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
Tuesday, August 29, 2006
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
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
Monday, August 28, 2006
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!!!
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
(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!!!
Sunday, August 27, 2006
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.
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.
Friday, August 25, 2006
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.
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.
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."
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."
Thursday, August 24, 2006
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.
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.
"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)
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)
Tuesday, August 22, 2006
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
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
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
Monday, August 21, 2006
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!
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!
Sunday, August 20, 2006
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!
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.
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.
Roger Penrose's diagram for Minkowski Space-Time of Special Relativity - Prelude to Einstein's General Relativity of Gravity
From my book Star Gate under construction (following Hawking & Ellis "The Large Scale Structure of Space-Time", Cambridge.
The intrinsic space-time geometry is only in the non-gravity force-free geodesic structure. There is no objective intrinsic gravity force in Einstein's theory of gravity. There is such an objective gravity force in Newton's older theory. Einstein eliminates Newton's pure gravity force acting at a distance replacing it with local variable curvature, i.e. geodesic deviations of neighboring passive test particles. Any attempt to restore Newton's gravity in Einstein's theory as another valid way of interpreting Einstein's theory is crackpot, inconsistent and displays a fundamental lack of understanding of what John Archibald Wheeler called "Einstein's Vision." Non-geodesics have no fundamental relation to the intrinsic geometry of spacetime. You cannot have non-geodesic paths of test particles without a non-gravity force like the long-range electromagnetic force. You cannot "pull g's" i.e. feel "weight" without a non-gravity force pushing you off a timelike geodesic inside the local light cone.
Geodesics are the straightest EXTREMAL paths in curved space-time.
Note that timelike geodesics are the longest paths in experienced proper time along them in the sense of the action principle of particle mechanics from the calculus of variations, i.e. neighboring bundle of paths with same starting and ending points. Virtual nongeodesic paths without non-gravity forces in this sense are quantum gravity zero point vacuum fluctuations in the Feynman path integral expression for the quantum amplitude of a classical geodesic path. Spacelike geodesics are the shortest straightest paths outside the light cone. Null geodesics have zero length. Real on-mass-shell faster than light tachyons do not exist in globally flat quantum field theories. They signal a vacuum instability as in the Higgs mechanism for the macro-quantum coherent origin of inertia and gravity as curvature. The Haisch-Puthoff model for the origin of inertia and gravity from random locally incoherent electromagnetic zero point fluctuations is wrong IMO.
A useful local nongeodesic "LNIF" frame in curved spacetime is the HOVERING non-geodesic "shell frame" at a fixed distance from a source. However such a frame does not always exist, e.g. inside the black hole null surface event horizon one-way membrane trapped surfaces containing null geodesics. Misunderstanding the contingent nature of the this admittedly useful frame, when it exists, leads one to delusionary ideas that, for example, with the SSS source M
g = GM/r^2
is an objective gravity force even in Einstein's GR. That is not true at all. That formula simply tells you how much rocket thrust you need in space to keep at a fixed distance from the source. It also tells you your weight per mass if you stand on a rigid surface of circumference 2pir encircling mass M.
The "Hilbert error" claim that there are no SSS event horizons is also crackpot IMO.
1. Globally flat Minkowski space-time
The metric in Cartesian coordinates is (c = 1)
ds^2 = -(dx^4)^2 + (dx^1)^2+ (dx^2)^2 + (dx^3)^2
Here the geodesics of maximal proper time are
x^a(affine parameter) = b^a(affine parameter) + c^a
Theorem: any two points in globally flat spacetime are connected by a unique geodesic.
Proof needs fancy formal stuff about exponential map of tangent space to manifold. See Hawking & Ellis for details.
Use the global coordinate transformation to spherical polar coordinates
x^4 = t
x^3 = rcostheta
x^2 = rsinthetacosphi
x^3 = rsinthetasinphi
theta is latitude on celestial sphere centered at r = 0
phi is longitude
Do the differential calculus with product rule to get
ds^2 = - dt^2 + dr^2 + r^2[(dtheta)^2 + sin^2theta(dphi)^2]
There is a non-physical coordinate singularity at r = 0 where the two angles theta & phi are undefined.
Theta ranges from 0 to pi, phi from 0 to 2pi, r from zero to infinity.
The choice of r = 0 in this unstable pre-inflationary pre Big Bang globally flat false vacuum is arbitrary here of course.
2. Wheeler-Feynman type of trick
Use the past to future retarded and future to past advanced light cone radial "null coordinates"
v = t + r i.e. advanced destiny wave back from the future (retro-causal future light cone)
w = t - r i.e. retarded history wave toward the future (past light cone)
Both v & w range from -infinity to + infinity
the GLOBAL FRAME INVARIANT metric field is then
ds^2 = -dudv - (1/4)(v - w)^2[(dtheta)^2 + sin^2theta(dphi)^2]
note that [(dtheta)^2 + sin^2theta(dphi)^2] describes a unit 2D spherical surface S2. Every "point" in the t-r plane is actually an S2 with radius r.
The v = constant, w = constant hypersurfaces are made from light cone null geodesics. Their intersection is a sphere
i.e. all the tangent vectors inside those hypersurfaces are null because no dv^2 & dw^2 terms.
v(w),av(w),bn^a^b = 0
,a is ordinary partial derivative
Penrose diagram for globally flat Minkowski spacetime to make infinity finite.
v = tanp
w = tanq
both p & q range from - pi/2 to + pi/2
Therefore, algebra & trig give
ds^2 = sec^2p sec^2q{-dpdq + (1/4)sin^2(p - q)[(dtheta)^2 + sin^2theta(dphi)^2]}
There exists a conformal map to
ds*^2 = -4dpdq + sin^2(p - q)[(dtheta)^2 + sin^2theta(dphi)^2]
i.e.
ds^2 = (1/4)sec^2(t' + r')sec^2(t' - r')ds*^2
Where we define
t' = p + q
r' = p - q
t' + r' ranges from -pi to pi
t' - r' ranges from -pi to pi
r' > 0
Therefore, algebra demands
ds*^2 = - (dt')^2 + (dr')^2 + sin^2r'[(dtheta)^2 + sin^2theta(dphi)^2]
which is LOCALLY a piece of the Einstein static universe.
Thus the WHOLE OF GLOBALLY FLAT MINKOWSKI SPACE-TIME is given by the FINITE REGION
t' + r' ranges from -pi to pi
t' - r' ranges from -pi to pi
r' > 0
of
ds^2 = (1/4)sec^2(t' + r')sec^2(t' - r')ds*^2
The original coordinates t & r are in
2t = tan[(1/2)(t'+r')] + tan[(1/2)(t'-r')]
2r = tan[(1/2)(t'+r')] - tan[(1/2)(t'-r')]
Suppress theta & phi, then the 1 + 1 string analog Einstein universe is globally equivalent to the unit circle S1, i.e. x^2 + y^2 = 1 imbedded in ANYONIC quantum well 2 + 1 Minkowski with
ds^2 = - dt^2 + dx^2 + dy^2
Note we really mean (ds)^2, (dt)^2 etc.
The full 4D Einstein static universe with his original cosmological constant /\ is the unit S^3
x^2 + y^2 + z^2 + w^2 = 1
imbedded in Kaluza-Klein 5D hyperspace
ds^2 = - dt^2 + dx^2 + dy^2 + dz^2 + dw^2
"One therefore has the situation: the whole of Minkowski space-time is conformal to the region
t' + r' ranges from -pi to pi
t' - r' ranges from -pi to pi
r' > 0
of the Einstein static universe, that is the shaded region of Fig 14. The boundary of this region may therefore be thought of as representing the conformal structure of infinity of Minkowski spacetime. It consists of the null surfaces p = +pi/2 labeled I^+ and q = -pi/2 labeled I^-, together with the points (p = pi/2,q = pi/2) (labeled i^+), (p = pi/2,q = - pi/2) (labeled i^0) and (p = -pi/2,q = -pi/2) (labeled i^-). Any future directed timelike geodesic in Minkowski space approaches i^+(i^-) for large positive (negative) values of its affine parameter, so one can regard any timelike geodesic as originating at i^- and finishing at i^+. Similarly one can regard null geodesics as originating at I^- and ending on I^+, while spacelike geodesics both originate and end at i^0. Thus one may regard i^+ and i^- as representing future and past timelike infinity, I^+ and I^- as representing future and past null infinity, and i^0 as representing spacelike infinity. (However nongeodesics do not obey these rules; e.g. nongeodesic timelike curves may start on I^- and end on I^+.) Since any Cauchy surface intersects all timelike and null geodesics, it is clear it will appear as a cross-section of the space everywhere reaching the boundary at i^0. One can also represent the conformal structure at infinity by drawing a diagram of the (t',r') plane. Each point of this diagram represents a sphere S2 and radial null geodesics are represented as lines at +- pi/4. In fact, the structure of infinity of any spherically symmetric spacetime can be represented by a diagram of this sort, which we call a Penrose diagram. On such diagrams, we shall represent infinity by single lines, the origin of polar coordinates by dotted lines, and irremovable singularities of the metric by double lines. ... Finally, ... one can obtain spaces locally identical to (Minkowski) but with different large scale topological properties by identifying points which are equivalent under a discrete isometry without fixed point ..." 5.1 Hawking and Ellis.
http://content.answers.com/main/content/wp/en/thumb/7/7c/180px-Penrose.PNG
From my book Star Gate under construction (following Hawking & Ellis "The Large Scale Structure of Space-Time", Cambridge.
The intrinsic space-time geometry is only in the non-gravity force-free geodesic structure. There is no objective intrinsic gravity force in Einstein's theory of gravity. There is such an objective gravity force in Newton's older theory. Einstein eliminates Newton's pure gravity force acting at a distance replacing it with local variable curvature, i.e. geodesic deviations of neighboring passive test particles. Any attempt to restore Newton's gravity in Einstein's theory as another valid way of interpreting Einstein's theory is crackpot, inconsistent and displays a fundamental lack of understanding of what John Archibald Wheeler called "Einstein's Vision." Non-geodesics have no fundamental relation to the intrinsic geometry of spacetime. You cannot have non-geodesic paths of test particles without a non-gravity force like the long-range electromagnetic force. You cannot "pull g's" i.e. feel "weight" without a non-gravity force pushing you off a timelike geodesic inside the local light cone.
Geodesics are the straightest EXTREMAL paths in curved space-time.
Note that timelike geodesics are the longest paths in experienced proper time along them in the sense of the action principle of particle mechanics from the calculus of variations, i.e. neighboring bundle of paths with same starting and ending points. Virtual nongeodesic paths without non-gravity forces in this sense are quantum gravity zero point vacuum fluctuations in the Feynman path integral expression for the quantum amplitude of a classical geodesic path. Spacelike geodesics are the shortest straightest paths outside the light cone. Null geodesics have zero length. Real on-mass-shell faster than light tachyons do not exist in globally flat quantum field theories. They signal a vacuum instability as in the Higgs mechanism for the macro-quantum coherent origin of inertia and gravity as curvature. The Haisch-Puthoff model for the origin of inertia and gravity from random locally incoherent electromagnetic zero point fluctuations is wrong IMO.
A useful local nongeodesic "LNIF" frame in curved spacetime is the HOVERING non-geodesic "shell frame" at a fixed distance from a source. However such a frame does not always exist, e.g. inside the black hole null surface event horizon one-way membrane trapped surfaces containing null geodesics. Misunderstanding the contingent nature of the this admittedly useful frame, when it exists, leads one to delusionary ideas that, for example, with the SSS source M
g = GM/r^2
is an objective gravity force even in Einstein's GR. That is not true at all. That formula simply tells you how much rocket thrust you need in space to keep at a fixed distance from the source. It also tells you your weight per mass if you stand on a rigid surface of circumference 2pir encircling mass M.
The "Hilbert error" claim that there are no SSS event horizons is also crackpot IMO.
1. Globally flat Minkowski space-time
The metric in Cartesian coordinates is (c = 1)
ds^2 = -(dx^4)^2 + (dx^1)^2+ (dx^2)^2 + (dx^3)^2
Here the geodesics of maximal proper time are
x^a(affine parameter) = b^a(affine parameter) + c^a
Theorem: any two points in globally flat spacetime are connected by a unique geodesic.
Proof needs fancy formal stuff about exponential map of tangent space to manifold. See Hawking & Ellis for details.
Use the global coordinate transformation to spherical polar coordinates
x^4 = t
x^3 = rcostheta
x^2 = rsinthetacosphi
x^3 = rsinthetasinphi
theta is latitude on celestial sphere centered at r = 0
phi is longitude
Do the differential calculus with product rule to get
ds^2 = - dt^2 + dr^2 + r^2[(dtheta)^2 + sin^2theta(dphi)^2]
There is a non-physical coordinate singularity at r = 0 where the two angles theta & phi are undefined.
Theta ranges from 0 to pi, phi from 0 to 2pi, r from zero to infinity.
The choice of r = 0 in this unstable pre-inflationary pre Big Bang globally flat false vacuum is arbitrary here of course.
2. Wheeler-Feynman type of trick
Use the past to future retarded and future to past advanced light cone radial "null coordinates"
v = t + r i.e. advanced destiny wave back from the future (retro-causal future light cone)
w = t - r i.e. retarded history wave toward the future (past light cone)
Both v & w range from -infinity to + infinity
the GLOBAL FRAME INVARIANT metric field is then
ds^2 = -dudv - (1/4)(v - w)^2[(dtheta)^2 + sin^2theta(dphi)^2]
note that [(dtheta)^2 + sin^2theta(dphi)^2] describes a unit 2D spherical surface S2. Every "point" in the t-r plane is actually an S2 with radius r.
The v = constant, w = constant hypersurfaces are made from light cone null geodesics. Their intersection is a sphere
i.e. all the tangent vectors inside those hypersurfaces are null because no dv^2 & dw^2 terms.
v(w),av(w),bn^a^b = 0
,a is ordinary partial derivative
Penrose diagram for globally flat Minkowski spacetime to make infinity finite.
v = tanp
w = tanq
both p & q range from - pi/2 to + pi/2
Therefore, algebra & trig give
ds^2 = sec^2p sec^2q{-dpdq + (1/4)sin^2(p - q)[(dtheta)^2 + sin^2theta(dphi)^2]}
There exists a conformal map to
ds*^2 = -4dpdq + sin^2(p - q)[(dtheta)^2 + sin^2theta(dphi)^2]
i.e.
ds^2 = (1/4)sec^2(t' + r')sec^2(t' - r')ds*^2
Where we define
t' = p + q
r' = p - q
t' + r' ranges from -pi to pi
t' - r' ranges from -pi to pi
r' > 0
Therefore, algebra demands
ds*^2 = - (dt')^2 + (dr')^2 + sin^2r'[(dtheta)^2 + sin^2theta(dphi)^2]
which is LOCALLY a piece of the Einstein static universe.
Thus the WHOLE OF GLOBALLY FLAT MINKOWSKI SPACE-TIME is given by the FINITE REGION
t' + r' ranges from -pi to pi
t' - r' ranges from -pi to pi
r' > 0
of
ds^2 = (1/4)sec^2(t' + r')sec^2(t' - r')ds*^2
The original coordinates t & r are in
2t = tan[(1/2)(t'+r')] + tan[(1/2)(t'-r')]
2r = tan[(1/2)(t'+r')] - tan[(1/2)(t'-r')]
Suppress theta & phi, then the 1 + 1 string analog Einstein universe is globally equivalent to the unit circle S1, i.e. x^2 + y^2 = 1 imbedded in ANYONIC quantum well 2 + 1 Minkowski with
ds^2 = - dt^2 + dx^2 + dy^2
Note we really mean (ds)^2, (dt)^2 etc.
The full 4D Einstein static universe with his original cosmological constant /\ is the unit S^3
x^2 + y^2 + z^2 + w^2 = 1
imbedded in Kaluza-Klein 5D hyperspace
ds^2 = - dt^2 + dx^2 + dy^2 + dz^2 + dw^2
"One therefore has the situation: the whole of Minkowski space-time is conformal to the region
t' + r' ranges from -pi to pi
t' - r' ranges from -pi to pi
r' > 0
of the Einstein static universe, that is the shaded region of Fig 14. The boundary of this region may therefore be thought of as representing the conformal structure of infinity of Minkowski spacetime. It consists of the null surfaces p = +pi/2 labeled I^+ and q = -pi/2 labeled I^-, together with the points (p = pi/2,q = pi/2) (labeled i^+), (p = pi/2,q = - pi/2) (labeled i^0) and (p = -pi/2,q = -pi/2) (labeled i^-). Any future directed timelike geodesic in Minkowski space approaches i^+(i^-) for large positive (negative) values of its affine parameter, so one can regard any timelike geodesic as originating at i^- and finishing at i^+. Similarly one can regard null geodesics as originating at I^- and ending on I^+, while spacelike geodesics both originate and end at i^0. Thus one may regard i^+ and i^- as representing future and past timelike infinity, I^+ and I^- as representing future and past null infinity, and i^0 as representing spacelike infinity. (However nongeodesics do not obey these rules; e.g. nongeodesic timelike curves may start on I^- and end on I^+.) Since any Cauchy surface intersects all timelike and null geodesics, it is clear it will appear as a cross-section of the space everywhere reaching the boundary at i^0. One can also represent the conformal structure at infinity by drawing a diagram of the (t',r') plane. Each point of this diagram represents a sphere S2 and radial null geodesics are represented as lines at +- pi/4. In fact, the structure of infinity of any spherically symmetric spacetime can be represented by a diagram of this sort, which we call a Penrose diagram. On such diagrams, we shall represent infinity by single lines, the origin of polar coordinates by dotted lines, and irremovable singularities of the metric by double lines. ... Finally, ... one can obtain spaces locally identical to (Minkowski) but with different large scale topological properties by identifying points which are equivalent under a discrete isometry without fixed point ..." 5.1 Hawking and Ellis.
http://content.answers.com/main/content/wp/en/thumb/7/7c/180px-Penrose.PNG
Anyons, Weyl Curvature & Arrow of Time
1. The Weyl curvature tensor is zero in 2 + 1 spacetime.
2. Therefore, the gravity entropy is zero there. There is only a Ricci tensor.
3. In the World Hologram, the anyonic 2 + 1 spacetime boundary of 3 + 1 space-time is more fundamental.
4. The 2 + 1 space-time can only have zero gravity entropy if Penrose is right.
This suggests the the initial singularity is 2 + 1 space-time with zero-entropy in order to have the correct Arrow of Time.
5. Note that the dark energy and dark matter as zero point energy of negative and positive pressures respectively on larger and short scales respectively are virtual sources of zero entropy Ricci tensor.
This mathematical concept becomes useful in the physics of two-dimensional systems such as sheets of graphite or the quantum Hall effect. In space of three dimensions (or more), elementary particles have tightly constrained quantum numbers and, in particular, are restricted to being fermions or bosons. In two-dimensional systems, however, quasiparticles are observed whose quantum states range continuously between fermionic and bosonic, taking on any quantum value in between. Frank Wilczek coined the term "anyons" in 1982 to describe such particles.
Let's say we have two identical particles on a plane. If we interchange both particles so that each particle travels counterclockwise for half a cycle around the center of both particles, the wave function of the system changes by a factor of eiθ where θ is an angle which only depends upon the type of particle in question. If θ is zero, we have a boson and if θ is π we have a fermion. For any other value, we have an anyon. If we have two particles a and b, which may or may not be identical, then their mutual statistics is the change in the phase factor, which is picked up after particle b is rotated counterclockwise around particle a for one full cycle. The mutual statistics may be completely unrelated to the interchange angle between two identical particles.
http://en.wikipedia.org/wiki/Anyon
Weyl curvature hypothesis
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This article or section is in need of attention from an expert on the subject.
Please help recruit one, or improve this page yourself if you can. See discussion page for details.
This article concerns Roger Penrose's 1979 Weyl curvature hypothesis, which would justify spatial homogeneity and isotropy of the observable part of the Universe in the Big Bang model. A different article discusses Weyl's postulate, which is an assumption relating to separation of space and time in the Big Bang model.
The Weyl curvature hypothesis, which arises in the application of Albert Einstein's general theory of relativity to physical cosmology, was introduced by the British mathematician and theoretical physicist Sir Roger Penrose in an article in 1979 [1] in an attempt to provide explanations for two of the most fundamental issues in physics. On the one hand one would like to account for a Universe which on its largest observational scales appears remarkably spatially homogeneous and isotropic in its physical properties (and so can be described by a simple Friedmann-Lemaître model), on the other hand there is the deep question on the origin of the second law of thermodynamics.
Penrose suggests that the resolution of both of these problems is rooted in a concept of the entropy content of gravitational fields. Near the initial cosmological singularity (the Big Bang), he proposes, the entropy content of the cosmological gravitational field was extremely low (compared to what it theoretically could have been), and started rising monotonically thereafter. This process manifested itself e.g. in the formation of structure through the clumping of matter to form galaxies and clusters of galaxies. Penrose associates the initial low entropy content of the Universe with the effective vanishing of the Weyl curvature tensor of the cosmological gravitational field near the Big Bang. From then on, he proposes, its dynamical influence gradually increased, thus being responsible for an overall increase in the amount of entropy in the Universe, and so inducing a cosmological arrow of time.
The Weyl curvature represents such gravitational effects as tidal fields and gravitational radiation. Mathematical treatments of Penrose's ideas on the Weyl curvature hypothesis have been given in the context of isotropic initial cosmological singularities e.g. in the articles [2] ,[3] ,[4] ,[5]. Penrose views the Weyl curvature hypothesis as a physically more credible alternative to cosmic inflation (a hypothetical phase of accelerated expansion in the early life of the Universe) in order to account for the presently observed almost spatial homogeneity and isotropy of our Universe [6].
http://en.wikipedia.org/wiki/Weyl_curvature_hypothesis
Weyl tensor
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In differential geometry, the Weyl curvature tensor, named after Hermann Weyl, is the traceless component of the Riemann curvature tensor. In other words, it is a tensor that has the same symmetries as the Riemann curvature tensor with the extra condition that its Ricci curvature must vanish.
In dimensions 2 and 3 the Weyl curvature tensor vanishes identically. In dimensions ≥ 4, the Weyl curvature is generally nonzero.
The Weyl tensor can be obtained from the full curvature tensor by subtracting out various traces. This is most easily done by writing the Riemann tensor as a (0,4) valent tensor (by contracting with the metric). The (0,4) valent Weyl tensor is then
where n is the dimension of the manifold, g is the metric, R is the Riemann tensor, Ric is the Ricci tensor, s is the scalar curvature, and hOk denotes the Kulkarni-Nomizu product of two symmetric (0,2) tensors:
The ordinary (1,3) valent Weyl tensor is then given by contracting the above with the inverse of the metric.
The Weyl tensor has the special property that it is invariant under conformal changes to the metric. That is, if g′ = f g for some positive scalar function then the (1,3) valent Weyl tensor satisfies W′ = W. For this reason the Weyl tensor is also called the conformal tensor. It follows that a necessary condition for a Riemannian manifold to be conformally flat is that the Weyl tensor vanish. It turns out that in dimensions ≥ 4 this condition is sufficient as well. In dimension 3 the vanishing of the Cotton tensor is a necessary and sufficient condition for the Riemannian manifold being conformally flat.
The Weyl tensor is given in components by
where Rabcd is the Riemann tensor, Rab is the Ricci tensor, R is the Ricci scalar (the scalar curvature) and [] refers to the antisymmetric part.
[edit]
1. The Weyl curvature tensor is zero in 2 + 1 spacetime.
2. Therefore, the gravity entropy is zero there. There is only a Ricci tensor.
3. In the World Hologram, the anyonic 2 + 1 spacetime boundary of 3 + 1 space-time is more fundamental.
4. The 2 + 1 space-time can only have zero gravity entropy if Penrose is right.
This suggests the the initial singularity is 2 + 1 space-time with zero-entropy in order to have the correct Arrow of Time.
5. Note that the dark energy and dark matter as zero point energy of negative and positive pressures respectively on larger and short scales respectively are virtual sources of zero entropy Ricci tensor.
This mathematical concept becomes useful in the physics of two-dimensional systems such as sheets of graphite or the quantum Hall effect. In space of three dimensions (or more), elementary particles have tightly constrained quantum numbers and, in particular, are restricted to being fermions or bosons. In two-dimensional systems, however, quasiparticles are observed whose quantum states range continuously between fermionic and bosonic, taking on any quantum value in between. Frank Wilczek coined the term "anyons" in 1982 to describe such particles.
Let's say we have two identical particles on a plane. If we interchange both particles so that each particle travels counterclockwise for half a cycle around the center of both particles, the wave function of the system changes by a factor of eiθ where θ is an angle which only depends upon the type of particle in question. If θ is zero, we have a boson and if θ is π we have a fermion. For any other value, we have an anyon. If we have two particles a and b, which may or may not be identical, then their mutual statistics is the change in the phase factor, which is picked up after particle b is rotated counterclockwise around particle a for one full cycle. The mutual statistics may be completely unrelated to the interchange angle between two identical particles.
http://en.wikipedia.org/wiki/Anyon
Weyl curvature hypothesis
From Wikipedia, the free encyclopedia
Jump to: navigation, search
This article or section is in need of attention from an expert on the subject.
Please help recruit one, or improve this page yourself if you can. See discussion page for details.
This article concerns Roger Penrose's 1979 Weyl curvature hypothesis, which would justify spatial homogeneity and isotropy of the observable part of the Universe in the Big Bang model. A different article discusses Weyl's postulate, which is an assumption relating to separation of space and time in the Big Bang model.
The Weyl curvature hypothesis, which arises in the application of Albert Einstein's general theory of relativity to physical cosmology, was introduced by the British mathematician and theoretical physicist Sir Roger Penrose in an article in 1979 [1] in an attempt to provide explanations for two of the most fundamental issues in physics. On the one hand one would like to account for a Universe which on its largest observational scales appears remarkably spatially homogeneous and isotropic in its physical properties (and so can be described by a simple Friedmann-Lemaître model), on the other hand there is the deep question on the origin of the second law of thermodynamics.
Penrose suggests that the resolution of both of these problems is rooted in a concept of the entropy content of gravitational fields. Near the initial cosmological singularity (the Big Bang), he proposes, the entropy content of the cosmological gravitational field was extremely low (compared to what it theoretically could have been), and started rising monotonically thereafter. This process manifested itself e.g. in the formation of structure through the clumping of matter to form galaxies and clusters of galaxies. Penrose associates the initial low entropy content of the Universe with the effective vanishing of the Weyl curvature tensor of the cosmological gravitational field near the Big Bang. From then on, he proposes, its dynamical influence gradually increased, thus being responsible for an overall increase in the amount of entropy in the Universe, and so inducing a cosmological arrow of time.
The Weyl curvature represents such gravitational effects as tidal fields and gravitational radiation. Mathematical treatments of Penrose's ideas on the Weyl curvature hypothesis have been given in the context of isotropic initial cosmological singularities e.g. in the articles [2] ,[3] ,[4] ,[5]. Penrose views the Weyl curvature hypothesis as a physically more credible alternative to cosmic inflation (a hypothetical phase of accelerated expansion in the early life of the Universe) in order to account for the presently observed almost spatial homogeneity and isotropy of our Universe [6].
http://en.wikipedia.org/wiki/Weyl_curvature_hypothesis
Weyl tensor
From Wikipedia, the free encyclopedia
Jump to: navigation, search
In differential geometry, the Weyl curvature tensor, named after Hermann Weyl, is the traceless component of the Riemann curvature tensor. In other words, it is a tensor that has the same symmetries as the Riemann curvature tensor with the extra condition that its Ricci curvature must vanish.
In dimensions 2 and 3 the Weyl curvature tensor vanishes identically. In dimensions ≥ 4, the Weyl curvature is generally nonzero.
The Weyl tensor can be obtained from the full curvature tensor by subtracting out various traces. This is most easily done by writing the Riemann tensor as a (0,4) valent tensor (by contracting with the metric). The (0,4) valent Weyl tensor is then
where n is the dimension of the manifold, g is the metric, R is the Riemann tensor, Ric is the Ricci tensor, s is the scalar curvature, and hOk denotes the Kulkarni-Nomizu product of two symmetric (0,2) tensors:
The ordinary (1,3) valent Weyl tensor is then given by contracting the above with the inverse of the metric.
The Weyl tensor has the special property that it is invariant under conformal changes to the metric. That is, if g′ = f g for some positive scalar function then the (1,3) valent Weyl tensor satisfies W′ = W. For this reason the Weyl tensor is also called the conformal tensor. It follows that a necessary condition for a Riemannian manifold to be conformally flat is that the Weyl tensor vanish. It turns out that in dimensions ≥ 4 this condition is sufficient as well. In dimension 3 the vanishing of the Cotton tensor is a necessary and sufficient condition for the Riemannian manifold being conformally flat.
The Weyl tensor is given in components by
where Rabcd is the Riemann tensor, Rab is the Ricci tensor, R is the Ricci scalar (the scalar curvature) and [] refers to the antisymmetric part.
[edit]
Saturday, August 19, 2006
Wikipedia articles on physics by Chris Hillman who works with John Baez
Critique of Yilmaz theory I agree 100% with Chris Hillman on
Yilmaz theory of gravitation
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The Yilmaz theory of gravitation is an attempt by Huseyin Yilmaz and a handful of coworkers to formulate a classical field theory of gravitation which closely mimics general relativity in weak-field conditions, but in which event horizons cannot appear.
(Orthographic caveat: in Turkish, Yilmaz's name is properly written Hüseyin Yılmaz; we will avoid this spelling because English-speaking readers are likely to misread the ı as i, which could cause technical difficulties. The spelling we use is the one Yilmaz adopts in the arXiv.)
Yilmaz's work has been sharply criticized on various grounds, including the claims that
his proposed field equation is ill-defined,
the two desiderata above are incompatible (event horizons can occur in weak field situations according to gtr, in the case of a supermassive black hole).
Yilmaz vigorously disputes these criticisms. Nonetheless, apart from Yilmaz's own papers, the theory has apparently received no attention in the research literature, apart from two critical papers. Yilmaz claims that his critics have misunderstood him, but it has been suggested that his papers are too murky in crucial places to admit a single clear interpretation. Yilmaz's credibility has also been badly damaged by what appear to be serious misstatements about general relativity.
It is well known that naive attempts to quantize general relativity along the same lines which lead from Maxwell's classical field theory of electromagnetism to quantum electrodynamics fail, and that it has proven very difficult to construct a theory of quantum gravity which goes over to general relativity in an appropriate limit. Yilmaz has claimed that, in contrast, his theory is in some sense 'compatible with quantum mechanics'. He even suggests that it might be an alternative to superstring theory. These claims have apparently been given no credence by physicists other than Yilmaz and a handful of his coworkers.
Yilmaz has offered several descriptions of the alleged field equation for his 'theory', which his critics feel are neither entirely consistent with each other nor well-defined. To understand one of the most basic criticisms of Yilmaz's work, one needs to be familiar with
the statement of the Einstein field equation,
the distinction between coordinate dependent and coordinate independent quantities,
well known facts concerning integration in curved spacetimes,
well known facts concerning gravitational energy-momentum pseudotensors in general relativity.
With this background in hand, one can say that Yilmaz apparently wishes to keep the left hand side of the Einstein field equation (namely the Einstein tensor, which is well defined for any Lorentzian manifold, independent of general relativity) but to modify the right hand side, the stress-energy tensor, by adding a kind of gravitational contribution. According to Yilmaz's critics, this additional term is not well-defined, and cannot be made well defined.
Yilmaz has apparently failed to produce a convincing proposal for an observational or experimental test of his theory, and it would appear that no astronomers have contemplated any attempts to test his ideas. On the other hand, astronomers are very interested indeed in testing theoretically solid competitors of general relativity; see Category:Tests of general relativity.
http://en.wikipedia.org/w/index.php?title=Yilmaz_theory_of_gravitation&oldid=45631271
Polarizable vacuum
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Revision as of 02:37, 3 June 2006; Hillman (Talk | contribs)
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In theoretical physics, particularly fringe physics, polarizable vacuum (PV) refers to a proposal by Harold Puthoff, which has been various characterized as
an attempt to reformulate general relativity in terms of a purely formal analogy with the propagation of light through an optical medium,
an attempt to replace general relativity with a scalar theory of gravitation featuring formal analogies with Maxwell's theory of electromagnetism,
an attempt to unify gravitation and electromagnetism in a theory of electrogravity,
an attempt to provide a physical mechanism for how spacetime gets curved in general relativity, which suggests (to Puthoff) the possibility of "metric engineering" for such purposes as spacecraft propulsion (see Breakthrough Propulsion Physics Program).
Puthoff himself has apparently offered various characterizations of his proposal, which has not been accepted in mainstream physics.
Contents [hide]
1 Related work
2 Puthoff's claims
3 A unified field theory?
4 External links
5 References
Related work
Antecedents of PV and more recent related proposals include the following:
A proposal in 1921 by H. A. Wilson to reduce gravitation to electromagnetism by pursuing the formal analogy between "light bending" in metric theories of gravitation and propagation of light through an optical medium having a spatially varying refractive index. Wilson's approach to a unified field theory is not considered viable today.
An attempt (roughly 1960-1970) by Robert Dicke and Fernando de Felice to resurrect and improve Wilson's idea of an optical analogue of gravitational effects. If interpreted conservatively as an attempt to provide an alternative approach to gtr, rather than as work toward a theory unifying electromagnetism and gravitation, this is not an unreasonable approach, although most likely of rather limited utility.
The 1967 proposal of Andrei Sakharov that gravitation might arise from underlying quantum field theory effects, in a manner somewhat analogous to the way that the (simple) classical theory of elasticity arises from (complicated) particle physics. This work is generally regarded as mainstream and not entirely implausible, but highly speculative, and most physicists seem to feel that little progress has been made.
My work is along the lines of Sakharov 1967.
In a series of papers, Bernard Haisch and Alfonso Rueda have proposed that the inertia of massive objects arises as a "electromagnetic reaction force", due to interaction with the so-called zero point field. According to mainstream physics, their claims rest upon incorrect computations using quantum field theory.
I agree with Hillman's assessment here.
Recent work, motivated in large part by the discoveries of the Unruh effect, Hawking radiation, and black hole thermodynamics, to work out a complete theory of physical analogues such as optical black holes. This is not work toward a unified field theory, but in another sense can be regarded as work towards an even more ambitious unification, in which some of the most famous effects usually ascribed to general relativity (but actually common to many metric theories of gravitation) would be seen as essentially thermodynamical effects, not specifically gravitational effects. This work has excited great interest because it might enable experimental verification of the basic concept of Hawking radiation, which is widely regarded as one of the most revolutionary proposals in twentieth century physics, but which in its gravitational incarnation seems to be impossible to verify in experiments in earthly laboratories.
Uh Oh
The 1999 proposal by Keith Watt and Charles W. Misner of a scalar theory of gravitation which postulates a stratified conformally flat metric of the form
, given with respect to a Cartesian chart, where φ satisfies a certain partial differential equation which reduces in a vacuum region to the flat spacetime wave equation
. This is a "toy theory", not a fully fledged theory of gravitation, since as Watt and Misner pointed out, while this theory does have the correct Newtonian limit, it disagrees with the result of certain observations.
Puthoff's claims
Disputed science:
Polarizable vacuum
Disciplines:
physics
Core tenets:
Gravitation can be described via a scalar theory of gravitation, using a stratified conformally flat metric, in which the field equation arises from the notion that the vacuum behaves like a optical polarizable medium.
Year proposed:
* 1998
Original proponents:
Harold Puthoff, Bernard Haisch
Current proponents:
ditto
In essence, Puthoff proposes that the presence of mass alters the electric permittivity and the magnetic permeability of flat spacetime, εo and μo respectively by multiplying them by a scalar function, K:
εo→ε = Kεo, μo→μ = Kμo
Puthoff argues that this will affect the lengths of rulers made of ordinary matter, so that (he argues), in the presence of a gravitational field, the spacetime metric of Minkowski spacetime is replaced by
where κ2 = K is the so-called "dialetric constant of the vacuum". This is a "diagonal" metric given in terms of a Cartesian chart and having the same stratified conformally flat form in the Watt-Misner theory of gravitation. However, according to Puthoff, κ must satisfy a field equation which differs from the field equation of the Watt-Misner theory. In the case of a static spherically symmetric vacuum, this reduces to
which happens to agree with the analogous situation in the Watt-Misner theory. This yields the asymptotically flat solution
The resulting Lorentzian spacetime has the same weak-field limit (and the same far-field) as the Schwarzschild vacuum solution in general relativity, and it satisfies three of the four classical tests of relativistic gravitation (redshift, deflection of light, precession of the perihelion of Mercury) to within the limit of observational accuracy. However, it yields a different prediction for the inspiral of test particles due to gravitational radiation.
However, requiring stratified-conformally flat metrics rules out the possibility of recovering the weak-field Kerr metric, and is certainly inconsistent with the claim that PV can give a general "approximation" of gtr. In particular, this theory exhibits no frame-dragging effects.
This explains why Puthoff has not been able to describe a rotating source in PV theory.
Also, the effect of gravitational radiation on test particles differs profoundly between scalar theories and tensor theories of gravitation such as general relativity. LIGO is not intended primarily as a test ruling out scalar theories, but is widely expected to do so as a side benefit once it detects unambiguous gravitational wave signals exhibiting the characteristics expected in general relativity.
Ibison has considered a "cosmological solution" of PV, analogous to the Friedmann dust solution (with flat orthogonal hyperslices) in general relativity, and argues that this model is inconsistent with various observational and theoretical constraints. He also finds a rate of inspiral disagreeing with observation, but apparently his result disagrees with that of Watt and Misner (who studied the same Lorentzian manifold in the context of their own scalar theory of gravitation).
It is widely appreciated in physics that, contrary to Puthoff's claims, no scalar theory of gravitation can reproduce all of general relativity's successes. It might be noted that De Felice uses constitutive relations to obtain a susceptability tensor which lives in spatial hyperslices; this provides extra degrees of freedom which help make up for the degree of freedom lacking in PV (and other scalar theories).
A unified field theory?
Ibison feels that Puthoff has never claimed to provide a unified field theory which combines gravitation and electromagnetism. However, Puthoff has coauthored papers with Bernard Haisch which apparently do make this claim, and Puthoff's other papers apparently fail to explicitly disavow any such intention.
In any case, whether or not Puthoff intends any such claim, mainstream physicists agree that PV is
not viable as a unification of gravitation and electromagnetism
not a "reformulation" of general relativity,
not a viable theory of gravitation, since it violates observational and theoretical requirements.
In addition, while this point is presumably moot, Puthoff's arguments for his field equations are highly suspect.
I agree with Hillman's assessment of Puthoff's PV theory 100%.
External links
H. E. Puthoff, M. Ibison, Polarizable Vacuum "Metric Engineering" Approach to GR-Type Effects, MITRE Conference, McLean, VA, May 8, 2003. From the website of EarthTech, a company founded by Puthoff.
References
Visser, Matt (2005). Analog Gravity. Living Reviews in Relativity. Retrieved on 2006-06-02.
Ibison, M. (2003). "Investigation of the polarizable vacuum cosmology." 2003.
Watt, Keith; and Misner, Charles (1999). "Relativistic Scalar Gravity: A Laboratory for Numerical Relativity." 10 Oct 1999.
Puthoff, H. E. (2002). "Polarizable-Vacuum (PV) representation of general relativity". Found. of Phys. 32: 927-943. arXiv eprint
de Felice, F. (1971). "On the gravitational field acting as an optical medium". General Relativity and Gravitation 2: 347-.
Dicke, R. H. (1957). "Gravitation without a principle of equivalence". Reviews of Modern Physics 29: 363-376.
Wilson, H. A. (1921). "An electromagnetic theory of gravitation". Physical Review 17: 54-59.
http://en.wikipedia.org/w/index.php?title=Polarizable_vacuum&oldid=56603531
Stochastic electrodynamics
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Revision as of 23:30, 4 June 2006; Hillman (Talk | contribs)
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In theoretical physics, Stochastic electrodynamics (SED) refers to a more or less controversial theory which posits that the interaction of elementary particles with the vacuum radiation field, or zero point field, is ultimately responsible for various familiar quantum phenonmena.
SED has been developed by a number of physicists; their contributions can generally be characterized as speculative proposals within mainstream physics, but widely popularized work by Haisch and Rueda (especially as portrayed in various cranky websites) is often considered fringe science.
Contents [hide]
1 Brief history
2 Nature of SED
3 The work of Haisch and Rueda
4 Internet culture
5 See also
6 External links
7 References
Brief history
Stochastic electrodynamics is usually credited to Timothy H. Boyer, but builds upon the notions of stochastic optics proposed by T. W. Marshall and the notion of induced gravity proposed by Andrei Sakharov. Boyer's ideas have been further developed by L. de la Pena and A. M. Cetto, who introduced linear stochastic electrodyamics (LSED).
This work is generally regarded as more or less mainstream physics. However, starting in about 1984, Bernard Haisch and Alfonso Rueda, sometimes joined by Harold E. Puthoff, have championed the notion the inertia of a massive object arises via an electromagnetic reaction force via interaction with the so-called zero point field. This builds upon a much earlier proposal by Walther Nernst, but is highly controversial; even more controversial is their proposal that this putative effect can be used for spacecraft propulsion and might even explain the UFO phenomenon.
I agree with Puthoff and Haisch that UFOs are real and need explaining. I do not agree with their explanation.
Nature of SED
The zero point field can be thought of, roughly speaking, as a superposition of electromagnetic waves with random frequencies, phases and directions, with a distribution proportional to the cube of frequency, up to a cutoff frequency on the order of the reciprocal of the Planck time. Planck's constant then appears as a kind of typical amplitude for quantum fluctuations in the zero point field.
The original motivation for SED is that it seeks to provide a local realist foundation for various mysterious effects of quantum field theory, including
Casimir force
van der Waals forces,
diamagnetism
cavity effects
Unruh effect
radiative corrections in the theory of the quantum harmonic oscillator
More controversially, Haisch and Rueda have tried to use SED to provide explanations for the phenomena of
inertia
gravitation
The work of Haisch and Rueda
According to Haisch and Rueda, inertia arises as an electromagnetic drag force on accelerating particles, produced by interaction with the zero-point field. In their 1998 Ann. Phys. paper (see citations), they speak of a "Rindler flux", presumably meaning the Unruh effect, and claim to have computed a nonzero "z.p.f. momentum". This computation rests upon their claim to compute a nonzero "z.p.f. Poynting vector", but according to Bill Unruh this computation is incorrect.
Haisch and Rueda also claim that gravitation arises from an electromagnetic induced dipole shielding similar to the Van der Waals force. They claim to explain the equality of gravitational and inertial mass, which is assumed but not derived in general relativity, and they claim to compute thereby the value of the Planck constant from the gravitational constant, or vice versa.
Haisch and Rueda claim that the structure of atoms arises from a thermal equilibrium between between a particle in a potential well and the zero point field. They claim that this resolves the radiation paradox of the Bohr model, a well known shortcoming of that model. This paradox states that an orbiting classical electron will quickly radiate all its energy away and collapse into the nucleus, which is in drastic disagreement with observation. According to Haisch and Rueda, however, in their theory, each orbiting electron absorbs exactly as much energy from the zero-point field as it radiates. They claim that the absorption and re-emission by the electrons in an atom preserves both the frequency distribution and isotropic random phase character of the zero-point field. They suggest an this intuitive picture: the electron is constantly trying to collapse into the nucleus but is blown off course by "gusts" from the background field and so maintains a stable orbit.
Haisch and Rueda claim that the Heisenberg uncertainty principle also arises from interaction of particles with the zero-point field, which, they say, randomly changes the position and velocity of every particle.
These claims are vigorously disputed by other physicists.
The Haisch/Rueda version of SED appears to incorrectly predict no deflection of light in a gravitational field. Their theory also appears to predict an enormous value for the cosmological constant. Haisch and Rueda propose to solve this problem by assuming that the zero-point field does not itself have gravitational mass; rather, they say, the gravitational mass of a massive object is created by the interaction between this object and the zero-point field. Issues which they have apparently not yet addressed include the homogeneous and isotropic nature of their notion of the zero point field.
Of course this is a serious error in the Haisch-Puthoff theory as the discovery of dark energy accelerating the universe proves. Tensor GCT covariance and equivalence principle imply that virtual quanta gravitate if spin 1/2 and anti-gravitate if spin 1. This follows from w = -1 (neglecting boundary effects) and quantum statistics in 3 + 1 space-time. What happens for anyons in 2 + 1 spacetime in quantum wells with fractional statistics is an interesting question I am thinking about. The world hologram idea is that 2 + 1 space-time is more fundamental than 3 + 1 spacetime.
Internet culture
The proposals of Haisch and Rueda have been eagerly promoted at many websites by new energy fans, who hope that the notion of zero point energy might ultimately provide no cost "energy from the vacuum", thereby solving many current problems in contemporary human society. Others claim that the work of Haisch, Rueda, and Puthoff holds out hope of developing an "inertial-less drive" (see Dean drive) which can be used to enable humans to visit far distant regions of the universe. According to a newstory which appeared in the Washington Post, a paper by Haisch played a key role in the bizarre story of the life-changing encounter of Joe Firmage with a (possibly imaginary) "luminous being".
Yes, this is a true story.
See also
Casimir effect
Polarizable vacuum
Rindler coordinates
Unruh effect
Vacuum energy
Zero-point energy
Andrei Sakharov
Bernard Haisch
Harold E. Puthoff
External links
California Institute for Physics and Astrophysics, a fringe physics organization founded by Bernard Haisch
The CEO from Cyberspace: Joe Firmage, a master of the Universe at 28, Wants to Defy Gravity and Visit the Far Corners Of His Realm, by Joel Achenbach, Washington Post, March 31, 1999, from the anticult website of Rick Ross
H. E. Puthoff, Quantum Vacuum Fluctuations: A New Rosetta Stone of Physics? from Lambert Dolphin's website; Dolphin has claimed that the speed of light has measurably decreased during the past 300 years, that special relativity is incorrect, has promoted the claims of Tom Van Flandern, and so on
References
Marshall, T. W. (1963). "TITLE NEEDED". Proc. Roy. Soc. A: 475.
Sakharov, A. D. (1968). "Vacuum Quantum Fluctuations in Curved Space and the Theory of Gravitation". Sov. Phys. Doklady: 1040.
Boyer, Timothy H. (1975). "Random electrodynamics: The theory of classical electrodynamics with classical electromagnetic zero-point radiation". Phys. Rev.: 790-808.
Boyer, T. H. (1980). "A Brief Survey of Stochastic Electrodynamics". Foundations of Radiation Theory and Quantum Electrodynamics. ISBN 0306402777
Boyer, Timothy H. (1985). "The Classical Vacuum". Scientific American. online version from PADRAK, the website of Patrick Bailey, who publishes New Energy News in Salt Lake City, UT, and who promotes a cranky theory of "plasmoids", which he says "contradict theories about gravity and 'mass' "
Milonni, Peter W. (1994). The Quantum Vacuum: An introduction to quantum electrodynamics. San Diego: Academic Press. ISBN 0-124-98080-5.
Haisch, B.; Rueda, A.; and Puthoff, H. E. (1994). "Inertia as a zero-point-field Lorentz force". Phys. Rev. A: 678-694. on-line version from Haisch's website
de la Pena, L.; and Cetto, A. M. (1996). The Quantum Dice: An Introduction to Stochastic Electrodynamics. Dordrecht: Kluwer. ISBN 0792338189. amazon page
Rueda, Alfonso; and Haisch, Bernard (1998). "Contribution to inertial mass by reaction of the vacuum to accelerated motion". Found. Phys.: 1057-1108. physics/9802030
Rueda, Alfonso, and Haisch, Bernard (2005). "Gravity and the Quantum Vacuum Inertia Hypothesis". Ann. Phys.: 479-498. gr-qc/0504061
de la Pena, L.; and Cetto, A. M. (2005). "Contribution from stochastic electrodynamics to the understanding of quantum mechanics." 4 Jan 2005., a review paper
See Stochastic_electrodynamics/Bibliography for more research papers.
http://en.wikipedia.org/w/index.php?title=Stochastic_electrodynamics&oldid=56907094
to be continued
Critique of Yilmaz theory I agree 100% with Chris Hillman on
Yilmaz theory of gravitation
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Revision as of 00:18, 27 March 2006; Hillman (Talk | contribs)
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The Yilmaz theory of gravitation is an attempt by Huseyin Yilmaz and a handful of coworkers to formulate a classical field theory of gravitation which closely mimics general relativity in weak-field conditions, but in which event horizons cannot appear.
(Orthographic caveat: in Turkish, Yilmaz's name is properly written Hüseyin Yılmaz; we will avoid this spelling because English-speaking readers are likely to misread the ı as i, which could cause technical difficulties. The spelling we use is the one Yilmaz adopts in the arXiv.)
Yilmaz's work has been sharply criticized on various grounds, including the claims that
his proposed field equation is ill-defined,
the two desiderata above are incompatible (event horizons can occur in weak field situations according to gtr, in the case of a supermassive black hole).
Yilmaz vigorously disputes these criticisms. Nonetheless, apart from Yilmaz's own papers, the theory has apparently received no attention in the research literature, apart from two critical papers. Yilmaz claims that his critics have misunderstood him, but it has been suggested that his papers are too murky in crucial places to admit a single clear interpretation. Yilmaz's credibility has also been badly damaged by what appear to be serious misstatements about general relativity.
It is well known that naive attempts to quantize general relativity along the same lines which lead from Maxwell's classical field theory of electromagnetism to quantum electrodynamics fail, and that it has proven very difficult to construct a theory of quantum gravity which goes over to general relativity in an appropriate limit. Yilmaz has claimed that, in contrast, his theory is in some sense 'compatible with quantum mechanics'. He even suggests that it might be an alternative to superstring theory. These claims have apparently been given no credence by physicists other than Yilmaz and a handful of his coworkers.
Yilmaz has offered several descriptions of the alleged field equation for his 'theory', which his critics feel are neither entirely consistent with each other nor well-defined. To understand one of the most basic criticisms of Yilmaz's work, one needs to be familiar with
the statement of the Einstein field equation,
the distinction between coordinate dependent and coordinate independent quantities,
well known facts concerning integration in curved spacetimes,
well known facts concerning gravitational energy-momentum pseudotensors in general relativity.
With this background in hand, one can say that Yilmaz apparently wishes to keep the left hand side of the Einstein field equation (namely the Einstein tensor, which is well defined for any Lorentzian manifold, independent of general relativity) but to modify the right hand side, the stress-energy tensor, by adding a kind of gravitational contribution. According to Yilmaz's critics, this additional term is not well-defined, and cannot be made well defined.
Yilmaz has apparently failed to produce a convincing proposal for an observational or experimental test of his theory, and it would appear that no astronomers have contemplated any attempts to test his ideas. On the other hand, astronomers are very interested indeed in testing theoretically solid competitors of general relativity; see Category:Tests of general relativity.
http://en.wikipedia.org/w/index.php?title=Yilmaz_theory_of_gravitation&oldid=45631271
Polarizable vacuum
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Revision as of 02:37, 3 June 2006; Hillman (Talk | contribs)
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In theoretical physics, particularly fringe physics, polarizable vacuum (PV) refers to a proposal by Harold Puthoff, which has been various characterized as
an attempt to reformulate general relativity in terms of a purely formal analogy with the propagation of light through an optical medium,
an attempt to replace general relativity with a scalar theory of gravitation featuring formal analogies with Maxwell's theory of electromagnetism,
an attempt to unify gravitation and electromagnetism in a theory of electrogravity,
an attempt to provide a physical mechanism for how spacetime gets curved in general relativity, which suggests (to Puthoff) the possibility of "metric engineering" for such purposes as spacecraft propulsion (see Breakthrough Propulsion Physics Program).
Puthoff himself has apparently offered various characterizations of his proposal, which has not been accepted in mainstream physics.
Contents [hide]
1 Related work
2 Puthoff's claims
3 A unified field theory?
4 External links
5 References
Related work
Antecedents of PV and more recent related proposals include the following:
A proposal in 1921 by H. A. Wilson to reduce gravitation to electromagnetism by pursuing the formal analogy between "light bending" in metric theories of gravitation and propagation of light through an optical medium having a spatially varying refractive index. Wilson's approach to a unified field theory is not considered viable today.
An attempt (roughly 1960-1970) by Robert Dicke and Fernando de Felice to resurrect and improve Wilson's idea of an optical analogue of gravitational effects. If interpreted conservatively as an attempt to provide an alternative approach to gtr, rather than as work toward a theory unifying electromagnetism and gravitation, this is not an unreasonable approach, although most likely of rather limited utility.
The 1967 proposal of Andrei Sakharov that gravitation might arise from underlying quantum field theory effects, in a manner somewhat analogous to the way that the (simple) classical theory of elasticity arises from (complicated) particle physics. This work is generally regarded as mainstream and not entirely implausible, but highly speculative, and most physicists seem to feel that little progress has been made.
My work is along the lines of Sakharov 1967.
In a series of papers, Bernard Haisch and Alfonso Rueda have proposed that the inertia of massive objects arises as a "electromagnetic reaction force", due to interaction with the so-called zero point field. According to mainstream physics, their claims rest upon incorrect computations using quantum field theory.
I agree with Hillman's assessment here.
Recent work, motivated in large part by the discoveries of the Unruh effect, Hawking radiation, and black hole thermodynamics, to work out a complete theory of physical analogues such as optical black holes. This is not work toward a unified field theory, but in another sense can be regarded as work towards an even more ambitious unification, in which some of the most famous effects usually ascribed to general relativity (but actually common to many metric theories of gravitation) would be seen as essentially thermodynamical effects, not specifically gravitational effects. This work has excited great interest because it might enable experimental verification of the basic concept of Hawking radiation, which is widely regarded as one of the most revolutionary proposals in twentieth century physics, but which in its gravitational incarnation seems to be impossible to verify in experiments in earthly laboratories.
Uh Oh
The 1999 proposal by Keith Watt and Charles W. Misner of a scalar theory of gravitation which postulates a stratified conformally flat metric of the form
, given with respect to a Cartesian chart, where φ satisfies a certain partial differential equation which reduces in a vacuum region to the flat spacetime wave equation
. This is a "toy theory", not a fully fledged theory of gravitation, since as Watt and Misner pointed out, while this theory does have the correct Newtonian limit, it disagrees with the result of certain observations.
Puthoff's claims
Disputed science:
Polarizable vacuum
Disciplines:
physics
Core tenets:
Gravitation can be described via a scalar theory of gravitation, using a stratified conformally flat metric, in which the field equation arises from the notion that the vacuum behaves like a optical polarizable medium.
Year proposed:
* 1998
Original proponents:
Harold Puthoff, Bernard Haisch
Current proponents:
ditto
In essence, Puthoff proposes that the presence of mass alters the electric permittivity and the magnetic permeability of flat spacetime, εo and μo respectively by multiplying them by a scalar function, K:
εo→ε = Kεo, μo→μ = Kμo
Puthoff argues that this will affect the lengths of rulers made of ordinary matter, so that (he argues), in the presence of a gravitational field, the spacetime metric of Minkowski spacetime is replaced by
where κ2 = K is the so-called "dialetric constant of the vacuum". This is a "diagonal" metric given in terms of a Cartesian chart and having the same stratified conformally flat form in the Watt-Misner theory of gravitation. However, according to Puthoff, κ must satisfy a field equation which differs from the field equation of the Watt-Misner theory. In the case of a static spherically symmetric vacuum, this reduces to
which happens to agree with the analogous situation in the Watt-Misner theory. This yields the asymptotically flat solution
The resulting Lorentzian spacetime has the same weak-field limit (and the same far-field) as the Schwarzschild vacuum solution in general relativity, and it satisfies three of the four classical tests of relativistic gravitation (redshift, deflection of light, precession of the perihelion of Mercury) to within the limit of observational accuracy. However, it yields a different prediction for the inspiral of test particles due to gravitational radiation.
However, requiring stratified-conformally flat metrics rules out the possibility of recovering the weak-field Kerr metric, and is certainly inconsistent with the claim that PV can give a general "approximation" of gtr. In particular, this theory exhibits no frame-dragging effects.
This explains why Puthoff has not been able to describe a rotating source in PV theory.
Also, the effect of gravitational radiation on test particles differs profoundly between scalar theories and tensor theories of gravitation such as general relativity. LIGO is not intended primarily as a test ruling out scalar theories, but is widely expected to do so as a side benefit once it detects unambiguous gravitational wave signals exhibiting the characteristics expected in general relativity.
Ibison has considered a "cosmological solution" of PV, analogous to the Friedmann dust solution (with flat orthogonal hyperslices) in general relativity, and argues that this model is inconsistent with various observational and theoretical constraints. He also finds a rate of inspiral disagreeing with observation, but apparently his result disagrees with that of Watt and Misner (who studied the same Lorentzian manifold in the context of their own scalar theory of gravitation).
It is widely appreciated in physics that, contrary to Puthoff's claims, no scalar theory of gravitation can reproduce all of general relativity's successes. It might be noted that De Felice uses constitutive relations to obtain a susceptability tensor which lives in spatial hyperslices; this provides extra degrees of freedom which help make up for the degree of freedom lacking in PV (and other scalar theories).
A unified field theory?
Ibison feels that Puthoff has never claimed to provide a unified field theory which combines gravitation and electromagnetism. However, Puthoff has coauthored papers with Bernard Haisch which apparently do make this claim, and Puthoff's other papers apparently fail to explicitly disavow any such intention.
In any case, whether or not Puthoff intends any such claim, mainstream physicists agree that PV is
not viable as a unification of gravitation and electromagnetism
not a "reformulation" of general relativity,
not a viable theory of gravitation, since it violates observational and theoretical requirements.
In addition, while this point is presumably moot, Puthoff's arguments for his field equations are highly suspect.
I agree with Hillman's assessment of Puthoff's PV theory 100%.
External links
H. E. Puthoff, M. Ibison, Polarizable Vacuum "Metric Engineering" Approach to GR-Type Effects, MITRE Conference, McLean, VA, May 8, 2003. From the website of EarthTech, a company founded by Puthoff.
References
Visser, Matt (2005). Analog Gravity. Living Reviews in Relativity. Retrieved on 2006-06-02.
Ibison, M. (2003). "Investigation of the polarizable vacuum cosmology." 2003.
Watt, Keith; and Misner, Charles (1999). "Relativistic Scalar Gravity: A Laboratory for Numerical Relativity." 10 Oct 1999.
Puthoff, H. E. (2002). "Polarizable-Vacuum (PV) representation of general relativity". Found. of Phys. 32: 927-943. arXiv eprint
de Felice, F. (1971). "On the gravitational field acting as an optical medium". General Relativity and Gravitation 2: 347-.
Dicke, R. H. (1957). "Gravitation without a principle of equivalence". Reviews of Modern Physics 29: 363-376.
Wilson, H. A. (1921). "An electromagnetic theory of gravitation". Physical Review 17: 54-59.
http://en.wikipedia.org/w/index.php?title=Polarizable_vacuum&oldid=56603531
Stochastic electrodynamics
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Revision as of 23:30, 4 June 2006; Hillman (Talk | contribs)
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In theoretical physics, Stochastic electrodynamics (SED) refers to a more or less controversial theory which posits that the interaction of elementary particles with the vacuum radiation field, or zero point field, is ultimately responsible for various familiar quantum phenonmena.
SED has been developed by a number of physicists; their contributions can generally be characterized as speculative proposals within mainstream physics, but widely popularized work by Haisch and Rueda (especially as portrayed in various cranky websites) is often considered fringe science.
Contents [hide]
1 Brief history
2 Nature of SED
3 The work of Haisch and Rueda
4 Internet culture
5 See also
6 External links
7 References
Brief history
Stochastic electrodynamics is usually credited to Timothy H. Boyer, but builds upon the notions of stochastic optics proposed by T. W. Marshall and the notion of induced gravity proposed by Andrei Sakharov. Boyer's ideas have been further developed by L. de la Pena and A. M. Cetto, who introduced linear stochastic electrodyamics (LSED).
This work is generally regarded as more or less mainstream physics. However, starting in about 1984, Bernard Haisch and Alfonso Rueda, sometimes joined by Harold E. Puthoff, have championed the notion the inertia of a massive object arises via an electromagnetic reaction force via interaction with the so-called zero point field. This builds upon a much earlier proposal by Walther Nernst, but is highly controversial; even more controversial is their proposal that this putative effect can be used for spacecraft propulsion and might even explain the UFO phenomenon.
I agree with Puthoff and Haisch that UFOs are real and need explaining. I do not agree with their explanation.
Nature of SED
The zero point field can be thought of, roughly speaking, as a superposition of electromagnetic waves with random frequencies, phases and directions, with a distribution proportional to the cube of frequency, up to a cutoff frequency on the order of the reciprocal of the Planck time. Planck's constant then appears as a kind of typical amplitude for quantum fluctuations in the zero point field.
The original motivation for SED is that it seeks to provide a local realist foundation for various mysterious effects of quantum field theory, including
Casimir force
van der Waals forces,
diamagnetism
cavity effects
Unruh effect
radiative corrections in the theory of the quantum harmonic oscillator
More controversially, Haisch and Rueda have tried to use SED to provide explanations for the phenomena of
inertia
gravitation
The work of Haisch and Rueda
According to Haisch and Rueda, inertia arises as an electromagnetic drag force on accelerating particles, produced by interaction with the zero-point field. In their 1998 Ann. Phys. paper (see citations), they speak of a "Rindler flux", presumably meaning the Unruh effect, and claim to have computed a nonzero "z.p.f. momentum". This computation rests upon their claim to compute a nonzero "z.p.f. Poynting vector", but according to Bill Unruh this computation is incorrect.
Haisch and Rueda also claim that gravitation arises from an electromagnetic induced dipole shielding similar to the Van der Waals force. They claim to explain the equality of gravitational and inertial mass, which is assumed but not derived in general relativity, and they claim to compute thereby the value of the Planck constant from the gravitational constant, or vice versa.
Haisch and Rueda claim that the structure of atoms arises from a thermal equilibrium between between a particle in a potential well and the zero point field. They claim that this resolves the radiation paradox of the Bohr model, a well known shortcoming of that model. This paradox states that an orbiting classical electron will quickly radiate all its energy away and collapse into the nucleus, which is in drastic disagreement with observation. According to Haisch and Rueda, however, in their theory, each orbiting electron absorbs exactly as much energy from the zero-point field as it radiates. They claim that the absorption and re-emission by the electrons in an atom preserves both the frequency distribution and isotropic random phase character of the zero-point field. They suggest an this intuitive picture: the electron is constantly trying to collapse into the nucleus but is blown off course by "gusts" from the background field and so maintains a stable orbit.
Haisch and Rueda claim that the Heisenberg uncertainty principle also arises from interaction of particles with the zero-point field, which, they say, randomly changes the position and velocity of every particle.
These claims are vigorously disputed by other physicists.
The Haisch/Rueda version of SED appears to incorrectly predict no deflection of light in a gravitational field. Their theory also appears to predict an enormous value for the cosmological constant. Haisch and Rueda propose to solve this problem by assuming that the zero-point field does not itself have gravitational mass; rather, they say, the gravitational mass of a massive object is created by the interaction between this object and the zero-point field. Issues which they have apparently not yet addressed include the homogeneous and isotropic nature of their notion of the zero point field.
Of course this is a serious error in the Haisch-Puthoff theory as the discovery of dark energy accelerating the universe proves. Tensor GCT covariance and equivalence principle imply that virtual quanta gravitate if spin 1/2 and anti-gravitate if spin 1. This follows from w = -1 (neglecting boundary effects) and quantum statistics in 3 + 1 space-time. What happens for anyons in 2 + 1 spacetime in quantum wells with fractional statistics is an interesting question I am thinking about. The world hologram idea is that 2 + 1 space-time is more fundamental than 3 + 1 spacetime.
Internet culture
The proposals of Haisch and Rueda have been eagerly promoted at many websites by new energy fans, who hope that the notion of zero point energy might ultimately provide no cost "energy from the vacuum", thereby solving many current problems in contemporary human society. Others claim that the work of Haisch, Rueda, and Puthoff holds out hope of developing an "inertial-less drive" (see Dean drive) which can be used to enable humans to visit far distant regions of the universe. According to a newstory which appeared in the Washington Post, a paper by Haisch played a key role in the bizarre story of the life-changing encounter of Joe Firmage with a (possibly imaginary) "luminous being".
Yes, this is a true story.
See also
Casimir effect
Polarizable vacuum
Rindler coordinates
Unruh effect
Vacuum energy
Zero-point energy
Andrei Sakharov
Bernard Haisch
Harold E. Puthoff
External links
California Institute for Physics and Astrophysics, a fringe physics organization founded by Bernard Haisch
The CEO from Cyberspace: Joe Firmage, a master of the Universe at 28, Wants to Defy Gravity and Visit the Far Corners Of His Realm, by Joel Achenbach, Washington Post, March 31, 1999, from the anticult website of Rick Ross
H. E. Puthoff, Quantum Vacuum Fluctuations: A New Rosetta Stone of Physics? from Lambert Dolphin's website; Dolphin has claimed that the speed of light has measurably decreased during the past 300 years, that special relativity is incorrect, has promoted the claims of Tom Van Flandern, and so on
References
Marshall, T. W. (1963). "TITLE NEEDED". Proc. Roy. Soc. A: 475.
Sakharov, A. D. (1968). "Vacuum Quantum Fluctuations in Curved Space and the Theory of Gravitation". Sov. Phys. Doklady: 1040.
Boyer, Timothy H. (1975). "Random electrodynamics: The theory of classical electrodynamics with classical electromagnetic zero-point radiation". Phys. Rev.: 790-808.
Boyer, T. H. (1980). "A Brief Survey of Stochastic Electrodynamics". Foundations of Radiation Theory and Quantum Electrodynamics. ISBN 0306402777
Boyer, Timothy H. (1985). "The Classical Vacuum". Scientific American. online version from PADRAK, the website of Patrick Bailey, who publishes New Energy News in Salt Lake City, UT, and who promotes a cranky theory of "plasmoids", which he says "contradict theories about gravity and 'mass' "
Milonni, Peter W. (1994). The Quantum Vacuum: An introduction to quantum electrodynamics. San Diego: Academic Press. ISBN 0-124-98080-5.
Haisch, B.; Rueda, A.; and Puthoff, H. E. (1994). "Inertia as a zero-point-field Lorentz force". Phys. Rev. A: 678-694. on-line version from Haisch's website
de la Pena, L.; and Cetto, A. M. (1996). The Quantum Dice: An Introduction to Stochastic Electrodynamics. Dordrecht: Kluwer. ISBN 0792338189. amazon page
Rueda, Alfonso; and Haisch, Bernard (1998). "Contribution to inertial mass by reaction of the vacuum to accelerated motion". Found. Phys.: 1057-1108. physics/9802030
Rueda, Alfonso, and Haisch, Bernard (2005). "Gravity and the Quantum Vacuum Inertia Hypothesis". Ann. Phys.: 479-498. gr-qc/0504061
de la Pena, L.; and Cetto, A. M. (2005). "Contribution from stochastic electrodynamics to the understanding of quantum mechanics." 4 Jan 2005., a review paper
See Stochastic_electrodynamics/Bibliography for more research papers.
http://en.wikipedia.org/w/index.php?title=Stochastic_electrodynamics&oldid=56907094
to be continued
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