Summary of Vacuum Coherence Theory
On Jan 6, 2005, at 1:17 AM, Carlos Perelman wrote:
Dear Jack :
Okay, so everything is fine then with setting the infrared scale to be given by the *throat* size of the
hyperboloid (that describes de Sitter, Anti de Sitter space), which is a *constant* parameter.
OK good. It must be *constant*; because w = -1 demands it.
Okay, we agree then on this.
Yes, we agree. I will cite you on that on any publication. It's important that w = -1 severely constrains the possible choices in the model. Do you know if that point is mentioned explicitly in the literature? I don't know this field that well, but Lenny Susskind definitely writes a lot about the (anti) de Sitter space in context of his hologram idea. George Chapline Jr does not like that approach for some reason - he does not like Bekenstein black hole thermodynamics. George is concerned with 3rd law of thermo I think and the fact that condensates (both real and virtual) have zero entropy. Of course I use that to explain why early universe has small entropy.
We can still use hologram idea from Bekenstein -> Hawking -> t'Hooft-Susskind
Entropy of Universe/kB ~ R(t)^2 BITS
to explain the Arrow of Time problem in inflationary cosmology defined by Roger Penrose in "Fashion, Faith & Fantasy" GR 17 Dublin, 2005
However, independent of that
Einstein's Cosmological Constant /\ is CONTINGENT in sense of WEP Anthropic Landscape Darwinism with an infinity of "Level 1" (Max Tegmark) Hubble parallel "material" (Wheeler's "IT") universes in hyperspace as given by chaotic inflation.
/\ = (Constant Throat Size)^-2 = 10^-56 cm^-2
Vacuum Dark Energy Density = (hc/Lp^2)/\ ~ 10^-17 10^66 10^-56 ~ 10^-7 ergs/cc
In my Vacuum Coherence Theory
/\ = Lp^-2(1 - Lp^n|Vacuum Coherence|^2)
n = 2 for World Hologram Paradigm, where Vacuum Coherence (Macro-Quantum Tsunami) is normalized as [length]^-n/2
At large scale FLRW homogeneous isotropic scale 10^2 -> 10^4 Megaparsecs |Vacuum Coherence| = constant independent of R(t) where
energy density of "stuff" real and virtual ~ R(t)^-3(1 + w)
w = 0 for cold matter
w = + 1/3 for real photons
w = -1 for random incoherent micro-quantum zero point energy vacuum fluctuations of all fields that can be quantized.
w = -1 demands that /\ = constant independent of R(t) on large-scale (not on small scale)
guv CANNOT be quantized because it is an emergent ODLRO "superfluid" field (Sakharov). However, it does have a "normal fluid" residue that huv that can be quantized, i.e. perturbation theory on the dynamical emergent c-number curved background guv. It's like BCS theory in the Gorkov formalism (Nambu-Jona Lasino).
Local ODLRO parameter Vacuum Coherence = |Higgs Amplitude|e^i(Goldstone Phase)
(suppress internal indices like in Yang-Mills type theories e.g. NASA space-probe gravity anomaly UNIFORM radial
a_g = - cH toward Sun suggests S2 space for Vacuum Coherence with hedgehog point topological defect starting 20AU from Sun.
All of this is scale-dependent like ZOOM IN-OUT wavelet transforms (renormalization group flows to fixed points, emergence of symmetries in low energy effective field theories such as here for Einstein's ODLRO 1916 GR)
Completing Andrei Sakharov's 1967 idea with PW Anderson's 1967 "More is different" emergent complexity thesis for ODLRO spontaneous broken ground state symmetries with emergent quasi-particles and collective mode excitations of the effective fields at the new levels of spontaneous self-organization:
guv(LNIF) = (Minkowski)uv + Lp^2(Goldstone Phase)(,u,v)
Pre-inflationary unstable vacuum is zero lepto-quark rest mass conformal vacuum of Penrose's twistors with no gravity at all.
Local Goldstone Phase transformations (transition functions for overlapping local coordinate charts) -> Diff(4) tensor GCTs.
Goldstone Phase(x^u) -> Goldstone Phase(x^u') = Goldstone Phase(x^u') + Chi(x^u,x^u')
GCT Jacobian Matrix
Xu'^u = Chi(x^u,x^u'),u,u' transition function for overlapping local coordinate charts
gu'v'(LNIF') = Xu'^uXv'^vguv(LNIF)
Note 16 second order ordinary partial derivatives of RIGID Goldstone Phase
64 third-order partial derivatives for connection Cartan 1-forms
256 fourth-order partial derivatives for curvature Cartan 2-forms
In general mixed partials need not commute (anholonomy).
Note that Wigner quantum limit of measuring space time with clocks of mass m + condition that no black hole forms in the measurement demands that the quantum gravity uncertainty &l in measurement of distance l is
&l > (Lp^2l)^1/3
If l = throat size ~ 10^28 cm = /\^-1/2
&l = (10^-66 10^28)^1/3 ~ 10^38/3 ~ 10^-13 cm ~ 1 fermi where hadron physics and classical electron radius e^2/mc^2 is.
Universal Regge Slope ~ (1/1Gev)^2 ~ (&l)^2 _ (1 fermi)^2 "quantum of area", i.e. Witten's "alpha'" for hadronic strings not superstrings. (My 1973 paper in "Collective Phenomena").
On Jan 6, 2005, at 1:17 AM, Carlos Perelman wrote:
Dear Jack :
Okay, so everything is fine then with setting the infrared scale to be given by the *throat* size of the
hyperboloid (that describes de Sitter, Anti de Sitter space), which is a *constant* parameter.
OK good. It must be *constant*; because w = -1 demands it.
Okay, we agree then on this.
I can send you a copy of my Mod. Phys. Letts A paper if you wish ?
Yes. You have it in pdf? Just e-mail it. :-)
Stay in touch
Carlos
Thursday, January 06, 2005
Wednesday, January 05, 2005
Holographic Universe and Dark Energy
On Jan 5, 2005, at 4:28 PM, Carlos Perelman wrote:
Dear Christian (Jack and Tony):
In the paper by Zee and Hsu : hep-th/0406142
they discuss the issue of the time dependence of the infrared scale and Cohen, Kaplan and Nelson paper in Phys. Rev. Letts (1999), but these authors do not derive the geometric mean relationship.
Note that In de Sitter or Anti de Sitter space, as I have shown, you set the infrared scale to be given by the *throat* size of the hyperboloid (that describes de Sitter, Anti de Sitter space), which is a *constant* parameter.
OK good. It must be "constant" because w = -1 demands it.
Energy Density ~ R(t)^-3(1 + w)
OK what I am saying is that
"throat size" = Lp/(1 - Lp^n|Vacuum Coherence|^2)^1/2 ~ 10^28 cm
Einstein Cosmological Constant /\ = (throat size)^-2
n = 2 in World Hologram picture - that George Chapline Jr rejects BTW.
n = 3 in usual space picture
Normalize macro-quantum Vacuum Coherence ODLRO parameter to 1/(Length)^n/2 like micro-quantum waves in n space dimensions.
The people who advocate Holography say that you equate the infrared scale with the size of the future event horizon of de Sitter space = an asymptotic unreachable scale.
Of course, we know that the Hubble radius is time dependent. Thus to be precise, we must use the geometric mean relationship using an ulraviolet Planck scale and an asymptotic infrared (constant) scale (throat size of hyperboloid).
The point is that you cannot have any dependence of Einstein's cosmological constant /\ on the scale factor R(t) or on H(t) = R(t)^-1dR(t)/dt.
Note, the quantum gravity world hologram uncertainty formula
(Uncertainty in measurement of length l)^2 = &l^2 > hl/mc Wigner quantum clock of mass m
&l > Gm/c^2 to avoid forming a quantum black hole
multiply
&l^3 > lhG/c^3 = lLp^2
Uncertainty in measurement of throat size is then
&l > [(throat size)(Planck area)]^1/3
If throat size ~ c/H ~ 10^28 cm
&l > (10^28x10^-66)^1/3 = 10^38/3 ~ 10^-13 cm ~ 1 fermi, i.e. 1Gev scale of universal Regge slope of hadronic resonances that are in some ways like rotating black holes in strong short-range gravity as I published in "Collective Phenomena" edited by Herbert Frohlich & F.W. Cummings, 1973.
hardly a random coincidence.
In my paper I have an underlying 5-dimensional Topological theory, and as Dirac pointed out long ago, when you have higher dimensions, one cannot exclude the possibility of a time variation of the four-dimensional fundamental constants in Nature, like the Planck scale (Newton's constant) resulting from compactifications of the extra dimensions.
The problem is w = -1 is a strong constraint from covariance and the principle of equivalence. That hit me in the I lika bigga piece of Pi in The Sky only today! :-)
Best wishes
Carlos
On Jan 5, 2005, at 1:40 PM, Jack Sarfatti wrote:
1. The entropy of universe from World Hologram as
S(Universe)/kB ~ R(t)^2
has nice feature that it solves Roger Penrose's problem with inflation of why early universe has low entropy, i.e. why Arrow of Time is in direction of accelerated expansion of space since
R(initial singularity) ~ 0 << R(today) ~ 10^61
However, George Chapline Jr objects to the whole Bekenstein-Hawking entropy ~ surface idea that is the basis of the t'Hooft-Susskind hologram. I sit on the fence on that for the moment.
However, I retract my hologram model where
/\ = (LpR(t))^-2
because it violates w = -1 for zero point energy.
That is the energy density of any "stuff" both real and virtual obeys
energy density ~ R(t)^-3(1 + w)
w = 0 for v/c << 1 real matter
w = +1/3 for radiation (real photons)
w = -1 for RANDOM INCOHERENT virtual quanta of all kinds
The energy density for ordinary matter ~ 1/R(t)^3 and ~ 1/R(t)^4 for radiation. But the dark energy density must be truly constant i.e. independent of R(t).
In my theory, Einstein's Cosmological Constant is
/\ = Lp^-2(1 - Lp^n|Vacuum Coherence|^2) ~ 10^-56 cm^-2
n is either 2 or 3 depending if you believe t'Hooft-Susskind hologram or not.
The formula must be more like what Carlos Perelman is saying
/\ = (H/c)^2
Where H is some truly constant asymptotic value of H = R(t)^-1dR(t)/dt
So that the future of our Universe is quasi-inflationary
R(t) ~ e^Ht
In that case.
OR alternatively we do not use H, but introduce another contingent CONSTANT parameter /\ in the sense of the WEP and the infinity of parallel material IT worlds as explained by Max Tegmark on his website.
On Jan 5, 2005, at 4:05 AM, Carlos Perelman wrote:
Dear Christian, Brian, Jack and Tony :
I recall that Christian ( Beck ) wrote a very nice paper about vacuum fluctuations related also to
Brian's ( Josephson ) work. In any case, let me tell Christian ( since he does not know ) about the origins of the Geometric mean relationship among the vacuum energy density
involving the upper and lower scales that is also related to the *neutrino* mass :
rho = ( L_Planck )^{ -2 } ( R_Hubble )^{ -2 } =
Oh OK you mean in my notation, using truly constant throat size
Dark Energy Density = hc/Lp^2(throat size)^2
Where in my Vacuum Condensate theory
1/(throat size)^2 = (1/Lp^2)(1 - Lp^n|Vacuum Coherence|^2) ~ 10^-56 cm^-2
( L_Planck )^{ -4 } ( L_Planck / R_Hubble )^{ 2 } ~
10^{ - 122 } (M_Planck )^4 = ( neutrino mass )^4 = agrees with Observations !
The neutrino mass you get from the above relationship is about 10^{- 3} electron volts = okay
Christian can see the *derivation* from first principles of
such geometric mean relationship described above in my paper :
Mod. Phys A vol 17 , No. 32 ( 2002 ) 2095-2103.
Anti de Sitter Gravity from ( topological ) BF-Chern-Simons-Higgs Theories
In page 2098 I provide the derivation of such geometric mean relation from scratch.
The throat size of Anti de Sitter also coincides with the throat size of de Sitter space and one can take the future horizon scale of the FRW metric ( Jack's model ) to coincide with the de Sitter throat size.
Anyway, I will not bore you anymore with these messages. It is very curious these results.
Happy New year
Carlos Castro Perelman
On Jan 5, 2005, at 4:28 PM, Carlos Perelman wrote:
Dear Christian (Jack and Tony):
In the paper by Zee and Hsu : hep-th/0406142
they discuss the issue of the time dependence of the infrared scale and Cohen, Kaplan and Nelson paper in Phys. Rev. Letts (1999), but these authors do not derive the geometric mean relationship.
Note that In de Sitter or Anti de Sitter space, as I have shown, you set the infrared scale to be given by the *throat* size of the hyperboloid (that describes de Sitter, Anti de Sitter space), which is a *constant* parameter.
OK good. It must be "constant" because w = -1 demands it.
Energy Density ~ R(t)^-3(1 + w)
OK what I am saying is that
"throat size" = Lp/(1 - Lp^n|Vacuum Coherence|^2)^1/2 ~ 10^28 cm
Einstein Cosmological Constant /\ = (throat size)^-2
n = 2 in World Hologram picture - that George Chapline Jr rejects BTW.
n = 3 in usual space picture
Normalize macro-quantum Vacuum Coherence ODLRO parameter to 1/(Length)^n/2 like micro-quantum waves in n space dimensions.
The people who advocate Holography say that you equate the infrared scale with the size of the future event horizon of de Sitter space = an asymptotic unreachable scale.
Of course, we know that the Hubble radius is time dependent. Thus to be precise, we must use the geometric mean relationship using an ulraviolet Planck scale and an asymptotic infrared (constant) scale (throat size of hyperboloid).
The point is that you cannot have any dependence of Einstein's cosmological constant /\ on the scale factor R(t) or on H(t) = R(t)^-1dR(t)/dt.
Note, the quantum gravity world hologram uncertainty formula
(Uncertainty in measurement of length l)^2 = &l^2 > hl/mc Wigner quantum clock of mass m
&l > Gm/c^2 to avoid forming a quantum black hole
multiply
&l^3 > lhG/c^3 = lLp^2
Uncertainty in measurement of throat size is then
&l > [(throat size)(Planck area)]^1/3
If throat size ~ c/H ~ 10^28 cm
&l > (10^28x10^-66)^1/3 = 10^38/3 ~ 10^-13 cm ~ 1 fermi, i.e. 1Gev scale of universal Regge slope of hadronic resonances that are in some ways like rotating black holes in strong short-range gravity as I published in "Collective Phenomena" edited by Herbert Frohlich & F.W. Cummings, 1973.
hardly a random coincidence.
In my paper I have an underlying 5-dimensional Topological theory, and as Dirac pointed out long ago, when you have higher dimensions, one cannot exclude the possibility of a time variation of the four-dimensional fundamental constants in Nature, like the Planck scale (Newton's constant) resulting from compactifications of the extra dimensions.
The problem is w = -1 is a strong constraint from covariance and the principle of equivalence. That hit me in the I lika bigga piece of Pi in The Sky only today! :-)
Best wishes
Carlos
On Jan 5, 2005, at 1:40 PM, Jack Sarfatti wrote:
1. The entropy of universe from World Hologram as
S(Universe)/kB ~ R(t)^2
has nice feature that it solves Roger Penrose's problem with inflation of why early universe has low entropy, i.e. why Arrow of Time is in direction of accelerated expansion of space since
R(initial singularity) ~ 0 << R(today) ~ 10^61
However, George Chapline Jr objects to the whole Bekenstein-Hawking entropy ~ surface idea that is the basis of the t'Hooft-Susskind hologram. I sit on the fence on that for the moment.
However, I retract my hologram model where
/\ = (LpR(t))^-2
because it violates w = -1 for zero point energy.
That is the energy density of any "stuff" both real and virtual obeys
energy density ~ R(t)^-3(1 + w)
w = 0 for v/c << 1 real matter
w = +1/3 for radiation (real photons)
w = -1 for RANDOM INCOHERENT virtual quanta of all kinds
The energy density for ordinary matter ~ 1/R(t)^3 and ~ 1/R(t)^4 for radiation. But the dark energy density must be truly constant i.e. independent of R(t).
In my theory, Einstein's Cosmological Constant is
/\ = Lp^-2(1 - Lp^n|Vacuum Coherence|^2) ~ 10^-56 cm^-2
n is either 2 or 3 depending if you believe t'Hooft-Susskind hologram or not.
The formula must be more like what Carlos Perelman is saying
/\ = (H/c)^2
Where H is some truly constant asymptotic value of H = R(t)^-1dR(t)/dt
So that the future of our Universe is quasi-inflationary
R(t) ~ e^Ht
In that case.
OR alternatively we do not use H, but introduce another contingent CONSTANT parameter /\ in the sense of the WEP and the infinity of parallel material IT worlds as explained by Max Tegmark on his website.
On Jan 5, 2005, at 4:05 AM, Carlos Perelman wrote:
Dear Christian, Brian, Jack and Tony :
I recall that Christian ( Beck ) wrote a very nice paper about vacuum fluctuations related also to
Brian's ( Josephson ) work. In any case, let me tell Christian ( since he does not know ) about the origins of the Geometric mean relationship among the vacuum energy density
involving the upper and lower scales that is also related to the *neutrino* mass :
rho = ( L_Planck )^{ -2 } ( R_Hubble )^{ -2 } =
Oh OK you mean in my notation, using truly constant throat size
Dark Energy Density = hc/Lp^2(throat size)^2
Where in my Vacuum Condensate theory
1/(throat size)^2 = (1/Lp^2)(1 - Lp^n|Vacuum Coherence|^2) ~ 10^-56 cm^-2
( L_Planck )^{ -4 } ( L_Planck / R_Hubble )^{ 2 } ~
10^{ - 122 } (M_Planck )^4 = ( neutrino mass )^4 = agrees with Observations !
The neutrino mass you get from the above relationship is about 10^{- 3} electron volts = okay
Christian can see the *derivation* from first principles of
such geometric mean relationship described above in my paper :
Mod. Phys A vol 17 , No. 32 ( 2002 ) 2095-2103.
Anti de Sitter Gravity from ( topological ) BF-Chern-Simons-Higgs Theories
In page 2098 I provide the derivation of such geometric mean relation from scratch.
The throat size of Anti de Sitter also coincides with the throat size of de Sitter space and one can take the future horizon scale of the FRW metric ( Jack's model ) to coincide with the de Sitter throat size.
Anyway, I will not bore you anymore with these messages. It is very curious these results.
Happy New year
Carlos Castro Perelman
Corrections to World Hologram & Einstein's Vacuum Dark Energy
1. The entropy of universe from World Hologram as
S(Universe)/kB ~ R(t)^2
has nice feature that it solves Roger Penrose's problem with inflation of why early universe has low entropy, i.e. why Arrow of Time is in direction of accelerated expansion of space since
R(initial singularity) ~ 0 << R(today) ~ 10^61
However, George Chapline Jr objects to the whole Bekenstein-Hawking entropy ~ surface idea that is the basis of the t'Hooft-Susskind hologram. I sit on the fence on that for the moment.
However, I retract my hologram model where
/\ = (LpR(t))^-2
because it violates w = -1 for zero point energy.
That is the energy density of any "stuff" both real and virtual obeys
energy density ~ R(t)^-3(1 + w)
w = 0 for v/c << 1 real matter
w = +1/3 for radiation (real photons)
w = -1 for RANDOM INCOHERENT virtual quanta of all kinds
The energy density for ordinary matter ~ 1/R(t)^3 and ~ 1/R(t)^4 for radiation. But the dark energy density must be truly constant i.e. independent of R(t).
In my theory, Einstein's Cosmological Constant is
/\ = Lp^-2(1 - Lp^n|Vacuum Coherence|^2) ~ 10^-56 cm^-2
n is either 2 or 3 depending if you believe t'Hooft-Susskind hologram or not.
The formula must be more like what Carlos Perelman is saying
/\ = (H/c)^2
Where H is some truly constant asymptotic value of H = R(t)^-1dR(t)/dt
So that the future of our Universe is quasi-inflationary
R(t) ~ e^Ht
In that case.
OR alternatively we do not use H but introduce another contingent CONSTANT parameter /\ in the sense of the WEP and the infinity of parallel material IT worlds as explained by Max Tegmark on his website.
On Jan 5, 2005, at 4:05 AM, Carlos Perelman wrote:
Dear Christian, Brian, Jack and Tony :
I recall that Christian ( Beck ) wrote a very nice paper about vacuum fluctuations related also to
Brian's ( Josephson ) work. In any case, let me tell Christian ( since he does not know ) about the origins of the Geometric mean relationship among the vacuum energy density
involving the upper and lower scales that is also related to the *neutrino* mass :
rho = ( L_Planck )^{ -2 } ( R_Hubble )^{ -2 } =
( L_Planck )^{ -4 } ( L_Planck / R_Hubble )^{ 2 } ~
10^{ - 122 } (M_Planck )^4 = ( neutrino mass )^4 = agrees with Observations !
The neutrino mass you get from the above relationship is about 10^{ - 3 } electron volts = okay
Christian can see the *derivation* from first principles of
such geometric mean relationship described above in my paper :
Mod. Phys A vol 17 , No. 32 ( 2002 ) 2095-2103.
Anti de Sitter Gravity from ( topological ) BF-Chern-Simons-Higgs Theories
In page 2098 I provide the derivation of such geometric mean relation from scratch.
The throat size of Anti de Sitter also coincides with the throat size of de Sitter space and one can take the future horizon scale of the FRW metric ( Jack's model ) to coincide with the de Sitter throat size.
Anyway, I will not bore you anymore with these messages. It is very curious these results.
Happy New year
Carlos Castro Perelman
1. The entropy of universe from World Hologram as
S(Universe)/kB ~ R(t)^2
has nice feature that it solves Roger Penrose's problem with inflation of why early universe has low entropy, i.e. why Arrow of Time is in direction of accelerated expansion of space since
R(initial singularity) ~ 0 << R(today) ~ 10^61
However, George Chapline Jr objects to the whole Bekenstein-Hawking entropy ~ surface idea that is the basis of the t'Hooft-Susskind hologram. I sit on the fence on that for the moment.
However, I retract my hologram model where
/\ = (LpR(t))^-2
because it violates w = -1 for zero point energy.
That is the energy density of any "stuff" both real and virtual obeys
energy density ~ R(t)^-3(1 + w)
w = 0 for v/c << 1 real matter
w = +1/3 for radiation (real photons)
w = -1 for RANDOM INCOHERENT virtual quanta of all kinds
The energy density for ordinary matter ~ 1/R(t)^3 and ~ 1/R(t)^4 for radiation. But the dark energy density must be truly constant i.e. independent of R(t).
In my theory, Einstein's Cosmological Constant is
/\ = Lp^-2(1 - Lp^n|Vacuum Coherence|^2) ~ 10^-56 cm^-2
n is either 2 or 3 depending if you believe t'Hooft-Susskind hologram or not.
The formula must be more like what Carlos Perelman is saying
/\ = (H/c)^2
Where H is some truly constant asymptotic value of H = R(t)^-1dR(t)/dt
So that the future of our Universe is quasi-inflationary
R(t) ~ e^Ht
In that case.
OR alternatively we do not use H but introduce another contingent CONSTANT parameter /\ in the sense of the WEP and the infinity of parallel material IT worlds as explained by Max Tegmark on his website.
On Jan 5, 2005, at 4:05 AM, Carlos Perelman wrote:
Dear Christian, Brian, Jack and Tony :
I recall that Christian ( Beck ) wrote a very nice paper about vacuum fluctuations related also to
Brian's ( Josephson ) work. In any case, let me tell Christian ( since he does not know ) about the origins of the Geometric mean relationship among the vacuum energy density
involving the upper and lower scales that is also related to the *neutrino* mass :
rho = ( L_Planck )^{ -2 } ( R_Hubble )^{ -2 } =
( L_Planck )^{ -4 } ( L_Planck / R_Hubble )^{ 2 } ~
10^{ - 122 } (M_Planck )^4 = ( neutrino mass )^4 = agrees with Observations !
The neutrino mass you get from the above relationship is about 10^{ - 3 } electron volts = okay
Christian can see the *derivation* from first principles of
such geometric mean relationship described above in my paper :
Mod. Phys A vol 17 , No. 32 ( 2002 ) 2095-2103.
Anti de Sitter Gravity from ( topological ) BF-Chern-Simons-Higgs Theories
In page 2098 I provide the derivation of such geometric mean relation from scratch.
The throat size of Anti de Sitter also coincides with the throat size of de Sitter space and one can take the future horizon scale of the FRW metric ( Jack's model ) to coincide with the de Sitter throat size.
Anyway, I will not bore you anymore with these messages. It is very curious these results.
Happy New year
Carlos Castro Perelman
Tuesday, January 04, 2005
ETs in their Magnificent Flying Machines
On Jan 4, 2005, at 7:36 PM, Jack Sarfatti wrote:
Einstein's guv(curved space time) ~ (Minkowski)uv Lp^2(Goldstone Phase)(,u,v)
Should be for non-inertial observers using non-gravity forces to hover (i.e. stand still as it were) at a fixed distance from a "source":
Einstein's guv(curved space time) ~ (Minkowski)uv + Lp^2(Goldstone Phase)(,u,v)
When the vacuum coherence -> 0, then we get back globally flat Minkowski spacetime, which is what we have in the pre-inflationary highly unstable completely incoherent false conformal vacuum.
What does curved spacetime mean operationally? One thing it means for space travelers is that they have to fire their rockets in order to HOVER at a fixed distance from some compact source. This is independent of measuring tidal stretch-squeeze relative accelerations between closely spaced geodesic test particles. If you fire a rocket in flat spacetime you move Bhubba, you buggy and you feel inertial g-force! Not so in curved spacetime where you move weightlessly in a geodesic glide relative to the distant stars or to the local cosmic black body microwave background radiation.
What the ETs know how to do is to geodesically glide in whatever direction they desire using small amounts of onboard power in their Magnificent Unconventional Flying Machines. That's what we are after!
http://stardrive.org/cartoon/MagicBean.html
We have the nonlocal "curvature without curvature" effect, analogous to the Bohm-Aharonov effect from non-simply connected global topology on locally observable physics (e.g. shift in a fringe pattern). As shown by R. Kiehn this comes from closed inexact Cartan form structure in the "gravity field", i.e. the Levi-Civita connection field for parallel transport of objects in the standard 1916 Einstein theory with zero torsion, zero nonmetricity and zero other exotic field effects.
On Jan 4, 2005, at 7:36 PM, Jack Sarfatti wrote:
Einstein's guv(curved space time) ~ (Minkowski)uv Lp^2(Goldstone Phase)(,u,v)
Should be for non-inertial observers using non-gravity forces to hover (i.e. stand still as it were) at a fixed distance from a "source":
Einstein's guv(curved space time) ~ (Minkowski)uv + Lp^2(Goldstone Phase)(,u,v)
When the vacuum coherence -> 0, then we get back globally flat Minkowski spacetime, which is what we have in the pre-inflationary highly unstable completely incoherent false conformal vacuum.
What does curved spacetime mean operationally? One thing it means for space travelers is that they have to fire their rockets in order to HOVER at a fixed distance from some compact source. This is independent of measuring tidal stretch-squeeze relative accelerations between closely spaced geodesic test particles. If you fire a rocket in flat spacetime you move Bhubba, you buggy and you feel inertial g-force! Not so in curved spacetime where you move weightlessly in a geodesic glide relative to the distant stars or to the local cosmic black body microwave background radiation.
What the ETs know how to do is to geodesically glide in whatever direction they desire using small amounts of onboard power in their Magnificent Unconventional Flying Machines. That's what we are after!
http://stardrive.org/cartoon/MagicBean.html
We have the nonlocal "curvature without curvature" effect, analogous to the Bohm-Aharonov effect from non-simply connected global topology on locally observable physics (e.g. shift in a fringe pattern). As shown by R. Kiehn this comes from closed inexact Cartan form structure in the "gravity field", i.e. the Levi-Civita connection field for parallel transport of objects in the standard 1916 Einstein theory with zero torsion, zero nonmetricity and zero other exotic field effects.
Giant Quantum Vacuum Tsunami Wave
Yes, thanks I did know about that actually. Good suggestion you make at bottom. I am curious to see how Schwinger would do the flat neutral conducting plate (area A, separation d) problem as ~ hc(A/d^4) the RANDOM ZPF photon pressure way, or ~ e^2(A/d^4) electro-static way that Ian Peterson of Coventry University advocates as the less misleading way - apparently Landau agreed says Werbos. Puthoff uses wrong POSITIVE pressure for his ZPF calculations of Ken Shoulders' charge clusters. In fact w = -1, so that the pressure is NEGATIVE since virtual photon energy density is POSITIVE from boson commutation rules. Some of the text books make same mistake treating the off-mass-shell virtual photons as if they were on-mass-shell real photons with the entirely different w = +1/3.
According to Einstein's GR, i.e. EEP + GCT tensor covariance (Puthoff gets them BOTH wrong in his PV dielectric model sold by Eric Davis in the USAF "teleportation report", in weak curvature slow speed Newtonian limit, neglecting gravimagnetic rotation of sources etc, the Poisson eq is
Laplacian of Gravity Potential per unit test mass = (G/c^2)(Energy Density of Source)(1 + 3w)
for BOTH REAL ON-MASS-SHELL sources and VIRTUAL OFF-MASS-SHELL EXOTIC VACUUM "dark energy" and "dark matter" sources.
It's only the VACUUM COHERENCE that can HIDE the effect of RANDOM ZPF sources by absorbing their direct gravity influence (either attractive or repulsive) into the vacuum condensate. The RANDOM ZPF is like "normal fluid" in the "two fluid model" of macro-quantum liquids and solids. The physical vacuum covariant "aether" is a 4D Super Solid (Kleinert's picture) with curvature and torsion from disclination and dislocation defect densities. The vacuum coherence TSUNAMI wave must be single-valued round closed loops just like superfluid order parameters are when they show quantized circulations and quantized magnetic fluxes. The NASA Pioneer 10 & 11 gravitational anomaly as a UNIFORM g-force tug back to Sun a_g = -cH = 10^-7 cm/sec^2 is a good example - in that case the "hedgehog" defect (David Thouless) with a UNIFORM RADIAL GRADIENT, in this case a gradient in the dark energy field between the two concentric spherical boundaries, the first at 20 AU from the NASA data.
So in the case of zero point forces we must have something like
ZPF ENERGY DENSITY = (hc/Lp^4)(1 - Lp^n|Vacuum Coherence|^2)
n = 3 in my original formula, but now I lean toward n = 2 if t'Hooft-Susskind World Hologram is right. George Chapline, Jr rejects that BTW.
The macro-quantum ODLRO LOCAL vacuum coherence "More is different" (PW Anderson) order parameter is normalized as
[Vacuum Coherence] = (Length)^-n/2
Just like micro-quantum wave functions. However, the MACRO-QUANTUM TSUNAMIS are RIGID (PW Anderson) THEY DO NOT COLLAPSE! They can sustain SIGNAL NONLOCALITY in A. Valentini's sense. They are IMMUNE FROM ENVIRONMENTAL DECOHERENCE! Indeed the Vacuum Coherence Goldstone Phase Rigidity = Super String Tension = c^4/G ~ 10^19Gev per 10^-33 cm = Space-Time Stiffness
Einstein's guv(curved space time) ~ (Minkowski)uv Lp^2(Goldstone Phase)(,u,v)
GCTs of Diff(4) are derived from local phase transformations (same as in other local gauge field theories)
Goldstone Phase (x^u) -> Goldstone Phase (x^u') = Goldstone Phase (x^u) + Chi(x^u,x^u')
Chi is the transition function for overlapping local coordinate charts in the atlas of the curved manifold.
Jacobian Matrix of the GCT Tensor multi-linear transformation is
Xu^u' = Chi,u^,u'
Vacuum Coherence generally lives in a multi-component order parameter space of dimension = order of G/H factor group where H is the broken symmetry subgroup. I suppress those "Yang-Mills" indices for simplicity. In this case G = Conformal Group.
gu'v' = Xu'^uXv'^vguv
AT SAME LOCAL EVENT P for COINCIDENT geodesic LIFS & non-geodesic LNIFS. "Geodesics" relative to (LC) connection only as yet. No torsion, no nonmetricity here - not yet anyway. Maybe later. We only use the (LC) covariant derivative ;
i.e. ; = , + (LC)
, is the ordinary partial derivative
This is analogous to minimal coupling in QED where
; = , + (e/ihc)A
(LC) is to curved spacetime what A is to internal space.
Both (LC) and A are Cartan connection 1-forms.
Kiehn decomposition
form = exact + closed non-exact + non-closed
exact is trivial CONTINGENT coordinate change, i.e. ARBITRARY MANNER of how detectors are set up!
This solves Zielinski's Problem when it is properly posed in terms of Cartan's exterior calculus including Wheeler's dual dictum for all field theories
"The boundary of a boundary is zero" as the essence of the ACTION PRINCIPLE.
closed non-exact is NONLOCAL influence of NON-TRIVIAL COHOMOLOGY (Betti numbers ...) of manifold on local physics
e.g. Bohm-Aharonov effect, Berry phases, Vilenken-Taub "curvature without curvature" as in brief existence of a thin flat wall of exotic vacuum dark energy
non-closed is LOCAL "classical" "curvature with curvature" e.g.
B = CurlA
Conformal Vacuum Tidal Stretch-Squeeze Curvature = (LC) Curl of itself
On Jan 4, 2005, at 4:40 PM, Tony Smith wrote:
Jack, you ask "... Did Schwinger write about Casimir force? ...".
Yes.
For example, see the paper at
http://xxx.lanl.gov/abs/quant-ph/9805031
by S. Liberati, F. Belgiorno, Matt Visser, and D.W. Sciama
entitled
Sonoluminescence as a QED vacuum effect: Probing Schwinger's proposal
The abstract states:
"... Several years ago Schwinger proposed a physical mechanism
for sonoluminescence in terms of photon production due to
changes in the properties of the quantum-electrodynamic (QED) vacuum
arising from a collapsing dielectric bubble.
This mechanism can be re-phrased in terms of the Casimir effect
and has recently been the subject of considerable controversy.
The present paper probes Schwinger's suggestion in detail:
Using the sudden approximation we calculate Bogolubov coefficients
relating the QED vacuum in the presence of the expanded bubble
to that in the presence of the collapsed bubble.
In this way
we derive an estimate for the spectrum and total energy emitted.
We verify that in the sudden approximation
there is an efficient production of photons,
and further that the main contribution to this dynamic Casimir effect
comes from a volume term, as per Schwinger's original calculation.
However,
we also demonstrate that the timescales required
to implement Schwinger's original suggestion are not physically relevant
to sonoluminescence.
Although Schwinger was correct in his assertion
that changes in the zero-point energy lead to photon production,
nevertheless his original model is not appropriate for sonoluminescence.
In other works (see
quant-ph/9805023, quant-ph/9904013, quant-ph/9904018, quant-ph/9905034)
we have developed a variant of Schwinger's model
that is compatible with the physically required timescales. ...".
It might be interesting to compare
Schwinger's (ordinary incoherent Casimir) / sonoluminescence relationship
with
the (vacuum coherence coherent Casimir) / dark energy relationship
that you are discussing.
Maybe they are related like
incoherent sonoluminescent light
is related to
coherent laser light.
Tony
PS - I asked a while back about what, in your model,
corresponds to the conventional scalar inflation field.
What does so correspond ?
Yes, thanks I did know about that actually. Good suggestion you make at bottom. I am curious to see how Schwinger would do the flat neutral conducting plate (area A, separation d) problem as ~ hc(A/d^4) the RANDOM ZPF photon pressure way, or ~ e^2(A/d^4) electro-static way that Ian Peterson of Coventry University advocates as the less misleading way - apparently Landau agreed says Werbos. Puthoff uses wrong POSITIVE pressure for his ZPF calculations of Ken Shoulders' charge clusters. In fact w = -1, so that the pressure is NEGATIVE since virtual photon energy density is POSITIVE from boson commutation rules. Some of the text books make same mistake treating the off-mass-shell virtual photons as if they were on-mass-shell real photons with the entirely different w = +1/3.
According to Einstein's GR, i.e. EEP + GCT tensor covariance (Puthoff gets them BOTH wrong in his PV dielectric model sold by Eric Davis in the USAF "teleportation report", in weak curvature slow speed Newtonian limit, neglecting gravimagnetic rotation of sources etc, the Poisson eq is
Laplacian of Gravity Potential per unit test mass = (G/c^2)(Energy Density of Source)(1 + 3w)
for BOTH REAL ON-MASS-SHELL sources and VIRTUAL OFF-MASS-SHELL EXOTIC VACUUM "dark energy" and "dark matter" sources.
It's only the VACUUM COHERENCE that can HIDE the effect of RANDOM ZPF sources by absorbing their direct gravity influence (either attractive or repulsive) into the vacuum condensate. The RANDOM ZPF is like "normal fluid" in the "two fluid model" of macro-quantum liquids and solids. The physical vacuum covariant "aether" is a 4D Super Solid (Kleinert's picture) with curvature and torsion from disclination and dislocation defect densities. The vacuum coherence TSUNAMI wave must be single-valued round closed loops just like superfluid order parameters are when they show quantized circulations and quantized magnetic fluxes. The NASA Pioneer 10 & 11 gravitational anomaly as a UNIFORM g-force tug back to Sun a_g = -cH = 10^-7 cm/sec^2 is a good example - in that case the "hedgehog" defect (David Thouless) with a UNIFORM RADIAL GRADIENT, in this case a gradient in the dark energy field between the two concentric spherical boundaries, the first at 20 AU from the NASA data.
So in the case of zero point forces we must have something like
ZPF ENERGY DENSITY = (hc/Lp^4)(1 - Lp^n|Vacuum Coherence|^2)
n = 3 in my original formula, but now I lean toward n = 2 if t'Hooft-Susskind World Hologram is right. George Chapline, Jr rejects that BTW.
The macro-quantum ODLRO LOCAL vacuum coherence "More is different" (PW Anderson) order parameter is normalized as
[Vacuum Coherence] = (Length)^-n/2
Just like micro-quantum wave functions. However, the MACRO-QUANTUM TSUNAMIS are RIGID (PW Anderson) THEY DO NOT COLLAPSE! They can sustain SIGNAL NONLOCALITY in A. Valentini's sense. They are IMMUNE FROM ENVIRONMENTAL DECOHERENCE! Indeed the Vacuum Coherence Goldstone Phase Rigidity = Super String Tension = c^4/G ~ 10^19Gev per 10^-33 cm = Space-Time Stiffness
Einstein's guv(curved space time) ~ (Minkowski)uv Lp^2(Goldstone Phase)(,u,v)
GCTs of Diff(4) are derived from local phase transformations (same as in other local gauge field theories)
Goldstone Phase (x^u) -> Goldstone Phase (x^u') = Goldstone Phase (x^u) + Chi(x^u,x^u')
Chi is the transition function for overlapping local coordinate charts in the atlas of the curved manifold.
Jacobian Matrix of the GCT Tensor multi-linear transformation is
Xu^u' = Chi,u^,u'
Vacuum Coherence generally lives in a multi-component order parameter space of dimension = order of G/H factor group where H is the broken symmetry subgroup. I suppress those "Yang-Mills" indices for simplicity. In this case G = Conformal Group.
gu'v' = Xu'^uXv'^vguv
AT SAME LOCAL EVENT P for COINCIDENT geodesic LIFS & non-geodesic LNIFS. "Geodesics" relative to (LC) connection only as yet. No torsion, no nonmetricity here - not yet anyway. Maybe later. We only use the (LC) covariant derivative ;
i.e. ; = , + (LC)
, is the ordinary partial derivative
This is analogous to minimal coupling in QED where
; = , + (e/ihc)A
(LC) is to curved spacetime what A is to internal space.
Both (LC) and A are Cartan connection 1-forms.
Kiehn decomposition
form = exact + closed non-exact + non-closed
exact is trivial CONTINGENT coordinate change, i.e. ARBITRARY MANNER of how detectors are set up!
This solves Zielinski's Problem when it is properly posed in terms of Cartan's exterior calculus including Wheeler's dual dictum for all field theories
"The boundary of a boundary is zero" as the essence of the ACTION PRINCIPLE.
closed non-exact is NONLOCAL influence of NON-TRIVIAL COHOMOLOGY (Betti numbers ...) of manifold on local physics
e.g. Bohm-Aharonov effect, Berry phases, Vilenken-Taub "curvature without curvature" as in brief existence of a thin flat wall of exotic vacuum dark energy
non-closed is LOCAL "classical" "curvature with curvature" e.g.
B = CurlA
Conformal Vacuum Tidal Stretch-Squeeze Curvature = (LC) Curl of itself
On Jan 4, 2005, at 4:40 PM, Tony Smith wrote:
Jack, you ask "... Did Schwinger write about Casimir force? ...".
Yes.
For example, see the paper at
http://xxx.lanl.gov/abs/quant-ph/9805031
by S. Liberati, F. Belgiorno, Matt Visser, and D.W. Sciama
entitled
Sonoluminescence as a QED vacuum effect: Probing Schwinger's proposal
The abstract states:
"... Several years ago Schwinger proposed a physical mechanism
for sonoluminescence in terms of photon production due to
changes in the properties of the quantum-electrodynamic (QED) vacuum
arising from a collapsing dielectric bubble.
This mechanism can be re-phrased in terms of the Casimir effect
and has recently been the subject of considerable controversy.
The present paper probes Schwinger's suggestion in detail:
Using the sudden approximation we calculate Bogolubov coefficients
relating the QED vacuum in the presence of the expanded bubble
to that in the presence of the collapsed bubble.
In this way
we derive an estimate for the spectrum and total energy emitted.
We verify that in the sudden approximation
there is an efficient production of photons,
and further that the main contribution to this dynamic Casimir effect
comes from a volume term, as per Schwinger's original calculation.
However,
we also demonstrate that the timescales required
to implement Schwinger's original suggestion are not physically relevant
to sonoluminescence.
Although Schwinger was correct in his assertion
that changes in the zero-point energy lead to photon production,
nevertheless his original model is not appropriate for sonoluminescence.
In other works (see
quant-ph/9805023, quant-ph/9904013, quant-ph/9904018, quant-ph/9905034)
we have developed a variant of Schwinger's model
that is compatible with the physically required timescales. ...".
It might be interesting to compare
Schwinger's (ordinary incoherent Casimir) / sonoluminescence relationship
with
the (vacuum coherence coherent Casimir) / dark energy relationship
that you are discussing.
Maybe they are related like
incoherent sonoluminescent light
is related to
coherent laser light.
Tony
PS - I asked a while back about what, in your model,
corresponds to the conventional scalar inflation field.
What does so correspond ?
Vacuum Tsunami in Dirac Sea to Higgs Ocean
The Vacuum Coherence is primarily a GIANT QUANTUM TSUNAMI WAVE of bound virtual electro-positron pairs formed from the "EARTHQUAKE" underneath the Dirac Sea to form The Higgs Ocean!
On Jan 4, 2005, at 7:03 AM, Paul J. Werbos, Dr. wrote:
At 03:09 PM 1/3/2005, Jack Sarfatti wrote:
On Jan 3, 2005, at 11:30 AM, Paul J. Werbos, wrote:
At 01:48 PM 1/3/2005, Jack Sarfatti wrote:
Paul is being too mystical in (2) the gravitational effects of zero point energy density are now completely understood. A good reference is Mike Turner's Op Ed in April 2003 Physics Today.
The basic equation is Einstein's
Guv + /\zpfguv = 0
Werbos "Certainly the gravitational implications of assuming (1/2)hw zero point energy, as an energy source term, according to Einstein's theory, are very straightforward, at least to within issues like renormalization. I did not realize that your pieces on "dark energy" vacuum-breaking warp drive were rooted in that idea, which is exactly what Bob Forward's lighter discussions talk about. (The book "Indistinguishable from magic.) I have read some but not all of your pieces."
Jack: I know what Bob Forward did because it was based on Hermann Bondi's idea of negative mass. I heard Bondi lecture on that at Cornell either ~ 1960 or maybe 1963-4? They had no idea back then about "dark energy" or even Kip Thorne's (1986) "exotic matter". It was very primitive. Basic idea back then was two parallel plates of equal and opposite "mass" will self-accelerate. It was not then realized that this was a free-float geodesic glider vacuum propeller like Alcubierre's solution with no time dilation. Of course it is that from the Einstein Equivalence Principle. Indeed, this idea fits George Trimble's "G-Engine" (1956) and Paul Hill's "acceleration field".
Dr. Werbos wrote:
"Hi, Jack!
Many of us pursue more than one idea in a lifetime -- Forward included.
His cheap mass-market paperback "Indistinguishable From Magic" mainly talked about
what you could do in engineering -- especially in space propulsion -- by exploiting
the gravitational effects you get, based on a model of gravity where it is assumed that
zero point energy plays a major role."
Jack: Yes, I know. But Bob Forward did not have the correct theory of the precise relationship of the zero point energy to gravity back then in terms of battle-tested Einstein GR, Heisenberg quantum uncertainty principle, and most important of all the "More is different" (P.W. Anderson 1967) "vacuum coherence" for the (Sakharov 1967) macro-quantum emergence of Einstein's GR field equations from the partial vacuum cohering of the random micro-quantum vacuum fluctuations in the pre -> post inflationary breaking of translational continuous symmetry whose energy release formed the Big Bang. It was not until the discovery of dark energy in 1999 or so that all the pieces of the mystery could be put together. The basic physics, without the vacuum coherence missing link is on pp 25-26 of John Peacock's "Cosmological Physics".
Werbos:
"At least that's what I remember several years after
a light reading of the book. I also remember he was very excited about how he had gotten
support for a kind of DOD black program in the area, and was going to an important highly
secret government meeting he could tell me nothing about to really make things happen.
Forward's book was extremely readable -- and that was a major factor in SOMEONE
paying a lot of attention."
Jack: I think Hal Puthoff knows a lot about that. I met Forward at SF Airport about that.
Werbos: "One of the key ideas was the use of Hawking-style "white black holes." It all depended on
the prediction that "quantum effects" (ala (1/2)hw stuff as best I recall -- sorry for the
fuzziness of my memory) would free us from Einstein's prediction that black holes grow forever."
Jack: He got that out of my 1975 book "Space-Time and Beyond" (E.P. Dutton) with Fred Alan Wolf. But all that stuff is not any good. We understand it all much better today.
Werbos: "I did note at the time that some of us do NOT regard such predictions as proven.
Thus if one tries to build such a device on earth (or even in a lot orbit which eventually decays),
and if the ZPE effects are not there (as I would expect)... such experiments could simply terminate Earth."
Jack: Yes, Andrei Sakharov worried about this. See famous remark from his student Okun. British Astronomer Royal, Martin Rees (Master of Trinity College, Cambridge) talks about it in "Our Final Hour" - a kind of exotic vacuum Ice 9 effect. The cosmological constant problem is part of this. The point is that without vacuum coherence the zero point energy density is MUCH TOO BIG of order hc/Lp^4 where Lp^2 = hG/c^3. In fact, the large-scale averaged zero point ANTI-GRAVITATING "dark energy" ACCELERATING THE UNIVERSE is 122 POWERS OF TEN smaller. That is, Einstein's cosmological constant /\ is not /\ = 1/Lp^2, but is, in fact, OBSERVED to be /\ = 1/(LpR(t))^2 where R(t) is the dimensionless cosmological space expansion factor R(today) = 10^61, R(Big Bang) = 1 using the t'Hooft-Susskind quantized area Holographic Entropy Conjecture from Bekenstein and Hawking's generalized "Black Hole Thermodynamics" that 3D space is really a holographic projection from a 2D screen. What is the World Hologram? Answer: The Vacuum Coherence where Einstein's exotic vacuum local c-number field equation
Guv + /\guv = 0
emerges from the RIGID Goldstone Phase of the Vacuum Coherence.
I get (on large scale, can be different on small scales!) TENTATIVELY
/\ = Lp^-2(1 - Lp^3|Vacuum Coherence|^2)
Note, if we really believe that the (3+1) fabric of space-time is really a holographic projection from the (2+1) hologram "screen" as it were, then I should NORMALIZE the Vacuum Coherence LOCAL ODLRO parameter to a surface not a volume to get
/\ = Lp^-2(1 - Lp^2|Vacuum Coherence|^2)
Like the quantum wave of an electron confined to a surface rather than in a box. Here we have GIANT QUANTUM TSUNAMIS inside the vacuum.
Therefore, only in this FRW large-scale average sense, taking the World Hologram idea seriously
R(t)^2 = (1 - Lp^2|Vacuum Coherence|^2)^-1
Note that we can have R(t)^2 < 0 which is Hawking's topological signature change from Lorentzian space time with causal light cones to instanton Euclidean space time without light cones.
Inflation requires flat 3D space so that
Omega(on-mass-shell matter w = 0) + Omega (near EM MHD fields) + Omega(on-mass-shell-photons w = +1/3) + Omega(off-mass-shell exotic vacua w = -1) + Omega(vacuum coherence) = 1
Omega(off-mass shell exotic vacua) + Omega(vacuum coherence) = Omega(dark energy w = -1 negative pressure) + Omega(dark matter|w = -1 positive pressure mimics w = 0)
(Entropy of Universe/kB) ~ R(t)^2 BITS
IT FROM BIT
explains Arrow of Time for irreversibility of Second Law of Thermodynamics in same direction as expanding accelerating space of our universe.
Pioneer 10&11 Gravity Anomaly UNIFORM RADIAL a_g = -cH = 10^-7 cm/sec^2 to Sun is a hedgehog topological defect in vacuum coherence at Sun, i.e. dark energy field between two concentric bounding spherical surfaces about Sun, first boundary surface starts at 20 AU from Sun. All stars should have this feature is my prediction.
See book by David Thouless on hedgehog where Vacuum Coherence lives in S^2 space for point defects.
Galactic Halo also a topological exotic vacuum defect of another kind.
Werbos: "Brin has a very nice science fiction novel, called "Earth," which starts out that way. (I forget whether the strategy used to save earth in that novel would have any real hope of working in reality.) In the meantime, Forward has died, as best I recall, so I do not know any rational way to probe further. My best guess is that it never got as far as he intended. In any case,producing black holes is not the easiest challenge to engineering.
Jack: Forward was grasping at straws. He was an engineer not a physicist. He died just when the observational breakthrough was emerging. He yearned of course, but did not have the right information. No one did back then.
Werbos: "Negative mass-energy is a different idea. I don't recall the book talking about it.
I did write something to NASA (well-received by a key guy) circa 1968, and
a paper in a very obscure journal circa 1973/74, on that... and a somewhat more
visible book chapter in 1994. (In Pribram's book Origins, bound next to the chapter by Prigogine.)"
Jack: I don't know the book. I am talking about Forward's paper "Negative Matter Propulsion" based on the ideas of Herman Bondi and Stalin's Physics Atomic Bomb Spy Master Yakov Terletski. See Sudoplatov "Special Tasks" revised paperback edition with foreword by Robert Conquest.
Werbos: "In 1968, I did mention what I thought was obvious. If you COULD somehow contain a major chunk of negative mass-energy... you get a craft of zero net mass, as close as you like, so that you would have access to space... just like... "cavorite" was it? Was that H.G. Wells? And with zero inertial mass, you don't exceed c objectively, but you can get very close to c and experience subjective speeds which feel to YOU like Star Trek... We have not proven it exists, of course, but as you hint, there is some evidence in astrophysics which makes the idea more plausible than the pure speculations you hear more about these days..."
Jack: Interesting. Can you send me that paper? We have come a long way since then. Read Saul-Paul Sirag's "Contact" in my autobiography "Destiny Matrix" (on Amazon).
1986 Kip Thorne's Star Gate Time Travel with "exotic matter".
Hawking's prohibition of time travel to past proved wrong by UFOs?
1991 or so? Alcubierre's SUPERLUMINAL timelike geodesic glider warp drive - no g-force no time dilation.
1999 discovery of anti-gravity "dark energy" almost 3/4 of universe IS EXOTIC MATTER! (misnamed)
Dark Matter Detectors will not click with Right Stuff - my prediction.
Dark Energy is virtual ZPF exotic vacuum with negative pressure
w = pressure/(energy density) = -1 from Lorentz covariance + equivalence principle
Dark Matter is virtual ZPF exotic vacuum with positive pressure w = -1 still, but from a distance it mimics w = 0 CDM.
Einstein's field equation in Newtonian limit is Poisson eq
Grad^2(Gravity Potential Energy per unit test mass) ~ (G/c^2)(Energy Density)(1 + 3w)
For ZPF w = -1 and Energy Density < 0 for RANDOM virtual electron-positron PV vacuum fluctuations, and Energy Density > 0 for RANDOM virtual photon vacuum fluctuations. Incoherent virtual photons anti-gravitate like dark energy. Incoherent virtual electron-positron pairs gravitate like dark matter. Virtual quanta cannot make electromagnetic detectors click, but they do make pure gravity detectors click and can be seen by EM detection of those gravity perturbations.
The Vacuum Coherence is primarily a GIANT QUANTUM TSUNAMI WAVE of bound virtual electro-positron pairs formed from the "EARTHQUAKE" underneath the Dirac Sea to form The Higgs Ocean!
Werbos:
By the way, the place where I first learned of Landau's
dipole analysis of the Casimir effect was:
Høye, J.SD., Brevik , I. && Aarseth,J.B. [2000], “The Casimir problem of spherical dielectrics: Quantum statistical and field theoretical approaches,” paper quant-ph/0008088 at xxx.lanl.gov and [2001] Physical Review E 63 051101
But in retrospect, it should have been obvious directly from
the equation of the strength of the Casimir effect!
I think I did a simple search on "Casimir" at arXiv.org, and scanned through a couple
dozen papers, and verified my conclusions via email with folks like Milton
(a fellow former student of Schwinger). The pattern was clear."
Did Schwinger write about Casimir force?
" As I checked my reference file here, I noted that Vigier was not a collaborator on
the particular book I have been citing on DeBroglie's final ideas, the book
which guided some of my thought circa 1970:
Louis DeBroglie, Nonlinear Wave Mechanics: A Causal Interpretation (A.Knodel & J.C.Miller,
tr). Elsevier, 1960.
But perhaps he might have sent me a reprint where Vigier was coauthor. I certainly remember
seeing Vigier's name as a coauthor with DeBroglie back then, but again... I am sorry it
is not so complete in my memory..
----------------
Best of luck to all...
Paul"
The Vacuum Coherence is primarily a GIANT QUANTUM TSUNAMI WAVE of bound virtual electro-positron pairs formed from the "EARTHQUAKE" underneath the Dirac Sea to form The Higgs Ocean!
On Jan 4, 2005, at 7:03 AM, Paul J. Werbos, Dr. wrote:
At 03:09 PM 1/3/2005, Jack Sarfatti wrote:
On Jan 3, 2005, at 11:30 AM, Paul J. Werbos, wrote:
At 01:48 PM 1/3/2005, Jack Sarfatti wrote:
Paul is being too mystical in (2) the gravitational effects of zero point energy density are now completely understood. A good reference is Mike Turner's Op Ed in April 2003 Physics Today.
The basic equation is Einstein's
Guv + /\zpfguv = 0
Werbos "Certainly the gravitational implications of assuming (1/2)hw zero point energy, as an energy source term, according to Einstein's theory, are very straightforward, at least to within issues like renormalization. I did not realize that your pieces on "dark energy" vacuum-breaking warp drive were rooted in that idea, which is exactly what Bob Forward's lighter discussions talk about. (The book "Indistinguishable from magic.) I have read some but not all of your pieces."
Jack: I know what Bob Forward did because it was based on Hermann Bondi's idea of negative mass. I heard Bondi lecture on that at Cornell either ~ 1960 or maybe 1963-4? They had no idea back then about "dark energy" or even Kip Thorne's (1986) "exotic matter". It was very primitive. Basic idea back then was two parallel plates of equal and opposite "mass" will self-accelerate. It was not then realized that this was a free-float geodesic glider vacuum propeller like Alcubierre's solution with no time dilation. Of course it is that from the Einstein Equivalence Principle. Indeed, this idea fits George Trimble's "G-Engine" (1956) and Paul Hill's "acceleration field".
Dr. Werbos wrote:
"Hi, Jack!
Many of us pursue more than one idea in a lifetime -- Forward included.
His cheap mass-market paperback "Indistinguishable From Magic" mainly talked about
what you could do in engineering -- especially in space propulsion -- by exploiting
the gravitational effects you get, based on a model of gravity where it is assumed that
zero point energy plays a major role."
Jack: Yes, I know. But Bob Forward did not have the correct theory of the precise relationship of the zero point energy to gravity back then in terms of battle-tested Einstein GR, Heisenberg quantum uncertainty principle, and most important of all the "More is different" (P.W. Anderson 1967) "vacuum coherence" for the (Sakharov 1967) macro-quantum emergence of Einstein's GR field equations from the partial vacuum cohering of the random micro-quantum vacuum fluctuations in the pre -> post inflationary breaking of translational continuous symmetry whose energy release formed the Big Bang. It was not until the discovery of dark energy in 1999 or so that all the pieces of the mystery could be put together. The basic physics, without the vacuum coherence missing link is on pp 25-26 of John Peacock's "Cosmological Physics".
Werbos:
"At least that's what I remember several years after
a light reading of the book. I also remember he was very excited about how he had gotten
support for a kind of DOD black program in the area, and was going to an important highly
secret government meeting he could tell me nothing about to really make things happen.
Forward's book was extremely readable -- and that was a major factor in SOMEONE
paying a lot of attention."
Jack: I think Hal Puthoff knows a lot about that. I met Forward at SF Airport about that.
Werbos: "One of the key ideas was the use of Hawking-style "white black holes." It all depended on
the prediction that "quantum effects" (ala (1/2)hw stuff as best I recall -- sorry for the
fuzziness of my memory) would free us from Einstein's prediction that black holes grow forever."
Jack: He got that out of my 1975 book "Space-Time and Beyond" (E.P. Dutton) with Fred Alan Wolf. But all that stuff is not any good. We understand it all much better today.
Werbos: "I did note at the time that some of us do NOT regard such predictions as proven.
Thus if one tries to build such a device on earth (or even in a lot orbit which eventually decays),
and if the ZPE effects are not there (as I would expect)... such experiments could simply terminate Earth."
Jack: Yes, Andrei Sakharov worried about this. See famous remark from his student Okun. British Astronomer Royal, Martin Rees (Master of Trinity College, Cambridge) talks about it in "Our Final Hour" - a kind of exotic vacuum Ice 9 effect. The cosmological constant problem is part of this. The point is that without vacuum coherence the zero point energy density is MUCH TOO BIG of order hc/Lp^4 where Lp^2 = hG/c^3. In fact, the large-scale averaged zero point ANTI-GRAVITATING "dark energy" ACCELERATING THE UNIVERSE is 122 POWERS OF TEN smaller. That is, Einstein's cosmological constant /\ is not /\ = 1/Lp^2, but is, in fact, OBSERVED to be /\ = 1/(LpR(t))^2 where R(t) is the dimensionless cosmological space expansion factor R(today) = 10^61, R(Big Bang) = 1 using the t'Hooft-Susskind quantized area Holographic Entropy Conjecture from Bekenstein and Hawking's generalized "Black Hole Thermodynamics" that 3D space is really a holographic projection from a 2D screen. What is the World Hologram? Answer: The Vacuum Coherence where Einstein's exotic vacuum local c-number field equation
Guv + /\guv = 0
emerges from the RIGID Goldstone Phase of the Vacuum Coherence.
I get (on large scale, can be different on small scales!) TENTATIVELY
/\ = Lp^-2(1 - Lp^3|Vacuum Coherence|^2)
Note, if we really believe that the (3+1) fabric of space-time is really a holographic projection from the (2+1) hologram "screen" as it were, then I should NORMALIZE the Vacuum Coherence LOCAL ODLRO parameter to a surface not a volume to get
/\ = Lp^-2(1 - Lp^2|Vacuum Coherence|^2)
Like the quantum wave of an electron confined to a surface rather than in a box. Here we have GIANT QUANTUM TSUNAMIS inside the vacuum.
Therefore, only in this FRW large-scale average sense, taking the World Hologram idea seriously
R(t)^2 = (1 - Lp^2|Vacuum Coherence|^2)^-1
Note that we can have R(t)^2 < 0 which is Hawking's topological signature change from Lorentzian space time with causal light cones to instanton Euclidean space time without light cones.
Inflation requires flat 3D space so that
Omega(on-mass-shell matter w = 0) + Omega (near EM MHD fields) + Omega(on-mass-shell-photons w = +1/3) + Omega(off-mass-shell exotic vacua w = -1) + Omega(vacuum coherence) = 1
Omega(off-mass shell exotic vacua) + Omega(vacuum coherence) = Omega(dark energy w = -1 negative pressure) + Omega(dark matter|w = -1 positive pressure mimics w = 0)
(Entropy of Universe/kB) ~ R(t)^2 BITS
IT FROM BIT
explains Arrow of Time for irreversibility of Second Law of Thermodynamics in same direction as expanding accelerating space of our universe.
Pioneer 10&11 Gravity Anomaly UNIFORM RADIAL a_g = -cH = 10^-7 cm/sec^2 to Sun is a hedgehog topological defect in vacuum coherence at Sun, i.e. dark energy field between two concentric bounding spherical surfaces about Sun, first boundary surface starts at 20 AU from Sun. All stars should have this feature is my prediction.
See book by David Thouless on hedgehog where Vacuum Coherence lives in S^2 space for point defects.
Galactic Halo also a topological exotic vacuum defect of another kind.
Werbos: "Brin has a very nice science fiction novel, called "Earth," which starts out that way. (I forget whether the strategy used to save earth in that novel would have any real hope of working in reality.) In the meantime, Forward has died, as best I recall, so I do not know any rational way to probe further. My best guess is that it never got as far as he intended. In any case,producing black holes is not the easiest challenge to engineering.
Jack: Forward was grasping at straws. He was an engineer not a physicist. He died just when the observational breakthrough was emerging. He yearned of course, but did not have the right information. No one did back then.
Werbos: "Negative mass-energy is a different idea. I don't recall the book talking about it.
I did write something to NASA (well-received by a key guy) circa 1968, and
a paper in a very obscure journal circa 1973/74, on that... and a somewhat more
visible book chapter in 1994. (In Pribram's book Origins, bound next to the chapter by Prigogine.)"
Jack: I don't know the book. I am talking about Forward's paper "Negative Matter Propulsion" based on the ideas of Herman Bondi and Stalin's Physics Atomic Bomb Spy Master Yakov Terletski. See Sudoplatov "Special Tasks" revised paperback edition with foreword by Robert Conquest.
Werbos: "In 1968, I did mention what I thought was obvious. If you COULD somehow contain a major chunk of negative mass-energy... you get a craft of zero net mass, as close as you like, so that you would have access to space... just like... "cavorite" was it? Was that H.G. Wells? And with zero inertial mass, you don't exceed c objectively, but you can get very close to c and experience subjective speeds which feel to YOU like Star Trek... We have not proven it exists, of course, but as you hint, there is some evidence in astrophysics which makes the idea more plausible than the pure speculations you hear more about these days..."
Jack: Interesting. Can you send me that paper? We have come a long way since then. Read Saul-Paul Sirag's "Contact" in my autobiography "Destiny Matrix" (on Amazon).
1986 Kip Thorne's Star Gate Time Travel with "exotic matter".
Hawking's prohibition of time travel to past proved wrong by UFOs?
1991 or so? Alcubierre's SUPERLUMINAL timelike geodesic glider warp drive - no g-force no time dilation.
1999 discovery of anti-gravity "dark energy" almost 3/4 of universe IS EXOTIC MATTER! (misnamed)
Dark Matter Detectors will not click with Right Stuff - my prediction.
Dark Energy is virtual ZPF exotic vacuum with negative pressure
w = pressure/(energy density) = -1 from Lorentz covariance + equivalence principle
Dark Matter is virtual ZPF exotic vacuum with positive pressure w = -1 still, but from a distance it mimics w = 0 CDM.
Einstein's field equation in Newtonian limit is Poisson eq
Grad^2(Gravity Potential Energy per unit test mass) ~ (G/c^2)(Energy Density)(1 + 3w)
For ZPF w = -1 and Energy Density < 0 for RANDOM virtual electron-positron PV vacuum fluctuations, and Energy Density > 0 for RANDOM virtual photon vacuum fluctuations. Incoherent virtual photons anti-gravitate like dark energy. Incoherent virtual electron-positron pairs gravitate like dark matter. Virtual quanta cannot make electromagnetic detectors click, but they do make pure gravity detectors click and can be seen by EM detection of those gravity perturbations.
The Vacuum Coherence is primarily a GIANT QUANTUM TSUNAMI WAVE of bound virtual electro-positron pairs formed from the "EARTHQUAKE" underneath the Dirac Sea to form The Higgs Ocean!
Werbos:
By the way, the place where I first learned of Landau's
dipole analysis of the Casimir effect was:
Høye, J.SD., Brevik , I. && Aarseth,J.B. [2000], “The Casimir problem of spherical dielectrics: Quantum statistical and field theoretical approaches,” paper quant-ph/0008088 at xxx.lanl.gov and [2001] Physical Review E 63 051101
But in retrospect, it should have been obvious directly from
the equation of the strength of the Casimir effect!
I think I did a simple search on "Casimir" at arXiv.org, and scanned through a couple
dozen papers, and verified my conclusions via email with folks like Milton
(a fellow former student of Schwinger). The pattern was clear."
Did Schwinger write about Casimir force?
" As I checked my reference file here, I noted that Vigier was not a collaborator on
the particular book I have been citing on DeBroglie's final ideas, the book
which guided some of my thought circa 1970:
Louis DeBroglie, Nonlinear Wave Mechanics: A Causal Interpretation (A.Knodel & J.C.Miller,
tr). Elsevier, 1960.
But perhaps he might have sent me a reprint where Vigier was coauthor. I certainly remember
seeing Vigier's name as a coauthor with DeBroglie back then, but again... I am sorry it
is not so complete in my memory..
----------------
Best of luck to all...
Paul"
Monday, January 03, 2005
Precision Cosmology
On Jan 3, 2005, at 10:48 AM, Jack Sarfatti wrote:
"On Jan 3, 2005, at 8:22 AM, Paul J. Werbos, Dr. wrote:
Good morning, folks!
This morning I feel I am finally beginning to make REAL sense of some of the
real fundamental issues suggested by the subject line here.
Some of you may wonder why it too me so long. But physics has become such a huge
and tangled subject that being too quick to draw conclusions won't work so well
any more. Sorting out the tangle, while maintaining high standards of understanding
things, is not so easy. Clearly there are many basic themes which no one earth fully understands as yet.
So let me start with zero point.
I was cheered greatly when Jack started to emphasize the distinction between two KINDS
of "energy from vacuum":
(1) the more classical notion of zero point energy (ZPE) based effectively on the "(1/2)hw" terms which emerge in some formulations of quantum field theory (QFT) as H0- ::H0::, the raw free Hamiltonian versus the normal form of that Hamiltonian. (The exact same ZPE noise is assumed in texts on semiclassical models of quantum optics.)
(2) more sophisticated but less definite ideas, such as vacuum breakdown or forces
linked to dark energy or negative energy.
.... I think he is basically right that the first seems very unlikely, while the second has a very real chance of
working out somehow, someday, if we can figure out what is going on more precisely and more completely."
Jack Sarfatti writes: Let me clarify this.
(1) Ian Peterson of University of Coventry has shown that there is energy available from the Casimir force
F(Casimir) = hc(A/d^4) for flat neutral plates area A separated by d
but it is VERY WEAK limited to the electrostatic potential energy of the mutually induced dipoles in each plate. In no sense does the Casimir force tap the zero point energy density whose naive estimate is ~ hc/Lp^4, Lp = 10^-33 cm. Nanotechnology using Casimir force? Yes. Warp drive using Casimir force? No.
Note that [hc] = [e^2] dimensionally so really
F(Casimir) ~ e^2(A/d^4)
is the less misleading way to write the formula, which is the same physics as in F(Coulomb) ~ e^2/r^2.
That one can get a result close to experiment from counting the difference in (1/2)hf modes inside vs outside the plates seems to be a fluke. See Milonni "The Quantum Vacuum"
Paul is being too mystical in (2) the gravitational effects of zero point energy density are now completely understood. A good reference is Mike Turner's Op Ed in April 2003 Physics Today.
The basic equation is Einstein's
Guv + /\zpfguv = 0
Where the stress-energy density tensor of the zpf is
tuv(zpf) = (hc/8piLp^2)/\zpfguv
Lp^2 = hG/c^3
In the weak curvature slow speed (neglect gravimagnetism) limit we get the Poisson equation
Grad^2V(zpf) ~ c^2/\zpf
V(zpf) = effective gravity energy per unit test particle mass of any NET zero point energy density from all quantum fields of all spins and species.
The Question is why is /\zpf so small, especially in large-scale cosmology limit where it is the Einstein cosmological constant that I compute to be for the FRW limit of homogeneous isotropy
/\(Einstein) = (LpR(t))^-2
R(t) is the dimensionless FRW scale factor
R(today) = 10^61
R(Big Bang) = "0" i.e. 1 if you quantize space time in areas ~ Lp^2
The t'Hooft-Susskind World Hologram Entropy of the Inflationary Universe S is
S(Universe)/kB ~ R(t)^2
This explains the Arrow of Time automatically.
The corresponding zero point energy density is then
~ (S(Universe)/kB)(hc/LpR(t))(LpR(t))^-3
giving /\ = (LpR(t))^-2
It is the vacuum coherence of the random ZPF that allows the cosmological constant to be small and which is the origin of the Holographic Universe.
R(t)^2 = [1 - Lp^3|Vacuum Coherence|^2]^-1
Where
R(Big Bang) = 1 BIT
because Vacuum Coherence = 0 pre-inflation False Vacuum
Vacuum Coherence = (Higgs Amplitude)e^i(Goldstone Phase)
Paul Werbos writes: "NEVERTHELESS -- even though I do not believe that the (1/2)hw noise is really there,
the first major theme of my cond-mat 2004 paper is description of a chip that should
be able to prove that it is there and exploit its energy **IF** it should be there."
Jack: Yes, nanotech applications are feasible, but they will not be "free energy devices" solving the energy crisis.
On Jan 2, 2005, at 9:59 PM, Tony Smith wrote:
Jack, you ask a lot of questions about what has Paula Zizzi done.
I will not try to speak for her on all of them,
but,
for example,
your first question is
"... Does she explicitly write Entropy(Universe)/kB ~ R(t)^2 =
Number of World Hologram BITS? ...".
I think that she does do that. For example in her paper at
http://xxx.lanl.gov/abs/gr-qc/0008049
she says
"... quantum information must play a relevant role in Quantum Gravity
(the "It from qubit" proposal).
The conjecture is that Quantum Gravity, the theory which will reconcile
Quantum Mechanics with General Relativity, can be formulated in terms of
quantum bits of information (qubits) stored in space at the Planck scale.
... entropy ... turns out to be a quarter of the area of the horizon,
(in units of Planck area), in accordance with the holographic principle. ..."
That's not good enough Tony. Does she write the EXACT formula I wrote? The quote above is obvious qualitatively given the Hologram Anzatz,
Does she write
S(Universe)/kB ~ R(t)^2
NOT BTW
S(Universe)/kB ~ (c/H(t)Lp)^2
Where
H(t) = R(t)^-1dR(t)/dt
My formula solves Penrose's Arrow of Time problem for Inflationary Universe using c/H does not. There is a very big difference here.
"You will have to read her work for yourself to get a proper
understanding of it. For me (or anyone else) to presume to
describe her work to you would in my opinion be a disservice
to both her and you. I have done my part by calling her work
to your attention. Whether or not you read her work is up to you."
I sent her this so if she thinks she should be cited she will respond. My precise equations were not at all influenced by her papers that I never read except for a very fast skim of a few seconds on the computer screen. I basically read very few papers by other people. I am a Lazy Dog Rogue Scholar.
"If you read her work, I think that you will find that she
has for some years had some of the ideas you are now using.
If you don't read her work, then you won't know what she has done,
and will not be able to give her proper historical credit."
I have been thinking about this independently long before she did. However, if she has written my precise formulae before me I will of course cite her. I will cite her even if she wrote it after me. The currency is the equations not the words. This stuff is in the air.
The important original idea I have is
R(t)^2 = [1 - Lp^3|Vacuum Coherence|^2]^-1
which EXPLAINS the t'Hooft-Susskind hologram and also DERIVES Einstein's GR in Sakharov's sense from the rigid "More is Different" (PW Anderson) Goldstone phase information in the Vacuum Coherence that damps out the random zero point energy. That's THE REALLY BIG IDEA. I don't think Zizzi has that?
On Jan 3, 2005, at 10:48 AM, Jack Sarfatti wrote:
"On Jan 3, 2005, at 8:22 AM, Paul J. Werbos, Dr. wrote:
Good morning, folks!
This morning I feel I am finally beginning to make REAL sense of some of the
real fundamental issues suggested by the subject line here.
Some of you may wonder why it too me so long. But physics has become such a huge
and tangled subject that being too quick to draw conclusions won't work so well
any more. Sorting out the tangle, while maintaining high standards of understanding
things, is not so easy. Clearly there are many basic themes which no one earth fully understands as yet.
So let me start with zero point.
I was cheered greatly when Jack started to emphasize the distinction between two KINDS
of "energy from vacuum":
(1) the more classical notion of zero point energy (ZPE) based effectively on the "(1/2)hw" terms which emerge in some formulations of quantum field theory (QFT) as H0- ::H0::, the raw free Hamiltonian versus the normal form of that Hamiltonian. (The exact same ZPE noise is assumed in texts on semiclassical models of quantum optics.)
(2) more sophisticated but less definite ideas, such as vacuum breakdown or forces
linked to dark energy or negative energy.
.... I think he is basically right that the first seems very unlikely, while the second has a very real chance of
working out somehow, someday, if we can figure out what is going on more precisely and more completely."
Jack Sarfatti writes: Let me clarify this.
(1) Ian Peterson of University of Coventry has shown that there is energy available from the Casimir force
F(Casimir) = hc(A/d^4) for flat neutral plates area A separated by d
but it is VERY WEAK limited to the electrostatic potential energy of the mutually induced dipoles in each plate. In no sense does the Casimir force tap the zero point energy density whose naive estimate is ~ hc/Lp^4, Lp = 10^-33 cm. Nanotechnology using Casimir force? Yes. Warp drive using Casimir force? No.
Note that [hc] = [e^2] dimensionally so really
F(Casimir) ~ e^2(A/d^4)
is the less misleading way to write the formula, which is the same physics as in F(Coulomb) ~ e^2/r^2.
That one can get a result close to experiment from counting the difference in (1/2)hf modes inside vs outside the plates seems to be a fluke. See Milonni "The Quantum Vacuum"
Paul is being too mystical in (2) the gravitational effects of zero point energy density are now completely understood. A good reference is Mike Turner's Op Ed in April 2003 Physics Today.
The basic equation is Einstein's
Guv + /\zpfguv = 0
Where the stress-energy density tensor of the zpf is
tuv(zpf) = (hc/8piLp^2)/\zpfguv
Lp^2 = hG/c^3
In the weak curvature slow speed (neglect gravimagnetism) limit we get the Poisson equation
Grad^2V(zpf) ~ c^2/\zpf
V(zpf) = effective gravity energy per unit test particle mass of any NET zero point energy density from all quantum fields of all spins and species.
The Question is why is /\zpf so small, especially in large-scale cosmology limit where it is the Einstein cosmological constant that I compute to be for the FRW limit of homogeneous isotropy
/\(Einstein) = (LpR(t))^-2
R(t) is the dimensionless FRW scale factor
R(today) = 10^61
R(Big Bang) = "0" i.e. 1 if you quantize space time in areas ~ Lp^2
The t'Hooft-Susskind World Hologram Entropy of the Inflationary Universe S is
S(Universe)/kB ~ R(t)^2
This explains the Arrow of Time automatically.
The corresponding zero point energy density is then
~ (S(Universe)/kB)(hc/LpR(t))(LpR(t))^-3
giving /\ = (LpR(t))^-2
It is the vacuum coherence of the random ZPF that allows the cosmological constant to be small and which is the origin of the Holographic Universe.
R(t)^2 = [1 - Lp^3|Vacuum Coherence|^2]^-1
Where
R(Big Bang) = 1 BIT
because Vacuum Coherence = 0 pre-inflation False Vacuum
Vacuum Coherence = (Higgs Amplitude)e^i(Goldstone Phase)
Paul Werbos writes: "NEVERTHELESS -- even though I do not believe that the (1/2)hw noise is really there,
the first major theme of my cond-mat 2004 paper is description of a chip that should
be able to prove that it is there and exploit its energy **IF** it should be there."
Jack: Yes, nanotech applications are feasible, but they will not be "free energy devices" solving the energy crisis.
On Jan 2, 2005, at 9:59 PM, Tony Smith wrote:
Jack, you ask a lot of questions about what has Paula Zizzi done.
I will not try to speak for her on all of them,
but,
for example,
your first question is
"... Does she explicitly write Entropy(Universe)/kB ~ R(t)^2 =
Number of World Hologram BITS? ...".
I think that she does do that. For example in her paper at
http://xxx.lanl.gov/abs/gr-qc/0008049
she says
"... quantum information must play a relevant role in Quantum Gravity
(the "It from qubit" proposal).
The conjecture is that Quantum Gravity, the theory which will reconcile
Quantum Mechanics with General Relativity, can be formulated in terms of
quantum bits of information (qubits) stored in space at the Planck scale.
... entropy ... turns out to be a quarter of the area of the horizon,
(in units of Planck area), in accordance with the holographic principle. ..."
That's not good enough Tony. Does she write the EXACT formula I wrote? The quote above is obvious qualitatively given the Hologram Anzatz,
Does she write
S(Universe)/kB ~ R(t)^2
NOT BTW
S(Universe)/kB ~ (c/H(t)Lp)^2
Where
H(t) = R(t)^-1dR(t)/dt
My formula solves Penrose's Arrow of Time problem for Inflationary Universe using c/H does not. There is a very big difference here.
"You will have to read her work for yourself to get a proper
understanding of it. For me (or anyone else) to presume to
describe her work to you would in my opinion be a disservice
to both her and you. I have done my part by calling her work
to your attention. Whether or not you read her work is up to you."
I sent her this so if she thinks she should be cited she will respond. My precise equations were not at all influenced by her papers that I never read except for a very fast skim of a few seconds on the computer screen. I basically read very few papers by other people. I am a Lazy Dog Rogue Scholar.
"If you read her work, I think that you will find that she
has for some years had some of the ideas you are now using.
If you don't read her work, then you won't know what she has done,
and will not be able to give her proper historical credit."
I have been thinking about this independently long before she did. However, if she has written my precise formulae before me I will of course cite her. I will cite her even if she wrote it after me. The currency is the equations not the words. This stuff is in the air.
The important original idea I have is
R(t)^2 = [1 - Lp^3|Vacuum Coherence|^2]^-1
which EXPLAINS the t'Hooft-Susskind hologram and also DERIVES Einstein's GR in Sakharov's sense from the rigid "More is Different" (PW Anderson) Goldstone phase information in the Vacuum Coherence that damps out the random zero point energy. That's THE REALLY BIG IDEA. I don't think Zizzi has that?
Physics of Matter, Mind and Consciousness
Yes, I agree with Dr. Werbos here. I was planning to say essentially the same thing but was too busy. The real issue here was brought up by Brian Josephson and Fotini Pallikari ~ 1993, then by me at Tucson II 1996 on two-way self-organizing "back-action" (implicit in p. 30 & 14.6 of Bohm & Hiley's Undivided Universe) - also of course by Stapp in his Phys Rev A paper on retro-PK, where he was burned at the stake by The Physics Fascists :-), Penrose's OR is not R, and finally clarified by A. Valentini. The issue is SIGNAL LOCALITY vs SIGNAL NONLOCALITY. Micro-quantum theory has SIGNAL LOCALITY i.e. NO CONSCIOUSNESS, NO PRESPONSE, NO REMOTE VIEWING EVER! This is why QUANTUM MIND is a Malapropism - a non-starter. As Basil Hiley says "Consciousness as collapse replaces one mystery by another." Max Tegmark shows that decoherence shuts you down much too fast.
However MACRO-QUANTUM theory comes to the rescue. No decoherence problem there, and we have signal nonlocality in open non-equilibrium systems. The CONSCIOUS MIND is a "More is different" (PW Anderson) EMERGENT MACRO-QUANTUM OPEN NON-EQUILIBRIUM SYSTEM with SIGNAL NONLOCALITY (PRESPONSE) IMMUNE to EVIRONMENTAL DECOHERENCE from "Phase Rigidity". It is similar in some ways to the VACUUM COHERENCE of precision cosmology of dark energy in the accelerating univese which brings us to Hawking's final questions on THE MIND OF GOD at the end of A BRIEF HISTORY OF TIME. I will be lecturing on all this in Santa Fe New Mexico April 24, 2005 10:30 AM La Fonda Hotel
http://www.bizspirit.com
Werbos also has a signal nonlocality model whose details I have not studied.
On Jan 3, 2005, at 1:59 PM, Paul J. Werbos, Dr. wrote:
John Cramer's Transactional QM model seems to have an interpretation that comes close to fitting the facts about precognition. This interpretation also appears to fit some recent experimental data better than other QM interpretations. Here is part of the abstract from John Cramer's paper, The Transactional Interpretation of Quantum Mechanics.
"A new interpretation of the formalism of quantum mechanics, the Transactional Interpretation (TI), is presented. The basic element of TI is the transaction describing a quantum event as an exchange of advanced {backward in time} and retarded {forward in time} waves, as implied by the work of Wheeler and Feynman, Dirac, and others. The TI is explicitly nonlocal and thereby consistent with recent tests of the Bell Inequality, yet is relativistically invariant and fully causal. The TI permits quantum mechanical wave functions to be interpreted as real waves physically present in space rather than as "mathematical representations of knowledge". The TI is shown to provide insight into the complex character of the quantum mechanical state vector and the mechanism associated with its "collapse". The TI also leads in a natural way to justification of the Heisenberg uncertainty principle."
Cramer has consistently stated that his Transactional Interpretation yields predictions IDENTICAL to
those of the usual (Copenhagen or many-worlds) versions of quantum theory - and thus that one should
not expect it to allow us to explain phenomena one whit different. In many ways, it really
is an INTERPRETATION -- a set of words muttered as one meditates on the usual Feynman diagrams without
changing anything.
This is different from my Backwards-Time Interpretation or formulation (per 1973 Nuovo Cimento letters
paper and the more recent stuff I put into quant-ph, plus the 2004 cond-mat paper). Constructing
a new flavor of underlying theory is not so easy as holding a benediction over the Feynmann diagrams --
but it really does open the door to new phenomena and possible tests. The words you cite about
backwards light from the stars... are similar to Huw Price's writings, which I see as far closer to the Backwards
Time Interpretation than to Cramer's writings to date; Price's writings on cosmology really do point towards
new possible physical experiments, and can even be translated into more workable technological versions.
But even then... when you try to get into explaining remote viewing stuff... I do not think that
ANY nonspeculative version of quantum theory -- transactional, backwards time, Copenhagen
or many-worlds -- would be enough by itself. More precisely, I do not think
that quantum electrodynamics, in any version of quantum theory, has room for the full
spirit of what has been observed, if you take the empirical writings of folks like Puthoff and Targ
totally seriously. I am not trying to deduce that QED or remote viewing are wrong; rather,
I am saying that full remote viewing would require additional changes in physics
to explain it. (That is a major theme in my q-bio 2003 papers, one of which
was based on my plenary at the very large 1999 conference in Japan which involved
some of the same players as the various Tucson confernces.)
Best of luck, and Happy New Year,
Paul
Yes, I agree with Dr. Werbos here. I was planning to say essentially the same thing but was too busy. The real issue here was brought up by Brian Josephson and Fotini Pallikari ~ 1993, then by me at Tucson II 1996 on two-way self-organizing "back-action" (implicit in p. 30 & 14.6 of Bohm & Hiley's Undivided Universe) - also of course by Stapp in his Phys Rev A paper on retro-PK, where he was burned at the stake by The Physics Fascists :-), Penrose's OR is not R, and finally clarified by A. Valentini. The issue is SIGNAL LOCALITY vs SIGNAL NONLOCALITY. Micro-quantum theory has SIGNAL LOCALITY i.e. NO CONSCIOUSNESS, NO PRESPONSE, NO REMOTE VIEWING EVER! This is why QUANTUM MIND is a Malapropism - a non-starter. As Basil Hiley says "Consciousness as collapse replaces one mystery by another." Max Tegmark shows that decoherence shuts you down much too fast.
However MACRO-QUANTUM theory comes to the rescue. No decoherence problem there, and we have signal nonlocality in open non-equilibrium systems. The CONSCIOUS MIND is a "More is different" (PW Anderson) EMERGENT MACRO-QUANTUM OPEN NON-EQUILIBRIUM SYSTEM with SIGNAL NONLOCALITY (PRESPONSE) IMMUNE to EVIRONMENTAL DECOHERENCE from "Phase Rigidity". It is similar in some ways to the VACUUM COHERENCE of precision cosmology of dark energy in the accelerating univese which brings us to Hawking's final questions on THE MIND OF GOD at the end of A BRIEF HISTORY OF TIME. I will be lecturing on all this in Santa Fe New Mexico April 24, 2005 10:30 AM La Fonda Hotel
http://www.bizspirit.com
Werbos also has a signal nonlocality model whose details I have not studied.
On Jan 3, 2005, at 1:59 PM, Paul J. Werbos, Dr. wrote:
John Cramer's Transactional QM model seems to have an interpretation that comes close to fitting the facts about precognition. This interpretation also appears to fit some recent experimental data better than other QM interpretations. Here is part of the abstract from John Cramer's paper, The Transactional Interpretation of Quantum Mechanics.
"A new interpretation of the formalism of quantum mechanics, the Transactional Interpretation (TI), is presented. The basic element of TI is the transaction describing a quantum event as an exchange of advanced {backward in time} and retarded {forward in time} waves, as implied by the work of Wheeler and Feynman, Dirac, and others. The TI is explicitly nonlocal and thereby consistent with recent tests of the Bell Inequality, yet is relativistically invariant and fully causal. The TI permits quantum mechanical wave functions to be interpreted as real waves physically present in space rather than as "mathematical representations of knowledge". The TI is shown to provide insight into the complex character of the quantum mechanical state vector and the mechanism associated with its "collapse". The TI also leads in a natural way to justification of the Heisenberg uncertainty principle."
Cramer has consistently stated that his Transactional Interpretation yields predictions IDENTICAL to
those of the usual (Copenhagen or many-worlds) versions of quantum theory - and thus that one should
not expect it to allow us to explain phenomena one whit different. In many ways, it really
is an INTERPRETATION -- a set of words muttered as one meditates on the usual Feynman diagrams without
changing anything.
This is different from my Backwards-Time Interpretation or formulation (per 1973 Nuovo Cimento letters
paper and the more recent stuff I put into quant-ph, plus the 2004 cond-mat paper). Constructing
a new flavor of underlying theory is not so easy as holding a benediction over the Feynmann diagrams --
but it really does open the door to new phenomena and possible tests. The words you cite about
backwards light from the stars... are similar to Huw Price's writings, which I see as far closer to the Backwards
Time Interpretation than to Cramer's writings to date; Price's writings on cosmology really do point towards
new possible physical experiments, and can even be translated into more workable technological versions.
But even then... when you try to get into explaining remote viewing stuff... I do not think that
ANY nonspeculative version of quantum theory -- transactional, backwards time, Copenhagen
or many-worlds -- would be enough by itself. More precisely, I do not think
that quantum electrodynamics, in any version of quantum theory, has room for the full
spirit of what has been observed, if you take the empirical writings of folks like Puthoff and Targ
totally seriously. I am not trying to deduce that QED or remote viewing are wrong; rather,
I am saying that full remote viewing would require additional changes in physics
to explain it. (That is a major theme in my q-bio 2003 papers, one of which
was based on my plenary at the very large 1999 conference in Japan which involved
some of the same players as the various Tucson confernces.)
Best of luck, and Happy New Year,
Paul
Circular Reasoning
First Paul if you disinguish "Cartesian CS" from "Riemann normal CS" and other terms you have used without definition in context you need to give concrete examples of each in math notation, otherwise what you write is unintelligible vague and useless.
I do admit Paul that this subject gets confusing because there are several different connections each with a different covariant derivative. Visser even gets confused on that in his notes. His key equation for
A = (LC) + S + Q
is wrong.
When I asked you what Del means in the definition of nonmetricity S you said |w and that is wrong as I will show in a simple case directly. You were, however, citing Visser correctly. Visser got sloppy easy to do. In 1916 GR this is not a problem because S = Q = 0 by hypothesis.
The point is if you write
A = (LC) + S + Q
Then S and Q must be GCT tensors, i.e. defined not with respect to the A covariant derivative |w but, rather, with respect to the (LC) covariant derivative ;w.
In general if you have any connection C and wish to add a C-tensor field to it like B so that
C' = C + B
Then you must define B in terms of |c not in terms of |c'. This is an ITERATIVE PROCEDURE to avoid circular reasoning here equivalent to dividing by zero to get 1 = 0 or anything you like without logic. It's not unlike the Russell Paradox.
Example 1 1916 GR
For example, 1916 GR itself where we use the ordinary flat covariant ,w to define the (LC) curved covariant ;w.
(LC)^abc = (1/2)g^a^d(gdc,b + gbd,c - gbc,d)
Note that ,b are ordinary flat spacetime partial derivatives.
Essentially the ; curved spacetime covariant derivative is of the form
; = , + (LC)
Like in EM where
p = mv - (e/c)A
The EM vector potential is in internal fiber space with S1 circle fiber what (LC) is in the curved spacetime of 1916 GR. The EM magnetic field curlA is like the vacuum conformal curvature (LC) curl of itself. The Bohm-Aharonov effect is like the Vilenken-Taub "curvature without curvature" from a closed non-exact connection 1-form (R. Kiehn).
Now, if you use what Visser wrote in his notes literally in the case Q = S = 0 for 1916 GR then one gets the NONSENSE result
(LC)^abc = (1/2)g^a^d(gdc;b + gbd;c - gbc;d) = 0
Since S is from gdc;b = 0 in 1916 GR.
Therefore, ignoring the iterative emergence of new orders results in the absurd result (LC) = 0 if you use Visser's erroneous formula in this simplest of all cases.
Example 2 Alex Poltorak's theory, torsion Q = 0 but non-metricity =/= 0.
A = (LC) + S
But what is S?
Sabc = (1/2)(Dagbc + Dbgac - Dcgab)
The problem is what is D?
We have two choices
1. D = ; = , + (LC)
2. D = | = ; + S
Visser says use 2, but as shown in Example 1 that leads to nonsense. One must use 1
i.e.
Sabc = (1/2)(gbc;a + gac;b - gab;c)
Sabc is a GCT tensor. It is not consistent with 1916 GR unless Sabc = 0, but you can consider a new larger theory where Sabc is a new dynamical field from HYPERSPACE for example. It is not RIGID. It is not NONDYNAMICAL. It is not "just differential geometry". So I do not understand Alex's "physics" here.
Suppose we use Visser's wrong formula literally, so that
S'abc = (1/2)(gbc|a + gac|b - gab|c)
where | = ; + S
Symbolically (forgetting sums and indices) this is
S' = g| = g; + S'g
Putting in the indices, you will get a God-Awful MESS that I bet has no consistent solution other than S' = 0.
Iterate
S' = g| = g; + (g; + S'g)g = g; + g;g + S'gg
Indeed this is an infinite series. I suspect its only consistent solution is S' = 0.
Also there is no reason to think that this S' even if you could get a consistent solution S' =/= 0 is a GCT tensor, which you need for your problem!
Indeed, this is close to a rigorous proof that you are barking up the wrong tree.
Of course none of this happens in Einstein's 1916 GR, which is why it is unfamiliar.
First Paul if you disinguish "Cartesian CS" from "Riemann normal CS" and other terms you have used without definition in context you need to give concrete examples of each in math notation, otherwise what you write is unintelligible vague and useless.
I do admit Paul that this subject gets confusing because there are several different connections each with a different covariant derivative. Visser even gets confused on that in his notes. His key equation for
A = (LC) + S + Q
is wrong.
When I asked you what Del means in the definition of nonmetricity S you said |w and that is wrong as I will show in a simple case directly. You were, however, citing Visser correctly. Visser got sloppy easy to do. In 1916 GR this is not a problem because S = Q = 0 by hypothesis.
The point is if you write
A = (LC) + S + Q
Then S and Q must be GCT tensors, i.e. defined not with respect to the A covariant derivative |w but, rather, with respect to the (LC) covariant derivative ;w.
In general if you have any connection C and wish to add a C-tensor field to it like B so that
C' = C + B
Then you must define B in terms of |c not in terms of |c'. This is an ITERATIVE PROCEDURE to avoid circular reasoning here equivalent to dividing by zero to get 1 = 0 or anything you like without logic. It's not unlike the Russell Paradox.
Example 1 1916 GR
For example, 1916 GR itself where we use the ordinary flat covariant ,w to define the (LC) curved covariant ;w.
(LC)^abc = (1/2)g^a^d(gdc,b + gbd,c - gbc,d)
Note that ,b are ordinary flat spacetime partial derivatives.
Essentially the ; curved spacetime covariant derivative is of the form
; = , + (LC)
Like in EM where
p = mv - (e/c)A
The EM vector potential is in internal fiber space with S1 circle fiber what (LC) is in the curved spacetime of 1916 GR. The EM magnetic field curlA is like the vacuum conformal curvature (LC) curl of itself. The Bohm-Aharonov effect is like the Vilenken-Taub "curvature without curvature" from a closed non-exact connection 1-form (R. Kiehn).
Now, if you use what Visser wrote in his notes literally in the case Q = S = 0 for 1916 GR then one gets the NONSENSE result
(LC)^abc = (1/2)g^a^d(gdc;b + gbd;c - gbc;d) = 0
Since S is from gdc;b = 0 in 1916 GR.
Therefore, ignoring the iterative emergence of new orders results in the absurd result (LC) = 0 if you use Visser's erroneous formula in this simplest of all cases.
Example 2 Alex Poltorak's theory, torsion Q = 0 but non-metricity =/= 0.
A = (LC) + S
But what is S?
Sabc = (1/2)(Dagbc + Dbgac - Dcgab)
The problem is what is D?
We have two choices
1. D = ; = , + (LC)
2. D = | = ; + S
Visser says use 2, but as shown in Example 1 that leads to nonsense. One must use 1
i.e.
Sabc = (1/2)(gbc;a + gac;b - gab;c)
Sabc is a GCT tensor. It is not consistent with 1916 GR unless Sabc = 0, but you can consider a new larger theory where Sabc is a new dynamical field from HYPERSPACE for example. It is not RIGID. It is not NONDYNAMICAL. It is not "just differential geometry". So I do not understand Alex's "physics" here.
Suppose we use Visser's wrong formula literally, so that
S'abc = (1/2)(gbc|a + gac|b - gab|c)
where | = ; + S
Symbolically (forgetting sums and indices) this is
S' = g| = g; + S'g
Putting in the indices, you will get a God-Awful MESS that I bet has no consistent solution other than S' = 0.
Iterate
S' = g| = g; + (g; + S'g)g = g; + g;g + S'gg
Indeed this is an infinite series. I suspect its only consistent solution is S' = 0.
Also there is no reason to think that this S' even if you could get a consistent solution S' =/= 0 is a GCT tensor, which you need for your problem!
Indeed, this is close to a rigorous proof that you are barking up the wrong tree.
Of course none of this happens in Einstein's 1916 GR, which is why it is unfamiliar.
Sunday, January 02, 2005
On Roger Penrose's Fashion, Faith & Fantasy in Physics Today
On Jan 2, 2005, at 2:11 PM, Tony Smith wrote:
Jack, you said that you '... give an actual QED mechanism for the vacuum instability causing inflation'
"In your model, why is there a transition from inflation to our present slower expansion mode ? In other words, why does inflation end ?"
For the same reason it ends in the mainstream model. I am simply giving an explanation for the success of the phenomenological mainstream model which contains a lot more on smaller scale phenomena that fit the observations at least qualitatively and yield Einstein's field equation as a world hologram phase effect.
"In Paula Zizzi's model, the end of inflation is something like the decoherence of a conscious thought a la Penrose-Hameroff etc."
I don't need that. However, I do have a model for consciousness that is also macro-quantum and is formally similar. Big things do not "collapse". It's all in the NOVA book up to early 2003.
"You have said that your universe begins with ' R(Initial Singularity) = 1 i.e. 1 Bit thinking of universe as cosmic computer with David Finkelstein's chronons 10^-44 sec of erasures - resetting the register so to speak.' That actually sounds to me more like Paula Zizzi's model in
http://xxx.lanl.gov/abs/gr-qc/0007006
where she says:
'during inflation, the universe can be described as a superposed state of quantum registers. ... we can indulge in speculating about the brain-universe, with ... quantum gravity registers, and a coherence time 10^(-34) sec ... which might have a conscious experience ...'
I did hear Zizzi speak in Paris 2003 Vigier. However, my thought has not been strongly influenced by hers. I did not understand her talk very well. She spoke too softly. Also I have not spent time trying to read her papers. This stuff is in the air and I have been thinking about such stuff since at least 1973 as Saul-Paul Sirag writes about in "Destiny Matrix"
"In a later paper at
http://xxx.lanl.gov/abs/gr-qc/0103002
she says:
'We consider a quantum gravity register that is a particular quantum memory register which grows with time, and whose qubits are pixels of area of quantum de Sitter horizons. At each time step, the vacuum state of this quantum register grows because of the uncertainty in quantum information induced by the vacuum quantum fluctuations. The resulting virtual states,
(responsible for the speed up of growth, i.e., inflation), are operated on by quantum logic gates and transformed into qubits.
The model of quantum growing network (QGN) described here is exactly solvable ... We also show that the bound on the speed of computation, the bound on clock precision, and the holographic bound, are saturated by the QGN.'
Yeah, that's all in same ballpark. Does she explicitly talk of vacuum coherence of the false vacuum ZPF prior to formation of gravity?
1. Does she explicitly write
Entropy(Universe)/kB ~ R(t)^2 = Number of World Hologram BITS?
2. Does she use this to solve Penrose's Arrow of Time problem?
3. Does she explicitly calculate the Dark Energy Density as
R(t)^2(hc/LpR(t))(1/LpR(t))^3 ?
4. Does she explicitly write Einstein's cosmological constant /\ as
/\ = (LpR(t))^-2 ?
5. Note that this comes directly from Einstein's exotic vacuum field equation
Guv + /\guv = 0
6. tuv(Exotic Vacuum) = (hc/Lp^4)(1/R(t))^2guv = (hc/Lp^2)/\guv
that I derive directly from t'Hooft-Susskind Hologram + Arrow of Time Constraint where in FRW large-scale homogeneous-isotropic limit
7. /\ = Lp^-2[1 - Lp^3|Vacuum Coherence|^2]
8. R(t)^2 = [1 - Lp^3|Vacuum Coherence|^2]^-1
9. (Vacuum Coherence);uu^;u + a(Vacuum Coherence) + b|Vacuum Coherence|^2(Vacuum Coherence) = 0
;u is (LC) covariant partial derivative
;uu^;u is (LC) covariant divergence "wave operator" D'Alembertian
10. (Vacuum Coherence) = |Higgs Amplitude|e^i(Goldstone Hologram Phase)
11. In pre -> post inflation vacuum phase transition
a > 0, b > 0 pre-inflation FALSE VACUUM no gravity, all rest masses = 0
a < 0, b > 0 post-inflation
12. Add the usual Linde friction terms as in mainstream models.
13. |Higgs Field| ~ e^-1/(Virtual Exchange Photon Energy)(Density of Virtual Electron States at False Vacuum Fermi Surface E = 0)
as in Nambu-Jona Lasino BCS models.
14. eu = eu^aea
eu^a = tetrads
15. eu = (Kronecker Delta)u^aea + Lp^2(Goldstone Phase),u
,u is ordinary partial derivative in flat Minkowski spacetime.
16. guv(Curved) = (Minkowski)uv + (Lp^2/2)(Goldstone Phase)(,u,v)
= eu^a(Minkowski)abev^b
( , ) is symmetrizer
17. U(1) local gauge symmetry, given two local coordinate charts x^u & x^u' at event P
Goldstone Phase(x^u) -> Goldstone Phase(x^u') = Goldstone Phase(x^u) + Chi(x^u|x^u')
18. Chi(x^u|x^u') = Canonical Transformation Generating Function Analog
= Transition Function for overlapping coordinate charts in the curved manifold
19. GCT Jacobian Matrices for GCT Tensor Transformations are
Xu^u' = Chi,u^u' etc.
20. Mixed partial derivative in a single coordinate chart need not commute.
21. Local metric effects of global non-trivial topology like Bohm-Aharonov (BA) effect from closed non-exact connection 1-forms (R. Kiehn) where the p = 1 Betti number =/= 0 for example Vilenken-Taub "curvature without curvature" from an unstable thin flat wall of exotic vacuum anti-gravitating dark energy where (LC) curl of (LC) with itself = 0, but (LC) =/=0 for HOVERING LNIFs. This is analogous to BA fringe shift where electrons only move in curlA = 0 region, but still feel the QUANTIZED enclosed curlA magnetic flux nonlocally. That is, A is felt locally in spite of gauge freedom. The electron canonical momentum p = mv - (e/c)A = (h/i)(U(1) Covariant Gradient of Micro-Quantum Phase of Electron) is gauge invariant.
22. Similarly AS ABOVE SO BELOW the Micro-Quantum Phase of the single real electron is replaced by the Macro-Quantum Goldstone Phase of the Virtual Electron-Positron Vacuum Condensate.
23. (Vacuum Coherence) ~ (Virtual Electron-Positron Condensate)
in the dominant approximation.
Does Zizzi have all that explicit in my Breaking the Real Da Vinci Code?
See story of Carlo Suares in Paris 1973 in the book "Destiny Matrix". :-)
I agree that torsion fields may be required experimentally. Too soon to tell. I refer also to Kleinert below. My basic Bohm guidance equation above
guv(Curved) = (Minkowski)uv + (Lp^2/2)(Goldstone Phase)(,u,v)
was inspired by Kleinert's idea that you cite below.
On Jan 2, 2005, at 2:11 PM, Tony Smith wrote:'
"Carlos, you say that you 'do NOT set the Torsion to zero by hand like Mansouri-MacDowell did. I *derive* it . ...".
Actually, in the variant of MacDowell-Mansouri that I use, I have non-zero torsion because I think that torsion is natural and necessary to build a model with spinor fermions. See for example http://xxx.lanl.gov/abs/gr-qc/0306029 entitled Einstein-Cartan theory as a theory of defects in space-time by M. L. Ruggiero and A. Tartaglia, where they say:
'Trautman ... introduced a characteristic length to estimate the effects of torsion, the "Cartan" radius. To achieve the condition ...[that] spin effects ... be of the same order as mass effects ... or, alternatively, when the matter density is [about] 10^47 g cm^(-3) for electron-like matter and 10^54 g cm^(-3) for nucleon-like matter, ... we can imagine that a nucleon of mass m should be squeezed so that its radius coincides with the Cartan radius r_Cart ... For a nucleon we obtain r_Cart = 10^(-26) cm, which is very small when compared with macroscopical scales, but it is larger than the Planck length. Hence, torsion must be taken into account to achieve a quantum theory of gravity. ... Kleinert ... adopted a linearized approach and showed that space-time with torsion and curvature can be generated from a flat space-time using "singular coordinate transformations," and is completely equivalent to a medium filled with dislocations and disclinations. In other words his singular coordinate transformations are the space-time equivalent of the plastic deformations which lead to incompatible states ... Hence, at least in this approximation, space-time can be thought of as a defect state, and defects are nothing but mass, mass current, and spin. The next important point is to try to go beyond the linear approximation. ... We can then say that Einstein-Cartan space-time can be considered as a defect state of a four-dimensional continuum ... In this analogy, the Poincare group ...[has]... six kinds of disclination-like deformations, and four kinds of dislocation-like deformations, which yield 10 different Riemann-Cartan spaces filled with topological defects. ... a Burgers vector B in T (4) and a Frank matrix G in SO(1,3) are defined by the parallel transport of a tetrad in the Riemann-Cartan space U4 around the line-like defect region. In this way, a space-time with curvature and torsion is thought of
as a distorted medium filled with dislocations and disclinations ..."
Tony
On Jan 2, 2005, at 2:11 PM, Tony Smith wrote:
Jack, you said that you '... give an actual QED mechanism for the vacuum instability causing inflation'
"In your model, why is there a transition from inflation to our present slower expansion mode ? In other words, why does inflation end ?"
For the same reason it ends in the mainstream model. I am simply giving an explanation for the success of the phenomenological mainstream model which contains a lot more on smaller scale phenomena that fit the observations at least qualitatively and yield Einstein's field equation as a world hologram phase effect.
"In Paula Zizzi's model, the end of inflation is something like the decoherence of a conscious thought a la Penrose-Hameroff etc."
I don't need that. However, I do have a model for consciousness that is also macro-quantum and is formally similar. Big things do not "collapse". It's all in the NOVA book up to early 2003.
"You have said that your universe begins with ' R(Initial Singularity) = 1 i.e. 1 Bit thinking of universe as cosmic computer with David Finkelstein's chronons 10^-44 sec of erasures - resetting the register so to speak.' That actually sounds to me more like Paula Zizzi's model in
http://xxx.lanl.gov/abs/gr-qc/0007006
where she says:
'during inflation, the universe can be described as a superposed state of quantum registers. ... we can indulge in speculating about the brain-universe, with ... quantum gravity registers, and a coherence time 10^(-34) sec ... which might have a conscious experience ...'
I did hear Zizzi speak in Paris 2003 Vigier. However, my thought has not been strongly influenced by hers. I did not understand her talk very well. She spoke too softly. Also I have not spent time trying to read her papers. This stuff is in the air and I have been thinking about such stuff since at least 1973 as Saul-Paul Sirag writes about in "Destiny Matrix"
"In a later paper at
http://xxx.lanl.gov/abs/gr-qc/0103002
she says:
'We consider a quantum gravity register that is a particular quantum memory register which grows with time, and whose qubits are pixels of area of quantum de Sitter horizons. At each time step, the vacuum state of this quantum register grows because of the uncertainty in quantum information induced by the vacuum quantum fluctuations. The resulting virtual states,
(responsible for the speed up of growth, i.e., inflation), are operated on by quantum logic gates and transformed into qubits.
The model of quantum growing network (QGN) described here is exactly solvable ... We also show that the bound on the speed of computation, the bound on clock precision, and the holographic bound, are saturated by the QGN.'
Yeah, that's all in same ballpark. Does she explicitly talk of vacuum coherence of the false vacuum ZPF prior to formation of gravity?
1. Does she explicitly write
Entropy(Universe)/kB ~ R(t)^2 = Number of World Hologram BITS?
2. Does she use this to solve Penrose's Arrow of Time problem?
3. Does she explicitly calculate the Dark Energy Density as
R(t)^2(hc/LpR(t))(1/LpR(t))^3 ?
4. Does she explicitly write Einstein's cosmological constant /\ as
/\ = (LpR(t))^-2 ?
5. Note that this comes directly from Einstein's exotic vacuum field equation
Guv + /\guv = 0
6. tuv(Exotic Vacuum) = (hc/Lp^4)(1/R(t))^2guv = (hc/Lp^2)/\guv
that I derive directly from t'Hooft-Susskind Hologram + Arrow of Time Constraint where in FRW large-scale homogeneous-isotropic limit
7. /\ = Lp^-2[1 - Lp^3|Vacuum Coherence|^2]
8. R(t)^2 = [1 - Lp^3|Vacuum Coherence|^2]^-1
9. (Vacuum Coherence);uu^;u + a(Vacuum Coherence) + b|Vacuum Coherence|^2(Vacuum Coherence) = 0
;u is (LC) covariant partial derivative
;uu^;u is (LC) covariant divergence "wave operator" D'Alembertian
10. (Vacuum Coherence) = |Higgs Amplitude|e^i(Goldstone Hologram Phase)
11. In pre -> post inflation vacuum phase transition
a > 0, b > 0 pre-inflation FALSE VACUUM no gravity, all rest masses = 0
a < 0, b > 0 post-inflation
12. Add the usual Linde friction terms as in mainstream models.
13. |Higgs Field| ~ e^-1/(Virtual Exchange Photon Energy)(Density of Virtual Electron States at False Vacuum Fermi Surface E = 0)
as in Nambu-Jona Lasino BCS models.
14. eu = eu^aea
eu^a = tetrads
15. eu = (Kronecker Delta)u^aea + Lp^2(Goldstone Phase),u
,u is ordinary partial derivative in flat Minkowski spacetime.
16. guv(Curved) = (Minkowski)uv + (Lp^2/2)(Goldstone Phase)(,u,v)
= eu^a(Minkowski)abev^b
( , ) is symmetrizer
17. U(1) local gauge symmetry, given two local coordinate charts x^u & x^u' at event P
Goldstone Phase(x^u) -> Goldstone Phase(x^u') = Goldstone Phase(x^u) + Chi(x^u|x^u')
18. Chi(x^u|x^u') = Canonical Transformation Generating Function Analog
= Transition Function for overlapping coordinate charts in the curved manifold
19. GCT Jacobian Matrices for GCT Tensor Transformations are
Xu^u' = Chi,u^u' etc.
20. Mixed partial derivative in a single coordinate chart need not commute.
21. Local metric effects of global non-trivial topology like Bohm-Aharonov (BA) effect from closed non-exact connection 1-forms (R. Kiehn) where the p = 1 Betti number =/= 0 for example Vilenken-Taub "curvature without curvature" from an unstable thin flat wall of exotic vacuum anti-gravitating dark energy where (LC) curl of (LC) with itself = 0, but (LC) =/=0 for HOVERING LNIFs. This is analogous to BA fringe shift where electrons only move in curlA = 0 region, but still feel the QUANTIZED enclosed curlA magnetic flux nonlocally. That is, A is felt locally in spite of gauge freedom. The electron canonical momentum p = mv - (e/c)A = (h/i)(U(1) Covariant Gradient of Micro-Quantum Phase of Electron) is gauge invariant.
22. Similarly AS ABOVE SO BELOW the Micro-Quantum Phase of the single real electron is replaced by the Macro-Quantum Goldstone Phase of the Virtual Electron-Positron Vacuum Condensate.
23. (Vacuum Coherence) ~ (Virtual Electron-Positron Condensate)
in the dominant approximation.
Does Zizzi have all that explicit in my Breaking the Real Da Vinci Code?
See story of Carlo Suares in Paris 1973 in the book "Destiny Matrix". :-)
I agree that torsion fields may be required experimentally. Too soon to tell. I refer also to Kleinert below. My basic Bohm guidance equation above
guv(Curved) = (Minkowski)uv + (Lp^2/2)(Goldstone Phase)(,u,v)
was inspired by Kleinert's idea that you cite below.
On Jan 2, 2005, at 2:11 PM, Tony Smith wrote:'
"Carlos, you say that you 'do NOT set the Torsion to zero by hand like Mansouri-MacDowell did. I *derive* it . ...".
Actually, in the variant of MacDowell-Mansouri that I use, I have non-zero torsion because I think that torsion is natural and necessary to build a model with spinor fermions. See for example http://xxx.lanl.gov/abs/gr-qc/0306029 entitled Einstein-Cartan theory as a theory of defects in space-time by M. L. Ruggiero and A. Tartaglia, where they say:
'Trautman ... introduced a characteristic length to estimate the effects of torsion, the "Cartan" radius. To achieve the condition ...[that] spin effects ... be of the same order as mass effects ... or, alternatively, when the matter density is [about] 10^47 g cm^(-3) for electron-like matter and 10^54 g cm^(-3) for nucleon-like matter, ... we can imagine that a nucleon of mass m should be squeezed so that its radius coincides with the Cartan radius r_Cart ... For a nucleon we obtain r_Cart = 10^(-26) cm, which is very small when compared with macroscopical scales, but it is larger than the Planck length. Hence, torsion must be taken into account to achieve a quantum theory of gravity. ... Kleinert ... adopted a linearized approach and showed that space-time with torsion and curvature can be generated from a flat space-time using "singular coordinate transformations," and is completely equivalent to a medium filled with dislocations and disclinations. In other words his singular coordinate transformations are the space-time equivalent of the plastic deformations which lead to incompatible states ... Hence, at least in this approximation, space-time can be thought of as a defect state, and defects are nothing but mass, mass current, and spin. The next important point is to try to go beyond the linear approximation. ... We can then say that Einstein-Cartan space-time can be considered as a defect state of a four-dimensional continuum ... In this analogy, the Poincare group ...[has]... six kinds of disclination-like deformations, and four kinds of dislocation-like deformations, which yield 10 different Riemann-Cartan spaces filled with topological defects. ... a Burgers vector B in T (4) and a Frank matrix G in SO(1,3) are defined by the parallel transport of a tetrad in the Riemann-Cartan space U4 around the line-like defect region. In this way, a space-time with curvature and torsion is thought of
as a distorted medium filled with dislocations and disclinations ..."
Tony
Rewriting The Bible, The Koran And All That
The Creation
IN THE BEGINNING WAS THE BIT
IT FROM BIT
On Jan 2, 2005, at 3:36 AM, Carlos Perelman wrote:
"Dear Jack , Tony ( Brian and Gary ) :
Thank you very much for your last mails. The number 26 depicted by Brian is very curous."
Jack wrote :
Vacuum Coherence obeys a GCT covariant Landau-Ginzburg equation depending on metric guv, which, in turn, depends on the Goldstone Phase of the Vacuum Coherence in a nonlinear self-organizing feedback-control loop.
"It is very interesting that you wrote this because in my paper :
Mod. Phys. A vol 17, no. 32 ( 2002 ) 2095-2103
Anti de Sitter Gravity from BF-Chern-Simons-Higgs theoriesThe Higgs mechanism is *essential* to break the SO(3, 2 ) symmetry down to the Lorentz group SO(3,1 ). I think there is something going on definitely, which deserves to be studied further. I studied Anti de Sitter space for many reasons ( Maldacena conjecture AdS/CFT and holography ) . But I guess one could have de Sitter space as well with a future horizon ( accelerated universe ) . After all, I equated the Anti de Sitter's (de Sitter's) throat-scale-parameter with the Hubble scale radius horizon in order to derive the geometric mean relationship."
But you could have used LpR(t) instead of c/H(t) (H(t) = R(t)^-1dR(t)/dt) equally at this decision point. If you did we have essentially the same end product. The convention here is that the R(t) FRW scale factor dimensionless in FLAT k = 0 post-inflation FRW Big Bang cosmological metric
ds^2 = (cdt)^2 - R(t)^2[dr^2 + r^2(dtheta^2 + sin^2thetadphi^2)
For "now" we have essentially same number since my R(now) = 10^61, but my choice has many added advantages
1. It fits t'Hooft-Susskind World Hologram Conjecture in which the Bekenstein-Hawking ENTROPY OF THE UNIVERSE S is
S(Universe)/kB ~ R(t)^2 BITS
2. This automatically explains the Arrow of Time synchronization with Expanding Universe posed for Inflation Theory in Roger Penrose's GR 17 & Princeton lectures "Fashion, Faith and Fantasy". Since in the continuum approximation R(pre->post inflation initial singularity) = 0 OR essentially 1 BIT in a discrete lattice quantum geometry (Ashtekar & Co) i.e.
R(Creation of the Universe)/R(Now) ~ 10^-61
3. To ERASE each BIT inside the coherent vacuum i.e. reset register of cosmic computer each "chronon" 10^-44 sec with a virtual ZERO POINT QUANTUM that does have DIRECT GRAVITY EFFECT via
Guv + /\zpfguv = 0
Even though ZPF does not cause EM detector clicks it does gravitate (or anti-gravitate), i.e. Cosmological Constant Problem here solved through Vacuum Coherence of the ZPF in the Flat Conformally Symmetric False Vacuum.
4. Therefore, the TOTAL VACUUM DARK ENERGY OF THE HOLOGRAPHIC UNIVERSE is
(ENTROPY OF UNIVERSE/kB)(MEAN ZERO POINT ENERGY PER BIT) ~ R(t)^2(hc/LpR(t)) = R(t)hc/Lp
R(Now)hc/Lp = 10^61x10^-5x10^21 = 10^77 ergs
5. VACUUM DARK ENERGY DENSITY OF THE HOLOGRAPHIC UNIVERSE = R(t)(hc/Lp)(1/Lp^3R(t)^3) = (hc/Lp^4)(1/R(t))^2
VACUUM DARK ENERGY DENSITY OF UNIVERSE TODAY = 10^-5x10^21x10^99x10^-122 = 10^(117 - 122) ~ 10^-7 ergs/cm^3
Where INFLATION demands
Omega(Matter w ~ 0) + Omega(Radiation w = +1/3) + Omega(Dark Matter i.e. w = -1 mimicking w ~ 0) + Omega(Dark Energy) + Omega(Vacuum Coherence) = 1
6. Note my NEW TERM to the cosmological balance sheet Omega(Vacuum Coherence).
7. Prediction dark matter detectors will never click with The Right Stuff, i.e. dark matter is virtual w = -1 mimic of w = 0 CDM in gravity lensing.
8. Einstein's local field equation emerges from the RIGID Goldstone Phase of the Vacuum Coherence solving Andrei Sakharov's problem of 1967 with P.W. Anderson's (also 1967 - a Good Vintage Year for Physics) "More is different".
"rho ( vaccum energy density ) ~ ( L_Planck )^{ -2 } ( R_Hubble )^{ - 2 } ~
10^{ - 122 } ( Planck Mass )^4 ( that Nottale gets using Scale Relativity )
Not suprisingly, the number 10^{122 } counts the *bits* of Planck areas contained in the
Area = (R_Hubble)^2. Some authors use 10^{123}, no big change.
When you [ Jack ] visit Santa Barbara, lets talk. The reason I wanted Tony to look at this paper ( that i sent him ) is because it explains the Topological origins behind the McDowell-Mansouri formulation of Gravity that Tony likes a lot. But I do NOT set the Torsion to zero by hand like Mansouri-MacDowell did. I *derive* it ."
9. I get the topology vacuum defects directly from the local macro-quantum vacuum ODLRO order parameter as in David Thouless's book on Topological Quantum Theory, e.g. NASA Pioneer Anomaly a_g = - cH as a uniform gradient dark energy hedge
"Anyway, I had to write to Susskind, Padmanabhan, Fischler ( whom I know ) and to Zee, Banks...because these people totally ignore the previous published work of others ( Nottale, me, Jack ) in their papers. I don't know if they will ever refer to my work, Jack's or Nottale's work. At least, I told them and YOU are witnesess of it.
Happy New year
Carlos"
The Creation
IN THE BEGINNING WAS THE BIT
IT FROM BIT
On Jan 2, 2005, at 3:36 AM, Carlos Perelman wrote:
"Dear Jack , Tony ( Brian and Gary ) :
Thank you very much for your last mails. The number 26 depicted by Brian is very curous."
Jack wrote :
Vacuum Coherence obeys a GCT covariant Landau-Ginzburg equation depending on metric guv, which, in turn, depends on the Goldstone Phase of the Vacuum Coherence in a nonlinear self-organizing feedback-control loop.
"It is very interesting that you wrote this because in my paper :
Mod. Phys. A vol 17, no. 32 ( 2002 ) 2095-2103
Anti de Sitter Gravity from BF-Chern-Simons-Higgs theoriesThe Higgs mechanism is *essential* to break the SO(3, 2 ) symmetry down to the Lorentz group SO(3,1 ). I think there is something going on definitely, which deserves to be studied further. I studied Anti de Sitter space for many reasons ( Maldacena conjecture AdS/CFT and holography ) . But I guess one could have de Sitter space as well with a future horizon ( accelerated universe ) . After all, I equated the Anti de Sitter's (de Sitter's) throat-scale-parameter with the Hubble scale radius horizon in order to derive the geometric mean relationship."
But you could have used LpR(t) instead of c/H(t) (H(t) = R(t)^-1dR(t)/dt) equally at this decision point. If you did we have essentially the same end product. The convention here is that the R(t) FRW scale factor dimensionless in FLAT k = 0 post-inflation FRW Big Bang cosmological metric
ds^2 = (cdt)^2 - R(t)^2[dr^2 + r^2(dtheta^2 + sin^2thetadphi^2)
For "now" we have essentially same number since my R(now) = 10^61, but my choice has many added advantages
1. It fits t'Hooft-Susskind World Hologram Conjecture in which the Bekenstein-Hawking ENTROPY OF THE UNIVERSE S is
S(Universe)/kB ~ R(t)^2 BITS
2. This automatically explains the Arrow of Time synchronization with Expanding Universe posed for Inflation Theory in Roger Penrose's GR 17 & Princeton lectures "Fashion, Faith and Fantasy". Since in the continuum approximation R(pre->post inflation initial singularity) = 0 OR essentially 1 BIT in a discrete lattice quantum geometry (Ashtekar & Co) i.e.
R(Creation of the Universe)/R(Now) ~ 10^-61
3. To ERASE each BIT inside the coherent vacuum i.e. reset register of cosmic computer each "chronon" 10^-44 sec with a virtual ZERO POINT QUANTUM that does have DIRECT GRAVITY EFFECT via
Guv + /\zpfguv = 0
Even though ZPF does not cause EM detector clicks it does gravitate (or anti-gravitate), i.e. Cosmological Constant Problem here solved through Vacuum Coherence of the ZPF in the Flat Conformally Symmetric False Vacuum.
4. Therefore, the TOTAL VACUUM DARK ENERGY OF THE HOLOGRAPHIC UNIVERSE is
(ENTROPY OF UNIVERSE/kB)(MEAN ZERO POINT ENERGY PER BIT) ~ R(t)^2(hc/LpR(t)) = R(t)hc/Lp
R(Now)hc/Lp = 10^61x10^-5x10^21 = 10^77 ergs
5. VACUUM DARK ENERGY DENSITY OF THE HOLOGRAPHIC UNIVERSE = R(t)(hc/Lp)(1/Lp^3R(t)^3) = (hc/Lp^4)(1/R(t))^2
VACUUM DARK ENERGY DENSITY OF UNIVERSE TODAY = 10^-5x10^21x10^99x10^-122 = 10^(117 - 122) ~ 10^-7 ergs/cm^3
Where INFLATION demands
Omega(Matter w ~ 0) + Omega(Radiation w = +1/3) + Omega(Dark Matter i.e. w = -1 mimicking w ~ 0) + Omega(Dark Energy) + Omega(Vacuum Coherence) = 1
6. Note my NEW TERM to the cosmological balance sheet Omega(Vacuum Coherence).
7. Prediction dark matter detectors will never click with The Right Stuff, i.e. dark matter is virtual w = -1 mimic of w = 0 CDM in gravity lensing.
8. Einstein's local field equation emerges from the RIGID Goldstone Phase of the Vacuum Coherence solving Andrei Sakharov's problem of 1967 with P.W. Anderson's (also 1967 - a Good Vintage Year for Physics) "More is different".
"rho ( vaccum energy density ) ~ ( L_Planck )^{ -2 } ( R_Hubble )^{ - 2 } ~
10^{ - 122 } ( Planck Mass )^4 ( that Nottale gets using Scale Relativity )
Not suprisingly, the number 10^{122 } counts the *bits* of Planck areas contained in the
Area = (R_Hubble)^2. Some authors use 10^{123}, no big change.
When you [ Jack ] visit Santa Barbara, lets talk. The reason I wanted Tony to look at this paper ( that i sent him ) is because it explains the Topological origins behind the McDowell-Mansouri formulation of Gravity that Tony likes a lot. But I do NOT set the Torsion to zero by hand like Mansouri-MacDowell did. I *derive* it ."
9. I get the topology vacuum defects directly from the local macro-quantum vacuum ODLRO order parameter as in David Thouless's book on Topological Quantum Theory, e.g. NASA Pioneer Anomaly a_g = - cH as a uniform gradient dark energy hedge
"Anyway, I had to write to Susskind, Padmanabhan, Fischler ( whom I know ) and to Zee, Banks...because these people totally ignore the previous published work of others ( Nottale, me, Jack ) in their papers. I don't know if they will ever refer to my work, Jack's or Nottale's work. At least, I told them and YOU are witnesess of it.
Happy New year
Carlos"
Saturday, January 01, 2005
Dark Energy from Entropy of World Hologram
On Jan 1, 2005, at 3:05 PM, Jack Sarfatti wrote:
On Dec 31, 2004, at 4:36 PM, Carlos Perelman wrote:
Dear Antonio, Jack, Matti and Tony :
Thank you very for your most recent messages about your work and the new, full moon.
Jack, about the notation. The whole purpose of my paper
Mod. Phys. A vol 17, no. 32 ( 2002 ) 2095-2103
Anti de Siter Gravity from BF-Chern-Simons-Higgs theories
was to show that the MacDowell-Mansouri formulation of gravity
I don't know that work.
can be embedded in a
*more* fundamental Topological BF theory
or that.
... and of course to DERIVE the relationship that
rho (vacuum ) = (L_Planck)^ { -2 } (R_Hubble )^ { -2 } ~ 10^{ - 122 } (Planck mass)^4 .
What is rho? Energy density?
Do you mean
Vacuum Energy Density = hc/Lp^2(c/H)^2 ~ 10^-17x10^66x10^-56 ergs/cc = 10^-7 ergs/cc
Here H = R(t)^-1dR(t)/dt
R dimensionless in usual FRW metric convention.
OK I think I see.
In my theory that seems to fit t'Hooft-Susskind Hologram quite well I get the same number, but with a very different time dependence
I get
Vacuum Energy Density = hc/Lp^4R(t)^2
That is
/\(Sarfatti) = 1/(LpR(t))^2 ~ 10^-56 cm^-2
In contrast
/\(Castro) = (H/c)^2 = (1/c^2R(t)^2)(dR(t)/dt)^2 ~ 10^-56 cm^2
So we are close numerically, but there is an essential difference. I do not use c/H(t) as the cosmic length scale, instead I use LpR(t) (R(t) is a pure number)
My theory says that the t'Hooft-Susskind-Hawking-Bekenstein Hologram Entropy of the Universe is
S(Universe)/kB = R(t)^2 ~ 10^122 BITS (now)
Where
R(t)^2 = [1 - Lp^3|Vacuum Coherence|^2 - 1]^-1
Therefore R(pre -> post inflation vacuum phase transition) ~ 1 BIT at initial singularity where |Vacuum Coherence| = 0.
The mean energy to erase a BIT in the vacuum is ~ hc/LpR(t)
Therefore the vacuum dark energy density is
~ (Entropy of Universe/kB)(hc/LpR(t))(1/LpR(t))^3 = hc/Lp^4(1/R(t))^2
~ 10^-17x10^132x10^-122 = 10^-7 ergs/cc
Furthermore, my model explains why the entropy of the early universe is low from the formation of the vacuum coherence. This explains the Arrow of Time and solves the problem with inflation raised by Roger Penrose.
Vacuum Coherence obeys a GCT covariant Landau-Ginzburg equation depending on metric guv, which, in turn, depends on the Goldstone Phase of the Vacuum Coherence in a nonlinear self-organizing feedback-control loop.
On Dec 31, 2004, at 1:13 PM, Jack Sarfatti wrote:
R(t)^2 = [1 - Lp^3|Vacuum Coherence|^2]^-1
Note when Vacuum Coherence = 0 PRE-INFLATION
R(Initial Singularity) = 1
i.e. 1 Bit thinking of universe as cosmic computer with David Finkelstein's chronons 10^-44 sec of erasures - resetting the register so to speak.
As the large-scale Vacuum Coherence limits to
|Vacuum Coherence|^2 -> 1/Lp^3
R(t) -> infinity
Vacuum Coherence can exceed this limit on smaller non-cosmological scales.
On Dec 31, 2004, at 12:43 PM, Jack Sarfatti wrote:
Inflation demands total stuff is at critical density for flat 3D space, i.e. k = 0 in large-scale FRW metric
Omega(random ZPF) + Omega(matter) + Omega(radiation) + Omega(vacuum coherence) = 1
Omega(on-mass-shell matter) ~ 1/R(t)^3, i.e. w = 0 in R(t)^-3(1 + w) for v/c << 1
Omega(on-mass-shell radiation) ~ 1/R(t)^4, i.e. w = +1/3
with Omega(random zpf) + Omega(vacuum coherence) ~ 1/R(t)^0 independent of R(t) since w = -1 for both random "normal fluid" zpf and condensate (vacuum coherence)
/\ is from random zpf causing both dark energy (negative pressure) and dark matter (positive pressure) exotic vacuum phases.
Clumps of w = -1 positive pressure, possibly like the Galactic Halo mimic w = 0 dark matter in their gravity lensing. Positive and negative pressure exotic vacua can each either universally attract or repel depending on their detailed distribution relative to the test particle. However localized negative pressure exotic vacuum clumps anti-gravitate for test particles outside their domain of support. Similarly, localized positive pressure clumps gravitate for test particles outside their support. The effective gravity strength G* of clumps of exotic vacuum regions can be larger than Newton's G.
Guv + /\zpfguv = 0
is the zero torsion field GR Poisson equation for exotic vacua.
In the Newtonian weak-field slow-speed limit, neglecting gravimagnetism, this is
Grad^2(Potential Energy per unit test mass of exotic vacuum field) ~ c^2/\zpf
Susskind's World Hologram Conjecture requires
Einstein's cosmological constant /\ ~ [LpR(t)]^-2
With critical energy density hc/Lp^4R(t)^2 = (mpc^2/Lp^3)R(t)^-2
Therefore Omega(/\) is independent of R(t) consistent with w = -1 Lorentz covariance and EEP of GR. Similarly for Omega(Vacuum Coherence), which is my new term.
OK trash what I wrote late last night on this when I was very tired. I woke up fresh with a start with the correct way to think about the problem - after taking a 600 mg ibuprofen for shoulder ache from over exercise at the health club.
Here is how Lenny Susskind's world hologram really does work and how it explains the dark energy!
1. Trash H. We don't need it.
2. The FRW space expansion factor R(t) is dimensionless. Everything is in units of Lp.
3. The Susskind-Hawking-Bekenstein-t'Hooft hologram entropy of the Universe is simply
S/kB = (1/4)R(t)^2
I have written this before of course.
R(now) = 10^61
This is a nice formula because it also explains the Arrow of Time since the entropy of the universe is 0 at the initial singularity here, i.e. R(initial singularity) = 0 or, if you prefer Finkelstein's chronons it is 1-bit at t = 0.
4. OK roughly model everything as photons.
The photon thermal distribution is
hf/(e^hf/kBT - 1) + hf/2
But the dark energy is, to first approximation virtual photons hf/2 whose mean value is hc/LpR(t).
5. Therefore we need virtual energy hf/2 to "erase" each bit every time the cosmic quantum computer clears its register to step forward another chronon to compute the history of the universe
Therefore, the dark energy density the vacuum fabric of curved spacetime needs to compute itself is
(R(t)^2/4)(hc/LpR(t))(1/Lp^3R(t))^3 = (hc/Lp^4)1/4R(t)^2 = (hc/4Lp^2)/
Einstein's cosmological constant /\ = 1/Lp^2R(t)^2 = 10^-56 cm^-2 NOW
hc/Lp^2 = c^4/G
6. So this says that Einstein's cosmological constant /\ is getting smaller as the Universe expands. On the other hand, w = pressure/(energy density) = -1 for random micro-quantum zero point energy.
The energy density of cosmic stuff scales as R(t)^-3(1 + w)
For example w = 0 for ordinary matter so that Omega(matter) ~ R(t)^-3
w = +1/3 for cosmic black body real photons so that Omega(CMB) ~ R(t)^-4
w = -1 for RANDOM micro-quantum vacuum zero point fluctuations (from covariance) so that
Omega(ZPF) ~ R(t)^-0 = constant.
7. However in my macro-quantum theory of the world hologram
/\ = (1/Lp^2)[1 - Lp^3|Vacuum Coherence|^2]
Equating this with the world hologram formula in the large-scale FRW metric limit
1/Lp^2R(t)^2 = (1/Lp^2)[1 - Lp^3|Vacuum Coherence|^2]
1/R(t)^2 = [1 - Lp^3|Vacuum Coherence|^2]
R(t)^2 = [1 - Lp^3|Vacuum Coherence|^2]^-1
Where from inflation
Omega(random ZPF) + Omega(matter) + Omega(radiation) + Omega(vacuum coherence) = 1
On Jan 1, 2005, at 3:06 PM, Jack Sarfatti wrote:
re: http://www.arXiv.org/abs/gr-qc/0407060
Zielinski has been making over-simplified naive exaggerated unjustified claims about Alex Potorak's theory that need to be checked. Alex presented "Gravity as Nonmetricity" at GR 17. I make a few initial queries. These equations are all from Alex's handout at GR 17.
AFFINE CONNECTION = LEVI-CIVITA CONNECTION + NONMETRICITY + TORSION
You need to specify which connection is used to define the covariant derivative.
Einstein's 1916 GR only used the LEVI-CIVITA CONNECTION, therefore Alex's theory is an extended theory beyond Einstein's and is physically and mathematically not at all equivalent to Einstein's theory.
Alex defines a "gravitational field" as the "nonmetricity of the affine connection". What this really means physically must be spelled out in great detail.
In 1916 GR the LEVI-CIVITA CONNECTION "gravitational field" (LC) =/= 0 only in Local Non-Inertial Frames (LNIF) and certain combinations of components of it are the INERTIAL FORCES. The Einstein equivalence principle EEP asserts that (LC) = 0 in any Local Inertial Frame (LIF). The LOCAL TETRAD eu^a MAP
guv(LNIF) = eu^anab(LIF)ev^b
is between COINCIDENT LIFs and LNIFs at same event P. nab is the constant Minkowski metric. Therefore, at the extremum of the point test particle dynamical action
guv(P),w = 0
, = ordinary partial derivative
gab(P'|LIF) ~ nab(LIF) + (1/2)gab(P|LIF),c,d(P'-P)^c(P'-P)^d + ...
This is the EEP Ansatz! Note that the second order terms in the Taylor series contain the tidal stretch-squeeze curvature information in the relative coordinates of an extended test particle in the LIF whose center of mass moves on a timelike geodesic extremum in the curved spacetime. There are NO INERTIAL FORCES in LIF's including the REST LIF of a test particle whose center of mass is on a geodesic where "weight" vanishes.
In contrast
guv(P'|LNIF)
~ guv(P|LNIF) + guv(P|LNIF),w(P'-P)^w + (1/2)guv(P|LNIF),w,l(P'-P)^w(P'-P)^l
Similarly one can Taylor expand the Jacobian matrices at P' of the GCTs connecting coincident LNIF's in overlapping coordinate charts x^u & x^u' in same neighborhood of the common physical event P.
Alex's nonmetricity theory, like Gennady Shipov's torsion theory is what Einstein would call attempts at a unified geometrodynamic theory. The physical motivation of Alex's theory is not clear to me at present time from his paper. He does claim that in nonertial frames:
"Inertial forces play the role of a gauge field whose potential is the affine connection". He also claims to have a local pure gravity energy density and a cosmological constant in terms of the affine connection that includes both torsion and nonmetricity fields defined, not with respect to the 1916 Levi-Civita connection, but with respect to the affine connection in a self-consistent way. However, the physics of all this remains obscure.
Nonmetricity in the sense of the smaller 4D (LC) connection is expected from extra space dimensions of Kaluza-Klein "hyperspace". Torsion comes from locally gauging the 6 Lorentz space-time rotations beyond 1916 GR, which is merely the local gauging of the 4 translations generated from 4-momentum. One can also locally gauge the 4 conformal boosts to uniform proper accelerated hyperbolic motion and the 1 dilation.
Relation to the metric engineering of Warp, Wormhole & WMD AKA W^3:
In 1916 GR, with only the (LC) connection, in 4D with zero torsion and zero nonmetricity. The 2 Bianchi identities give vanishing GCT covariant divergences
Guv(vacuum)^;v = 0
This means that the pure vacuum stress-energy current densities are locally conserved all by themselves and, therefore, in the presence of matter
Tuv(matter)^;v = 0
Metric engineering practical warp drive stargate time travel is impossible to achieve under these tight restrictions. The alleged "fact" of "alien" UFOs suggests that such restrictions are not absolute. We cannot ignore such "data".
In contrast when we add exotic vacuum dark zero point energy corrections, and ignore Tuv(matter) as a good approximation we get for the exotic vacuum
Guv + /\zpfguv = 0
where
Guv(exotic dark energy zpf vacuum)^;v + /\zpf^,vguv = 0
using only the (LC) connection. Using the AFFINE CONNECTION will obviously give more torsion field and nonmetricity field correction terms. I ignore those here. We are no longer constrained by the enormous spacetime stiffness factor c^4/G = string tension = 10^19Gev/per 10^-33 cm since we do not try to tweak the Tuv(matter) term the way Hal Puthoff and Eric Davis propose to do in their entirely, in my opinion, dead end impractical strategy for metric engineering W^3 as we see in the UFO phenomenon.
The idea of practical metric engineering the fabric of spacetime for W^3 is that /\zpf depends on the VACUUM COHERENCE, which can be controlled with small power requirements on board the "Unconventional Flying Object" (Paul Hill) by Josephson-Berry phase coupling not unlike Ray Chiao's intriguing idea for the macro-quantum gravimagnetic-electromagnetic superconducting high-efficiency transducers applied to the non-propagating virtual near fields of gravity and electromagnetism.
On the physical meaning of gauge transformation and general coordinate transformations.
All connection field are also Cartan 1-forms in addition to the their metrical structure.
R. Kiehn points out that for any p-form there are three qualitatively different contributions (similarly for dual co-form manifolds for Hodge-DeRham integrals in curved spacetime and beyond) where
Integral of dp-form on p+1 co-form = Integral of p-form on boundary of p+1 co-form
d^2 = 0
d = Cartan exterior derivative
Boundary & dual to d
&^2 = 0
Boundary of a boundary = 0
Exact form f means
f = dg
Closed form means
df = 0
All exact forms are closed, but not all closed forms are exact.
Quotient space of closed forms mod exact forms = HOMOLOGY
Closed co-forms have &f* = 0, exact p co-forms are boundaries of p+1 co-forms.
Quotient space of nonbounding closed p co-forms mod bounding p co-forms is the co-Homology whose dimension is the Betti number of p-dim wormholes.
A traversable wormhole stargate is in a p = 3 co-form needing dark energy to sustain it for practical time travel "teleportation" "Beam me up Scotty!" Making Star Trek Real.
General p-form
= Trivial Gauge Exact p-form
+ Bohm-Aharonov-Josephson-Berry Nonlocal Wilson Phase Factor closed not-exact p-form
+ LOCAL non-closed p-form
The first term, i.e. trivial gauge exact p-forms are simply the CONTINGENT CHOICE of a local coordinate chart in the neighborhood of physical event E. This contingent choice has direct operational physical meaning and is not simply a formal virtual choice. In the case of Einstein's general relativity this choice specifies the set of generically local noninertial detectors MEASURING event E. In the case of say U(1) EM one can imagine a similar choice in the extra Kaluza-Klein space dimension, or, alternatively, setting an absolute phase on a one-handed clock in internal fiber bundle S1 circle space.
The second term is the non-local global topology term from, for example, non-vanishing Betti numbers of multiple-connectivity in the p-dim slice of the n-dim manifold. This seems to give the Vilenken-Taub curvature-without-curvature for a thin unstable wall of dark energy where the third local "curl" term above vanishes for p = 1 but, nevertheless, non-inertial observers must fire rocket motors with jets pointing away from the wall to hover motionless at fixed distance from the thin wall of dark energy that is antigravitating. That is we have a "gravitational" (LC) =/= 0 field even though the local covariant curl of (LC) (AKA curvature-with-curvature) vanishes! This reminds us of the Bohm-Aharonov effect.
For example an electron beam takes both paths where curl A = 0, but A =/= 0 and there is a shift in the position of the fringes proportional to the quantized flux of magnetic curlA threading the two paths even though no curl A ever touches the electrons. A is like the (LC) connection "universal g-force" and curlA is like the local tidal stretch-squeeze curvature. The Bohm-Aharonov effect is "magnetism without magnetism", the Vilenken-Taub effect (1983) is "curvature without curvature".
Choosing the local gauge in this case is selecting HOVERING NONINERTIAL OBSERVERS who must use non-gravity forces to keep off the timelike geodesics in the vacuum. This is very direct local meaning of the connection field in GR where each contingent choice of local coordinate chart has direct physical visualization. How to visualize the locality of the connection A field in electromagnetism is not so obvious until we focus on the test charge where the canonical momentum is
p = mv - (e/c)A
In that case we can associate A with a pseudo-Galilean transformation
v -> v' = v - (e/mc)A
mv = kinetic momentum
(e/c)A = electromagnetic field momentum of the virtual photon cloud of the test charge
This only really begins to make sense quantum mechanically where
mv = (h/i)d/dx on the qubit Bohm pilot wave of the test charge.
On Jan 1, 2005, at 3:05 PM, Jack Sarfatti wrote:
On Dec 31, 2004, at 4:36 PM, Carlos Perelman wrote:
Dear Antonio, Jack, Matti and Tony :
Thank you very for your most recent messages about your work and the new, full moon.
Jack, about the notation. The whole purpose of my paper
Mod. Phys. A vol 17, no. 32 ( 2002 ) 2095-2103
Anti de Siter Gravity from BF-Chern-Simons-Higgs theories
was to show that the MacDowell-Mansouri formulation of gravity
I don't know that work.
can be embedded in a
*more* fundamental Topological BF theory
or that.
... and of course to DERIVE the relationship that
rho (vacuum ) = (L_Planck)^ { -2 } (R_Hubble )^ { -2 } ~ 10^{ - 122 } (Planck mass)^4 .
What is rho? Energy density?
Do you mean
Vacuum Energy Density = hc/Lp^2(c/H)^2 ~ 10^-17x10^66x10^-56 ergs/cc = 10^-7 ergs/cc
Here H = R(t)^-1dR(t)/dt
R dimensionless in usual FRW metric convention.
OK I think I see.
In my theory that seems to fit t'Hooft-Susskind Hologram quite well I get the same number, but with a very different time dependence
I get
Vacuum Energy Density = hc/Lp^4R(t)^2
That is
/\(Sarfatti) = 1/(LpR(t))^2 ~ 10^-56 cm^-2
In contrast
/\(Castro) = (H/c)^2 = (1/c^2R(t)^2)(dR(t)/dt)^2 ~ 10^-56 cm^2
So we are close numerically, but there is an essential difference. I do not use c/H(t) as the cosmic length scale, instead I use LpR(t) (R(t) is a pure number)
My theory says that the t'Hooft-Susskind-Hawking-Bekenstein Hologram Entropy of the Universe is
S(Universe)/kB = R(t)^2 ~ 10^122 BITS (now)
Where
R(t)^2 = [1 - Lp^3|Vacuum Coherence|^2 - 1]^-1
Therefore R(pre -> post inflation vacuum phase transition) ~ 1 BIT at initial singularity where |Vacuum Coherence| = 0.
The mean energy to erase a BIT in the vacuum is ~ hc/LpR(t)
Therefore the vacuum dark energy density is
~ (Entropy of Universe/kB)(hc/LpR(t))(1/LpR(t))^3 = hc/Lp^4(1/R(t))^2
~ 10^-17x10^132x10^-122 = 10^-7 ergs/cc
Furthermore, my model explains why the entropy of the early universe is low from the formation of the vacuum coherence. This explains the Arrow of Time and solves the problem with inflation raised by Roger Penrose.
Vacuum Coherence obeys a GCT covariant Landau-Ginzburg equation depending on metric guv, which, in turn, depends on the Goldstone Phase of the Vacuum Coherence in a nonlinear self-organizing feedback-control loop.
On Dec 31, 2004, at 1:13 PM, Jack Sarfatti wrote:
R(t)^2 = [1 - Lp^3|Vacuum Coherence|^2]^-1
Note when Vacuum Coherence = 0 PRE-INFLATION
R(Initial Singularity) = 1
i.e. 1 Bit thinking of universe as cosmic computer with David Finkelstein's chronons 10^-44 sec of erasures - resetting the register so to speak.
As the large-scale Vacuum Coherence limits to
|Vacuum Coherence|^2 -> 1/Lp^3
R(t) -> infinity
Vacuum Coherence can exceed this limit on smaller non-cosmological scales.
On Dec 31, 2004, at 12:43 PM, Jack Sarfatti wrote:
Inflation demands total stuff is at critical density for flat 3D space, i.e. k = 0 in large-scale FRW metric
Omega(random ZPF) + Omega(matter) + Omega(radiation) + Omega(vacuum coherence) = 1
Omega(on-mass-shell matter) ~ 1/R(t)^3, i.e. w = 0 in R(t)^-3(1 + w) for v/c << 1
Omega(on-mass-shell radiation) ~ 1/R(t)^4, i.e. w = +1/3
with Omega(random zpf) + Omega(vacuum coherence) ~ 1/R(t)^0 independent of R(t) since w = -1 for both random "normal fluid" zpf and condensate (vacuum coherence)
/\ is from random zpf causing both dark energy (negative pressure) and dark matter (positive pressure) exotic vacuum phases.
Clumps of w = -1 positive pressure, possibly like the Galactic Halo mimic w = 0 dark matter in their gravity lensing. Positive and negative pressure exotic vacua can each either universally attract or repel depending on their detailed distribution relative to the test particle. However localized negative pressure exotic vacuum clumps anti-gravitate for test particles outside their domain of support. Similarly, localized positive pressure clumps gravitate for test particles outside their support. The effective gravity strength G* of clumps of exotic vacuum regions can be larger than Newton's G.
Guv + /\zpfguv = 0
is the zero torsion field GR Poisson equation for exotic vacua.
In the Newtonian weak-field slow-speed limit, neglecting gravimagnetism, this is
Grad^2(Potential Energy per unit test mass of exotic vacuum field) ~ c^2/\zpf
Susskind's World Hologram Conjecture requires
Einstein's cosmological constant /\ ~ [LpR(t)]^-2
With critical energy density hc/Lp^4R(t)^2 = (mpc^2/Lp^3)R(t)^-2
Therefore Omega(/\) is independent of R(t) consistent with w = -1 Lorentz covariance and EEP of GR. Similarly for Omega(Vacuum Coherence), which is my new term.
OK trash what I wrote late last night on this when I was very tired. I woke up fresh with a start with the correct way to think about the problem - after taking a 600 mg ibuprofen for shoulder ache from over exercise at the health club.
Here is how Lenny Susskind's world hologram really does work and how it explains the dark energy!
1. Trash H. We don't need it.
2. The FRW space expansion factor R(t) is dimensionless. Everything is in units of Lp.
3. The Susskind-Hawking-Bekenstein-t'Hooft hologram entropy of the Universe is simply
S/kB = (1/4)R(t)^2
I have written this before of course.
R(now) = 10^61
This is a nice formula because it also explains the Arrow of Time since the entropy of the universe is 0 at the initial singularity here, i.e. R(initial singularity) = 0 or, if you prefer Finkelstein's chronons it is 1-bit at t = 0.
4. OK roughly model everything as photons.
The photon thermal distribution is
hf/(e^hf/kBT - 1) + hf/2
But the dark energy is, to first approximation virtual photons hf/2 whose mean value is hc/LpR(t).
5. Therefore we need virtual energy hf/2 to "erase" each bit every time the cosmic quantum computer clears its register to step forward another chronon to compute the history of the universe
Therefore, the dark energy density the vacuum fabric of curved spacetime needs to compute itself is
(R(t)^2/4)(hc/LpR(t))(1/Lp^3R(t))^3 = (hc/Lp^4)1/4R(t)^2 = (hc/4Lp^2)/
Einstein's cosmological constant /\ = 1/Lp^2R(t)^2 = 10^-56 cm^-2 NOW
hc/Lp^2 = c^4/G
6. So this says that Einstein's cosmological constant /\ is getting smaller as the Universe expands. On the other hand, w = pressure/(energy density) = -1 for random micro-quantum zero point energy.
The energy density of cosmic stuff scales as R(t)^-3(1 + w)
For example w = 0 for ordinary matter so that Omega(matter) ~ R(t)^-3
w = +1/3 for cosmic black body real photons so that Omega(CMB) ~ R(t)^-4
w = -1 for RANDOM micro-quantum vacuum zero point fluctuations (from covariance) so that
Omega(ZPF) ~ R(t)^-0 = constant.
7. However in my macro-quantum theory of the world hologram
/\ = (1/Lp^2)[1 - Lp^3|Vacuum Coherence|^2]
Equating this with the world hologram formula in the large-scale FRW metric limit
1/Lp^2R(t)^2 = (1/Lp^2)[1 - Lp^3|Vacuum Coherence|^2]
1/R(t)^2 = [1 - Lp^3|Vacuum Coherence|^2]
R(t)^2 = [1 - Lp^3|Vacuum Coherence|^2]^-1
Where from inflation
Omega(random ZPF) + Omega(matter) + Omega(radiation) + Omega(vacuum coherence) = 1
On Jan 1, 2005, at 3:06 PM, Jack Sarfatti wrote:
re: http://www.arXiv.org/abs/gr-qc/0407060
Zielinski has been making over-simplified naive exaggerated unjustified claims about Alex Potorak's theory that need to be checked. Alex presented "Gravity as Nonmetricity" at GR 17. I make a few initial queries. These equations are all from Alex's handout at GR 17.
AFFINE CONNECTION = LEVI-CIVITA CONNECTION + NONMETRICITY + TORSION
You need to specify which connection is used to define the covariant derivative.
Einstein's 1916 GR only used the LEVI-CIVITA CONNECTION, therefore Alex's theory is an extended theory beyond Einstein's and is physically and mathematically not at all equivalent to Einstein's theory.
Alex defines a "gravitational field" as the "nonmetricity of the affine connection". What this really means physically must be spelled out in great detail.
In 1916 GR the LEVI-CIVITA CONNECTION "gravitational field" (LC) =/= 0 only in Local Non-Inertial Frames (LNIF) and certain combinations of components of it are the INERTIAL FORCES. The Einstein equivalence principle EEP asserts that (LC) = 0 in any Local Inertial Frame (LIF). The LOCAL TETRAD eu^a MAP
guv(LNIF) = eu^anab(LIF)ev^b
is between COINCIDENT LIFs and LNIFs at same event P. nab is the constant Minkowski metric. Therefore, at the extremum of the point test particle dynamical action
guv(P),w = 0
, = ordinary partial derivative
gab(P'|LIF) ~ nab(LIF) + (1/2)gab(P|LIF),c,d(P'-P)^c(P'-P)^d + ...
This is the EEP Ansatz! Note that the second order terms in the Taylor series contain the tidal stretch-squeeze curvature information in the relative coordinates of an extended test particle in the LIF whose center of mass moves on a timelike geodesic extremum in the curved spacetime. There are NO INERTIAL FORCES in LIF's including the REST LIF of a test particle whose center of mass is on a geodesic where "weight" vanishes.
In contrast
guv(P'|LNIF)
~ guv(P|LNIF) + guv(P|LNIF),w(P'-P)^w + (1/2)guv(P|LNIF),w,l(P'-P)^w(P'-P)^l
Similarly one can Taylor expand the Jacobian matrices at P' of the GCTs connecting coincident LNIF's in overlapping coordinate charts x^u & x^u' in same neighborhood of the common physical event P.
Alex's nonmetricity theory, like Gennady Shipov's torsion theory is what Einstein would call attempts at a unified geometrodynamic theory. The physical motivation of Alex's theory is not clear to me at present time from his paper. He does claim that in nonertial frames:
"Inertial forces play the role of a gauge field whose potential is the affine connection". He also claims to have a local pure gravity energy density and a cosmological constant in terms of the affine connection that includes both torsion and nonmetricity fields defined, not with respect to the 1916 Levi-Civita connection, but with respect to the affine connection in a self-consistent way. However, the physics of all this remains obscure.
Nonmetricity in the sense of the smaller 4D (LC) connection is expected from extra space dimensions of Kaluza-Klein "hyperspace". Torsion comes from locally gauging the 6 Lorentz space-time rotations beyond 1916 GR, which is merely the local gauging of the 4 translations generated from 4-momentum. One can also locally gauge the 4 conformal boosts to uniform proper accelerated hyperbolic motion and the 1 dilation.
Relation to the metric engineering of Warp, Wormhole & WMD AKA W^3:
In 1916 GR, with only the (LC) connection, in 4D with zero torsion and zero nonmetricity. The 2 Bianchi identities give vanishing GCT covariant divergences
Guv(vacuum)^;v = 0
This means that the pure vacuum stress-energy current densities are locally conserved all by themselves and, therefore, in the presence of matter
Tuv(matter)^;v = 0
Metric engineering practical warp drive stargate time travel is impossible to achieve under these tight restrictions. The alleged "fact" of "alien" UFOs suggests that such restrictions are not absolute. We cannot ignore such "data".
In contrast when we add exotic vacuum dark zero point energy corrections, and ignore Tuv(matter) as a good approximation we get for the exotic vacuum
Guv + /\zpfguv = 0
where
Guv(exotic dark energy zpf vacuum)^;v + /\zpf^,vguv = 0
using only the (LC) connection. Using the AFFINE CONNECTION will obviously give more torsion field and nonmetricity field correction terms. I ignore those here. We are no longer constrained by the enormous spacetime stiffness factor c^4/G = string tension = 10^19Gev/per 10^-33 cm since we do not try to tweak the Tuv(matter) term the way Hal Puthoff and Eric Davis propose to do in their entirely, in my opinion, dead end impractical strategy for metric engineering W^3 as we see in the UFO phenomenon.
The idea of practical metric engineering the fabric of spacetime for W^3 is that /\zpf depends on the VACUUM COHERENCE, which can be controlled with small power requirements on board the "Unconventional Flying Object" (Paul Hill) by Josephson-Berry phase coupling not unlike Ray Chiao's intriguing idea for the macro-quantum gravimagnetic-electromagnetic superconducting high-efficiency transducers applied to the non-propagating virtual near fields of gravity and electromagnetism.
On the physical meaning of gauge transformation and general coordinate transformations.
All connection field are also Cartan 1-forms in addition to the their metrical structure.
R. Kiehn points out that for any p-form there are three qualitatively different contributions (similarly for dual co-form manifolds for Hodge-DeRham integrals in curved spacetime and beyond) where
Integral of dp-form on p+1 co-form = Integral of p-form on boundary of p+1 co-form
d^2 = 0
d = Cartan exterior derivative
Boundary & dual to d
&^2 = 0
Boundary of a boundary = 0
Exact form f means
f = dg
Closed form means
df = 0
All exact forms are closed, but not all closed forms are exact.
Quotient space of closed forms mod exact forms = HOMOLOGY
Closed co-forms have &f* = 0, exact p co-forms are boundaries of p+1 co-forms.
Quotient space of nonbounding closed p co-forms mod bounding p co-forms is the co-Homology whose dimension is the Betti number of p-dim wormholes.
A traversable wormhole stargate is in a p = 3 co-form needing dark energy to sustain it for practical time travel "teleportation" "Beam me up Scotty!" Making Star Trek Real.
General p-form
= Trivial Gauge Exact p-form
+ Bohm-Aharonov-Josephson-Berry Nonlocal Wilson Phase Factor closed not-exact p-form
+ LOCAL non-closed p-form
The first term, i.e. trivial gauge exact p-forms are simply the CONTINGENT CHOICE of a local coordinate chart in the neighborhood of physical event E. This contingent choice has direct operational physical meaning and is not simply a formal virtual choice. In the case of Einstein's general relativity this choice specifies the set of generically local noninertial detectors MEASURING event E. In the case of say U(1) EM one can imagine a similar choice in the extra Kaluza-Klein space dimension, or, alternatively, setting an absolute phase on a one-handed clock in internal fiber bundle S1 circle space.
The second term is the non-local global topology term from, for example, non-vanishing Betti numbers of multiple-connectivity in the p-dim slice of the n-dim manifold. This seems to give the Vilenken-Taub curvature-without-curvature for a thin unstable wall of dark energy where the third local "curl" term above vanishes for p = 1 but, nevertheless, non-inertial observers must fire rocket motors with jets pointing away from the wall to hover motionless at fixed distance from the thin wall of dark energy that is antigravitating. That is we have a "gravitational" (LC) =/= 0 field even though the local covariant curl of (LC) (AKA curvature-with-curvature) vanishes! This reminds us of the Bohm-Aharonov effect.
For example an electron beam takes both paths where curl A = 0, but A =/= 0 and there is a shift in the position of the fringes proportional to the quantized flux of magnetic curlA threading the two paths even though no curl A ever touches the electrons. A is like the (LC) connection "universal g-force" and curlA is like the local tidal stretch-squeeze curvature. The Bohm-Aharonov effect is "magnetism without magnetism", the Vilenken-Taub effect (1983) is "curvature without curvature".
Choosing the local gauge in this case is selecting HOVERING NONINERTIAL OBSERVERS who must use non-gravity forces to keep off the timelike geodesics in the vacuum. This is very direct local meaning of the connection field in GR where each contingent choice of local coordinate chart has direct physical visualization. How to visualize the locality of the connection A field in electromagnetism is not so obvious until we focus on the test charge where the canonical momentum is
p = mv - (e/c)A
In that case we can associate A with a pseudo-Galilean transformation
v -> v' = v - (e/mc)A
mv = kinetic momentum
(e/c)A = electromagnetic field momentum of the virtual photon cloud of the test charge
This only really begins to make sense quantum mechanically where
mv = (h/i)d/dx on the qubit Bohm pilot wave of the test charge.
Precision Cosmology
On Jan 1, 2005, at 3:39 PM, Jack Sarfatti wrote:
bcc
Don't know off hand. Is this a theory prediction or compilation of data? Remember I say dark matter and dark energy are the same thing only differing in sign of pressure and also on scale. Clumps of w = -1 dark matter WILL mimic w = 0 CDM as you and I discussed previously.
There is a covariant Landau-Ginsburg equation for vacuum coherence that is a self-organizing loop with Einstein's field equations. Requires counter-intuitive computer simulation - a major job for an army of workers.
On Jan 1, 2005, at 1:28 PM, Tony Smith wrote:
Jack, does your model predict the same evolution of the
ratio of dark energy to dark matter to ordinary matter
that is shown in the attached image taken from
http://dpf2004.ucr.edu/plenary/carroll.pdf
which is Carroll's presentation at the 2004 APS DPF meeting ?
If not, how would those pie charts look for your model ?
Tony
On Jan 1, 2005, at 3:39 PM, Jack Sarfatti wrote:
bcc
Don't know off hand. Is this a theory prediction or compilation of data? Remember I say dark matter and dark energy are the same thing only differing in sign of pressure and also on scale. Clumps of w = -1 dark matter WILL mimic w = 0 CDM as you and I discussed previously.
There is a covariant Landau-Ginsburg equation for vacuum coherence that is a self-organizing loop with Einstein's field equations. Requires counter-intuitive computer simulation - a major job for an army of workers.
On Jan 1, 2005, at 1:28 PM, Tony Smith wrote:
Jack, does your model predict the same evolution of the
ratio of dark energy to dark matter to ordinary matter
that is shown in the attached image taken from
http://dpf2004.ucr.edu/plenary/carroll.pdf
which is Carroll's presentation at the 2004 APS DPF meeting ?
If not, how would those pie charts look for your model ?
Tony
Thursday, December 30, 2004
Einstein's Cosmological Constant from The World Hologram
R(t)^2 = [1 - Lp^3|Vacuum Coherence|^2]^-1
Note when Vacuum Coherence = 0 PRE-INFLATION
R(Initial Singularity) = 1
i.e. 1 Bit thinking of universe as cosmic computer with David Finkelstein's chronons 10^-44 sec of erasures - resetting the register so to speak.
As the large-scale Vacuum Coherence limits to
|Vacuum Coherence|^2 -> 1/Lp^3
R(t) -> infinity
Vacuum Coherence can exceed this limit on smaller non-cosmological scales.
On Dec 31, 2004, at 12:43 PM, Jack Sarfatti wrote:
Inflation demands total stuff is at critical density for flat 3D space, i.e. k = 0 in large-scale FRW metric
Omega(random ZPF) + Omega(matter) + Omega(radiation) + Omega(vacuum coherence) = 1
Omega(on-mass-shell matter) ~ 1/R(t)^3, i.e. w = 0 in R(t)^-3(1 + w) for v/c << 1
Omega(on-mass-shell radiation) ~ 1/R(t)^4, i.e. w = +1/3
with Omega(random zpf) + Omega(vacuum coherence) ~ 1/R(t)^0 independent of R(t) since w = -1 for both random "normal fluid" zpf and condensate (vacuum coherence)
/\ is from random zpf causing both dark energy (negative pressure) and dark matter (positive pressure) exotic vacuum phases.
Clumps of w = -1 positive pressure, possibly like the Galactic Halo mimic w = 0 dark matter in their gravity lensing. Positive and negative pressure exotic vacua can each either universally attract or repel depending on their detailed distribution relative to the test particle. However localized negative pressure exotic vacuum clumps anti-gravitate for test particles outside their domain of support. Similarly, localized positive pressure clumps gravitate for test particles outside their support. The effective gravity strength G* of clumps of exotic vacuum regions can be larger than Newton's G.
Guv + /\zpfguv = 0
is the zero torsion field GR Poisson equation for exotic vacua.
In the Newtonian weak-field slow-speed limit, neglecting gravimagnetism, this is
Grad^2(Potential Energy per unit test mass of exotic vacuum field) ~ c^2/\zpf
Susskind's World Hologram Conjecture requires
Einstein's cosmological constant /\ ~ [LpR(t)]^-2
With critical energy density hc/Lp^4R(t)^2 = (mpc^2/Lp^3)R(t)^-2
Therefore Omega(/\) is independent of R(t) consistent with w = -1 Lorentz covariance and EEP of GR. Similarly for Omega(Vacuum Coherence), which is my new term.
OK trash what I wrote late last night on this when I was very tired. I woke up fresh with a start with the correct way to think about the problem - after taking a 600 mg ibuprofen for shoulder ache from over exercise at the health club.
Here is how Lenny Susskind's world hologram really does work and how it explains the dark energy!
1. Trash H. We don't need it.
2. The FRW space expansion factor R(t) is dimensionless. Everything is in units of Lp.
3. The Susskind-Hawking-Bekenstein-t'Hooft hologram entropy of the Universe is simply
S/kB = (1/4)R(t)^2
I have written this before of course.
R(now) = 10^61
This is a nice formula because it also explains the Arrow of Time since the entropy of the universe is 0 at the initial singularity here, i.e. R(initial singularity) = 0 or, if you prefer Finkelstein's chronons it is 1-bit at t = 0.
4. OK roughly model everything as photons.
The photon thermal distribution is
hf/(e^hf/kBT - 1) + hf/2
But the dark energy is, to first approximation virtual photons hf/2 whose mean value is hc/LpR(t).
5. Therefore we need virtual energy hf/2 to "erase" each bit every time the cosmic quantum computer clears its register to step forward another chronon to compute the history of the universe
Therefore, the dark energy density the vacuum fabric of curved spacetime needs to compute itself is
(R(t)^2/4)(hc/LpR(t))(1/Lp^3R(t))^3 = (hc/Lp^4)1/4R(t)^2 = (hc/4Lp^2)/
Einstein's cosmological constant /\ = 1/Lp^2R(t)^2 = 10^-56 cm^-2 NOW
hc/Lp^2 = c^4/G
6. So this says that Einstein's cosmological constant /\ is getting smaller as the Universe expands. On the other hand, w = pressure/(energy density) = -1 for random micro-quantum zero point energy.
The energy density of cosmic stuff scales as R(t)^-3(1 + w)
For example w = 0 for ordinary matter so that Omega(matter) ~ R(t)^-3
w = +1/3 for cosmic black body real photons so that Omega(CMB) ~ R(t)^-4
w = -1 for RANDOM micro-quantum vacuum zero point fluctuations (from covariance) so that
Omega(ZPF) ~ R(t)^-0 = constant.
7. However in my macro-quantum theory of the world hologram
/\ = (1/Lp^2)[1 - Lp^3|Vacuum Coherence|^2]
Equating this with the world hologram formula in the large-scale FRW metric limit
1/Lp^2R(t)^2 = (1/Lp^2)[1 - Lp^3|Vacuum Coherence|^2]
1/R(t)^2 = [1 - Lp^3|Vacuum Coherence|^2]
R(t)^2 = [1 - Lp^3|Vacuum Coherence|^2]^-1
Where from inflation
Omega(random ZPF) + Omega(matter) + Omega(radiation) + Omega(vacuum coherence) = 1
R(t)^2 = [1 - Lp^3|Vacuum Coherence|^2]^-1
Note when Vacuum Coherence = 0 PRE-INFLATION
R(Initial Singularity) = 1
i.e. 1 Bit thinking of universe as cosmic computer with David Finkelstein's chronons 10^-44 sec of erasures - resetting the register so to speak.
As the large-scale Vacuum Coherence limits to
|Vacuum Coherence|^2 -> 1/Lp^3
R(t) -> infinity
Vacuum Coherence can exceed this limit on smaller non-cosmological scales.
On Dec 31, 2004, at 12:43 PM, Jack Sarfatti wrote:
Inflation demands total stuff is at critical density for flat 3D space, i.e. k = 0 in large-scale FRW metric
Omega(random ZPF) + Omega(matter) + Omega(radiation) + Omega(vacuum coherence) = 1
Omega(on-mass-shell matter) ~ 1/R(t)^3, i.e. w = 0 in R(t)^-3(1 + w) for v/c << 1
Omega(on-mass-shell radiation) ~ 1/R(t)^4, i.e. w = +1/3
with Omega(random zpf) + Omega(vacuum coherence) ~ 1/R(t)^0 independent of R(t) since w = -1 for both random "normal fluid" zpf and condensate (vacuum coherence)
/\ is from random zpf causing both dark energy (negative pressure) and dark matter (positive pressure) exotic vacuum phases.
Clumps of w = -1 positive pressure, possibly like the Galactic Halo mimic w = 0 dark matter in their gravity lensing. Positive and negative pressure exotic vacua can each either universally attract or repel depending on their detailed distribution relative to the test particle. However localized negative pressure exotic vacuum clumps anti-gravitate for test particles outside their domain of support. Similarly, localized positive pressure clumps gravitate for test particles outside their support. The effective gravity strength G* of clumps of exotic vacuum regions can be larger than Newton's G.
Guv + /\zpfguv = 0
is the zero torsion field GR Poisson equation for exotic vacua.
In the Newtonian weak-field slow-speed limit, neglecting gravimagnetism, this is
Grad^2(Potential Energy per unit test mass of exotic vacuum field) ~ c^2/\zpf
Susskind's World Hologram Conjecture requires
Einstein's cosmological constant /\ ~ [LpR(t)]^-2
With critical energy density hc/Lp^4R(t)^2 = (mpc^2/Lp^3)R(t)^-2
Therefore Omega(/\) is independent of R(t) consistent with w = -1 Lorentz covariance and EEP of GR. Similarly for Omega(Vacuum Coherence), which is my new term.
OK trash what I wrote late last night on this when I was very tired. I woke up fresh with a start with the correct way to think about the problem - after taking a 600 mg ibuprofen for shoulder ache from over exercise at the health club.
Here is how Lenny Susskind's world hologram really does work and how it explains the dark energy!
1. Trash H. We don't need it.
2. The FRW space expansion factor R(t) is dimensionless. Everything is in units of Lp.
3. The Susskind-Hawking-Bekenstein-t'Hooft hologram entropy of the Universe is simply
S/kB = (1/4)R(t)^2
I have written this before of course.
R(now) = 10^61
This is a nice formula because it also explains the Arrow of Time since the entropy of the universe is 0 at the initial singularity here, i.e. R(initial singularity) = 0 or, if you prefer Finkelstein's chronons it is 1-bit at t = 0.
4. OK roughly model everything as photons.
The photon thermal distribution is
hf/(e^hf/kBT - 1) + hf/2
But the dark energy is, to first approximation virtual photons hf/2 whose mean value is hc/LpR(t).
5. Therefore we need virtual energy hf/2 to "erase" each bit every time the cosmic quantum computer clears its register to step forward another chronon to compute the history of the universe
Therefore, the dark energy density the vacuum fabric of curved spacetime needs to compute itself is
(R(t)^2/4)(hc/LpR(t))(1/Lp^3R(t))^3 = (hc/Lp^4)1/4R(t)^2 = (hc/4Lp^2)/
Einstein's cosmological constant /\ = 1/Lp^2R(t)^2 = 10^-56 cm^-2 NOW
hc/Lp^2 = c^4/G
6. So this says that Einstein's cosmological constant /\ is getting smaller as the Universe expands. On the other hand, w = pressure/(energy density) = -1 for random micro-quantum zero point energy.
The energy density of cosmic stuff scales as R(t)^-3(1 + w)
For example w = 0 for ordinary matter so that Omega(matter) ~ R(t)^-3
w = +1/3 for cosmic black body real photons so that Omega(CMB) ~ R(t)^-4
w = -1 for RANDOM micro-quantum vacuum zero point fluctuations (from covariance) so that
Omega(ZPF) ~ R(t)^-0 = constant.
7. However in my macro-quantum theory of the world hologram
/\ = (1/Lp^2)[1 - Lp^3|Vacuum Coherence|^2]
Equating this with the world hologram formula in the large-scale FRW metric limit
1/Lp^2R(t)^2 = (1/Lp^2)[1 - Lp^3|Vacuum Coherence|^2]
1/R(t)^2 = [1 - Lp^3|Vacuum Coherence|^2]
R(t)^2 = [1 - Lp^3|Vacuum Coherence|^2]^-1
Where from inflation
Omega(random ZPF) + Omega(matter) + Omega(radiation) + Omega(vacuum coherence) = 1
Nonlocal curvature without curvature
First think of superfluid helium. The "circulation" vector field v is a "connection" like the EM vector potential A. The vorticity curl v is like magnetic field curlA. Curlv is zero outside of the vortex core in the irrotational superflow. The quantized circulation vortices are multiply connected, i.e. winding numbers or Betti numbers for 1-forms & 2-forms. They are multiply connected because they have "micro-quantum normal fluid cores" where the macro-quantum coherence drops if not to zero to a much smaller value to make a Josephson weak link of sorts. In my macro-quantum theory of gravity for Super Cosmos the "normal fluid" is the exotic vacuum dark energy of negative micro-quantum zero point pressure or the dark matter of positive zero point pressure.
Therefore, we have a Bohm-Aharonov nonlocality in superfluid helium but we do not think it is amazing because we can picture a local circulation vector field of the fluid flow.
Now we have an isomorphism with elasticity theory as shown by Hagen Kleinert. We have a kind of tetrad world crystal elastic distortion field that is essentially related to the non-tensor Levi-Civita connection field (LC), which is like A in EM and like v in superfluid helium. We can, therefore, have non-vanishing "circulation" integrals (line integrals of local g-force) even though there is no interior (covariant) curl of (LC) because the unstable dark energy thin wall is an exotic vacuum "normal fluid" core. In terms of crystal distortion theory, there is a smooth distortion (LC) field outside the source region of a thin unstable dark energy slab inside of which there is Ricci tensor which is a bunch of disclination topological defects that influence at a distance the local (LC) field of vanishing curl.
Now in EM, we say vector potential is not a local observable because it is a inhomogeneous non-tensor under the U(1) local gauge transformations. In GR these are the GCT transition functions between overlapping local coordinate charts in the atlas covering the manifold like analytical continuation of complex functions of complex variable bypassing branch points. (A power series circle of convergence stops at a branch point but you can finagle around the obstruction with a different circle.) Note in my theory the (LC) connection comes from the 4^3 3rd order partial derivatives of the more is different emergent macro-quantum world hologram Goldstone rigid phase of the post-inflationary vacuum coherence field that is the fabric of smooth OLDLRO curved spacetime. So there is no reason at all to say that the (LC) connection is not a local observable even though it is not a GCT tensor.
It's nice, and of course necessary, that the metric as second order partial derivatives of the Goldstone phase and the connection as third order partial derivatives and curvature as 4th order partial derivatives have exactly the correct number of GCT tensor indices required by Einstein's GR!
First think of superfluid helium. The "circulation" vector field v is a "connection" like the EM vector potential A. The vorticity curl v is like magnetic field curlA. Curlv is zero outside of the vortex core in the irrotational superflow. The quantized circulation vortices are multiply connected, i.e. winding numbers or Betti numbers for 1-forms & 2-forms. They are multiply connected because they have "micro-quantum normal fluid cores" where the macro-quantum coherence drops if not to zero to a much smaller value to make a Josephson weak link of sorts. In my macro-quantum theory of gravity for Super Cosmos the "normal fluid" is the exotic vacuum dark energy of negative micro-quantum zero point pressure or the dark matter of positive zero point pressure.
Therefore, we have a Bohm-Aharonov nonlocality in superfluid helium but we do not think it is amazing because we can picture a local circulation vector field of the fluid flow.
Now we have an isomorphism with elasticity theory as shown by Hagen Kleinert. We have a kind of tetrad world crystal elastic distortion field that is essentially related to the non-tensor Levi-Civita connection field (LC), which is like A in EM and like v in superfluid helium. We can, therefore, have non-vanishing "circulation" integrals (line integrals of local g-force) even though there is no interior (covariant) curl of (LC) because the unstable dark energy thin wall is an exotic vacuum "normal fluid" core. In terms of crystal distortion theory, there is a smooth distortion (LC) field outside the source region of a thin unstable dark energy slab inside of which there is Ricci tensor which is a bunch of disclination topological defects that influence at a distance the local (LC) field of vanishing curl.
Now in EM, we say vector potential is not a local observable because it is a inhomogeneous non-tensor under the U(1) local gauge transformations. In GR these are the GCT transition functions between overlapping local coordinate charts in the atlas covering the manifold like analytical continuation of complex functions of complex variable bypassing branch points. (A power series circle of convergence stops at a branch point but you can finagle around the obstruction with a different circle.) Note in my theory the (LC) connection comes from the 4^3 3rd order partial derivatives of the more is different emergent macro-quantum world hologram Goldstone rigid phase of the post-inflationary vacuum coherence field that is the fabric of smooth OLDLRO curved spacetime. So there is no reason at all to say that the (LC) connection is not a local observable even though it is not a GCT tensor.
It's nice, and of course necessary, that the metric as second order partial derivatives of the Goldstone phase and the connection as third order partial derivatives and curvature as 4th order partial derivatives have exactly the correct number of GCT tensor indices required by Einstein's GR!
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