like IR quark force is

g(IR quark) = c^2/Lp*

Lp* ~ 1 fermi

/\zpf(IR quark) = -1/Lp*r

this is QUARK CONFINEMENT!

Then in UV limit

g(UV quark) = c^2r/Lp*^2

/\zpf(UV quark) = - 1/2Lp*^2

this is QUARK ASYMPTOTIC FREEDOM!

Note, for accelerating universe on IR cosmic scale

/\zpf(dark energy) = + (H/c)^2

Vzpf(dark energy) = -c^2(1/2)/\zpf(dark energy)R^2

g(dark energy) = H^2R = c^2/R ~ 1 nanometer/sec^2 - same number mod sign as NASA Pioneer anomalous acceleration, but pointing opposite direction to center of sun? In case of cosmology, think of a flat infinite rubber sheet in accelerating expansion same in all directions at each point of the sheet.

c/H ~ R

Area of future de Sitter WORLD HOLOGRAM horizon is NLp^2 = 4piR^2

N = Bekenstein c-bits ~ 10^122

N^1/2 ~ 10^61

R ~ 10^61 10^-33 ~ 10^28 cm

&R = (Lp^2R)^1/3 = N^1/6Lp ~ 1 fermi = size of Lp* quantum gravity "foam" bubble.

"equivalence principle" has several meanings.
Formally it is the tetrad idea as in the Rovelli quotes you sent to Kiehn.

zero g-force LIF <-> non-zero g-forceLNIF at same P local coincidence

a lot of confusion sets in about "gravity force" = "weight" in non-inertial frames that should not be confused with curvature. Basically in those discussions the static hovering frames are tacitly meant as when one writes

g00 = 1 - rs/r = - 1/grr

rs/r < 1

so for example

g ~ c^2rs/r^2

is what you need in an off-geodesic LNIF that stands still, as it were, in the curved spacetime in that simplest of metrics.

On Oct 22, 2007, at 6:48 PM, Paul Zielinski wrote:
If Einstein's equivalence principle is the cornerstone, then I think it's important to be clear about what it actually is and what parts of it can still be considered valid in the 1916 theory.

It looks to me that the tetrad model is built around Einstein's version of the principle as presented very clearly by Einstein himself in 1916, and not Pauli's.

Yes.

Einstein's version, unlike Pauli's, refers to uniform frame acceleration in a Minkowski spacetime.

No, it's more general, i.e. Pauli's. Look what Einstein says informally is not all that he had in mind.

Weight as gravity force (Newton's sense) is always an inertial force in a LNIF off-geodesic independent of the local curvature until and unless you contingently arbitrarily specify the static "shell" (Wheeler) frame which does not always exist. All inertial forces pushing test particles off timelike geodesics require non-gravity forces to create them.

However, in addition to this Mickey Mouse stuff I made a nice picture of quark forces today all from Sakharov's zero point energy induced gravity that is strong on short scale in 3D space - none of this extra-dimensional nonsense needed for this experimental problem - enough of excess mathematical baggage! Remember Feynman's "a beautiful theory is murdered by an ugly fact" - see Lee Smolin's "The Trouble With Physics" for examples.

Imagine two point monopole defects connected by a string "vortex" defect". By "defect" I mean Goldstone phase singularities (Michael Berry's term) in the several real Higgs fields of the vacuum. The "cores" of the point defects (the quarks) are spherically symmetric with uniform negative zero point energy density giving the induced Sakharov gravity potential energy per unit mass of

V(monopole quark) = -c^2(r/Lp*)^2

out to the coherence "annealing" length within which the quark force per unit mass is

f(UV) ~ c^2r/Lp*^2 -> 0 as r = distance between two point defects -> 0

this is UV "asymptotic freedom"

In the opposite IR limit of "confinement" assume that the zero point energy density in the line vortex core falls off as 1/Lp*r

This gives

f(IR) ~ c^2/Lp*

similar to the cosmic dark energy repulsion (but of different sign)

g(accelerating universe) ~ cH ~ 1 nanometer/sec^2 - same as Pioneer anomaly, but in opposite direction?

Note the UNIFORM large-scale dark energy density corresponds to /\zpf ~ 1/(Hubble radius)^2

i.e. V(cosmic) ~ c^2r^2/(Hubble)^2

~ c^2r/(Hubble)^2 ~ c^2/(Hubble) on large scale

compare to the IR quark force of similar origin c^2/Lp*

Newton saw the equivalence of the falling apple to the motion of the planets.

Sarfatti saw the equivalence of the quark force to the accelerating universe!

Supersymmetry? Extra dimensions? we don't need no damn supersymmetries and extra dimensions! ;-)

(well maybe we do :-))

The dark matter (negative zero point energy density in a vortex filament) induced IR long-wave quark-quark force per unit mass is

f(IR) = c^2/Lp* = constant

Lp* ~ 1 fermi ~ (Lp^2Hubble radius of future dark energy retro-causal de Sitter horizon)^1/3

Lp ~ 10^-33 cm

Hubble "radius" ~ 10^28 cm

This means that the dark matter vortex filament core zero point energy density scales as

1/Lp*r in IR limit

but scales as 1/Lp*^2 in the UV limit where

f(UV) ~ c^2r/Lp*^2 -> 0 as r -> 0

i.e. asymptotic freedom of QCD

Therefore, there is a connection of SU(3) internal symmetry with localized conformal group symmetry which may be there perhaps in Carlos Castro's model?

Obviously SU(3) is the symmetry of the 3D quantum harmonic oscillator which is precisely what we have in a sphere of uniform zpe density. Therefore, the two ends of the open string are point monopole defects with spherical symmetry connected by a dark matter zpe vortex filament tube - this is a pretty picture not needing extra space dimensions. Roger Penrose does not like extra space dimensions (e.g. "The Road to Reality") too much excess math baggage - that's "The Trouble With Physics" - what I just gave you is a Michael Faraday picture in 3D space consistent with Einstein's GR and ordinary QM.

On Oct 21, 2007, at 4:35 PM, Jack Sarfatti wrote:

What do they have in common?

"the force between two quarks approaches a constant strength as we pull the quarks apart ..."
p. 104 "The Trouble With Physics" Lee Smolin

In the simple weak curvature slow speed Galilean limit of Einstein's 1916 General Relativity (GR) with additional torsion, the quantum exotic vacuum zero point energy (ZPE) induced Sakharov (1967) gravity potential energy per unit test particle mass is (in a static spherically symmetric toy model)

Vzpf(r) = -(1/2)c^2/\zpf(r)r^2

In Einstein's GR

g00 = (1 + 2Vzpf/c^2) = - 1/grr

for static LNIF observers outside the event horizon g00 = 0.

ZPF induced Newtonian "gravity force per unit test mass is

f = - dVzpf/dr

In the case of the two NASA Pioneer space probes at the outer edge of the solar system now beyond Saturn in different directions on the celestial sphere the anomalous gravity pull fits the adhoc assumption

|/\zpf| = H/cr

H = Hubble's cosmological constant

Vzpf ~ cHr

f = cH ~ 1 nanometer/sec^2 agrees with observed data

this universal anomalous "gravity" force can point either radially inward or radially outward depending on the sign of the exotic vacuum zero point energy density (w = -1).

Dark matter has /\zpf < 0, i.e. negative zero point exotic vacuum energy with positive pressure and this gives the force pointing inwards to the center of the Sun if we imagine a possibly expanding hollow concentric spherical shell "pulse" starting presently around the orbit of Saturn - blown off in a "vacuum quake" from the center of the Sun. K Tangen says the anomaly is non-geodesic, this model says it's geodesic - however since there must be a torsion field to allow /\zpf to be variable, there may not be a conflict using the "auto-parallel" generalized "geodesic".

Carlos Castro has a new duality argument from localizing the full conformal group to explain why Hubble's parameter shows up at this small scale, i.e. in my paradigm this is tantamount to curvature + torsion + conformal boost and dilation compensating geometrodynamic gauge potentials.

Obviously this same picture can work for hadronic strings i.e. quarks at the end of a rubber band string that is a vortex filament whose "core" is dark matter but of larger density than in the Pioneer case.

i.e. /\zpf ~ 1/Lp*r

Lp*^2 ~ hG*/c^3

G* ~ 10^40G(Newton)

as in Abdus Salam's strong short-range f-gravity and my paper of 1973 "Collective Phenomena" ed. H. Frohlich & FW Cummings when I was at Salam's ICTP in Trieste, Italy.

This gives universal slope of hadronic resonance Regge trajectories

Spin ~ (1Gev)^-2E^2 + intercept

also interpreted as small Kerr black holes in strong short range zero point energy induced Sakharov gravity

What do they have in common?

"the force between two quarks approaches a constant strength as we pull the quarks apart ..."
p. 104 "The Trouble With Physics" Lee Smolin

In the simple weak curvature slow speed Galilean limit of Einstein's 1916 General Relativity (GR) with additional torsion, the quantum exotic vacuum zero point energy (ZPE) induced Sakharov (1967) gravity potential energy per unit test particle mass is (in a static spherically symmetric toy model)

Vzpf(r) = -(1/2)c^2/\zpf(r)r^2

In Einstein's GR

g00 = (1 + 2Vzpf/c^2) = - 1/grr

for static LNIF observers outside the event horizon g00 = 0.

ZPF induced Newtonian "gravity force per unit test mass is

f = - dVzpf/dr

In the case of the two NASA Pioneer space probes at the outer edge of the solar system now beyond Saturn in different directions on the celestial sphere the anomalous gravity pull fits the adhoc assumption

|/\zpf| = H/cr

H = Hubble's cosmological constant

Vzpf ~ cHr

f = cH ~ 1 nanometer/sec^2 agrees with observed data

this universal anomalous "gravity" force can point either radially inward or radially outward depending on the sign of the exotic vacuum zero point energy density (w = -1).

Dark matter has /\zpf < 0, i.e. negative zero point exotic vacuum energy with positive pressure and this gives the force pointing inwards to the center of the Sun if we imagine a possibly expanding hollow concentric spherical shell "pulse" starting presently around the orbit of Saturn - blown off in a "vacuum quake" from the center of the Sun. K Tangen says the anomaly is non-geodesic, this model says it's geodesic - however since there must be a torsion field to allow /\zpf to be variable, there may not be a conflict using the "auto-parallel" generalized "geodesic".

Carlos Castro has a new duality argument from localizing the full conformal group to explain why Hubble's parameter shows up at this small scale, i.e. in my paradigm this is tantamount to curvature + torsion + conformal boost and dilation compensating geometrodynamic gauge potentials.

Obviously this same picture can work for hadronic strings i.e. quarks at the end of a rubber band string that is a vortex filament whose "core" is dark matter but of larger density than in the Pioneer case.

i.e. /\zpf ~ 1/Lp*r

Lp*^2 ~ hG*/c^3

G* ~ 10^40G(Newton)

as in Abdus Salam's strong short-range f-gravity and my paper of 1973 "Collective Phenomena" ed. H. Frohlich & FW Cummings when I was at Salam's ICTP in Trieste, Italy.

This gives universal slope of hadronic resonance Regge trajectories

Spin ~ (1Gev)^-2E^2 + intercept

also interpreted as small Kerr black holes in strong short range zero point energy induced Sakharov gravity

Most of these issues are pseudo-problems based on the ambiguity of plain English and the unconscious shifts in meaning of the same nouns such as "gravitational field" that has at least two independent meanings. Also there is a paradigm shift between Newton and Einstein that causes a lot of confusion e.g. Puthoff's PV theory one example, string theory another. See L. Smolin "The Trouble with Physics" on "background-independence."

1. There is nothing wrong with Einstein's original formulation of the equivalence principle.

2. Equivalence principle is general not restricted to static uniform Newtonian gravity fields.

3. Operational definitions of g-force on the one hand, and curvature tidal effects on the other are completely orthogonal, independent, compatible, they "commute" to use quantum analogy.

4. Strictly speaking, "gravity force" is eliminated in Einstein, but not in Newton. Elementary particle theorists think of "gravity force" as a perturbation-based S-Matrix spin 2 RIGID Poincare group 2nd rank tensor force on a par with spin 1 RIGID Poincare group vector gauge force. The latter are renormalizable (t' Hooft ~ 1973), the former are not! This is also the string theory background-dependent approach with Minkowski spacetime as the Newtonian non-dynamical arena, rather than the Leibnizian background-independent where the geometrodynamic (GMD) field (fabric of 3D space changing in time for arbitrary slicing (foliations) of 4D spacetime) is on an equal ontological footing with all other matter fields on a pre-metrical manifold with minimal couplings - the latter a form of the equivalence principle.

5. My original idea is to use the tetrad fields because they are intrinsically spin 1 vector fields (in Poincare group sense) hence renormalizable if you use perturbation theory.

6. In addition another one of my original ideas is to apply P.W. Anderson's "More is different" = Sid Colman's "hidden symmetry" = Brout & Englert & Higgs "spontaneous broken symmetry" so that the c-number tetrad compensating fields from localizing 4D translations T4 and the dynamically independent c-number spin connections from localizing Lorentz group emerge from the coherent Goldstone phases of the post-inflation vacuum Higgs field order parameters in precisely the same way as does the coherent MACRO-QUANTUM CONDENSATE resistantless superfluid flow (more complex algebra of course). This leaves over the quantum zero point fields of virtual quanta that become "normal fluid" on-mass-shell.

7. The rules of MACRO-QUANTUM THEORY are "More is different" from micro-quantum theory - same as for General Relativity compared to Special Relativity.

Conservation of information = Unitarity? Yes for micro-qm, NO for MACRO-QM!

Signal locality? Yes for micro-qm, NO for MACRO-QM! This opens door to "consciousness" as well as paranormal "remote viewing" and other spooky techgnostic UFO super technology that scares the mainstream physics CSICOPS establishment - including even their most visionary thinkers like L. Smolin and Max Tegmark.

See A. Valentini's "violation of sub-quantal equilibrium" allowing use of nonlocal entanglement as a stand-alone C^3 as in Lawry Chickering's 1982 letter to Richard De Lauer Under Secretary of Defense about my work in the 80's. Contact Cap Weinberger Jr for details on this period. Chickering ran ICS a Reagan think tank with Cap Weinberger Sr, Brent Scowcroft, Milton Friedman, Ed Meese on their board ("The Buttoned Down Bohemians, SF Sunday Chronicle, 1986) Don Rumsfeld also ran it in mid-80's.

On Oct 20, 2007, at 9:33 AM, Paul Zielinski wrote:

Jack Sarfatti wrote:
The answer is yes and no depending on the context.

There is an objective local empirical measurable difference between un-accelerated zero-g force geodesics and accelerated non-geodesics with g-force. In this sense 1 "acceleration is absolute."

In other words there are still preferred frames in GR -- the inertial frames -- but what is and what is not an inertial frame now depends on the matter distribution?

Yes, if the meaning of "preferred" is "g-force". The key structure are the null geodesics. Obviously detectors on timelike geodesics measure zero g-force. Only a non-gravity force can push you off a timelike geodesic and then you feel g-force = weight AND you are TIME DILATED in a twin situation (action principle for test particles).

However, the key intrinsic GMD field LOCAL GCT (T4(x)) invariants e^a & S^a^b & R^a^b are FRAME-INVARIANT (also coordinate chart invariant) mod Lorentz group connecting coincident LIFs. These are LOCAL in sense of complete gauge orbits P not bare manifold points p connected by "active diffeomorphisms" (see Rovelli Ch 2 for pictures of this).

ds^2 = e^aea is absolute invariant of course under locally gauged Poincare group

P10(x) = T4(x)@ O1,3(x)

Curvature field = R^a^b = dS^a^b + S^ac/\S^cb

it's ACTION DENSITY is

{abcd}R^a^b/\e^c/\e^d

e^a = I^a + A^a

in 1905 SR, A^a = 0

1905 SR only includes GIF -> GIF' where

I^a = I^audx^u

Ia^u = 4x4 identity matrix = Kronecker delta in all GIFs (Global Inertial Frames).

A^a =/=0 in a GNIF even when R^a^b = 0

A^a = 0 in a LIF in 1916 GR

but A^a =/= 0 in a LNIF

and now R^a^b =/= 0 is possible unlike GNIF..

For examples see

http://en.wikipedia.org/wiki/Frame_fields_in_general_relativity


sigma = my e

this is for static non-geodesic LNIF "shell observers" (Wheeler's term)

e.g.

I^0t = 1

A^0t = (1 - 2m/r)^1/2 -1

Note that when m -> 0, A^0t -> 0

I^1r = 1

A^1r = (1 - 2m/r)^-1/2 -1

Note that when m -> 0, A^1r -> 0

etc.

Also in this case R^a^b =/= 0

Obviously these BACKGROUND-INDEPENDENT A^a is the fundamental spin 1 vector "Yang-Mills" compensating gravity field. The background-dependent spin 2 objects are not-fundamental but composite so no wonder they do not renormalize in perturbation theory. Note that in non-commutative geometry A^aPa do not commute. However, the full theory is non-commutative Yang-Mills anyway in ordinary commuting geometry since we must use the complete P10 Lie algebra
{A^aPa, S^a^bPab} in forming the minimally coupled covariant derivatives on the matter spinor fields (Rovelli Ch 2) to agree with the equivalence principle.

The latter always require a non-gravity force.
Yes, it requires a non-gravity force to push a freely falling test object off a GR geodesic.
Note also the action principle that timelike geodesics have the longest elapsed time compared to all other neighboring world lines that intersect them in two coincidences. Most popular discussions of "gravity field" are sloppy in this regard - even Lee Smolin's "The Trouble With Physics". The "gravity field" = g-force = "shell static observer" (Schwarzschild solution outside event horizon). That is, you cannot locally distinguish a non-geodesic g-force from the non-gravity force needed to keep you stationary in simple situations like a static spherically symmetric curvature field. The non-geodesic Center Of Mass (COM) force is sloppily called the "gravity force" - it vanishes on the free-float geodesic. The curvature as tidal geodesic deviation (in coordinates relative to COM) is measured in the absence of any g-force.
The geodesic deviation of freely falling test particles can also be measured in the presence of a net "g-force".

Yes, but it's Rube Goldberg messy way to do it. R^a^b is T4(x) INVARIANT - same for LIF & LNIF at same local coincidence P


In addition, the field GCT tensor and spinor equations of classical and quantum physics including the background-independent geometrodynamic field for evolving 3D space (no matter how 4D space-time is sliced or "foliated') on an equal footing with the electromagnetic and all matter fields have the same local frame invariant forms whether the frames are unaccelerated geodesic or accelerated non-geodesic. In this last sense 2 "acceleration is relative." The equivalence principle is not restricted to uniform static fields.

Depends on which version you are talking about.

I mean the time record of g-force on a single detector is locally equivalent to some dynamic GMD field for a some LNIF observer.

Note the equivalence principle is a two-sided coin:

i) COM g-forces in flat 4D spacetime are locally indistinguishable from the non-gravity forces needed to keep one fixed relative to the source in curved spacetime. The world line of a test particle fixed relative to the source (e.g. confirmed by Doppler radar) is off-(timelike) geodesic (always a local g-force).

ii) COM g-forces vanish on unaccelerated timelike geodesics.

Observed net g-forces vanish along geodesics.

"net" has no meaning - excess verbal baggage

Localizing the rigid translation gauge group T4 universally the same way for all non-gravity matter fields introduces the compensating tetrad fields A^a that encode the non-geodesic accelerating local frames and also the curvature if present - it need not be.

Where the compensation acts to restore the original T4 symmetry?

If you like. What that means precisely is that you now have a larger action which is invariant under the large localized T4(x) group - with new curvature field dynamics in addition to the original lepton-quark-EM-weak-strong fields of the standard model.

Am I correct to call T4 a group of coordinate transformations?

If you are careful. The redundant p -> p' coordinate maps on SAME gauge orbit P are factored out!
This is Fadeev-Popov trick taken over from Yang-Mills quantization case (with ghosts violating spin-statistics in Feynman path integrals - so it's already set up for quantizing residual zero point - normal excitations in and out of condensate (Gorkov) in my emergent gravity model. Holography is looking at 2D + 1 non-bounding cycles surrounding 3D + 1 spacetime regions with GMD point monopoles and

&L ~ (Lp^2L)^1/3 (Wigner-Salecker-Bohr-Rosenfeld)

L ~ N^1/2Lp (hologram)

&L ~ N^1/6Lp

N = # Bekenstein c-bits on FUTURE dark energy pumped retro-causal de Sitter horizon with signal nonlocality in A. Valentini's sense.

P orbits are the vertical solid curves, the dots are p, p', p" etc.


e^a = I^a + A^a

ds^2 = guvdx^udx^v = nabe^a^eb = e^aea

nab = Minkowski constant metric of absolutely non-accelerating frames

guv is the curvilinear metric of absolutely accelerating frames

1905 SR only permits unaccelerated global frames where

I^a = I^audx^u

I^au = Kronecker delta 4x4 identity matrix

As soon as we have an accelerated frame A^a =/= 0

So A^a, like the LC connection, is not a GCT tensor?

Exactly. Same as in EM where the vector potential is not a tensor relative to the internal U(1) group.

e.g.

simple example 1+1 spacetime Galilean relativity limit

gt/c << 1

x' = x - (1/2)gt^2

t' = t

(x,t) = GIF

(x',t') = GNIF

dx' = dx - gtdt

dt' = dt

ds^2 = (cdt)^2 - dx^2 = (cdt')^2 - (dx' + gt'dt')^2

= c^2[1 - (gt'/c)^2]dt'^2 - 2gt'dx'dt' - dx'^2

gt't' = [1 - (gt'/c)^2]

gt'x' = -2gt'/c

gx'x' = -1

gtt = 1

gxt = 0

gxx = -1

The tetrad components are

e^tt' = &t/&t' = + 1

dx = dx' - gt'dt'

e^tx' = &t/&x' = 0

e^xx' = &x/&x' = 1

e^xt' = -gt'/c

e^t = dt' = I^t

e^x = dx' - gt'dt' = I^x + A^x

I^x = dx'

Where did you get this expression for I^x?

from the above equations - if it's not obvious you are missing something. I would have to do it in math text standard symbols - it's elementary calculus of partial derivatives and gradient directional derivatives etc.

A^x = -gt'dt' = gravimagnetic tetrad field

Where did you get this expression for A^x?

ditto - it should be obvious

All you've given us is

e^a = I^a + A^a

which is not enough to get I^x = dx', A^a = -gt'dt'.

Yes it is. You are not understanding the calculus.

e.g.

df(x,y) = (&f/&x)dx + (&f/&y)dy

e^au means &x^a(IF)/&x^u(NIF)

x' = x - (1/2)gt^2

t' = t

(x,t) = GIF

(x',t') = GNIF

x^a(IF) = (x,t)

x^u(NIF) = (x',t')

PS of course the local classical laws of physics (tensor and spinor equations) are still independent of the local coincident frames either unaccelerated LIFs or absolutely accelerated LNIFs. Note however, that the LNIF detectors see the Unruh-Hawking black body thermal photons not seen by the LIF detectors. This is a non-classical quantum effect.

On Oct 18, 2007, at 3:23 PM, Jack Sarfatti wrote:

In both Galilean relativity and 1905 Einstein special relativity non-accelerated "geodesic" motion is globally relative. The same is not true in 1916 Einstein general relativity. Non-accelerated geodesic motion means no g-force, weightless free-float. Note that a uniform motion at constant speed in a fixed direction in curved spacetime is not a local non-accelerated geodesic. For example, drive your car on a straight road at constant speed (Earth's surface curvature ignorable for small distances). You are not weightless. When you fall off a ladder you are on a locally non-accelerated geodesic motion momentarily. Your local unaccelerated motion looks "accelerated" to Bob fixed to Earth's surface, which is, in fact, an accelerated off-curved geodesic LNIF. Therefore, there is an absolute test for local geodesic unaccelerated center-of-mass (COM) motion, i.e. free-float weightlessness. In this sense acceleration is locally absolute. If you feel g-force your motion is locally accelerated relative to the intrinsic geodesic structure of the local geometrodynamic field. The key geodesics are the null geodesics ds^2 = 0 of light rays. The intrinsic local frame-invariant 1916 (zero torsion) geometrodynamic field curvature is in the relative tilt of neighboring invariant light cones as shown by Roger Penrose. Note that curvature is "geodesic deviation," i.e. nonlocal relative acceleration between two slightly separated geodesic weightless observers, neither feel local COM g-force. That is, two free-float weightless observers with zero local objective accelerations in their point centers of mass, nevertheless, detect a nonlocal relative acceleration as shown, for example, by the drift of Doppler radar signals - that is the essential operational definition of curvature.

The theory seems to contradict Einstein's equivalence principle that all forms of stress-energy current densities, including locally random virtual zero point vacuum fluctuations bend spacetime equallly. Introducing a high frequency cutoff is a clear violation.

On Oct 15, 2007, at 4:50 PM, Jack Sarfatti wrote:

I am taking a second look at this paper and it deserves close study.

http://www.arxiv.org/abs/0707.1797

What about General Relativity GR?

Argument #1
LIF is same result as below for SR. Use the EQUIVALENCE PRINCIPLE tetrad transformation e^au to go from 1905 SR LIF to LOCALLY COINCIDENT 1916 LNIF. A GCT scalar invariant remains an invariant. For example, given a first rank LIF tensor Ta (LIF) then Tu(LNIF) = eu^aTa, but a LIF scalar has no LIF "a-indices" therefore the scalar remains a scalar.

But is the above really correct? Remember, the Unruh effect
http://en.wikipedia.org/wiki/Unruh_effect
(~ Black Hole temperature, entropy & Hawking radiation) tetrad map LIF -> LNIF = accelerated non-inertial frame off-curved spacetime geodesic, hence g-forces (universal weight) and according to Unruh a black body temperature depending on the actual off-geodesic acceleration caused by a non-gravity translational force and/or a conserved orbital angular momentum in vacuum. Temperature ~ surface gravity in case of event horizon of a black hole.
http://en.wikipedia.org/wiki/Black_hole_thermodynamics

Begin forwarded message:

From: physnews@aip.org
Date: October 18, 2007 8:46:43 AM PDT
To: sarfatti@well.com
Subject: Physics News Update 843
Reply-To: physnews@aip.org


PHYSICS NEWS UPDATE
The American Institute of Physics Bulletin of Physics News
Number 843 October 18, 2007 by Phillip F. Schewe
www.aip.org/pnu

RELATIVISTIC THERMODYNAMICS. Einstein*s special theory of
relativity has formulas, called Lorentz transformations, that
convert time or distance intervals from a resting frame of reference
to a frame zooming by at nearly the speed of light. But how about
temperature? That is, if a speeding observer, carrying her
thermometer with her, tries to measure the temperature of a gas in a
stationary bottle, what temperature will she measure? A new look at
this contentious subject suggests that the temperature will be the
same as that measured in the rest frame. In other words, moving
bodies will not appear hotter or colder.
You*d think that such an issue would have been settled decades ago,
but this is not the case. Einstein and Planck thought, at one time,
that the speeding thermometer would measure a lower temperature,
while others thought the temperature would be higher. One problem
is how to define or measure a gas temperature in the first place.
James Clerk Maxwell in 1866 enunciated his famous formula predicting
that the distribution of gas particle velocities would look like a
Gaussian-shaped curve. But how would this curve appear to be for
someone flying past? What would the equivalent average gas
temperature be to this other observer? Jorn Dunkel and his
colleagues at the Universitat Augsburg (Germany) and the Universidad
de Sevilla (Spain) could not exactly make direct measurements (no
one has figured out how to maintain a contained gas at relativistic
speeds in a terrestrial lab), but they performed extensive
simulations of the matter. Dunkel
(joern.dunkel@physik.uni-augsburg.de ) says that some astrophysical
systems might eventually offer a chance to experimentally judge the
issue. In general the effort to marry thermodynamics with special
relativity is still at an early stage. It is not exactly known how
several thermodynamic parameters change at high speeds. Absolute
zero, Dunkel says, will always be absolute zero, even for
quickly-moving observers. But producing proper Lorentz
transformations for other quantities such as entropy will be
trickier to do. (Cubero et al., Physical Review Letters, 26 October
2007; text available to journalists at www.aip.org/physnews/select)

On Oct 2, 2007, at 5:31 PM, Paul Zielinski wrote:

Jack Sarfatti wrote:
#3
On Oct 2, 2007, at 1:31 PM, Paul Zielinski wrote:

In other words, linear coordinate substitutions?

yes

I^u is a homogeneous affine tensor under the above i.e.

I^au to I^au' = C^uu'I^au

Which is analogous to a "Cartesian tensor" under orthogonal transformations in ordinary 3D space?

yes

Therefore

I^audx^u is an affine invariant (scalar) under I.

In addition, A^a is a Lorentz 4-vector under rigid O(1,3).

This could either mean that the components indexed by a are the components of a Lorentz vector, or
that there is a separate Lorentz vector for each value of a.

the former,

OK.
also "a" labels each GCT u-index tensor

e.g. e^au means 4 distinct first-rank GCT tensors whose components labeled by "u"
Right.
i.e. "a" are O(1,3) indices & u are GCT indices.

So the a-indexed qualtities are components of vectors under LLTs, and the u-indexed quantities
are components of vectors under GCTs?

yes, or more generally tensors (or non-tensor connections as the case may be) relative the respective groups if multiple indices of same type..

e^au means 4 Lorentz vectors in u-space and 4 u-vectors in a-space.

OK. And this is what they call the "flat" vs. "curved" indices?

Yes, u (curved) are also technically "tangent or co-tangent" and a(flat) Minkowski, I prefer "u" as non-geodesic LNIF and "a" as geodesic LIF to connect the formalism directly to the equivalence principle - using Wheeler's operational approach closest to actual experimental physics. In past I called "u" base space and "a" fiber" but I guess technically that's not what the mathematicians like. So basically "a,b ..." means zero g-force geodesic local observer-detector and "u,v ..." means non-zero g-force off-geodesic local observer detectors and all the transformations are "local" in the sense of almost colliding observers looking at the same processes - each observer is a point p on the same GCT gauge orbit P, i.e. p(Alice) ~ p'(Bob) belong to the same P - as in Rovelli's pictures in Ch 2 of "Quantum Gravity."

e^a' = O(1,3)^a'ae^a

eu' = (GCT)^uu'eu

e^a = e^audx^u

eu = e^au(d/dx^a)

eu = e^au(d/dx^a)?

yes, that was a typo


Then e^a = I^a + A^a remains scalar invariant under the larger NON-AFFINE transformations that include those conformal boosts to constant accelerating GNIFs as well as the full GCTs of 1916 GR

i.e. I^a to I^a + X^a under GCTs

A^a to A^a - X^a

just like gauge invariant P + eA in U1(x) electromagnetism.

So A^a to A^a - X^a cancels or "compensates" I^a to I^a + X^a under the "non-affine" transformations?
Such that I^a + A^a to I^a + A^a?

Yes.

OK.

And is that how you model an LIF in gauge gravity theory? Cancellation of the two spoiler non-homogeneous
terms X^a and -X^a in I^a and A^a?

No, A^a = 0 in a LIF, A^a =/= 0 in a LNIF.

OK. So A^a represents the net field observed in the LIF?

No, A^a = 0 in both a Minkowski GIF (R^a^b = 0) and a curved LIF (R^a^b =/= 0) where I^au = Kronecker delta (this is in Rovelli explicitly)

A^a =/= 0 in both a Minkowski GNIF (R^a^b = 0) and a curved LNIF (R^a^b =/= 0), therefore A^a =/= 0 is Shipov's "inertial geometrodynamic field" - even though it is zero in a LIF its gradients need not be zero so that R^a^b =/= 0. Remember this curvature field 2-form

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

where S^a^b = spin connection 1-form

is already of Yang-Mills form and it is a GCT local scalar invariant (zero rank GCT tensor) like ds^2 = e^aea is.

S^a^b is the compensating Yang-Mills type gauge potential from localizing the rigid 6-parameter Lorentz group SO(1,3)

R^a^b = - R^b^a is ALSO an antisymmetric second rank 6-parameter Lorentz group SO(1,3) tensor just like the EM field tensor is!

I was also trying to force the torsion field 2-form T^a into the Yang-Mills mold

e^a = I^a + A^a

T^a = d(I^a + A^a) + S^ac/\(I^a + A^a)

in 1905 SR only allowing GIF -> GIF' ("affine" global frame transformations)

A^a = 0 and S^a^b = 0

dI^a = 0

half-way to 1916 GR allowing GIF -> GNIF'

A^a =/= 0 and S^a^b =/= 0

but

R^a^b = 0

and

T^a = 0

Going all the way to 1916 GR, i.e. replace rigid T4 by local T4(x) (defines "GCT), i.e. LIF -> LNIF (tetrads) & LNIF -> LNIF' as well as LIF -> LIF' all at same P, i.e. on fixed GCT gauge orbit

R^a^b =/= 0 allowed

T^a = 0 enforced.

This gives a dummy redundant S^a^b(T4) (see Rovelli eq. 2.89) that I cannot put into Yang-Mills form

S^a^b(T4) = w^a^bce^c

Might be able to do it for the actual torsion field, but I am not sure - maybe not.

Einstein-Cartan theory is locally gauging full Poincare P10 to P10(x) so that T^a =/= 0

Note if T^a =/= 0 from localizing only SO(1,3) subgroup of P10 you do get a torsion induced curvature. This is what Utiyama did in 1956, but he did not have GCTs as a set of gauge transformations. He stuck them in ad-hoc because he did not localize T4.


e^a(LIF) = I^a

e^a(LNIF) = I'^a + A'^a

I'^a = I^a + X^a

A'^a = -X^a

The intrinsic curvature is in the gradients of A^a =/= 0 even when A^a = 0 in a LIF - same as Levi-Civita.

OK. So then it is A^a that should split up, in my model, into "curved-coordinate" and "intrinsic" parts -- as I thought.

Maybe, but why bother?

Consider the space of local frames on a fixed GCT gauge orbit (see pictures in Rovelli Ch 2) - each local frame is a point p on the orbit. A^a is a functional on this gauge orbit "space". LIFs are critical points with horizontal tangents (analogy) - intrinsic curvature is in the second order partial derivatives of the A^a inertial field.

Do a Taylor series. In a LIF starting point (remember "p" here is in the abstract space of local frames on a gauge orbit not physical spacetime)

A^a(LNIF at p') ~ 0 + 0(p' - p) + (1/2)(d^A^a(LIF at p)/dp^2)(p' - p)^2 + ...

If we expand around a LNIF at p to a LIF at p' then

0 ~ A^a(LNIF at p) + (dA^a(LNIF at p)/dp)(p' - p) + (1/2)(d^A^a(LNIF at p)/dp^2)(p' - p)^2 + ...

Then in this model the cancellation of the non-tidal g-field in an LIF is entirely a function of the coordinate
transformation properties of the tetrad basis? With no reference to the intrinsic spacetime geometry?

Exactly - g-forces are simply non-geodesic artifacts of those non-affine transformations to accelerating frames, curvature is completely irrelevant.

If by this you mean "...to local frames accelerating with respect to LIFs", then OK. That is certainly consistent with the position you've taken previously.

Yes. The LIFs are determined by the geodesics that depend on the curvature GCT invariants R^a^b =/= 0 i.e. relative tilts of neighboring light cones (e.g. R. Penrose, "The Road to Reality"). By definition LIFs defined relative to R^a^b =/= 0 are "nonaccelerating" (zero g-forces). If you force this into Minkowski spacetime like Puthoff & Yilmaz want to do then you change the meaning of "nonaccelerating" causing a lot of confusion! A curved (R^a^b =/= 0) geodesic LIF looks approximately like a Minkowski (R^a^b = 0 globally) GNIF! Hence a lot of useless arguments.

There are g-forces in Minkowski S-T GNIFs - what curvature does is to change what is meant by "geodesic".

If by "curvature" you mean "intrinsic stretch-squeeze deformation of the manifold", then I agree.

Yes, that is the Weyl vacuum curvature there is also the Ricci compression/expansion in the presence of real matter quanta and also virtual matter quanta, i.e. the gravitating dark matter and the anti-gravitating dark energy both!

Note that in 1905 SR X^a = 0 and A^a = 0 i.e. only GIF -> GIF'

Right. That's the easy part.


So A^a is a kind of "inertial field" in G. Shipov's sense.

I don't understand this. Why doesn't the term X^a (in I^a -> I^a + X^a) represent an inertial field?

OK I see what you mean as in my above

e^a(LIF) = I^a

e^a(LNIF) = I'^a + A'^a

I'^a = I^a + X^a

A'^a = -X^a

Therefore, you can think of X^a as a purely contingent "inertial field", because of the equivalence principle absent in internal Yang-Mills of weak flavor and strong color forces, the GCT (local T4(x)) gauge transformations on fixed gauge orbits have direct physical meaning in terms of what actual detectors register.