Baron Munchausen Meets Rube Goldberg in Einstein's Elevator

PS No matter how hard the Baron fires his rocket motor, his non-geodesic world line must be inside the forward light cone at each point on that world line. The field of light cones is not parallel in curved space-time so that the bundle of non-geodesics available to the Baron is not identical to what it would be in globally flat space-time. Therefore, one must take the connection field of the source in some global coordinates like the asymptotic flat "Book Keeper coordinates" (Wheeler's term) in

ds^2 = (1 - 2M/r)dt^2 - (1 - 2M/r)^-1dr^2 + r^2(dtheta^2 + sin^2thetadphi^2)

to make the problem simpler let theta = pi/2 equatorial orbit

x^1 is radial r, x^3 is azimuthal phi, the only non-zero LC-connection components then are

(^010) = (M/r^2)(1 - 2M/r)^-1

(^133) = -r(1 - 2M/r)

(^100) = (M/r^2)(1 - 2M/r)

(^313) = 1/r

For the fiducial hovering LNIF shell observers at fixed r

dt(shell) = (1 - 2M/r)^1/2dt

dr(shell) = (1 - 2M/r)^-1/2dr

dphi(shell) = dphi

So for an arbitrary motion of the Baron subject to the above causal light cone restriction, one needs to find the GCT from the shell observer to the Baron to do find the Baron's coincident connection field relative to the shell observer.

i.e. symbolically we have the CONTINGENT inhomogeneous non-tensor transformation from non-geodesic LNIF Shell Observer to the non-geodesic LNIF Baron

(Baron) = (GCT)(GCT)(GCT)(Shell Observer) + (GCT)Grad(GCT)

This is not intrinsic. This is not of any fundamental theoretical interest. It is contingent even though one can formally relate it to curvature, it's Fool's Gold. It's a Chimera. It's The Siren beckoning. Also it is a very complex calculation in general not worth the effort since the Baron would do better to directly measure his local g with a scale.


On Sep 3, 2006, at 8:23 PM, Jack Sarfatti wrote:

The word "fictitious" is a bad one like "hidden variables" in Bohm's reinterpretation of quantum theory. You certainly "feel" a "fictitious" g and it will cause a pointer on a suitable detector to move. Therefore, fictitious forces, or inertial forces, are physical in that they are detectable. However, they are not tensors relative to the relevant symmetry groups, therefore, one cannot construct objective frame-invariants from them under those symmetry groups. In this subtle sense I meant "g-forces are not physical" or "g-forces are fictitious" although in a pragmatic experiential sense they are real!



The covariant equation for the NON-geodesic in ALL frames is

D^2x^u(test)/ds^2 = d^2x^u(test)/ds^2 + (Connection)^uvw(dx^v(test)/ds)(dx^w(test)/ds) = F^u(non-gravity)/m(test)

If Alice is LIF her connection vanishes and she sees the special relativity F = ma

D^2x^u(test)/ds^2 = d^2x^u(test)/ds^2 = F^u(non-gravity)/m(test)

What does the Baron see in his own LNIF rest frame when he fires a small rocket motor on his cannon ball?

D^2x^u(Baron)/ds^2 = (Connection Baron)^u00(dx^0(Baron)/ds)(dx^0(Baron)/ds) = F^u(Baron)/m(Baron)

(Connection Baron)^u00(dx^0(test)/ds)(dx^0(test)/ds) - F^u(non-gravity)/m(Baron) = 0

(Connection Baron)^000(dx^0(test)/ds)(dx^0(test)/ds) - F^0(non-gravity)/m(Baron) = 0

(Connection Baron)^i00(dx^0(test)/ds)(dx^0(test)/ds) - F^i(non-gravity)/m(Baron) = 0

i = 1,2,3 spacelike

The experienced "fictitious" inertial nongeodesic g-force in the Baron's frame is simply

g-force = {(Connection Baron)^i00}

= {F^i(non-gravity)/m(Baron)}

Notice that curvature is completely irrelevant i.e. gradients of the connection play no role whatsoever.

Let the Baron in his LNIF rest frame look at a Alice who is on a geodesic. The Baron's version of Alice's geodesic equation is

D^2x^u(Alice)/ds^2

= d^2x^u(Alice)/ds^2 + (Connection Baron)^uvw(dx^v(Alice)/ds)(dx^w(Alice)/ds) = 0

This simplifies to

= d^2x^u(Alice)/ds^2 + (Connection Baron)^u00(dx^0(Alice)/ds)(dx^0(Alice)/ds) = 0

= d^2x^u(Alice relative to Baron)/ds^2

+ F^i(non-gravity on Baron)/m(Baron)(dx^0(Alice relative to Baron)/ds)^2 = 0

Now above assumes Minkowski space-time.

Suppose all of the above happens in the vacuum curvature field of an SSS source

g00 = (1 - 2M(source)/r) = - 1/grr etc.

in the usual asymptotic coordinates.

Let Alice and the Baron be momentarily close to a given r,theta, phi, t.

For example, in the equatorial plane theta = pi/2 "1" = "r"

(SSS connection)^100 = M/r^2(1 - 2M/r) etc.

One would then have to find the GCT connecting the nearly coincident static shell observer to the Baron. If, for example, the Baron adjusted his rocket motor to be a shell observer, then the GCT is the trivial identity transformation and one can then use

(SSS connection)^100 = M/r^2(1 - 2M/r)

Actually doing a detailed calculation is not trivial.


From: Jack Sarfatti
Date: September 3, 2006 4:58:01 PM PDT
To: Sarfatti_Physics_Seminars@yahoogroups.com
Subject: Re: Zielinski fails to grasp the subtle beauties of Einstein's Vision


On Sep 3, 2006, at 1:16 PM, xerberos2 wrote:


Jack wrote:You misread Einstein's text ...

I'm not misreading his text. Einstein's text is very clear. He is
proposing to treat a fictitious inertial field as if it were a real
gravitational field, so that he can pretend that the accelerating
frame K' is not accelerating.

By "real gravitational field" he means in the sense of Newton's theory.

K' that is non-geodesic in curved space-time is locally equivalent to a geodesic inertial frame in flat space-time with a "real" gravity field. This is Einstein's bridge back to Newton's theory. "geodesic" has two different meanings in the same sentence here.

"Real gravitational g-field" is meaningful in Newton's theory in flat Euclidean 3D space with absolute simultaneity (Galilean relativity v/c ---> 0) where the Newtonian geodesics are straight lines in flat Euclidean 3D space with point test particles moving at constant speed along them. That's the Newtonian geodesic. There is zero g-force on Newton's geodesic.

"g-field" in Einstein's theory means exactly the same thing as in Newton's theory except that the notion of geodesic has changed. An Einstein geodesic projected down into 3D space is generally not a straight line nor is the test particle speed constant. For example the Earth's elliptical orbit around the Sun is geodesic relative to the Sun's curvature field - to a good approximation. Curvature is geodesic deviation. g-forces are non-zero only on non-geodesics created by non-gravity (essentially electromagnetic) forces. There is no necessary intrinsic relationship of a g-force event to the local curvature.

Now, what confuses Zielinski is the following: consider a cannon ball in free fall as in


http://www.zonalibre.org/blog/diversovariable/archives/baron-munchausen.jpg

Newton's explanation: the Baron and the cannonball are NOT on a geodesic, therefore, there is a real gravitational force per unit test mass on both the Baron and the cannonball relative to the frame K' (surface of Earth) that is "inertial" to a good approximation. It is the same real gravitational force per unit test mass g for both

g-force(Newton) ~ GM(Earth)/r^2

Therefore, the Baron feels weightless, i.e. no pressure on his behind from the cannonball since each are falling in exactly the same way at every moment. That is, there is zero g-force in the common rest frame of the Baron and the cannonball.

Einstein's explanation: the Baron and the cannon ball are on a timelike geodesic in curved space-time.

The covariant equation for the geodesic in ALL frames is

D^2x^u(test)/ds^2 = d^2x^u(test)/ds^2 + (Connection)^uvw(dx^v(test)/ds)(dx^w(test)/ds) = 0

This is the covariant

F = ma

with

F = 0

This form-invariant (local frame covariant) equation means.

OBJECTIVE TENSOR TEST PARTICLE ACCELERATION = 0

This is the DEFINITION of a GEODESIC!

THIS IS TRUE IN ALL FRAMES FOR ALL POSSIBLE CURVATURES INCLUDING GLOBALLY FLAT ZERO EVERYWHERE-WHEN.

D^2x^u(test)/ds^2 is the GCT tensor acceleration of the test particle. Its local frame-invariant scalar is

g = (D^2x^u(test)/ds^2D^2xu(test)/ds^2)^1/2

g = 0 on a geodesic - universally true!

Look more closely at the meaning of the geodesic equation. Let Baron Munchausen be on the test particle that is the cannonball in the above picture.

D^2x^u(Baron)/ds^2 = d^2x^u(Baron)/ds^2 + (Connection)^uvw(dx^v(Baron)/ds)(dx^w(Baron)/ds) = 0


d^2x^u(Baron)/ds^2 = Newton's flat space + time kinematical acceleration that is not a GCT tensor.

(Connection)^uvw(dx^v(test)/ds)(dx^w(test)/ds) = inertial "force per test mass" that is a contingent artifact of the local frame of reference. This term even exists in globally flat spacetime when K' is accelerating from an electromagnetic force.

Let Alice be a nearly coincident to the Baron geodesic LIF in curved space-time. What Alice sees is

D^2x^u(Baron)/ds^2 = d^2x^u(Baron)/ds^2

= 0

(Connection Alice LIF) = 0

The size of Alice's LIF is such that the gradients in (Connection Alice LIF) are ignorable. You can think of the LIF as a ball at the bottom of a potential well with a very small zero point jiggle - this is only a rough analogy.


http://rsc.anu.edu.au/~sevick/groupwebpages/images/animations/capture_3D0282.jpg

Let Bob be a nearly coincident to the Baron non-geodesic LNIF observer, then in Bob's POV

D^2x^u(Baron)/ds^2

= d^2x^u(Baron)/ds^2 + (Connection Bob)^uvw(dx^v(Baron)/ds)(dx^w(Baron)/ds)

= 0

(Connection Bob) =/= 0

Because an electromagnetic force is acting on Bob.

Finally in the Baron's rest frame, which in this case is also geodesic

D^2x^u(Baron)/ds^2 = d^2x^u(Baron)/ds^2

= 0

dx^i/ds = 0

i = 1,2,3 spacelike

dx^0/ds = 1

This covers all of the cases.

Homework Problem: Put an external force on the Baron. Describe all the cases.

In answer to Z's question about Wheeler. When Wheeler says gravity is curvature he means tensor "geodesic deviation" he does not mean contingent non-tensor non-geodesic "g-force."

"Gravity" and "gravity field" mean different things in different contexts. Usually this is not a problem for physicists to get the nuance intended in each specific. It is a problem for Z.

Newton vs Einstein

On Sep 3, 2006, at 1:16 PM, xerberos2 wrote:


Jack wrote:You misread Einstein's text ...

I'm not misreading his text. Einstein's text is very clear. He is
proposing to treat a fictitious inertial field as if it were a real
gravitational field, so that he can pretend that the accelerating
frame K' is not accelerating.

By "real gravitational field" he means in the sense of Newton's theory.

K' that is non-geodesic in curved space-time is locally equivalent to a geodesic inertial frame in flat space-time with a "real" gravity field. This is Einstein's bridge back to Newton's theory. "geodesic" has two different meanings in the same sentence here.

"Real gravitational g-field" is meaningful in Newton's theory in flat Euclidean 3D space with absolute simultaneity (Galilean relativity v/c ---> 0) where the Newtonian geodesics are straight lines in flat Euclidean 3D space with point test particles moving at constant speed along them. That's the Newtonian geodesic. There is zero g-force on Newton's geodesic.

"g-field" in Einstein's theory means exactly the same thing as in Newton's theory except that the notion of geodesic has changed. An Einstein geodesic projected down into 3D space is generally not a straight line nor is the test particle speed constant. For example the Earth's elliptical orbit around the Sun is geodesic relative to the Sun's curvature field - to a good approximation. Curvature is geodesic deviation. g-forces are non-zero only on non-geodesics created by non-gravity (essentially electromagnetic) forces. There is no necessary intrinsic relationship of a g-force event to the local curvature.

Now, what confuses Zielinski is the following: consider a cannon ball in free fall as in


http://www.zonalibre.org/blog/diversovariable/archives/baron-munchausen.jpg

Newton's explanation: the Baron and the cannonball are NOT on a geodesic, therefore, there is a real gravitational force per unit test mass on both the Baron and the cannonball relative to the frame K' (surface of Earth) that is "inertial" to a good approximation. It is the same real gravitational force per unit test mass g for both

g-force(Newton) ~ GM(Earth)/r^2

Therefore, the Baron feels weightless, i.e. no pressure on his behind from the cannonball since each are falling in exactly the same way at every moment. That is, there is zero g-force in the common rest frame of the Baron and the cannonball.

Einstein's explanation: the Baron and the cannon ball are on a timelike geodesic in curved space-time.

The covariant equation for the geodesic in ALL frames is

D^2x^u(test)/ds^2 = d^2x^u(test)/ds^2 + (Connection)^uvw(dx^v(test)/ds)(dx^w(test)/ds) = 0

This is the covariant

F = ma

with

F = 0

This form-invariant (local frame covariant) equation means.

OBJECTIVE TENSOR TEST PARTICLE ACCELERATION = 0

This is the DEFINITION of a GEODESIC!

THIS IS TRUE IN ALL FRAMES FOR ALL POSSIBLE CURVATURES INCLUDING GLOBALLY FLAT ZERO EVERYWHERE-WHEN.

D^2x^u(test)/ds^2 is the GCT tensor acceleration of the test particle. Its local frame-invariant scalar is

g = (D^2x^u(test)/ds^2D^2xu(test)/ds^2)^1/2

g = 0 on a geodesic - universally true!

Look more closely at the meaning of the geodesic equation. Let Baron Munchausen be on the test particle that is the cannonball in the above picture.

D^2x^u(Baron)/ds^2 = d^2x^u(Baron)/ds^2 + (Connection)^uvw(dx^v(Baron)/ds)(dx^w(Baron)/ds) = 0


d^2x^u(Baron)/ds^2 = Newton's flat space + time kinematical acceleration that is not a GCT tensor.

(Connection)^uvw(dx^v(test)/ds)(dx^w(test)/ds) = inertial "force per test mass" that is a contingent artifact of the local frame of reference. This term even exists in globally flat spacetime when K' is accelerating from an electromagnetic force.

Let Alice be a nearly coincident to the Baron geodesic LIF in curved space-time. What Alice sees is

D^2x^u(Baron)/ds^2 = d^2x^u(Baron)/ds^2

= 0

(Connection Alice LIF) = 0

The size of Alice's LIF is such that the gradients in (Connection Alice LIF) are ignorable. You can think of the LIF as a ball at the bottom of a potential well with a very small zero point jiggle - this is only a rough analogy.


http://rsc.anu.edu.au/~sevick/groupwebpages/images/animations/capture_3D0282.jpg

Let Bob be a nearly coincident to the Baron non-geodesic LNIF observer, then in Bob's POV

D^2x^u(Baron)/ds^2

= d^2x^u(Baron)/ds^2 + (Connection Bob)^uvw(dx^v(Baron)/ds)(dx^w(Baron)/ds)

= 0

(Connection Bob) =/= 0

Because an electromagnetic force is acting on Bob.

Finally in the Baron's rest frame, which in this case is also geodesic

D^2x^u(Baron)/ds^2 = d^2x^u(Baron)/ds^2

= 0

dx^i/ds = 0

i = 1,2,3 spacelike

dx^0/ds = 1

This covers all of the cases.

Homework Problem: Put an external force on the Baron. Describe all the cases.

In answer to Z's question about Wheeler. When Wheeler says gravity is curvature he means tensor "geodesic deviation" he does not mean contingent non-tensor non-geodesic "g-force."

"Gravity" and "gravity field" mean different things in different contexts. Usually this is not a problem for physicists to get the nuance intended in each specific. It is a problem for Z.

Kibble's 1961 paper on gravity as a local gauge theory

Sean Carroll's text book lightly touches on this at the end. Sunny Auyang makes a short cryptic remark in her book on the philosophy of quantum field theory that is intriguing but too incomplete.

My original unique approach to gravity as an emergent collective phenomenon from the inflation process itself has the tetrads (AKA "vierbeins") as the macro-quantum emergent 4D covariant supersolid field in analogy with the 3D Galilean superfluid velocity field. The tetrad field is renormalizable spin 1 as a quantum field. Einstein's geometrodynamic field is quadratic in the tetrad field, therefore any residual zero point micro-quanta outside of the Bose-Einstein vacuum ODLRO condensate forming the random anti-gravitating dark energy are Einstein-Podolsky-Rosen entangled spin 2 triplet pair states of the spin 1 tetrad quanta.

T.W.B. Kibble's 1961 paper "Lorentz Invariance and the Gravitational Field" JMP 2, March-April 1961 was a marked improvement over Utiyama's partial solution of the problem that locally gauged only the 6-parameter homogeneous Lorentz group (AKA Poincare group) to get the spin connection 1-form w^ab = w^abudx^u for the parallel transport of orientations of the tetrad 1-forms e^a = e^audx^u, a = 0,1,2,3 AKA Cartan mobile frames. Utiyama had to stick in the curved metric ad-hoc - not very satisfactory. Kibble locally gauged the entire 10-parameter inhomogeneous Lorentz group. This was prior to the elegant math of fiber bundles in physics where the compensating local gauge potential comes from the principle bundle and the source fields come from an associated bundle. Gauge theories use internal symmetry groups G for action dynamics with the Poincare group as a rigid non-dynamical background enforcing globally flat spacetime without any gravity at all. The equivalence principle forces the Poincare group to be dynamical and this introduces an added layer of complexity, ambiguity and confusion when trying to cast gravity as a local gauge theory. One must use Dirac's idea of the "substratum" in which the tetrad fields are well-behaved spin 1 vector fields when quantized rather than the unrenormalizable spin 2 tensor fields. It is curious that Kibble, or Penrose later, did not locally gauge the 15-parameter massless conformal group that is the basis of twistor theory. Locally gauging the 4-parameter translation subgroup T4 of the 10-parameter Poincare group gives the Einstein-Cartan tetrads e^a as the compensating field. However, because of the equivalence principle, these tetrads are also in the associated bundle as source fields like the spinor electron field in U(1) QED. That is, the equivalence principle has a feature like Godel's self-reference. In a sense this is true of all non-Abelian gauge theories that are self-interacting forming "geons" or "solitons" or "glue balls" (QCD), i.e. the gauge field carries the source charge. In the case of gravity the source charge is stress-energy density. Although the spin 2 geometrodynamic field does not have a local stress-energy tensor, one cannot jump to that conclusion for the spin 1 tetrad field in the substratum. Locally gauging the 6-parameter homogeneous group O(1,3) gives a dynamically independent spin connection. Note, that in Einstein's 1916 theory, the spin connection is not dynamically independent. The tetrads are dynamically independent and forcing the constraint of zero torsion gaps to second order in closed loops of parallel transport means that the spin connection components are determined by the tetrad components. This is not so in the general case treated by Kibble in 1961.

"The extended transformations for which the 10 parameters become arbitrary functions of position may be interpreted as general coordinate transformations and rotations of the vierbein system."

Torsion Fields: Some toy model calculations
I. 1 + 1 string spacetime slice, neglecting Weyl conformal dilation but including energy and momentum translation generators i.e. A00 = Energy Generator, A11 = Linear Momentum Generator in sense of Noether's theorem relating symmetries to conservation laws for continuous groups. We mean appropriate matrix representations of the Lie algebra depending on what physical vector space they operate on, e.g. Cartan mobile tetrad local frames of reference for gravity and internal vector spaces for "charges" of U(1), SU(2) & SU(3).

The geometrodynamic gauge-covariant partial derivatives acting on Tuv(source) matter fields are

,u ---> ;u = ,u + (Connection)u^a^bAab

(use ' for base space indices)

;0' = ,0' + (Connection)0'^0^0A00 + (Connection)0'^1^1A11

+ (Connection)0'^1^0A10 + (Connection)0'^0^1A01

A01 = - A10 = space-time Lorentz boost

;0' = ,0' + (Connection)0'^0^0(Energy) + (Connection)0'^1^1(Linear Momentum)

+ [(Connection)0'^1^0 - (Connection)0'^0^1]A10

;0' = ,0' + (LC Connection)0'^0^0(Energy) + (LC Connection)0'^1^1(Linear Momentum)

+ (Tensor Torsion Field)0'^1^0(Lorentz Boost)

Note how the String Torsion Field is the Yang-Mills "Phase" of the Lorentz Boost.

The Equivalence Principle is encoded in the (LC Connection) terms.

Similarly for ;1

The tetrads tilt in infinitesimal displacements as:

ea(x + dx) = eb(x)(Connection at x)u^badx^u

e0(x + dx) = [(Connection at x)0'^00dx^0' + (Connection at x)1'^00dx^1']e0(x)

+ [(Connection at x)0'^10dx^0' + (Connection at x)1'^10dx^1']e1(x)

e1(x + dx) = [(Connection at x)0'^01dx^0' + (Connection at x)1'^01dx^1']e0(x)

+ [(Connection at x)0'^11dx^0' + (Connection at x)1'^11dx^1']e1(x)

II 2 + 1 slice for anyonic vacuum ODLRO fractional charge/quantum statistics "World Hologram Plate"

cc* + c*ce^i(Anyonic Phase) = 1

Anyonic Phase = 0 2D fermions

Anyonic Phase = pi 2D bosons

Control Anyonic Phase with perpendicular magnetic field on a 2D nano quantum well showing fractional quantum Hall effect.



Exotic matter effects are neither fermion nor boson.

What does that do to the spin-statistics connection?

Flux tubes pin to charged fermions. Effective charges are fractional like quarks, but only in 2D + 1 space-time "surfaces". In world holography there are no dynamically independent volume degrees of freedom for the geometrodynamic field, hence the Bekenstein bound for black hole thermodynamics and the amount of bits that can be packed into a Volume V ~ V^2/3/Lp^2 ~ (/\Lp^2)^-1 for our pocket universe on the cosmic landscape of parallel universes.

,u ---> ;u = ,u + (Connection)u^a^bAab

;0' = ,0' + (Connection)0'^a^bAab

;0' = ,0' + (Connection)0'^0^0A00 + (Connection)0'^1^1A11 + (Connection)0'^2^2A22

+ (Connection)0'^0^1A01 + (Connection)0'^1^0A10

+ (Connection)0'^0^2A02 + (Connection)0'^2^0A20

+ (Connection)0'^1^2A12 + (Connection)0'^2^1A21

;0' = ,0' + (Connection)0'^0^0(Energy) + (Connection)0'^1^1(Momentum1) +

(Connection)0'^2^2(Momentum2)

+ [(Connection)0'^0^1 - (Connection)0'^1^0]A01

+ [(Connection)0'^0^2 - (Connection)0'^2^0]A02

+ [(Connection)0'^1^2 - (Connection)0'^2^1]A12

;0' = ,0' + (Connection)0'^0^0(Energy) + (Connection)0'^1^1(Momentum1) +

(Connection)0'^2^2(Momentum2)

+ (TORSION)0'^0^1 (LORENTZ BOOST)01

+ (TORSION)0'^0^2 (LORENTZ BOOST)02

+ (TORSION)0'^1^2 (ROTATION)12

Similarly for ;1'

Note that in Einstein's 1916 theory, TORSION = 0, therefore the Lorentz boost and rotation terms vanish!

Homework, do this for 3D + 1.


On Aug 29, 2006, at 8:32 AM, Jack Sarfatti wrote:

Bottom Line
Gravity is "More is different" emergent from the Standard Model of quarks & leptons with gauge bosons. Standard quantum gravity theories are not even wrong, i.e. loop quantum gravity, string theory, canonical quantization are like trying to quantize elasticity theory.

This is the 11th dimension so to speak. 10 from the Poincare group.
From the principle fiber bundle

M(Base Space) = Cartan Mobile Tetrad Frame Fiber Bundle/(Poincare Group + Weyl Dilation)

dimM = 11?

This is intuitive - still thinking about it - non-rigorous.

That is, 4 translations of the tetrad local frame, 3 rotations, 3 boosts + 1 Weyl dilation. Each parameter "phase" "angle of rotation" is a "dimension" of M.

11 G-Orbit equivalence classes partition of the tetrad bundle.

G = Poincare Group + Weyl Dilation
(universal symmetry group for emergent spacetime physics)

Also an addition 4 special conformal transformations not accounted for (Tony Smith)

,u ---> ;u = ,u + (Connection)u^a^bAab

"Gauge covariant partial derivative" analog to internal symmetry Yang-Mills SU(2), SU(3) ...

{Aab} = Lie Algebra of G

The Cartan mobile tetrad frames tilt & stretch/contract relative to each other

ea(x + dx) = eb(x)(Connection at x)u^badx^u

(ea|eb) = (Minkowski metric)ab = nab

(eu|ev) = (Curvilinear Metric)uv = guv

e^a = eu^adx^u

eu = eu^a&a

Identity action = I = e^a&a = I' + B

F = dB ~ dTheta/\dPhi

Theta & Phi = Goldstone phases of vacuum ODLRO Higgs inflation field with 3 real components (in one toy model)

B ~ Theta/\dPhi - dTheta/\Phi

d^2 = 0

D = d + B/
DF = 0

D*F = *J

D*J = 0

Yang-Mills field equations for U(1)xSU(2)xSU(3) of standard model in false vacuum that is globally flat.

i.e. Gravity emergent from the Standard Model of quarks & leptons with gauge bosons.

On Aug 29, 2006, at 2:05 AM, Carlos Castro wrote:

Dear Jack :

Also in Weyl's geometry the non-metricity tensor Q is
zero as well.

The Weyl covariant derivative of the metric is zero.
Despite that the lengths of vectors change under
parallel transport (in Weyl spacetime )
the angle of two vectors remains the same ( conformal
property ) under paralell transport.

Best wishes

Carlos

Emergent Gravity from Quarks and Leptons
Bottom Line
Gravity is "More is different" emergent from the Standard Model of quarks & leptons with gauge bosons. Standard quantum gravity theories are not even wrong, i.e. loop quantum gravity, string theory, canonical quantization are like trying to quantize elasticity theory.

This is the 11th dimension so to speak. 10 from the Poincare group.
From the principle fiber bundle

M(Base Space) = Cartan Mobile Tetrad Frame Fiber Bundle/(Poincare Group + Weyl Dilation)

dimM = 11?

This is intuitive - still thinking about it - non-rigorous.

That is, 4 translations of the tetrad local frame, 3 rotations, 3 boosts + 1 Weyl dilation. Each parameter "phase" "angle of rotation" is a "dimension" of M.

11 G-Orbit equivalence classes partition of the tetrad bundle.

G = Poincare Group + Weyl Dilation
(universal symmetry group for emergent spacetime physics)

Also an addition 4 special conformal transformations not accounted for (Tony Smith)

,u ---> ;u = ,u + (Connection)u^a^bAab

"Gauge covariant partial derivative" analog to internal symmetry Yang-Mills SU(2), SU(3) ...

{Aab} = Lie Algebra of G

The Cartan mobile tetrad frames tilt & stretch/contract relative to each other

ea(x + dx) = eb(x)(Connection at x)u^badx^u

(ea|eb) = (Minkowski metric)ab = nab

(eu|ev) = (Curvilinear Metric)uv = guv

e^a = eu^adx^u

eu = eu^a&a

Identity action = I = e^a&a = I' + B

F = dB ~ dTheta/\dPhi

Theta & Phi = Goldstone phases of vacuum ODLRO Higgs inflation field with 3 real components (in one toy model)

B ~ Theta/\dPhi - dTheta/\Phi

d^2 = 0

D = d + B/
DF = 0

D*F = *J

D*J = 0

Yang-Mills field equations for U(1)xSU(2)xSU(3) of standard model in false vacuum that is globally flat.

i.e. Gravity emergent from the Standard Model of quarks & leptons with gauge bosons.

On Aug 29, 2006, at 2:05 AM, Carlos Castro wrote:

Dear Jack :

Also in Weyl's geometry the non-metricity tensor Q is
zero as well.

The Weyl covariant derivative of the metric is zero.
Despite that the lengths of vectors change under
parallel transport (in Weyl spacetime )
the angle of two vectors remains the same ( conformal
property ) under paralell transport.

Best wishes

Carlos

Graviity Emergent from the Dirac Substratum

Geodesic deviation is nonlocal even though the Riemann curvature tensor is
local.

How can that be? Since you can even measure it locally?

But you cannot. As soon as you measure geodesic deviation, the LIF
breaks down. You never measure the local curvature tensor itself only its nonlocal
footprint so to speak.

OK, then what about the water drop argument put forward by Ohanian and
Ruffini ("O&R") in their "Gravitation and Spacetime", Ch 1?

That's non-local!! The LIF is defined only to the extent that the geodesic deviation is below the threshold of detection! That's the whole point!!!!!! Ruvwl(x) is formally local but it is not directly measurable - it's inferred from

d^2(x-x)^u/ds^2 = (x-x')^l(dx^w/ds)(dx^v/ds)(Ruvwl)

All the quantities here apart from are independently measurable.

(Ruvwl) is a nonlocal smear or average over scale (x - x') invariant spacetime separation of the 2 geodesic test particles.

EEP is only good for a single test particle observer - as soon as geodesic detection is detectable LIF needs to be made smaller!

So when you detect geodesic deviation you no longer can use only ONE LIF - you have two mobile LIF geodesic tetrad frames tilted relative to each other.

e^j(x + dx) = e^i(x){i^ju|x}dx^u

(ej|ei) = (Minkowski)ij

(eu|ev) = guv curvilinear metric

All you did Paul was to CONTINGENTLY CHOOSE THE SHELL HOVERING LNIFs, that may not even exist in general, and call them INTRINSIC ACCELERATION.

All test particles do have invariant 4-acceleration magnitude of course. For geodesics it's ZERO.

Note that their are 6 "phases" for relative rotation of the tetrad frames and 4 more if you include infinitesimal translations. Add the Weyl dilatation to get the 11-dim manifold of M-theory.

It's the orientations of the mobile Cartan tetrad frames + dilation that is analogous to the internal gauge groups U(1), SU(2), SU(3) Yang-Mills.

As soon as you get a geodesic deviation signal filtered from the noise, that means your measurement is NO GOOD. You must reduce resolution or make your scale smaller until you hit rock bottom "Planck scale" that may be much larger than 10^-33 cm ending the hierarchy problem "desert." Wheeler's system is consistent!

PS in g00 = 1 + V(Newton)/c^2) static metrics

But from POV of LOCAL GAUGE THEORY here Poincare group is locally gauged as if it is internal Yang-Mills, the CONNECTION is the YANG-MILLS POTENTIAL

i.e
;u = ,u + {u|^i^j}Aij

where Aij are, in general the 10 generators of the global Poincare group

i.e. 4 translations + 3 space rotations + 3 space-time boosts

{u|^i^j} is the LC connection here with TORSION beyond Einstein 1916

LOCALLY GAUGE GL(4,R) to get 6 more generators and phases?

The connection field components are like the "phases" of Yang-Mills.

In simplest U(1) em

e^iPHASE(ELECTRIC CHARGE) operates on a matter source field

PHASE is like connection component or like 3 phases of SU(2) & 8 phases of SU(3) etc.

BUT MY EMERGENT GRAVITY has the DIRAC SUBSTRATUM!

THIS PART IS REALLY NEW ORIGINAL TO ME, AND ME ALONE.

e = I = I' + A

I is the IDENTITY action on the tangent bundle of mobile LIF Einstein-Cartan frames as Waldyr Rodrigues says.

Think of analogy in Hilbert space

I = Sum|i)(i| completeness

remember macro-quantum ODLRO is OVERCOMPLETE

Also remember MY SOLUTION to ~ 10^122 cosmological constant problem

Vacuum condensates PSI SUCK UP random zero point energy! They have zero entropy and zero quantum vacuum fluctuation!

(0|PSI|0) =/= 0 HIGGS FIELD

(0|PSI^2|0) - |(0|PSI|0)|^2 = 0 exactly

unlike electric field ZPF in Puthoff's & Haisch's theory.

I = eu^idx^u&i = IDENTITY Cartan 1-FORM

dA ~ dTheta/\dPhi

is my new discovery of the SPIN 1 renormalizable Dirac Substratum of emergent SPIN 2 gravity from EPR pairs of the A quanta!

A obey a Yang-Mills theory with A-balls like glue-balls & Wheeler geons.

dA is something like the loop quantum gravity area operator

There is no volume operator in sense of world hologram.

The key dimensionless parameter coupling is obviously

Lp*^2/\ = (hG*/c^3)/\ = (number of BITS of pocket universe)^-1

G* slides like renormalization group flow - weak at large scale, strong at small scale maybe from the extra dimensions from above?


The L-C connection is essentially a non-tensor gauge potential from
locally gauging the translation group. It has no covariant tensor
part! You confuse the transformation with the thing transformed.

So you say, but I think this was refuted by Poltorak.

He made a mistake of conception.

No, according to Poltorak, as a purely mathematical matter, you can
extract a (2,1) general tensor from the L-C connection. This is the
non-metricity tensor Q of the general affine connection A that effects
the L-C decomposition.

This is all in his papers.

This makes no physical sense at all. In Einstein's GR Q = 0!!!

The Illusion of "Gravity Force"
Paul, your fundamental confusion is as follows:
You have confused a contingent relation with a necessary relation.
This comes from garbling Newton's theory of gravity with Einstein's.
Also high energy physicists and science journalists talk about the 4-forces including gravity. Of course in special relativistic quantum field theory on a flat Minkowski background you can do that, but it misses the full nonlinearity of strong field gravity and the issue of "background independence."
Both have the same weak field limit that adds to the confusion.
Possibly Hal Puthoff shares this confusion with you? I don't know.
The meaning of the geodesic equation is that the invariant proper acceleration of a geodesic test particle is zero. This is true no matter what the curvature.
Curvature is geodesic deviation.
Consequently, only test particles on non-geodesics have non-vanishing proper acceleration and this is always caused by non-gravity forces, in effect the quantum electrodynamic force in macroscopic situations. Now this is true even in special relativity and Newtonian particle mechanics with the Galilean group of absolute simultaneity. Only the idea of "geodesic" as extremum path in the calculus of variations changes.
Therefore, in accord with Einstein's original version of the equivalence principle, all "gravity forces," i.e. "pulling g's" are 100% inertial forces on non-geodesics caused by non-gravity forces acting on the test particle. It's only when you ask for a stationary non-gedesic shell frame maintained by non-gravity forces do you get a contingent relationship to the local curvature. For example in SSS toy model

g(non-inertial Shell Frame) ~ GM/r^2 = c^2(GM/c^2r^3)r = c^2(SSS Curvature)r

You misinterpret this as "intrinsic". That's wrong. It's still an inertial force, in the particular non-inertial frame that keeps a fixed reduced circumference radial coordinate r. You can only do this outside the event horizon of the black hole.

For example, if the test particle is a rocket ship in space, the impulse engine is switched on and the ejected propellant pushes the rocket off its free-float geodesic path in the external local curved spacetime. In contrast, if the high Tc anyonic superconductor phase in the thin nano-engineered fuselage is locked to Goldstone phases of the residual vacuum coherent "inflation field" with large-scale mean dark energy ~ 10^-8 ergs/cm^3, to get weightless zero g geodesic warp drive

http://www.astrosciences.info/WarpDrive_files/image024.jpg

then no g-forces are felt even when the "saucer" makes hairpin turns in a dogfight with our jet fighters because the ship is able to control its own local geodesic with its propellantless propulsion "warp bubble." The Josephson phase lock bypasses the need for the huge energy densities needed in the brute force Tuv method using

Guv(Geometry) + kTuv(Applied Non-Gravity Field Energy) = 0

Rather we use

Guv(Geometry) + /\(Phase Lock)guv ~ 0

Additional torsion fields beyond Einstein's 1916 approximation of locally gauging only the 4-parameter translation group transform /\(Dark Energy/Matter) from a constant into a local scalar field that is controllable. That's my "conjecture" based on the UFO data.

On Aug 26, 2006, at 11:09 PM, Paul Zielinski wrote:

Jack Sarfatti wrote:

Hey Zielinski, I was with Creon Levit tonite from NASA AMES and we looked for you at Specs. Creon said that Hal Puthoff thought you were on the "right track." Maybe Hal can explain you since you can't and Creon said he is not able to understand what your point is either!

Z: I think I've now explained it very precisely and in concrete detail with reference to the Vilenkin solution. It's essentially the same kind of thing that Alex Poltorak has been talking and writing about, going back to his 1980 paper, where he showed that the physical gravitational field can be represented by the non-metricity tensor contained in the L-C connection, the decomposition being induced by an arbitrary generalized affine
connection. The general idea goes all the way back to de Sitter and Mie.

J: Irrelevant because non-metricity = 0 in Einstein's theory. This is a Red Herring. There is no such thing in the 1916 theory. That's Alex's error of conception IMHO. Of course if you want to make a unified field theory in Einstein's original classical sense - that is a different story.

Z: I'm developing a concrete geometric model for Alex's abstract decomposition in terms of tangent spaces so that it's easier for people like you and Creon to understand.

J: Chasing a mirage of endless delusion.
...

Z: It was Puthoff who thought my ideas were original and worth pursuing. That was all before I had ever heard of Alex Poltorak. The reason Hal Puthoff understands it is because he's an ether man.

J: Anesthetized? :-)
Yes, Hal's PV theory
1) violates the local equivalence principle
2) violates GCT tensor covariance
3) disagrees with observation except in the trivial weak field case where it's rigged to agree.

Z: It mystifies me that Einstein's 1918-1920 reversion to an ether interpretation of the 1916 theory has been ignored in this field. It also mystifies me that "general relativity" lives on as myth, even while Mach's principle went into the trash basket along with the rest of Mach's original program ~ 1916-1918.

J: Depends what you mean by "ether". Einstein never reverted to the Galilean group "ether" of the 19th century. Creon has some great data mining software he did at NASA "Viewpoints" that may confirm or falsify my theory on dark matter and dark energy "filamentary foam" with the latest NASA data coming in. CIA et-al like it also. It has all sorts of applications to all sorts of things including Homeland Security data mining.

Z: OK, too bad I missed you. Another time perhaps.

Vilenkin's Vacuum Defect

On Aug 25, 2006, at 7:02 PM, Paul Zielinski wrote:
Jack Sarfatti wrote:

OK what does in mean say for there to be a non-zero connection field with zero curvature field.

That's exactly what you get in a Minkowski spacetime in an accelerating observer frame (<=> curved spacetime coordinates).

Yes, I said that.

You get a non-zero LC connection. Since the Minkowski geometry is 100% uniform (in
Cartesian coordinates g_uv = n_uv everywhere) there is no geometric contribution to this connection field, which is thus 100% coordinate-originated.

Yes.

Same on an ordinary sphere.

How does that differ from a Minkowski spacetime?

If you start with a Minkowski spacetime (Cartesian g_uv = n_uv; R^u_vwl = 0) and construct a Cartesian (i.e. Lorentz) CS, and then while you hold the Cartesian CS fixed you deform the metric so that g_uv, w =/= 0 for some u, v, w, but still R^u_vwl = 0 everywhere in the manifold, then you get a non-zero LC connection *even in the Cartesian CS*.

That's what the vacuum defect Tuv does.

Since it is well known that a Cartesian CS on a flat manifold makes ZERO contribution to the LC connection, the LC connection is therefore *purely geometric* in origin.

It would mean LNIF observers would have to fire their rockets in order to keep a fixed distance from the vacuum wall source.

Exactly. That is the application of a non-gravity force that cancels the effect of the bending of the test particle geodesics by the source. But it is not the same as such bending. It is simply a *measure* of the physical effect of
the bending of the geodesics on the behavior of the rocket, compared to its behavior in a Minkowski spacetime.

This is same idea as shell frame in the SSS problem.

Yes, two distinct effects here.

The point is that no actual Rindler frame in a Minkowski spacetime (in the Vilenkin case an x-t (1 + 1) spacetime) can actually bend the test particle geodesics, either intrinsically or in relation to the gravitational source.

There is just no logical way out of this. Vilenkin's domain wall solution clearly exhibits test particle geodesics that are geometrically curved, both intrinsically and in relation to the wall, along the x-direction. So the Rindler metric that is
responsible for the true gravitational acceleration of test particle away from the wall cannot possibly represent a Rindler frame defined in a Minkowski x-t surface. What it actually represents is a geometrically deformed but still flat x-t manifold with *geometric* g_tt, x =/= 0 (in a Cartesian coordinate representation).

You have to be careful here. Geodesics are always zero proper acceleration for the test particles on them. The LNIF Rindler observers hover relative to the wall. They have proper acceleration g on their non-geodesic paths stationary relative to the source Tuv wall. Therefore, relative to them the geodesic particles appear to "accelerate" and indeed they really are repelled from the wall but their proper local invariant acceleration is zero. That's the meaning of the covariant geodesic equation.

The Tuv ~ /\&(x)diag(1,0,1,1) causes the effect Where the Rindler LNIF observers are hovering relative to the plane wall they see. Consequently they see the geodesic test particles repel from near the wall. Yes, those geodesics are intrinsically different from Minkowski because of the Tuv source that is absent in really sourceless globally flat space-tim.

A Rindler frame in Minkowski spacetime cannot do anything to the actual geometry of test-particle geodesics. A geometric deformation of a flat manifold to *another* geometrically inequivalent flat manifold can.

That is different from a Minkowski spacetime in which there is no source, so that firing rockets will not keep the observers at a fixed distance from some marker.

Right.

Z.

On Aug 25, 2006, at 6:34 PM, Jack Sarfatti wrote:

OK what does in mean say for there to be a non-zero connection field with zero curvature field? How does that differ from a Minkowski spacetime? It would mean LNIF observers would have to fire their rockets in order to keep a fixed distance from the vacuum wall source. That is different from a sourceless Minkowski spacetime without the vacuum wall below, so that firing rockets will not keep the observers at a fixed distance from some marker. That's the situation below for the hovering LNIF Rindler observers that are like the "shell frame" observers outside the event horizon of a non-rotating black hole.

On Aug 24, 2006, at 10:51 AM, Jack Sarfatti wrote:

"Geodesic" means straightest possible path. It's a relative idea depending on the space.

1. In Newton's 17th Century Theory of Gravity there is an objective gravity force field.
For example, the conservative gravity potential energy per unit test mass in Newton's geodesic global inertial frame of reference "the Lab frame" of Physics 101 for a sphere of mass M is

V(Newton) = - GM/r

The objectively real gravity force per unit test mass is

f(Newton) = - GradV(Newton) = - GM/r^2 pointing radially inward

A freely falling cannon ball is not on a Newtonian geodesic. It is generally on a parabolic path if it has initial speed perpendicular to the radial vector with the above f(Newton).



This interpretation changes completely in the switch to Einstein's General Relativity. Newton's above pure gravity force is completely eliminated because the path of the freely falling cannon ball is now a zero acceleration geodesic in the curved space-time. The Lab frame on surface Earth is not a Global Inertial Frame (GIF) it is a non-geodesic Local Non-Inertial Frame (LNIF) and the Lab Observer is objectively accelerating off geodesic from the quantum electrical forces pushing on him from the Earth's surface.

Locally frame-invariant objective accelerations vanish on geodesics.

Objective accelerations are contingent properties of contingent external quantun electrodynamical forces acting on the accelerating bodies on non-geodesic paths. Then and only then are 100% inertial g-forces detected as when a pilot "pulls g's" in a dogfight or when you step on a scale to weigh yourself. That is a non-intrinsic historical accident not a feature of the objective geometry of the curved spacetime.

Objective local frame invariant curved spacetime geometry is 100% geodesic deviation. It is only the zero objective acceleration geodesic structure that determines the objective geometry or geometrodynamic field. The accidental non-geodesics from external electrodynamic internal symmetry gauge fields have nothing to do with the objective geometry of the geometrodynamic field. The objectively real geometrodynamic field is the geodesic deviation tensor curvature field. That is the deep meaning of the equivalence principle misunderstood even by some professional physicists.

Now in the counter-intuitive example below from Vilenkin the situation is as follows.

The metric field guv looks different to different observers. For geodesic observers the metric field is actually globally flat Minkowski 3 + 1 space-time with zero curvature tensor everywhere except on an ideal zero thickness spherical 2D deSitter surface lightlike event horizon of coherent macroquantum vacuum topological vacuum defect that at time t = -infinity has infinite area. The sphere collapses and at time t = 0 it stops at a finite area /\^-1 = c^4/g^2 and then reverses expanding back to infinite area at t = + infinity. This is what the inertial GEODESIC observers INSIDE the collapsing-expanding vacuum defect sphere see. For them their spacetime patch is globally flat with zero 3+1 curvature tensor. The situation is very different for observers outside the sphere. Their spacetime patch is not globally flat.

Now there is a special class of uniformly non-accelerating LNIF "Rindler observers" with local frame invariant radial uniform acceleration g for which the really flat 3 + 1 Minkowski spacetime looks crazy with a complicated metric field. These observers see a plane wall instead of the sphere seen by the geodesic observers. If they compute the 3 + 1 curvature tensor they will get zero exactly like the geodesic observers. If they compute the radial slice they see a 1 + 1 Rindler submetric field. If they compute along planes parallel to the plane wall they get a 2 + 1 constant curvature /\ = c^4/g where to these non-inertial Rindler LNIF observers the geodesic test particles are in an effective Newtonian potential

V(Newton) = -gx + g^2x^2/2c^2

with illusional "gravity force" per unit test mass

f(Newton) = -dV/dx = +g (repulsive) - (g/c)^2x (attractive)

However, this is artificial because these Rindler LNIF observers must fire rockets (non gravity forces) to see this crazy artificial metric field. What they see is not fundamental but a wacky contingency in a Rube Goldberg contrived situation. The objective geometrodynamic field inside the deSitter spherical vacuum defect surface of Dirac delta function singularity is globally flat Minkowski spacetime. The so-called g-field above is 100% inertial not of fundamental geometrodynamic meaning.

Whenever the 3 + 1 curvature tensor vanishes in a region that region is Minkowski relative to geodesic local observers. There is no such thing as a Newtonian-like objective g-force in Einstein's theory ever. Any curvilinear metric representations that show a uniform g-force in particular must have zero objective curvature and such curvilinear representations are 100% illusionary artifacts of firing rockets in space in nutty ways like looking at an object through a Fun House Mirror in the Coney Island of a Demented Mind! ;-)

On Aug 23, 2006, at 10:07 PM, Jack Sarfatti wrote:

OK Paul you are right that Vilenkin does say the 3 + 1 curvature tensor R^uvwl = 0. But this 3 + 1 flat region is not the entire space-time of the exotic vacuum wall source tensor Tuv.

In fact he says that for inertial geodesic observers in this coordinate patch that does not cover the whole manifold

ds^2 = dt*^2 - dx*^2 - dy*^2 - dz*^2 Minkowski, but for them the wall is not flat, it is a sphere!

x*^2 + y*^2 + x*^2 = /\^-1 + t*^2

This vacuum bubble sphere for the geodesic observers is 2 + 1 DeSitter, it contracts from infinity to a minimum area /\^-1 then re-expands to infinity with constant acceleration g.

Also the metric in question only covers a fraction of the space-time of the source.

To review, the t-y,z slice is a 2 +1 DeSitter space. Therefore the 2 + 1 slice "parallel" to the plane is a subspace of constant positive curvature

/\ = g^2/c^4

embedded in the 3 + 1 flat space. So that's fine. No contradiction there. You can embed a curved subspace in a larger flat space. Also the 1 + 1 x-t slice is flat for a constantly accelerating Rindler observers. The metric field guv looks different for different sets of observers.

There are 3 separate metric fields here guv(3+1), gu'v'(2+1) & gu"v"(1 + 1) each with their own curvature tensors unto themselves.

We were talking apples and oranges.

The 3 + 1 curvature tensor of guv(3+1) can vanish and the curvature tensors of subspaces gu'v'(2+1) & gu"v"(1 + 1) not vanish! In particular the 2 + 1 slice parallel to the planar source is a DeSitter space of constant positive curvature /\. Its curvature tensor components are factors in the the larger 3 + 1 curvature tensor that vanishes. The algebra is complicated but the general idea is simple.

Nonzero Connection Fields with Zero Curvature Fields
OK what does in mean say for there to be a non-zero connection field with zero curvature field? How does that differ from a Minkowski spacetime? It would mean LNIF observers would have to fire their rockets in order to keep a fixed distance from the vacuum wall source. That is different from a sourceless Minkowski spacetime without the vacuum wall below, so that firing rockets will not keep the observers at a fixed distance from some marker. That's the situation below for the hovering LNIF Rindler observers that are like the "shell frame" observers outside the event horizon of a non-rotating black hole.

Physics Today

Why do the "Skeptics" ignore "string theory" and "loop quantum gravity"?

One wonders, however, what Feynman's reaction would have been had he lived to contemplate the contemporary scene in high energy theoretical physics almost twenty years later. String theory and its progeny still have yet to make a single, falsifiable prediction which can be tested by a physically plausible experiment. This isn't surprising, because after decades of work and tens of thousands of scientific publications, nobody really knows, precisely, what superstring (or M, or whatever) theory really is; there is no equation, or set of equations from which one can draw physical predictions. Leonard Susskind, a co-founder of string theory, observes ironically in his book The Cosmic Landscape (March 2006), “On this score, one might facetiously say that String Theory is the ultimate epitome of elegance. With all the years that String Theory has been studied, no one has ever found a single defining equation! The number at present count is zero. We know neither what the fundamental equations of the theory are or even if it has any.” (p. 204). String theory might best be described as the belief that a physically correct theory exists and may eventually be discovered by the research programme conducted under that name. -- J. Walker http://kelvin@fourmilab.ch/documents/reading_list/


Can we compare string theory to the war in Iraq?
Looking for the actual equations and contact with experiment
like looking for Saddam's WMD? ;-)


Key paper by A. Valentini
http://xxx.lanl.gov/abs/quant-ph/0203049

Also

http://www.signonsandiego.com/news/science/20060622-9999-lz1c22cause.html

Cramer and others (Srikanth, Hepp & Peacock ...) think signal nonlocality may be possible in orthodox QM i.e. cloning theorem wrong in some sense. This was what I had thought in 70's (Martin Gardner in "Magic and Paraphysics") but since changed my mind accepting the no-cloning theorem that linearity and unitarity precludes signal nonlocality in orthodox QM. My macro-quantum ODLRO theory is neither linear nor unitary in the orthodox QM sense - breakdown of Born interpretation for rigid local order parameter (PW Anderson's "More is different").
My views on all this are in my three books since 2002 (on Amazon)
Destiny Matrix
Space-Time and Beyond II
Super Cosmos (that has stuff from GR 17 BTW)
Physical Review does not publish this sort of thing. :-)

Basically I propose that all conscious matter needs signal nonlocality. You cannot have remote viewing without it. Therefore, orthodox quantum theory with no-cloning signal locality must break down in living matter. "Signal nonlocality" is analogous to "curvature" in relativity where zero curvature is the Special Relativity limit of General Relativity. In a similar sense, signal locality is the micro-quantum limit of a more general post-quantum theory with signal nonlocality in non-equilibrium macro-systems in sense of A. Valentini & Brian Josephson & Fotini Pallikari.

On a related front my theory of emergent gravity as a 4D covariant supersolid is formally similar to above. Note I published a prediction of the supersolid in 1969 before Tony Legget.

I claim Einstein's smooth c-number field equations emerge "More is different" very simply from the residual inflation vacuum ODLRO "Higgs" field's Goldstone phases (a kind of world hologram). You need at least two Goldstone phases to get GR unlike ordinary superfluids, which only have one Goldstone phase. You get something like Calabi-Yau adding 6 more Goldstone phases to the Higgs vacuum ODLRO field. So one need not posit GR + Inflation but derive GR from Inflation - that makes sense for the creation of curved spacetime of a pocket universe on the landscape of the megaverse in a bootstrap from the false vacuum. With signal nonlocality we can see into event and particle horizons so that the landscape is testable in principle with "remote viewing."

Through the Fun House Mirror

Look Paul, I explained the whole thing correctly earlier today.
Look at the metric from POV of the geodesic observers.
The exotic dark energy "quintessent" w = -2/3 vacuum ODLRO plane wall source

Tuv ~ (c^4/\/G)&(x)diag(1,0,1,1)

signature 1 -1,-1,-1

1 + 3w = 1 - 0 - 1 - 1 = -1

w = - 2/3

note that

c^4/\/G = c^4g^2/c^4G = g^2/G

The LIF geodesic observers INSIDE THE DYNAMIC DESITTER VACUUM 2D SPHERICAL SHELL see it collapsing at constant objective proper acceleration g from infinity down to finite area /\^-1 and re-expanding back out to infinity.

/\^-1 = c^4/g^2 is the minimum area of the vacuum spherical shell at t = 0 when it stops and reverses.

The zero proper invariant acceleration geodesic observers see the 3 + 1 Minkowski metric

ds^2 = c^2dt*^2 - dx*^2 - dy*^2 - dz*^2

Now the LNIF Rindler non-geodesic properly accelerating observers at g along x =/= x* see an infinite plane wall instead of the dynamic DeSitter spherical shell.
These Rindler observers must do work in order to exist. They need to fire rocket engines precisely unlike the LIF geodesic observers who get a free ride.

The interior 3 + 1 space-time is GLOBALLY FLAT, i.e. R^uvwl = 0 for ALL observers LNIF & LIF.

However, the LNIF Rindler observers see a DeSitter 2 + 1 transverse slice (t-y-z) and a Rindler longitudinal slice (t-x) where from the LNIF the geodesic test particles appear to be in a Newtonian force field

V(Newton) = -gx + (1/2)g^2x^2/c^2

f(Newton) = -dV/dx = + g(repulsive) - g^2x/c^2 attractive

With geodesic test particle event horizon(s) at

1 + V(Newton)/c^2 = 0

1 - gx/c^2 + (1/2)g^2x^2/c^3 = 0

The metric you wrote only covers the interior of the DeSitter spherical shell not the exterior.

On Aug 24, 2006, at 5:54 PM, Paul Zielinski wrote:

Let me re-word this.

Flat everywhere but at x = 0 does not *just* mean flat "in a 1-1 x-t slice".
It means the spacetime *as a whole* is locally Riemann flat *everywhere* except at x = 0."


Vilenkin makes it quite clear that the domain wall spacetime *as a whole* is Riemann flat (R^u_vwl = 0) everywhere *except* on the wall itself. If it is only flat on x-t surfaces then how could R^u_vwl = 0 everywhere outside of the wall?

However, you are right that in Vilenkin's 1983 solution each y-z, t hypersurface is a (2 + 1) de Sitter space embedded in a 4D Riemann-flat spacetime, which implies constant positive curvature along any y-z, t hypersurface.

The point is that the "Rindler" metric on the x, t surfaces is a Riemann-flat metric on those surfaces that results in real gravitational acceleration away from the wall along x. That means that this "Rindler" metric does not actually represent
a Rindler frame in a Minkowski spacetime, but instead represents a real geometric tilt of the metric along the x direction. According to the equivalence principle, the observable effects are the same either way; but the two cases are nevertheless not the same from a theoretic standpoint, since a coordinate tranformation cannot change the geometric relationship between test particle geodesics and the wall.

This is a Red Herring. No one ever said otherwise.

So while you have a valid point that this domain wall solution is not as simple as it looks at first glance, my argument still works in this example, since the effect of the flat x-t metric is to curve the actual geometry of the test particle geodesics and produce real gravitational acceleration away from the source along the x direction,

No, you keep misunderstanding this. The geodesic test particles in APPEAR to be in a conservative force field f(Newton)

V(Newton) = -gx + (1/2)g^2x^2/c^2

f(Newton) = -dV/dx = + g(repulsive) - g^2x/c^2 attractive

relative to the LNIF non-geodesic Rindler observers with constant proper g from firing rockets. It's exactly like the free falling cannon ball geodesic relative to the non-geodesic Earth in Einstein's POV - switch "geodesic" to get Newton's POV for same problem.
In any case the objective 3 + 1 Riemann curvature tensor is zero for everyone, but not the 2 + 1 DeSitter slice that for the LNIF guys looks curved i.e. /\. The LIF guys do not slice it in same way so one cannot directly compare these subspaces. What everyone agrees is that 3 + 1 curvature tensor vanishes.


which a coordinate transformation alone cannot do. So this is not actually a Minkowski spacetime, as you claim. Vilenkin doesn't actually say that it is; he only says "the metric is Minkowski", meaning that it is formally of the Minkowski type; just as when he
says that the x-t metric is a "Rindler metric", by which he means that it is *formally* the same as a metric that represents a Rindler frame in an actual Minkowski spacetime. So I think it is you, and not Vilenkin, who is confused here.

I think you are making a meaningless verbal distinction without any physical meaning.

You always get this effect locally in Riemann normal coordinates in a *curved* spacetime, since then the metric assumes its normal form [-1, 1, 1, 1] -- but in the curved case obviously this doesn't mean that you are actually in a Minkowski spacetime. The situation here is very similar, even though the net Riemann curvature of the spacetime outside the wall is zero. Here you have a real flat geometric metric gradient that remains constant, while the net *coordinate* gradient goes to zero in any free-fall frame. That does not mean that Vilenkin's solution is a Minkowski spacetime. It simply means that
the metric assumes its *normal form* in any free fall frame in the Riemann-flat region.

Sorry I don't understand what point you are making.

If the 4th rank curvature tensor = 0 at all points in a 4D simply connected space-time region then that is sufficient to say that the geodesic observers have metric

ds^2 = (cdt)^2 - dx^2 - dy^2 - dz^2

and that any curvilinear metric guv(x) in this manifold describes a set of non-geodesic local observers using non-gravity forces to maintain the given curvilinear representation i.e.

ds^2 = gu'v'(x)dx^u'dx^v' (LNIF') = (cdt)^2 - dx^2 - dy^2 - dz^2 (LIF)

R^u'v'w'l'(x') = R^uvwl(x) = 0 INVARIANT VANISHING OF ALL THE TENSOR COMPONENTS FOR ALL OBSERVERS.

In his 1981 paper on the weak field solution there is no mention of /\, and Vilenkin writes a linearized field equation

(Δ^2 - &_t^2) h_uv = 16πG (T_uv - 1/2η_uv T)

subject to harmonic coordinates. So why he jumps straight to an exact solution with /\ =/= 0 in the 1983 paper without even writing a new field equation is still a mystery to me

Z.

Coney Island of the Non-Inertial Mind
"Geodesic" means straightest possible path. It's a relative idea depending on the space.

1. In Newton's 17th Century Theory of Gravity there is an objective gravity force field.
For example, the conservative gravity potential energy per unit test mass in Newton's geodesic global inertial frame of reference "the Lab frame" of Physics 101 for a sphere of mass M is

V(Newton) = - GM/r

The objectively real gravity force per unit test mass is

f(Newton) = - GradV(Newton) = - GM/r^2 pointing radially inward

A freely falling cannon ball is not on a Newtonian geodesic. It is generally on a parabolic path if it has initial speed perpendicular to the radial vector with the above f(Newton).



This interpretation changes completely in the switch to Einstein's General Relativity. Newton's above pure gravity force is completely eliminated because the path of the freely falling cannon ball is now a zero acceleration geodesic in the curved space-time. The Lab frame on surface Earth is not a Global Inertial Frame (GIF) it is a non-geodesic Local Non-Inertial Frame (LNIF) and the Lab Observer is objectively accelerating off geodesic from the quantum electrical forces pushing on him from the Earth's surface.

Locally frame-invariant objective accelerations vanish on geodesics.

Objective accelerations are contingent properties of contingent external quantun electrodynamical forces acting on the accelerating bodies on non-geodesic paths. Then and only then are 100% inertial g-forces detected as when a pilot "pulls g's" in a dogfight or when you step on a scale to weigh yourself. That is a non-intrinsic historical accident not a feature of the objective geometry of the curved spacetime.

Objective local frame invariant curved spacetime geometry is 100% geodesic deviation. It is only the zero objective acceleration geodesic structure that determines the objective geometry or geometrodynamic field. The accidental non-geodesics from external electrodynamic internal symmetry gauge fields have nothing to do with the objective geometry of the geometrodynamic field. The objectively real geometrodynamic field is the geodesic deviation tensor curvature field. That is the deep meaning of the equivalence principle misunderstood even by some professional physicists.

Now in the counter-intuitive example below from Vilenkin the situation is as follows.

The metric field guv looks different to different observers. For geodesic observers the metric field is actually globally flat Minkowski 3 + 1 space-time with zero curvature tensor everywhere except on an ideal zero thickness spherical 2D deSitter surface lightlike event horizon of coherent macroquantum vacuum topological vacuum defect that at time t = -infinity has infinite area. The sphere collapses and at time t = 0 it stops at a finite area /\^-1 = c^4/g^2 and then reverses expanding back to infinite area at t = + infinity. This is what the inertial GEODESIC observers INSIDE the collapsing-expanding vacuum defect sphere see. For them their spacetime patch is globally flat with zero 3+1 curvature tensor. The situation is very different for observers outside the sphere. Their spacetime patch is not globally flat.

Now there is a special class of uniformly non-accelerating LNIF "Rindler observers" with local frame invariant radial uniform acceleration g for which the really flat 3 + 1 Minkowski spacetime looks crazy with a complicated metric field. These observers see a plane wall instead of the sphere seen by the geodesic observers. If they compute the 3 + 1 curvature tensor they will get zero exactly like the geodesic observers. If they compute the radial slice they see a 1 + 1 Rindler submetric field. If they compute along planes parallel to the plane wall they get a 2 + 1 constant curvature /\ = c^4/g where to these non-inertial Rindler LNIF observers the geodesic test particles are in an effective Newtonian potential

V(Newton) = -gx + g^2x^2/2c^2

with illusional "gravity force" per unit test mass

f(Newton) = -dV/dx = +g (repulsive) - (g/c)^2x (attractive)

However, this is artificial because these Rindler LNIF observers must fire rockets (non gravity forces) to see this crazy artificial metric field. What they see is not fundamental but a wacky contingency in a Rube Goldberg contrived situation. The objective geometrodynamic field inside the deSitter spherical vacuum defect surface of Dirac delta function singularity is globally flat Minkowski spacetime. The so-called g-field above is 100% inertial not of fundamental geometrodynamic meaning.

Whenever the 3 + 1 curvature tensor vanishes in a region that region is Minkowski relative to geodesic local observers. There is no such thing as a Newtonian-like objective g-force in Einstein's theory ever. Any curvilinear metric representations that show a uniform g-force in particular must have zero objective curvature and such curvilinear representations are 100% illusionary artifacts of firing rockets in space in nutty ways like looking at an object through a Fun House Mirror in the Coney Island of a Demented Mind! ;-)

On Aug 23, 2006, at 10:07 PM, Jack Sarfatti wrote:

OK Paul you are right that Vilenkin does say the 3 + 1 curvature tensor R^uvwl = 0. But this 3 + 1 flat region is not the entire space-time of the exotic vacuum wall source tensor Tuv.

In fact he says that for inertial geodesic observers in this coordinate patch that does not cover the whole manifold

ds^2 = dt*^2 - dx*^2 - dy*^2 - dz*^2 Minkowski, but for them the wall is not flat, it is a sphere!

x*^2 + y*^2 + x*^2 = /\^-1 + t*^2

This vacuum bubble sphere for the geodesic observers is 2 + 1 DeSitter, it contracts from infinity to a minimum area /\^-1 then re-expands to infinity with constant acceleration g.

Also the metric in question only covers a fraction of the space-time of the source.

To review, the t-y,z slice is a 2 +1 DeSitter space. Therefore the 2 + 1 slice "parallel" to the plane is a subspace of constant positive curvature

/\ = g^2/c^4

embedded in the 3 + 1 flat space. So that's fine. No contradiction there. You can embed a curved subspace in a larger flat space. Also the 1 + 1 x-t slice is flat for a constantly accelerating Rindler observers. The metric field guv looks different for different sets of observers.

There are 3 separate metric fields here guv(3+1), gu'v'(2+1) & gu"v"(1 + 1) each with their own curvature tensors unto themselves.

We were talking apples and oranges.

The 3 + 1 curvature tensor of guv(3+1) can vanish and the curvature tensors of subspaces gu'v'(2+1) & gu"v"(1 + 1) not vanish! In particular the 2 + 1 slice parallel to the planar source is a DeSitter space of constant positive curvature /\. Its curvature tensor components are factors in the the larger 3 + 1 curvature tensor that vanishes. The algebra is complicated but the general idea is simple.

Physicists Howl at Dark Matter

I saw the top minds in physics go crazy trying to understand the Dark Side!
"I saw the best minds of my generation destroyed by madness, starving hysterical naked,
dragging themselves through the negro streets at dawn looking for an angry fix,
angelheaded hipsters burning for the ancient heavenly connection to the starry dynamo in the machinery of night"
Alan Ginsburg "Howl"

New Scientist is competing now with The Onion.
http://www.theonion.com/content/

Even Bekenstein in desperation has become a Ptolemeist with epicycle fudge factors.

Plain vanilla covariant non-aether GR works just fine. Dark energy is zero point energy with w = -1 negative pressure. Dark matter is also zero point energy with w = -1 with positive pressure at smaller scales than dark energy because it clumps and mimics w = 0 CDM. Very simple. LHC will not find any exotic dark matter particles. Omega(ZPF) ~ 0.96, Omega(ordinary on shell quanta) ~ 0.04. Simple. End of story? Here I am defending the orthodoxy.

On Aug 24, 2006, at 8:54 AM, Jack Sarfatti wrote:


On Aug 24, 2006, at 7:25 AM, Gary S. Bekkum wrote:

Now Starkman's team has reproduced Bekenstein's results using just one field - the new ether (www.arxiv.org/astro-ph/ 0607411). Even more tantalisingly, the calculations reveal a close relationship between the threshold acceleration a0 - which depends on the ether - and the rate at which the universe's expansion is accelerating. Astronomers have attributed this acceleration to something called dark energy, so in a sense the ether is related to this entity. That they have found this connection is a truly profound thing, says Bekenstein. The team is now investigating how the ether might cause the universe's expansion to speed up. Public release date: 23-Aug-2006
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Contact: Claire Bowles
claire.bowles@rbi.co.uk
44-207-611-1210
New Scientist
Ether returns to oust dark matterFrom his office window, Glenn Starkman can see the site where Albert Michelson and Edward Morley carried out their famous 1887 experiment that ruled out the presence of an all-pervading "aether" in space, setting the stage for Einstein's special theory of relativity. So it seems ironic that Starkman, who is at Case Western Reserve University in Cleveland, Ohio, is now proposing a theory that would bring ether back into the reckoning. While this would defy Einstein, Starkman's ether would do away with the need for dark matter.Nineteenth-century physicists believed that just as sound waves move through air, light waves must move through an all-pervading physical substance, which they called luminiferous ("light-bearing") ether. However, the Michelson-Morley experiment failed to find any signs of ether, and 18 years after that, Einstein's special relativity argued that light propagates through a vacuum. The idea of ether was abandoned – but not discarded altogether, it seems.Starkman and colleagues Tom Zlosnik and Pedro Ferreira of the University of Oxford are now reincarnating the ether in a new form to solve the puzzle of dark matter, the mysterious substance that was proposed to explain why galaxies seem to contain much more mass than can be accounted for by visible matter. They posit an ether that is a field, rather than a substance, and which pervades space-time. "If you removed everything else in the universe, the ether would still be there," says Zlosnik. This ether field isn't to do with light, but rather is something that boosts the gravitational pull of stars and galaxies, making them seem heavier, says Starkman. It does this by increasing the flexibility of space-time itself . "We usually imagine space-time as a rubber sheet that's warped by a massive object," says Starkman. "The ether makes that rubber sheet more bendable in parts, so matter can seem to have a much bigger gravitational effect than you would expect from its weight." The team's calculations show that this ether-induced gravity boost would explain the observed high velocities of stars in galaxies, currently attributed to the presence of dark matter.This is not the first time that physicists have suggested modifying gravity to do away with this unseen dark matter. The idea was originally proposed by Mordehai Milgrom while at Princeton University in the 1980s. He suggested that the inverse-square law of gravity only applies where the acceleration caused by the field is above a certain threshold, say a0. Below that value, the field dissipates more slowly, explaining the observed extra gravity. "It wasn't really a theory, it was a guess," says cosmologist Sean Carroll at the University of Chicago in Illinois.Then in 2004 this idea of modified Newtonian dynamics (MOND) was reconciled with general relativity by Jacob Bekenstein at the Hebrew University in Jerusalem, Israel (New Scientist, 22 January 2005, p 10), making MOND a genuine contender in the eyes of some physicists. Bekenstein's work was brilliant, but fiendishly complicated, using many different and arbitrary fields and parameters," says Ferreira. "We felt that something so complicated couldn't be the final theory.Now Starkman's team has reproduced Bekenstein's results using just one field - the new ether (www.arxiv.org/astro-ph/ 0607411). Even more tantalisingly, the calculations reveal a close relationship between the threshold acceleration a0 - which depends on the ether - and the rate at which the universe's expansion is accelerating. Astronomers have attributed this acceleration to something called dark energy, so in a sense the ether is related to this entity. That they have found this connection is a truly profound thing, says Bekenstein. The team is now investigating how the ether might cause the universe's expansion to speed up.Andreas Albrecht, a cosmologist at the University of Calfornia, Davis, believes that this ether model is worth investigating further. "We've hit some really profound problems with cosmology Ð with dark matter and dark energy," he says. "That tells us we have to rethink fundamental physics and try something new."Both Bekenstein and Albrecht say Starkman's team must now carefully check whether the ether theory fits with the motions of planets within our solar system, which are known to a high degree of accuracy, and also explain what exactly this ether is. Ferreira agrees: "The onus is definitely on us to pin this theory down so it doesn't look like yet another fantastical explanation," he says.However, physicists may be reluctant to resurrect any kind of ether because it contradicts special relativity by forming an absolute frame of reference . "Interestingly, this controversial aspect should make it easy to test for experimentally," says Carroll. ###"This article is posted on this site to give advance access to other authorised media who may wish to quote extracts as part of fair dealing with this copyrighted material. Full attribution is required, and if reporting online a link to www.newscientist.com is also required. This story posted here is the EXACT text used in New Scientist magazine, therefore advance permission is required before any and every reproduction of each article in full. Please contact celia.guthrie@rbi.co.uk. Please note that all material is copyright of Reed Business Information Limited and we reserve the right to take such action as we consider appropriate to protect such copyright."THIS ARTICLE APPEARS IN NEW SCIENTIST MAGAZINE ISSUE: 26 AUGUST 2006Author: Zeeya MeraliIF REPORTING ON THIS STORY, PLEASE MENTION NEW SCIENTIST AS THE SOURCE AND, IF REPORTING ONLINE, PLEASE CARRY A HYPERLINK TO: http://www.newscientist.comUK CONTACT - Claire Bowles, New Scientist Press Office, London:Tel: 44-0-20-7611-1210 or email claire.bowles@rbi.co.ukUS CONTACT – New Scientist Boston office:Tel: 617-386-2190 or email kyre.austin@reedbusiness.com
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Astrophysics, abstract
astro-ph/0607411From: T.G Zlosnik [view email] Date: Tue, 18 Jul 2006 12:43:44 GMT (10kb)Modifying gravity with the Aether: an alternative to Dark MatterAuthors: T.G Zlosnik, P.G Ferreira, G.D Starkman
Comments: Submitted to Physical Review Letters
There is evidence that Newton and Einstein's theories of gravity cannot explain the dynamics of the universe on a wide range of physical scales. To be able to understand the properties of galaxies, clusters of galaxies and the universe on the whole it has become commonplace to invoke the presence of dark matter. An alternative approach is to modify the gravitational field equations to accommodate observations. We propose a new class of gravitational theories in which we add a new degree of freedom, the Aether, in the form of a vector field that is coupled covariantly, but non-minimally, with the space-time metric. We explore the Newtonian and non-Newtonian limits, discuss the conditions for these theories to be consistent and explore their effect on cosmology.Full-text: PostScript, PDF, or Other formats
References and citations for this submission:
SLAC-SPIRES HEP (refers to, cited by, arXiv reformatted);
NASA ADS;
CiteBase (autonomous citation navigation and analysis)

Subject: Gravity Fields of Dark Energy Exotic Vacuum Domain Walls.
http://disc.server.com/discussion.cgi?disc=68326;article=2819;
is the color version of the work below.
On Aug 22, 2006, at 3:54 PM, Paul Zielinski wrote:
The cosmic string and vacuum domain wall solutions are globally flat outside the sources.

Is this accurate? NO! Not for the vacuum wall at least.

The exotic vacuum ODLRO domain wall is an off-mass-shell virtual dark energy effect different from the on-mass-shell slab of ordinary matter.

"The gravitational field of a domain wall is rather unusual and is very different from that of an ordinary massive plane."

http://www.novelconceptsinc.com/picts/calculators-slab-thermal-resistance.gif


http://www.mrao.cam.ac.uk/ppeuc/astronomy/papers/axenides/node2.html
&
"Cosmic Strings and Other Topological Defects"
A. Vilenkin & E. Shellard 13.3

"the gravitational field of the wall is repulsive" p.378

"The Einstein equations [with vacuum ODLRO wall source] have no static solutions having planar and reflectional symmetry."

I. Vacuum domain wall

The vacuum wall is in the y-z plane and the source tensor Tuv has a Dirac delta function &(x). The metric solution can be represented as

ds^2 = (1 - g|x|/2c^2)^2(cdt)^2 + dx^2 + (1 - g|x|/2c^2)^2e^2(gt/c)(dy^2 + dz^2)

"The x-t part is a 1 + 1 Rindler metric describing a flat space in the frame of reference of a uniformly accelerated observer."

This is LNIF non-geodesic observer because the acceleration of a LIF geodesic observer is by construction zero. That is the geodesic is the straightest world line in space-time. It need not be "straight" in the projected spacelike hypersurface.

Note that the statement of flatness is only in the 1 + 1 x-t slice not in the whole 3 + 1 manifold so that Zielinski may be misunderstanding what "flatness" means in this problem.

"The observer at x = 0 will see (geodesic) test particles moving away from the wall with acceleration g in agreement with the Newtonian analysis."

When we see cannon balls in free fall almost parabolic orbit


http://www.zonalibre.org/blog/diversovariable/archives/baron-munchausen.jpg
We are LNIF observers on the non-geodesic world line of the rotating rigid Earth's surface whose center of mass is on a geodesic round the Sun at a focus of the slightly precessing elliptical orbit of that center. The cannon ball is geodesic in Einstein's theory, though not in Newton's where a gravity force is acting on the cannon ball. There is a bait and switch here as we flip paradigms to explain the same phenomenon in almost opposite ways. The word "geodesic" changes meaning. However, there is zero acceleration on "geodesics" in both Newton's and Einstein's informal language and in both cases the geodesic is the straightest possible path. Newton's space + time is flat Euclidean, Einstein's space-time is curved.

Look at the 1 + 1 Rindler metric slice warp factor more closely

(1 - g|x|/2c^2)^2 = 1 - g|x|/c^2 + (g|x|/2c^2)^2

The effective Newtonian potential per unit test mass is

V(Newton) = -g|x| + (g|x|/2c)^2

The "Newtonian" gravity force on the Einsteinian "geodesic" test particle in the POV of the LNIF Rindler uniformly accelerated observer is

- dV(Newton)/d|x| = + g - g^2|x|/2c^2

Note that Zielinski did misunderstand. The first term on the RHS is an approximately uniform repulsion seen by the LNIF observer looking at a test particle on a geodesic in this curved space-time. This approximation is only good when g|x|/c^2 << 1. The second term will give curvature to the spacetime in the Einstein description and it is an attraction. Note the balance at

+g - g^2|x|/2c^2 = 0

i.e.

1 = g|x|/2c^2

which is an infinite red shift horizon.

Note that the non-geodesic Rindler observer needs to apply a NON-GRAVITY FORCE, e.g. firing a rocket engine to maintain his privileged frame status in which the metric field is represented.

The total 3 + 1 is not globally flat as Zielinski wrongly said. Indeed, the x = constant slices form a 2 + 1 DeSitter space of positive zero point energy with negative pressure. This DeSitter space has constant positive curvature /\. It is not at all flat with a vanishing curvature tensor.

ds*^2 = dt^2 - e^gt/c(dy^2 + dz^2_

Note that the COSMOLOGICAL CONSTANT in the 2 + 1 slice here is

/\ = g^2/c^4

Note that the DARK ZERO POINT STRESS TENSOR of the Vacuum ODLRO "Wall" is

Tuv = Ttt&(x)diag(1,0,1,1)

Ttt = wall tension in the y-z plane

In the weak field limit the effective GR Einstein-corrected Poisson gravity equation is

Grad^2V(Newton) = 4piG(Ttt - Txx - Tyy - Tzz) = 4piGTtt(1 - 0 - 1 - 1) = -4piGTtt

i.e. repulsive for positive Ttt = energy density that has dominating negative pressure here by a factor of 2. The broken rotational symmetry has changed the usual pressure factor of 3 to 2.

1 + 3w = -1

w = - 2/3

in this problem

Note also that GTtt/c^4 = /\ = g^2/c^4

i.e. Ttt(Wall) = g^2/G

"Gravity Force" outmoded concept

The analogy of gravity force with electrical force is not very good. However, take a large flat charged conducting plate.

http://www.math.uni-bremen.de/~justen/Forschung/ie_condenser.jpg

Near its center the electric force field is approximately uniform in analogy with a uniform gravity force field in Newton's picture. Above picture is for a condenser with oppositely charge plates that give similar effect. I am talking about the RED region.

That is there is a finite region of space in which approximately from Gauss's law

Grad^2V ~ source density

doing integrals and using symmetry

V(Coulomb) ~ Ez

z is normal distance to plate

the force per unit mass on a test particle charge q and mass m is

a = -(q/m)dV/dz = - (q/m)E

E ~ spatially uniform in limited region

In Newtonian gravity from potential theory there is a similar Gauss law

V(Newton) ~ gz

a = g

Approximately uniform

What this means in Einstein's theory is the following.

The approximate metric can be written as (c = 1)

ds^2 ~ -(1 - gz)dt^2 + (1 - gz)^-1dz^2 + dx^2 + dy^2

gz << 1

For the rest "shell" LNIF hovering observers

dz(LNIF shell) = dz/(1 - gz)^1/2 ~ dz(1 + gz/2)

dt(LNIF shell) = dt(1 - gz)^1/2 ~ dt(1 - gz/2)

The z distance between stationary nongeodesic shell observers is larger than the "book keeping" amount (if there were no source) by gz/2

Note the approximation gz << 1.

i.e. gz/c^2 << 1

The gravity red shift is for a receiver far away and sender at z is for frequency of signal f

f(receiver) ~ f(sender)(1 - gz/2c^2)

only from that limited region.

The important part of the connection field here is

c^2{^z00} ~ g

but that is only in the non-geodesic SHELL FRAME.

It's not frame-invariant.

Note in electricity

The electromagnetic force is a tensor

f^u = (q/m)F^uvV^v

But in gravity in Einstein's theory

the Newtonian "gravity force" is not a tensor

g ~ c^2{z,00}

The shell LNIF observers must provide a non-gravity force to keep at fixed z in the above problem

This is CONTINGENT - not INTRINSIC.

There is no intrinsic gravity force in Einstein's theory. All gravity force is 100% inertial depending on arbitrary choice of the non-geodesic needing a non-gravity force to exist. The curvature field is intrinsic i.e. a tensor, but it is geodesic deviation independent of arbitrary choices of non-geodesics from non-gravity forces. There is never any "g-force" on a massive test particle on a timelike geodesic in curved space-time. The test particle acceleration on a geodesic is zero. The intrinsic classical geometrodynamic field is fully determined by the geodesic structure. Intrinsic curvature is "geodesic deviation". All non-geodesics are contingent not necessary and they require external non-gravity forces to create. Null event horizons are barriers (one-way membranes) to all timelike worldlines whether geodesic or nongeodesic). Spacelike worldlines pass through event horizons but on-mass-shell tachyons usually signal a vacuum ODLRO instability and are not themselves stable. Post-quantum signal nonlocality observed in the CIA SRI experiments of Puthoff & Targ and confirmed in other experiments
http://www.signonsandiego.com/news/science/20060622-9999-lz1c22cause.html
do not change the above considerations. That is, non-light signal based nonlocal C^3 will not provide "absolute simultaneity". Classical GR geometrodynamics is not affected by post-quantum signal nonlocality that is a mental process confined to living conscious matter far from thermal equilibrium.
http://xxx.lanl.gov/abs/quant-ph/0203049

Look at this another way

e^a = I^a(globally flat LNIF inertial force observer effect) + A^a(intrinsically curved geodesic deviation)

e^a = e^audx^u

these 4 tetrad fields are GCT group local frame invariant scalars, but they are Lorentz group O(1,3) 4-vectors.

e^au = I^au(globally flat LNIF inertial force observer effect) + A^au(intrinsically curved geodesic deviation)

The total O(3,1)xGCT scalar invariant e = Identity on Tangent Bundle is like

1 = Sum |i>
i.e. e = identity on tangent bundle is an invariant constraint in all local frames.

e = e(observer frame effect) + e(intrinsic curved geometry)

The two terms on RHS are not separately identity actions on the tangent bundle only their sum is. They are separately local frame invariants however.


On Aug 21, 2006, at 11:18 AM, Jack Sarfatti wrote:

Yes thanks for reminding me of course I should have explicitly mentioned that, but I split
e = I(LNIF observer) + A(intrinsic curved geometry)
where
A has the curvature information.
A ~ dTheta/\dPhi
e = I is simply the globally flat Minkowski spacetime trivial tetrad since

guv(curvilinear) equivalent to globally flat Minkowski metric in that case.

i.e.

e = Trivial Globally Flat Tetrad (LNIF Non-Geodesic Observer Inertial Force Contingencies) + Non-Trivial Geodesic Deviation Tetrad from modulation of the Goldstone phases of the vacuum ODLRO "inflation" Higgs field.

The electroweak Higgs and the inflation field may be closely related in my program for a theory.

All curvilinear effects when A = 0 are then simply non-geodesic LNIF observer effect inertial forces from non-gravity forces on the local detectors. There is no geodesic deviation when A = 0. That's the key idea that

A is analogous to v = (h/m)dTheta in superfluid helium

The formal issue is can we have things like

(p/q)/\(r/s) = (-1)^|pr/qs|(r/s)/\(p/q)

p,q,r,s all integers

If so, that begins to suggest anyons with fractional quantum statistics and fractional charges according to Frank Wilzcek.


On Aug 21, 2006, at 9:24 AM, Waldyr A. Rodrigues Jr. wrote:

Dear Jack,

Objects like (1/2) = (1/2)u^v^wdx^u/\&xv/\&xw have nothing to do with fractals. However they have a nice algebra. I call them Clifford valued-differential forms and use them in the attached paper which has been published in 2004 in the Int. J. Mod. Phys. D. You also can find it in the arXiv.

By the way, your e = eu^adx^u&a, is nothing more than the identity operator acting on the tangent bundle (or in the cotangent bundle). . . I already explained that, but it seems that you forgot.



Best regards,

Waldyr



-----Mensagem original-----
De: Jack Sarfatti [mailto:sarfatti@pacbell.net]
Enviada em: segunda-feira, 21 de agosto de 2006 12:16
Para: Sarfatti_Physics_Seminars
Assunto: What is a fractal Cartan form anyway?



Next question since the idea only popped into my mind for the first

time late last night.



For example what would a 1/2 form be?



Maybe



?



Where &xv is a dual basis to dx^u?



Then a (p,q) form has p covariant & q contravariant indices.



On Aug 20, 2006, at 9:49 PM, Jack Sarfatti wrote:



>

>>

>> e = eu^adx^u&a

>>

>> is contracted over both the GCT indices u and the tangent space

>> indices a.

>> Therefore it's locally frame invariant both under GCT Diff(4) for

>> COINCIDENT non-geodesic LNIFs at fixed physical event E as well as

>> for O(1,3) COINCIDENT LIF transformations at same E.

>>

>> Cartan's whole idea of differential forms is that they are local

>> frame invariants - local coordinate independent.

>>

>> A general 1 form is

>>

>> 1 = 1udx^u

>>

>> that's scalar invariant

>>

>> 1 = 1udx^u = 1u'dx^u'

>>

>> A general 2-form is

>>

>> 2 = 2uvdx^u/\dx^v

>>

>> 2uv = - 2vu

>>

>> etc.

>>

>> d(p/\q) = dp/\q + (-1)^|p|p/\dq

>>

>> d^2 = 0

>>

>> If p is a zero form scalar O

>>

>> d(O/\q) = dO/\g + O/\dq is a q + 1 form

>>

>> If p is a 1-form

>>

>> d(1/\q) = d1/\q - 1/\dq

>>

>> etc.

>>

>> p/\q = (-1)^|pq|q/\p

>>

>> If p & q are both 1-forms then they anti-commute sort of like

>> fermion operators.

>>

>> ckck' + ck'ck = 0

>>

>> when k = k' that's the Pauli exclusion principle.

>>

>> If p & q are both 0-forms then they commute like bosons.

>>

>> bkbk' - bk'bk = 0

>>

>> You get Heisenberg uncertainty principle by taking canonical

>> conjugates

>>

>> e.g. c*k = d/dck is conjugate to ck, one must assume c*K is also a

>> 1-form?

>>

>> c*kck + ckc*k = 1

>>

>> So now let p & q be rational numbers, i.e. fractal forms.

>>

>> This gives fractional quantum statistics & fractional charges!

What is a fractal Cartan form?

Next question since the idea only popped into my mind for the first time late last night.

For example what would a 1/2 form be?

Maybe

(1/2) = (1/2)u^v^wdx^u/\&xv/\&xw ?

Where &xv is a dual basis to dx^u?

Then a (p,q) form has p covariant & q contravariant indices.

Fractal Cartan Forms are Anyons

e = eu^adx^u&a

is contracted over both the GCT indices u and the tangent space indices a.
Therefore it's locally frame invariant both under GCT Diff(4) for COINCIDENT non-geodesic LNIFs at fixed physical event E as well as for O(1,3) COINCIDENT LIF transformations at same E.

Cartan's whole idea of differential forms is that they are local frame invariants - local coordinate independent.

A general 1 form is

1 = 1udx^u

that's scalar invariant

1 = 1udx^u = 1u'dx^u'

A general 2-form is

2 = 2uvdx^u/\dx^v

2uv = - 2vu

etc.

d(p/\q) = dp/\q + (-1)^|p|p/\dq

d^2 = 0

If p is a zero form scalar O

d(O/\q) = dO/\g + O/\dq is a q + 1 form

If p is a 1-form

d(1/\q) = d1/\q - 1/\dq

etc.

p/\q = (-1)^|pq|q/\p

If p & q are both 1-forms then they anti-commute sort of like fermion operators.

ckck' + ck'ck = 0

when k = k' that's the Pauli exclusion principle.

If p & q are both 0-forms then they commute like bosons.

bkbk' - bk'bk = 0

You get Heisenberg uncertainty principle by taking canonical conjugates

e.g. c*k = d/dck is conjugate to ck, one must assume c*K is also a 1-form?

c*kck + ckc*k = 1

So now let p & q be rational numbers, i.e. fractal forms.

This gives fractional quantum statistics & fractional charges!

Galactic Patrol Back From The Future
Hawking and Ellis show that anti-DeSitter space-time has closed timelike curves!
Dark energy corresponds to DeSitter space-time that is well behaved on cosmological scale with no closed timelike curves. However on a smaller scale like the galactic dark matter halos, if the dark matter densities are approximately uniform the dominating metric field they create may be approximately anti-DeSitter. This would fit Colonel Corso's remarks from his private notes that the alleged Roswell aliens were time travelers from our future. In that case they would have to be from our galaxy, i.e. within a spherical dark matter halo of approximately uniform negative zero point energy density and positive pressure. It's interesting that Hawking and Ellis had no inkling of the dark energy and dark matter as zero point vacuum energy of positive and negative energy density respectively when they wrote their book in 1973. The edition I have is 1995 and no mention of dark matter there in connection with anti-DeSitter spacetime. No inkling of dark energy as well a scant ten years ago.