- Gravitons for a Cosmological Constant /\ =/= 0
- /\ > 0 outside Gravitationally Bound Domains of Unispace
- ZeroPoint Energy and Josephson Junction Dark Energy and EVOs
- /\ and ZeroPoint Energy
- /\ Energy Magnitude
- /\ and Chiao QM-GR Transduction of EM-Gravity

In the D4-D5-E6-E7-E8 VoDou Physics model, Gravity and the Cosmological Constant come from the MacDowell-Mansouri Mechanism and the 15-dimensional Spin(2,4) = SU(2,2) Conformal Group, which is made up of:

- 3 Rotations;
- 3 Boosts;
- 4 Translations;
- 4 Special Conformal transformations; and
- 1 Dilatation.

According to gr-qc/9809061 by R. Aldrovandi and J. G. Peireira:

"... By the process of Inonu-Wigner group contraction with R -> oo ...[where R ]... the de Sitter pseudo-radius ... , both de Sitter groups ... with metric ... (-1,+1,+1,+1,-1) ...[or]... (-1,+1,+1,+1,+1) ... are reduced to the Poincare group P, and both de Sitter spacetimes are reduced to the Minkowski space M. As the de Sitter scalar curvature goes to zero in this limit, we can say that M is a spacetime gravitationally related to a vanishing cosmological constant.On the other hand, in a similar fashion but taking the limit R -> 0, both de Sitter groups are contracted to the group Q, formed by a semi-direct product between Lorentz and special conformal transformation groups, and both de Sitter spaces are reduced to the cone-space N, which is a space with vanishing Riemann and Ricci curvature tensors. As the scalar curvature of the de Sitter space goes to infinity in this limit, we can say that N is a spacetime gravitationally related to an infinite cosmological constant.

If the fundamental spacetime symmetry of the laws of Physics is that given by the de Sitter instead of the Poincare group, the P-symmetry of the weak cosmological-constant limit and the Q-symmetry of the strong cosmological-constant limit can be considered as limiting cases of the fundamental symmetry. ...

... Minkowski and the cone-space can be considered as dual to each other, in the sense that their geometries are determined respectively by a vanishing and an infinite cosmological constants. The same can be said of their kinematical group of motions: P is associated to a vanishing cosmological constant and Q to an infinite cosmological constant.

The dual transformation connecting these two geometries is the spacetime inversion x^u -> x^u / sigma^2 . Under such a transformation, the Poincare group P is transformed into the group Q, and the Minkowski space M becomes the cone-space N. The points at infinity of M are concentrated in the vertex of the cone-space N, and those on the light-cone of M becomes the infinity of N. It is interesting to notice that, despite presenting an infinite scalar curvature, the concepts of space isotropy and equivalence between inertial frames in the cone-space N are those of special relativity. The difference lies in the concept of uniformity as it is the special conformal transformations, and not ordinary translations, which act transitively on N. ...

... in the light of the recent supernovae results ... favoring possibly quite large values for the cosmological constant, the above results may acquire a further relevance to Cosmology ...".

Since the Cosmological Constant comes from the 10 Rotation, Boost,
and Special Conformal generators of the Conformal
Group Spin(2,4) = SU(2,2), **the fractional part of our Universe of
the Cosmological Constant should be about 10 / 15 = 67%**.

Since Black Holes, including Dark Matter Primordial
Black Holes, are curvature singularities in our 4-dimensional
physical spacetime, and since Einstein-Hilbert curvature comes from
the 4 Translations of the 15-dimensional Conformal
Group Spin(2,4) = SU(2,2) through the MacDowell-Mansouri Mechanism
(in which the generators
corresponding to the 3 Rotations and 3 Boosts do not propagate),
**the fractional part of our Universe of Dark Matter ****Primordial
Black Holes**** should be about 4 / 15 = 27%**.

Since Ordinary Matter gets mass from the Higgs mechanism which is
related to the 1 Scale Dilatation of the 15-dimensional Conformal
Group Spin(2,4) = SU(2,2), **the fractional part of our universe of
Ordinary Matter should be about 1 / 15 = 6%**.

Therefore, our Flat Expanding Universe should, according to the cosmology of the D4-D5-E6-E7-E8 VoDou Physics model, have, roughly:

- According to an article by Michael S. Turner in
Physics Today (April 2003, pp. 10-11): "... vacuum energy ... is
characterized by an "equation of state" ...[ w = pressure /
density = -1 for vacuum energy with negative pressure ]...[
that] determines how the energy density of dark energy ... vacuum
energy ... changes as the universe expands: ...[ **vacuum energy
density is proportional to 1 / R^3(1+w) = 1 = constant** ]...
for comparison, for nonrelativistic matter w = 0 and for radiation, w
= 1/3 ...[In]... Einstein's theory ... the strength of
gravity depends on pressure, p, [and density, rho,] with
**rho + 3p acting as the source of gravity** ...[so that
**vacuum energy with p = - rho < - rho / 3 ]... has gravity
that repels rather than attracts. ...[and is]... exotic**.
... The ratio of pressure to energy density is characterized by the
square of the internal velocity divided by c^2. thus ... vacuum
energy ... is intrinsically relativistic and is more like energy than
matter. ...[**If vacuum energy could be bottled up, we
could]... create an object with ****antigravity**.
...".

Some relevant observational results in cosmology are discussed by Subir Sakar in hep-ph/0201140, where he says:

"... The most exciting observational developments have undoubtedly been in measurements of thedeceleration parameter q = ( dH^(-1) / dt ) - 1, which equals 0.5 for the E-deS model where H ...[is proportional to]... t^(2/3), and -1 for a DeSitter (deS) model with OMEGA_m = 0, OMEGA_/\ = 1 which has H constant. ... for z>1 the cosmological constant becomes unimportant relative to the increasing matter density ( ...[proportional to]... (1+z)^3) so the expansion should be seen to be slowing down at such epochs; the transition from acceleration to deceleration occurs at z = ( 2 OMEGA_/\ / OMEGA_m )^(1/3) -1. ......[reference 44 is]... A.G. Riess et al., Astrophys. J. 560 (2001) 49; see also M.S. Turner and A.G. Riess, [astro-ph/0106051]. ...".

According to M.S. Turner and A.G. Riess, in astro-ph/0106051:

"... the SN data favor recent acceleration (z < 0.5) and past deceleration (z > 0.5) ... Specializing to a flat Universe, as indicated by recent CMB anisotropy measurements which determine OMEGA_0 = 1 ± 0.04 ... and constant w_X, these expressions becomeH(z)^2 = H_0^2 [ OMEGA_M (1+z)^3 + OMEGA_X (1+z)^3(1+w_X) ]

q(z) = (1/2) [ ( 1 + (OMEGA_X / OMEGA_M) (1+3w_X) (1+z)^3w_X ) /

/ ( 1 + (OMEGA_X / OMEGA_M) (1+z)^3w_X ) ) ]From this it follows that the redshift of transition from deceleration to acceleration ( = z_(q=0) ) is

1 + z_(q=0) = [ (1+3w_X)( OMEGA_M - 1) / OMEGA_M ]^(-1/(3w_X) ] =

= [ 2 OMEGA_/\ / OMEGA_M ]^(1/3)where the second equation is for vacuum energy (i.e., w_X = -1). ...".

Note that for the /\ Cosmological Constant - Cold Dark Matter - Ordinary Matter model that is favored by WMAP observations and the above calculations, OMEGA_/\ / OMEGA_M = 2 (approximately), so that 1 + z_(q=0) = [ 2 OMEGA_/\ / OMEGA_M ]^(1/3) = 4^(1/3) = 1.587 so that the redshift at the inflection point between decelerated and accelerated expansion is about z_(q=0) = 0.587.

As Dennnis Marks pointed out to me:

- since w = -1 for /\ and the average overall density of /\ remains constant with time and the expansion of our Universe; and
- w = 0 for nonrelativistic matter so that its overall average density declines as 1 / R^3 as our Universe expands; and
- primordial black hole dark matter, for black holes more massive than the Planck mass, decays as our Universe expands so that its overall average density declines somewhat faster than 1 / R^3 as our Universe expands;

the ratio of their overall average densities must vary with time, or scale factor R of our Universe, as it expands so that the above calculated ratio 0.67 : 0.27 : 0.06 is valid only for a particular time, or scale factor, of our Universe, and that is a time near our present time at which WMAP measures that ratio to be 0.73 : 0.23 : 0.04 (in my opinion very close to the above caculated ratio). His remarks are substantially equivalent to a question that Michael S. Turner, in astro-ph/0202005, calls "... The Nancy Kerrigan Problem ... in the past dark energy was unimportant and in the future it will be dominant! We just happen to live at the time when dark matter and dark energy have comparable densities. In the words of Olympic skater Nancy Kerrigan, "Why me? Why now?". In other words:

Since WMAP observes Ordinary Matter at 4% NOW, the time WHEN Ordinary Matter was 6% would be at redshift z such that 1 / (1+z)^3 = 0.04 / 0.06 = 2/3 , or (1+z)^3 = 1.5 , or 1+z = 1.145 , or z = 0.145. To translate redshift into time, in billions of years before present, or Gy BP, use this chart

from a
www.supernova.lbl.gov file SNAPoverview.pdf. to see that **the
time WHEN Ordinary Matter was 6% would have been a bit over 2 billion
years ago, or 2 Gy BP**.

**If****Cold Dark Matter = Primordial Black Holes (PBH)****If****Cold Dark Matter = MOND****If****Cold Dark Matter = PBH + MOND**

**If Cold Dark Matter = Primordial
****Black Holes**** (****P****B****H****):
**

The above calculation of 2 Gy BP for the ratio 0.67 : 0.27 : 0.06 is based only on the decline in the Ordinary Matter component with expansion of Space, so it is only a rough estimate, in that it ignores such things as decay of Ordinary Matter protons by GUT (10^31 year lifetime) or by Black Hole processes (10^64 year lifetime), which would be less important during the relevant time periods near NOW than in the Black Hole and Dark Eras of the distant future.

Jack Sarfatti said (in the context of his physics/cosmology model): "... "... I am also saying that lepto-quarks [leptons and quarks] have dark matter cores on small scale. It's /\zpf < 0 that keeps electron stable. Think, naively for the nonce, of electron as a shell of electric charge with an inner /\zpf < 0 core. It looks like a "point" from huge effective curvature of /\zpf. ...".That idea is not only interestingly similar to the idea of /\zpf < 0 haloes helping to hold galaxies together, but also seems very much like the Compton Radius Vortex model of leptons and quarks as Kerr-Newman black holes with no cosmic censorship of their naked singularities.

Also, perhaps the concept of Primordial Black Holes as Cold Dark Matter might be a particle manifestation of the part of /\zpf < 0 (or, perhaps equivalently, MOND Cold Dark Matter) that is not found in the center of /\ = 0 Ordinary Matter leptons and quarks. If that viewpoint is correct, in view of the WMAP ratio of 73% - 23% - 4% of /\ > 0 , /\ < 0, /\ = 0, there should be a lot more mass in /\ < 0 Primordial Black Holes than in /\ = 0 leptons and quarks.

Further, Cold Dark Matter cores of leptons and quarks seems consistent with an association of Ordinary Matter with production of MOND Cold Dark Matter in early times of our Universe, and it may be that PBH Cold Dark Matter and MOND Cold Dark Matter may be very closely related.

As to how the Dark Energy /\ and Cold Dark Matter terms have
evolved during the past 2 Gy, a rough estimate analysis would be,
**if Cold Dark matter = PBH**:

- /\ and CDM would be effectively created during expansion in their natural ratio 67 : 27 = 2.48 = 5 / 2, each having proportionate fraction 5 / 7 and 2 / 7, respectively;
- CDM Black Hole decay would be ignored; and
- pre-existing CDM Black Hole density would decline by the same 1 / R^3 factor as Ordinary Matter, from 0.27 to 0.27 / 1.5 = 0.18.

The Ordinary Matter excess 0.06 - 0.04 = 0.02 plus the first-order CDM excess 0.27 - 0.18 = 0.09 should be summed to get a total first-order excess of 0.11, which in turn should be distributed to the /\ and CDM factors in their natural ratio 67 : 27, producing, for NOW after 2 Gy of expansion:

- /\ factor = 0.67 + 0.11 x 5/7 = 0.67 + 0.08 = 0.75; and
- CDM Black Hole factor = 0.18 + 0.11 x 2/7 = 0.18 + 0.03 = 0.21

so that the **present ratio of 0.73 : 0.23 : 0.04 observed by
****WMAP**** seems to me
to be consistent with the ****cosmology****
of the ****D4-D5-E6-E7-E8 VoDou Physics
model** if Cold Dark Matter = PBH.

( Note that the equation of state for MOND might be similar to that for gravitational interactions from other Worlds of the Many-Worlds, so, in these calculations, MOND dark matter might be taken to include gravitational interactions from other Worlds of the Many-Worlds. )

The above calculation of 2 Gy BP for the ratio 0.67 : 0.27 : 0.06 is based only on the decline in the Ordinary Matter component with expansion of Space, so it is only a rough estimate, in that it ignores such things as decay of Ordinary Matter protons by GUT (10^31 year lifetime) or by Black Hole processes (10^64 year lifetime), which would be less important during the relevant time periods near NOW than in the Black Hole and Dark Eras of the distant future.

At first glance it might appear that if MOND obeys an equation of state with w = -1 similar to /\, as opposed to w = 0 similar to Ordinary matter, then MOND could not be the CDM of our Universe because, as Max Tegmark says: "... rho is proportional to (1+z)^3 for baryons and cold dark matter ...", while rho is constant if w = -1. However,Jack Sarfatti has suggested (in the context of his physics/cosmology model) that "... the galactic halos are huge spheres of exotic vacuum ...[ /\ < 0 Cold Dark Matter]... keeping the galaxies stable ..." (an idea interestingly similar to the idea of Dark Matter cores of leptons and quarks).

If Cold Dark Matter is concentrated around galaxies, then maybe Cosmological Constant /\ > 0 Dark Energy energy is concentrated in the (now much larger) volume of space that is mostly empty vacuum and maybe the reason for them to be located in different parts of our universe is that:

- Dark Stuff in empty space naturally has the full Conformal Degrees of Freedom of Cosmological Constant /\ > 0 Dark Energy, so that the local background spacetime is a conformal cone-space; but
- Dark Stuff in the presence of the gravitational field of ordinary matter (such as in galactic haloes) becomes MOND Cold Dark Matter, loses full Conformal Degrees of Freedom, and is reduced to the degrees of freedom of the Poincare group with Minkowski spacetime as local background.
As to how that would affect the evolution of MOND Cold Dark Matter:

- in the distant past, when Ordinary Matter was far more abundant than Cosmological Constant /\ > 0 Dark Energy, the MOND Cold Dark Matter may have been mostly generated by, and therefore proportional by 27 / 6 to, the gravitational field of Ordinary Matter. Therefore, at early times, MOND Cold Dark Matter would have its effective equation of state derived from that of ordinary matter, evolving consistently with the early universe asymptote (1+z)^3 shown on the Tegmark figure; while
- in the near present and the future, Cosmological Constant /\ > 0 Dark Energy dominates Ordinary Matter, and the rate of creation of MOND Cold Dark Matter will be proportional by 27 / 67 to Cosmological Constant /\ > 0 Dark Energy, although the MOND Cold Dark Matter will tend to fall into, and be concentrated near, Ordinary Matter such as is found in the galaxies of our universe.
In his physics/cosmology model, Jack Sarfatti describes Dark Matter as a gravitationally attractive exotic form of Dark Energy equivalent to a Cosmological Constant taking values /\ < 0, while he describes Ordinary Matter as corresponding to non-exotic /\ = 0 with equilibrium vaccuum fluctuations producing Born Rule quantum phenomena, and Dark Energy as corresponding to an anti-gravitating conventional Cosmological Constant with /\ > 0.

It may be that Jack Sarfatti's /\ < 0 Dark Matter may be substantially equivalent to my MOND Cold Dark Matter, and

it may also be that MOND Cold Dark Matter and PBH Cold Dark Matter may be very closely related.

As to how the Dark Energy /\ and Cold Dark Matter terms have
evolved during the past 2 Gy, a rough estimate analysis would be,
**if Cold Dark Matter = MOND**:

- /\ and CDM would be effectively created during expansion in their natural ratio 67 : 27 = 2.48 = 5 / 2, each having proportionate fraction 5 / 7 and 2 / 7, respectively; and
- pre-existing CDM density would not decline.

The Ordinary Matter excess 0.06 - 0.04 = 0.02 should be distributed to the /\ and CDM factors in their natural ratio 67 : 27, producing, for NOW after 2 Gy of expansion:

- /\ factor = 0.67 + 0.02 x 5/7 = 0.67 + 0.01 = 0.68; and
- CDM Black Hole factor = 0.27 + 0.02 x 2/7 = 0.18 + 0.01 = 0.28

so that the **present ratio of 0.73 : 0.23 : 0.04 observed by
****WMAP**** seems to me
to be roughly consistent with the ****cosmology****
of the ****D4-D5-E6-E7-E8 VoDou Physics
model** if Cold Dark Matter = MOND, although the correspondence
is not quite as close as for the case that Cold
Dark Matter = PBH.

( Note that the equation of state for MOND might be similar to that for gravitational interactions from other Worlds of the Many-Worlds, so, in these calculations, MOND dark matter might be taken to include gravitational interactions from other Worlds of the Many-Worlds. )

The above calculation of 2 Gy BP for the ratio 0.67 : 0.27 : 0.06
is based only on the decline in the Ordinary Matter component with
expansion of Space, so it is only a rough estimate, in that it
ignores such things as decay of Ordinary Matter protons by GUT
(10^31 year lifetime) or by Black Hole
processes (10^64 year lifetime), which would be less important
during the relevant time periods near NOW than in the
Black Hole and Dark Eras of the distant future. As to how the
Dark Energy /\ and Cold Dark Matter terms have evolved during the
past 2 Gy, a rough estimate analysis would be, **if Cold Dark Matter
= (1/2) ****PBH**** + (1/2) ****MOND**:

- /\ and CDM would be effectively created during expansion in their natural ratio 67 : 27 = 2.48 = 5 / 2, each having proportionate fraction 5 / 7 and 2 / 7, respectively;
- CDM Black Hole decay would be ignored;
- pre-existing CDM MOND density (1/2)(0.27) = 0.14 would not decline; and
- pre-existing CDM Black Hole density would decline by the same 1 / R^3 factor as Ordinary Matter, from (1/2)(0.27) = 0.13 to ( 0.13 / 1.5 ) = 0.09.

The Ordinary Matter excess 0.06 - 0.04 = 0.02 plus the first-order CDM excess 0.13 = 0.09 = 0.04 should be summed to get a total first-order excess of 0.06, which in turn should be distributed to the /\ and CDM factors in their natural ratio 67 : 27, producing, for NOW after 2 Gy of expansion:

- /\ factor = 0.67 + 0.06 x 5/7 = 0.67 + 0.04 = 0.71; and
- CDM Black Hole factor = 0.23 + 0.06 x 2/7 = 0.23 + 0.02 = 0.25

so that the **present ratio of 0.73 : 0.23 : 0.04 observed by
****WMAP**** seems to me
to be quite consistent with the ****cosmology****
of the ****D4-D5-E6-E7-E8 VoDou Physics
model** if Cold Dark Matter = PBH + MOND.

In my opinion, there are four Special Times in the history of our Universe:

- the
**Big Bang Beginning of Inflation**(about 13.7 Gy BP); - the
**End of Inflation**= Beginning of Decelerating Expansion (beginning of green line also about 13.7 Gy BP); - the
**End of Deceleration**(q=0) = Inflection Point = Beginning of Accelerating Expansion (purple vertical line at about z = 0.587 and about 7 Gy BP). According to a hubblesite web page credited to Ann Feild, the above diagram "... reveals changes in the rate of expansion since the universe's birth 15 billion years ago. The more shalow the curve, the faster the rate of expansion.**The curve changes noticeably about 7.5 billion years ago**, when objects in the universe began flying apart as a faster rate. ...". According to a CERN Courier web page: "... Saul Perlmutter, who is head of the Supernova Cosmology Project ... and his team have studied altogether some 80 high red-shift type Ia supernovae. Their results imply that**the universe was decelerating for the first half of its existence, and then began accelerating approximately 7 billion years ago**. ...". According to astro-ph/0106051 by Michael S. Turner and Adam G. Riess: "...**current supernova data ... favor deceleration at z > 0.5**...**SN 1997ff at z = 1.7**provides direct evidence for an early phase of slowing expansion if the dark energy is a cosmological constant ...". - the
**Last Intersection**of the Accelerating Expansion of our Universe with Linear Expansion (green line) from End of Inflation (first interesection) through Inflection Point (second intersection, at purple vertical line at about z = 0.587 and about 7 Gy BP) to the Third Intersection (at red vertical line at z = 0.145 and about 2 Gy BP), which is also around the times of the beginning of the Proterozoic Era and Eukaryotic Life, Fe2O3 Hematite ferric iron Red Bed formations, a Snowball Earth, and the start of the Oklo fission reactor. 2 Gy is also about 10 Galactic Years for our Milky Way Galaxy and is on the order of the time for the process of a collision of galaxies.

After the Last Intersection at the end of the Early Part of the Accelerating Expansion of our Universe, expansion of our Universe continues to accelerate with the Late Part of its Accelerating Expansion until New Universes are created by Quantum Fluctuation Black Holes. New Universe creation can happen many times at many Times (almost all of which are late).

Those four Special Times define four Special Epochs:

- The
**Inflation Epoch**, beginning with the Big Bang and ending with the End of Inflation. The Inflation Epoch is described by Zizzi Quantum Inflation, ending with Self-Decoherence of our Universe. - The
**Decelerating Expansion Epoch**, beginning with the Self-Decoherence of our Universe at the End of Inflation. During the Decelerating Expansion Epoch, the Radiation Era is succeeded by the Matter Era, and the Matter Components (Dark and Ordinary) remain more prominent than they would be under the "standard norm" conditions of Linear Expansion. - The
**Early Accelerating Expansion Epoch**, beginning with the End of Deceleration and ending with the Last Intersection of Accelerating Expansion with Linear Expansion. During Accelerating Expansion, the prominence of Matter Components (Dark and Ordinary) declines, reaching the "standard norm" condition of Linear Expansion at the end of the Early Accelerating Expansion Epoch at the Last Intersection with the Line of Linear Expansion. - The
**Late Accelerating Expansion Epoch**, beginning with the Last Intersection of Accelerating Expansion and continuing forever, with New Universe creation happening many times at Many Times. During the Late Accelerating Expansion Epoch, the Cosmological Constant /\ is more prominent than it would be under the "standard norm" conditions of Linear Expansion.

**NOW happens to be about 2 billion years **into the Late
Accelerating Expansion Epoch.

Our present insight that **the Time of Life on Earth, from the
Proterozoic begining of Eukaryotic Life to Present-Day Humanity,
covers the 2 billion years beginning with a ****Special
Time**** in the ****Time-History****
of our Universe** leads us to a better understanding of the
Unification of Gravity / Particle
Physics / Mathematics / Information
/ Consciousness, and perhaps to a better
understanding our our ultimate Fate.

Therefore:

and

It is interesting to compare the Special Time of the calculated ratio 0.67 : 0.27 : 0.06 with the D4-E5-E6-E7-E8 VoDou Physics model calculations of particle masses and force strength constants, because

- particle masses and force strength constants vary, due to renormalization, with ambient energy due to renormalization in much the same way as
- the cosmological ratio of densities of the Cosmological Constant /\, Cold Dark Matter, and Ordinary Matter vary with the Scale or Time of our expanding Universe.

For example, calculation of the QCD color force strength gives the number 0.6286, but that is only valid at the energy level of /\qcd = 245 MeV. To get the QCD force strength that you see around the W mass of about 91 GeV, you have to run the QCD force strength by renormalization equations, which, on a simple level, give a QCD force strength of about 0.106 at 91 GeV, which in my opinion may be a reasonably physically realistic result.

Zeldovich and Novikov say, in Stars and Relativity (Dover 1996, a reprint of their 1971 volume 1 of Relativistic Astrophysics), at page 33:

"... Often it is said that/\ =/= 0 means that gravitons have a nonzero rest mass.But /\ =/= 0 leads also to the result that, even in the absence of matter, spacetime cannot be flat everywhere. In curved spacetime the very definition of the mass of a graviton is no longer clear. ...".

Since /\ > 0 is necessary for the observed accelerating expansion of our Universe, and since around 67% of our Universe is made up /\ > 0 stuff, such as massive spin-2 gravitons related to Special Conformal transformations, and since our universe expansion is like pennies glued on a balloon, where the pennies ( gravitationally bound regions of clusters of galaxies and their galaxies, stars, and planets including Earth ) do NOT expand and the accelerated expansion is only of the balloon outside the pennies,

then

Zeldovich and Novikov say, in their 1983 volume 2 of Relativistic Astrophysics (Chicago 1983), at pages 668-669:

"... [A] side of the theory of gravitation consists of ascribing a definite "elasticity" to spacetime itself. The qualitative idea goes back to Clifford. If space can in principle be curved, then there must be a factor - the elasticity - by virtue of which space, with high precision, actually remains flat on the scales of the Earth, the solar system, and the Galaxy. Indeed, the elasticity idea corresponds to the termconst. INTEGRAL R dV in the GTR Lagrangian introduced by Einstein. Upon variation, this particular term gives the left-hand side of Einstein's equations, while the right-hand side of the equations represents the energy and momentum densities of real matter. ... According to ... an idea developed by Sakharov ...[in 1967]... the elasticity of space depends on vacuum polarization. From this point of view, the theory of gravity cannot even in principle exist without an account of all other fields (the electron, positron-electron, ... etc.), although the total practical contribution of these fields is expressed through the magnitude of the gravitational constant G.

The above account gives the situation as it was in 1971( see ...[ Zeldovich and Novikov, in Stars and Relativity (Dover 1996, a reprint of their 1971 volume 1 of Relativistic Astrophysics), at page 33, where they say "... In the vacuum, virtual particles with mass m and average separation L = hbar / mc are created. Their total proper energy is zero, so the gravitational interaction of the neighboring particles detemines the energy density of the vacuum:

... New developments that radically change the picture are allowed when one takes into account the conformal invariance of the fields describing the ... [photon], e+/-, ... and presumably the hadrons too. Indeed, it follows from the conformal invariance that the contribution of the enumerated fields and particles to the elasticity of the vacuum is negligibly small, of the order ofG m^2 / ( hbar c ) or ( G m^2 / ( hbar c ) ) ln( p_0 / m c ), where p_0 is a limiting momentum. Particles with zero rest mass contribute nothing at all; such a conclusion follows immediately from the realization that there is no vacuum polarization if m = 0 in a conformally flat space ...

... because the equation describing gravitational waves and their quanta, gravitons, is not conformally invariant ... a theory is possible in which only the spacetime is considered and in which interesting results are obtained concerning the gravitons and the curvature of the background spacetime due to the gravitational field of the gravitons. The gravitons, in addition, propagate in this background spacetime, so what is obtained is actually a closed picture for a graviton-background system ...".

In my opinion, contrary to my understanding of what Zeldovich and Novikov said in 1983, perhaps electron-positron phenomena could be useful when coupled with GraviPhotons of my D4-D5-E6-E7-E8 VoDou Physics model, which has 5 conformal graviphotons:

- 1 that scales/dilates spacetime, and its action is like just expanding or contracting space at a single given point, and its action is suppressed because of Feynman's factor of G / 3 c^2 that I use BOTH WAYS for input AND output of space warping; and
- 4 that do Special Conformal transformations. They have some GLOBAL NONLOCAL effects in which they can expand space at one point and produce a corresponding contraction of space at another point. In other words, their effects are globally conservative in that there is no total net input or output of energy, but they can take an energy input (space warp) at one point and "move it" to produce a corresponding energy output (space warp) at another point, sort of like the Fat Man plutonium bomb took in energy in the USA and released energy in Nagasaki.

If /\ = 0, with massless spin-2 gravitons and flat Minkowski background spacetime prevails in Gravitationally Bound Domains such as clusters of galaxies and their galaxies, stars, and planets including Earth, and corresponds to a Born Rule equilibrium vaccuum,

and

if /\ < 0, with massive spin-2 gravitons related to MOND and Black Holes are associated with Gravitationally Bound Domains such as clusters of galaxies and their galaxies, stars, and planets including Earth, but correspond to a non-Born Rule non-equilibrium vaccuum,

and

if /\ > 0, with massive spin-2 gravitons related to Special Conformal transformations and curved cone-space background spacetime, prevails in the rest of our Universe outside Gravitationally Bound Domains, and corresponds to a non-Born Rule non-equilibrium vacuum,

then

**is there a way for us here on Earth to use their ****different
vacuum energies**** ? **

Jack Sarfatti's physics/cosmology model has such a way that in my opinion is compatible with the conformal structure of the D4-D5-E6-E7-E8 VoDou Physics model. Here is a rough outline of how it might work:

There are 3 different vacua:

- 1 - a Born Rule equilibrium Ordinary Matter vacuum /\ = 0
- 2 - a non-Born Rule non-equilibrium Dark Energy vacuum /\ > 0
- 3 - a non-Born Rule non-equilibrium Dark Matter vacuum /\ < 0

Jack Sarfatti says "... They are different regions of the same unified local /\zpf(x) field - on different scales (Fourier transform, or in general a Wigner density and even a wavelet version of the Wigner density). /\zpf is a continuous variable with local stress-energy density tensor tuv(x)zpf = (c^4/8piG)/\zpf(x) ...".

Jack uses **a /\ = 0 Ordinary Matter superconductor as a
Josephson Junction to regulate the energy difference between /\ >
0 Dark Energy and /\ < 0 Dark Matter**. He says "... That's the
general idea. See Appendix C in ...[the
Sarfatti Nova paper]... . You use magnetic flux et-al phase
modulation to create exotic vacuum dark energy and dark matter
regions in the initial /\zpf = 0 non-exotic vacuum. ...

...[also]... There are clearly ...[possibly useful]... energy density differences ...[between /\ = 0 Ordinary vacuum and either or both of the /\ > 0 Dark Energy and /\ < 0 Dark Matter vacua]... if the different regions are there already in Nature as there are on large scale. ...

...[a rough estimate of the magnitude of the energies involved is]...

I use conventions where /\zpf > 0 gives positive zpf energy density with dominating equal and opposite negative zpf pressure (w = -1), but gravity effect in GR is ~ G(energy density + 3pressure) ...

...[in the equation

for the Josephson Junction regulator]... The giant wave local function is normalized to the actual superfluid number density like a single particle wave is normalized to probability density that integrates to 1. ... |< 0|e+(x)e-(x)|0 >|^2 = 1/Lp^3 ... corresponds to non-exotic /\zpf = 0 vacuum. ...".

As to how to construct such a Josephson Junction regulator, consider the related question:

which can be answered by opening Special Conformal Degrees of Freedom with electromagnetic currrents in 4 Rodin coils arranged in the geometry of a Fuller Vector Eqilibrium Cuboctahedron.

Such a Rodin Coil GateWay Junction might result from coupling of electron-positron phenomena with GraviPhotons of my D4-D5-E6-E7-E8 VoDou Physics model, which has 5 conformal graviphotons:

- 1 that scales/dilates spacetime, and its action is like just expanding or contracting space at a single given point. (Its action is suppressed because of Feynman's factor of G / 3 c^2.); and
- 4 that do Special Conformal transformations. (They have some global nonlocal effects in which they can expand space at one point and produce a corresponding contraction of space at another point. In other words, their effects are globally conservative in that there is no total net input or output of energy, but they can take an energy input (space warp) at one point and "move it" to produce a corresponding energy output (space warp) at another point, sort of like the Fat Man plutonium bomb took in the energy of construction of plutonium in the USA and released that energy as an explosion in Nagasaki.)

If a Rodin Coil Josephson Junction were used to access the energy of massive Special Conformal Cone-Space Vacuum Gravitons of /\ > 0 Dark Energy, it would be less like using a plutonium Fat Man bomb and more like using a U-235 Little Boy bomb or a deuterium/tritium fusion bomb, in that:

- U-235, deuterium, and tritium, like /\ > 0 Special Conformal Cone-Space Vacuum Gravitons, are far from the Earth-region prevailing stable state of nickle/iron nuclei or the /\ = 0 Flat Minkowski Vacuum, and
- U-235, deuterium, and tritium can with a small energy input be kicked out of their local stability to fall to a new (lower) level of local stability thus producing a large energy release, just as a small amount of electromagnetic energy might open a Rodin Coil GateWay Junction for large amounts of /\ > 0 Special Conformal Cone-Space Vacuum Energy to come to us on Earth from the underlying Vacuum.

The /\ = 0 Flat Minkowski vacuum here in our Gravitationally Bound Domain, including Earth, is very stable due to the prevailing Gravitational Binding Energy, so that spontaneous natural energy flows from the underlying /\ > 0 Special Conformal Cone-Space Vacuum are very rare or non-existent. That is fortunate for us here on Earth, because that any such spontaneous flow might cause our world to be flooded with huge amounts of energy, perhaps destroying our Earth.

If you try to use /\ > 0 Special Conformal Cone-Space Vacuum ZeroPoint Energy by using Rodin Coil GateWay Junctions, you must be careful to first solve the problem of storing the energetic /\ > 0 material in such a way that they do not blow up in your face (such as almost happened at Oak Ridge before Feynman stopped their practice of transporting U-235 in solution that was dangerously close to critical density, while over in the USSR, without Feynman, such "accidents" did actually occur).

Each Rodin coil of such a Rodin Coil GateWay Junction would have the geometry of a Hopf fibration of a 3-sphere S3 by Clifford circles.

There should be 4 coils, one for each of the 4 physical dimensions of SpaceTime, and they should be configured as 4 axes that are 3-dim projections of the 4-dim coordinate axes of the 4-dim 24-cell, i.e., as 4 axes of Fuller's Vector Equilibrium, the cuboctahedron,

The 4 Rodin Coil Clifford-Hopf Tori are indicated by the cyan, magenta, yellow, and green hexagonal "equators" of a cuboctahedron

which configuration is a 3-dimensional projection of the 4-dimensional 24-cell

Each of the 12 vertices of the cuboctahedron corresponds to 2 of the 24 vertices of the 24-cell, which 24 vertices are the vertices of a green cuboctahedron, a red octahedron, and a blue octahedron.

Here is a different perspective illustration, patterned after Fig. 172 of Geometry and the Imagination (Anschauliche Geometrie) by David Hilbert and S. Cohn-Vossen (Chelsea 1952), with 12 green vertices of a central cuboctahedron, 6 red vertices of an inner octahedron, and 6 blue vertices of an outer octahedron.

The 4 Rodin Coil Clifford-Hopf Tori of the cyan, magenta, yellow, and green hexagonal "equators" of a cuboctahedron appear on the 24-cell as four ( cyan, magenta, yellow, and green ) hexagonal rings. Since the 24-cell is self-dual, the 4 hexagonal rings can also be seen as 4 rings of 6 octahedral faces. Three such rings of octahedra are of the same type as the one illustrated here

where the common triangular faces of the 6 octahedra in the ring are shaded.

The fourth ring, corresponding to the green ring of 6 octahedra, all of which are in the central cuboctahedron, is of the type similarly illustrated here

The three similar rings can be thought of as space-like, while the distinct fourth ring can be thought of as timelike.

Note that the 6th octahderon of the distinct ring consists of the exterior of the outer octahedron, going all the way to infinity.

Note also that if you were to try to construct a Rodin coil, you would have to be careful that the loops are oriented correctly with respect to each other as shown in the 24-cell illustrations, and that the cuboctahedron projection illustration obscures some of that orientation information.

You should realize that flows through the Rodin coil would be described by the dual 24-cell to the 24-cell used in construction of the windings of the Rodin coil, and

**Such a Rodin Coil could be a GateWay Junction controlling .
**

As Jack Sarfatti has
noted, **the ****gravitationally
repulsive nature of /\ > 0**** material means that /\ >
0 material could be used as ****antigravity****
for transportation, etc., in ****Gravitationally
Bound Domains (including Earth)**.

As for regions of our Universe outside Gravitationally Bound
Domains, where /\ > 0 is the prevalent Vacuum State, **the
Special Conformal nature of /\ > 0 means that ****Special
Conformal SpaceWarp Drive**** could be used in regions of our
Universe outside ****Gravitationally
Bound Domains**.

As Richard Feynman says in Lecture 11.2 of his Feynman Lectures on Gravitation (Addison-Wesley 1995), at page 154:

"... we may give an interpretation of the theory of gravitation ... as follows: ... Consider a small three-dimensional sphere ... [ in a ] three-space perpendicular to the time axis ... Its actual radius exceeds the radius calculated by Euclidean geometry ... by an amount proportional ... [ by the factor ] G / 3 c^2 ... to the amount of matter inside the sphere ... one fermi per 4 billion metric tons ... we require the same result to hold in any coordinate system regardless of its velocity. ...".

The potential energy difference between the /\ > 0 Special Conformal Cone-Space Vacuum and the /\ = 0 Flat Minkowski Vacuum might be very great, on the order of Feynman's factor of G / 3 c^2 =

= 2 x 10^(-29) cm/g

The energy of an electromagnetic current needed for a Rodin Coil Josephson Junction GateWay might be very much smaller, so that a huge amount of energy might be obtainable here on Earth.

Perhaps Quantum Consciousness Resonance phenomena might be useful in making and controlling a Rodin Coil Josephson Junction GateWay (compare the energy sources of The Matrix and Akira).

"... It should be kept in mind that QM not only describes microscopic phenomena, but also macroscopic phenomena, such as superconductivity. Specifically, I would like to point out the following three conceptual tensions:

- (1) The spatial nonseparability of physical systems due to entangled states in QM, versus the complete spatial separability of all physical systems in GR ... which is a local realistic field theory. ...
- (2) The equivalence principle of GR, versus the uncertainty principle of QM.
- (3) The mixed state (e.g., of an entangled bipartite system, one part of which falls into a black hole; the other of which flies off to infinity) in GR, versus the pure state of such a system in QM. ...[this]... concerns the problem of the natures of information and entropy in QM and GR.

... These conceptual tensions originate from the superposition principle of QM, which finds its most dramatic expression in the entangled state of two or more spatially separated particles of a single physical system, which in turn leads to Einstein-Podolsky-Rosen (EPR) effects. It should be emphasized here that it is necessary to consider two or more particles for observing EPR phenomena, since only then does the configuration space of these particles no longer coincide with that of ordinary spacetime. ... This mathematical nonfactorizability implies a physical nonseparability of the system, and leads to instantaneous, space-like correlations-at-a-distance in the joint measurements of the properties (e.g., spin) of discrete events ... we have observed nonlocal features of the world. ... a fundamental spatial nonseparability of physical systems has been revealed ... the observed space-like EPR correlations occur on macroscopic, non-Planckian distance scales, where the conceptual tension (1) between QM and GR becomes most acute. ... there are new issues which crop up due to the long-range nature of the gravitational force, which are absent in special relativity, but present in general relativity. ... It is therefore natural to look to the realm of macroscopic phenomena associated with quantum fluids, rather than phenomena at microscopic, Planck length scales, in our search for ... experimental consequences. ...

... a macroscopically coherent quantum system, e.g., a quantum fluid such as the electron pairs inside a superconductor, usually possesses an energy gap which separates the ground state of the system from all possible excited states of the system. ... these quantum fluids are protectively entangled, in the sense that the existence of some sort of energy gap separates the nondegenerate ground state of the system from all excited states, and hence prevents any rapid decoherence due to the environment. Under these circumstances, the macroscopically entangled ground state of a quantum fluid, becomes a meaningful global concept, and the notion of nonlocality, that is, the spatial nonseparability of a system into its parts, enters in an intrinsic way into the problem of the interaction of matter with gravitational fields. ...

... there should exist a difference between classical and quantum matter in their respective responses to gravitational tidal fields. At a fundamental level, this difference arises from the quantum phase shift which is observable in the shift of the interference fringe pattern that results from an atom travelling coherently along two nearby, but intersecting, geodesics in the presence of spacetime curvature ...

... Another difference between a classical and a quantum liquid drop is the possibility of the presence of quantized vortices in the latter, along with their associated persistent, macroscopic current flows. These quantum flows possess quantized vorticities of ±h/m, where m is the mass of the superfluid atom. ...

... particles in a macroscopically coherent quantum many-body system, i.e., a quantum fluid, are entangled with each other in such a way that there arises an unusual "quantum rigidity" of the system, closely associated with what London called "the rigidity of the macroscopic wavefunction" ... One example of such a rigid quantum fluid is the "incompressible quantum fluid" in both the integer and the fractional quantum Hall effects ... This rigidity arises from the fact that there exists an energy gap (for example, the quantum Hall gap) which separates the ground state from all the low-lying excitations of the system. This gap, as pointed out above, also serves to protect the quantum entanglement present in the ground state from decoherence due to the environment, provided that the temperature of these quantum systems is sufficiently low. Thus these quantum fluids exhibit a kind of "gap-protected quantum entanglement." Furthermore, the gap leads to an evolution in accordance with the quantum adiabatic theorem: The system stays adiabatically in a rigidly unaltered ground state, which leads in first-order perturbation theory to quantum diamagnetic effects. Examples of consequences of this "rigidity of the wavefunction" are

- the Meissner effect in the case of superconductors, in which the magnetic field is expelled from their interiors, and
- the Chern-Simons effect in the quantum Hall fluid, in which the photon acquires a mass inside the fluid. ...

... The Meissner effect in a superconductor is closely analogous to the Higgs mechanism of high-energy physics, in which the physical vacuum also spontaneously breaks local gauge invariance, and can also be viewed as forming a condensate which possesses a single-valued complex order parameter with a well-defined local phase. From this viewpoint, the appearance of the London penetration depth for a superconductor is analogous in an inverse manner to the appearance of a mass for a gauge boson, such as that of the W or Z boson. Thus, the photon, viewed as a gauge boson, acquires a mass inside the superconductor, such that its Compton wavelength becomes the London penetration depth.

Similar considerations apply to the effect of the Chern-Simons term in the quantum Hall fluid. ...

... Closely related to this spontaneous symmetry breaking process is the appearance of Yang's off-diagonal long-range order (ODLRO) of the reduced density matrix in the coordinate-space representation for most of these macroscopically coherent quantum systems ... In particular, there seems to be no limit on how far apart Cooper pairs can be inside a single superconductor before they lose their quantum coherence. ODLRO and spontaneous symmetry breaking are both purely quantum concepts with no classical analogs. ...

... Due to its gyroscopic nature, the spin vector of an electron undergoes parallel transport during the passage of a GR wave. The spin of the electron is constrained to lie inside the space-like submanifold of curved spacetime. This is due to the fact that we can always transform to a co-moving frame, such that the electron is at rest at the origin of this frame. In this frame, the spin of the electron must be purely a space-like vector with no time-like component. This imposes an important constraint on the motion of the electron's spin, such that whenever the space-like submanifold of spacetime is disturbed by the passage of a gravitational wave, the spin must remain at all times perpendicular to the local time axis. If the spin vector is constrained to follow a conical trajectory during the passage of the gravitational wave, the electron picks up a Berry phase proportional to the solid angle subtended by this conical trajectory after one period of the GR wave. In a manner similar to the persistent currents induced by the Berry phase in systems with ODLRO ... such a Berry phase induces an electrical current in the quantum Hall fluid, which is in a macroscopically coherent ground state ... This macroscopic current generates an EM wave. Thus a GR wave can be converted into an EM wave. By reciprocity, the time-reversed process of the conversion from an EM wave to a GR wave must also be possible. ...

... While the precise form of the nonrelativistic Hamiltonian is not known for the many-body system in a weakly curved spacetime consisting of electrons in a strong magnetic field, I conjecture that it will have the form ...

where the particle index, the spin, and the tetrad indices have all been suppressed. Upon expanding the square, it follows that for a quantum Hall fluid of uniform density, there exists a cross-coupling or interaction Hamiltonian term of the form

which couples the electromagnetic a field to the gravitational b field. In the case of time-varying fields, a(t) and b(t) represent EM and GR radiation, respectively. ...

... In first-order perturbation theory, the quantum adiabatic theorem predicts that there will arise the cross-coupling energy between the two radiation fields mediated by the quantum fluid ... For the adiabatic theorem to hold, there must exist an energy gap Egap (e.g., the quantum Hall energy gap) separating the ground state from all excited states, in conjunction with the approximation that the time variation of the radiation fields must be slow compared to the gap time hbar / E_gap. This suggests that under these conditions, there might exist an interconversion process between these two kinds of classical radiation fields mediated by this quantum fluid ...

... The question immediately arises: EM radiation is fundamentally a spin 1(photon) field, but GR radiation is fundamentally a spin 2 (graviton) field. How is it possible to convert one kind of radiation into the other, and not violate the conservation of angular momentum? The answer: The EM wave converts to the GR wave through a medium. Here specifically, the medium of conversion consists of a strong DC magnetic field applied to a system of electrons. This system possesses an axis of symmetry pointing along the magnetic field direction, and therefore transforms like a spin 1 object. When coupled to a spin 1 (circularly polarized) EM radiation field, the total system can in principle produce a spin 2 (circularly polarized) GR radiation field, by the addition of angular momentum. However, it remains an open question as to how strong this interconversion process is between EM and GR radiation. ... the size of the conversion efficiency of this transduction process needs to be determined by experiment. ...

... We can see more clearly the physical significance of the interaction Hamiltonian H_int = a . b once we convert it into second quantized form and express it in terms of the creation and annihilation operators for the positive frequency parts of the two kinds of radiation fields, as in the theory of quantum optics, so that in the rotating-wave approximation

where the annihilation operator a and the creation operator a* of the single classical mode of the plane-wave EM radiation field corresponding the a term, obey the commutation relation [a, a*] = 1, and where the annihilation operator b and the creation operator b* of the single classical mode of the plane-wave GR radiation field corresponding to the b term, obey the commutation relation [b, b*] = 1. (This represents a crude, first attempt at quantizing the gravitational field, which applies only in the case of weak, linearized gravity.) The first term a* b then corresponds to the process in which a graviton is annihilated and a photon is created inside the quantum fluid, and similarly the second term b* a corresponds to the reciprocal process, in which a photon is annihilated and a graviton is created inside the quantum fluid. ...

... In the case of superconductors, Cooper pairs of electrons possess a macroscopic phase coherence, which can lead to an Aharonov-Bohm-type interference absent in the ionic lattice.

Similarly, in the quantum Hall fluid, the electrons will also possess macroscopic phase coherence, ... which can lead to Berry-phase-type interference absent in the lattice.

Furthermore, there exist ferromagnetic superfluids with intrinsic spin, in which an ionic lattice is completely absent, such in spin-polarized atomic BECs ... and in superfluid helium 3. In such ferromagnetic quantum fluids, there exists no ionic lattice to give rise to any classical response which could prevent a quantum response to tidal gravitational radiation fields. The Berry-phase-induced response of the ferromagnetic superfluid arises from the spin connection (see the above minimal-coupling rule, which can be generalized from an electron spin to a nuclear spin coupled to the curved spacetime associated with gravitational radiation), and leads to a purely quantum response to this radiation. The Berry phase induces time-varying macroscopic quantum flows in this ferromagnetic ODLRO system ... which transports time-varying orientations of the nuclear magnetic moments. This ferromagnetic superfluid can therefore also in principle convert gravitational into electromagnetic radiation, and vice versa, in a manner similar to the case discussed above for the ferromagnetic quantum Hall fluid.

Thus we expect there to exist differences between classical and quantum fluids in their respective linear responses to weak external perturbations associated with gravitational radiation.

Like superfluids, the quantum Hall fluid is an example of a quantum fluid which differs from a classical fluid in its current-current correlation function ... in the presence of GR waves. In particular, GR waves can induce a transition of the quantum Hall fluid out of its ground state only by exciting a quantized, collective excitation across the quantum Hall energy gap. This collective excitation would involve the correlated motions of a macroscopic number of electrons in this coherent quantum system. Hence the quantum Hall fluid is effectively incompressible and dissipationless, and is thus a good candidate for a quantum antenna. ...

... In general relativity, there exists in general no global time coordinate that can apply throughout a large system, since for nonstationary metrics, such as those associated with gravitational radiation, the local time axis varies from place to place in the system. It is therefore necessary to set up operationally a general laboratory frame by which an observer can measure the motion of slowly moving test particles in the presence of weak, time-varying gravitational radiation fields. For either a classical or quantum test particle, the result is that its mass m should enter into the Hamiltonian through the replacement of p - eA by p - eA - mN, where N is the small, local tidal velocity field induced by gravitational radiation on a test particle located at X_a relative to the observer at the origin (i.e., the center of mass) of this frame ... Due to the quadrupolar nature of gravitational tidal fields, the velocity field N for a plane wave grows linearly in magnitude with the distance of the test particle from the center of mass, as seen by the observer located at the center of mass of the system. Therefore, in order to recover the standard result of classical GR that only tidal gravitational fields enter into the coupling of radiation and matter, one expects in general that a new characteristic length scale L corresponding to the typical size of the distance X_a separating the test particle from the observer, must enter into the determination of the coupling constant between radiation and matter. For example, L can be the typical size of the detection apparatus (e.g., the length of the arms of the Michelson interferometer used in LIGO), or of the transverse Gaussian wave packet size of the gravitational radiation, so that the coupling constant associated with the Feynman vertex for a graviton-particle interaction becomes proportional to the extensive quantity sqrt(GL), instead of an intensive quantity involving only sqrt(G). For the case of superconductors, treating Cooper pairs of electrons as bosons, we would expect the above arguments would carry over with the charge e replaced by 2e and the mass m replaced by 2m. ...

... Returning to the general problem of quantum fields embedded in curved spacetime, we recall that the ground state of a superconductor, which possesses spontaneous symmetry breaking, and therefore ODLRO, is very similar to that of the physical vacuum, which is believed also to possess spontanous symmetry breaking through the Higgs mechanism. In this sense, therefore, the vacuum is "superconducting." The question thus arises: How does a ground or "vacuum" state of a superconductor, and other quantum fluids viewed as ground states of nonrelativistic quantum field theories with ODLRO, interact with dynamically changing spacetimes, e.g., a GR wave? ...

... we suspect that there might exist superconductors, viewed as quantum fluids, which are transducers between EM and GR waves ... If the quantum transducer conversion efficiency turns out to be high, this will lead to an avenue of research which could be called "gravity radio." ... We have obtained an upper limit on the conversion efficiency for YBCO at liquid nitrogen temperature of 1.6 x 10^(-5). Details of this experiment will be reported elsewhere ...[see gr-qc/0304026 ]...".

Perhaps Quantum Consciousness Resonance phenomena might be useful in using Chiao QM-GR Transduction of EM-Gravity to make and control a Rodin Coil Josephson Junction GateWay (compare the energy sources of The Matrix and Akira).

[ July 2004 note by Frank D. (Tony) Smith, Jr., on

Consider the experimental results mentioned in the Beck and Mackey paper at http://xxx.lanl.gov/abs/astro-ph/0406504 in which they say:

"... the zero-point term has proved important in

- explaining X-ray scattering in solids ... ;
- understanding of the Lamb shift ... in hydrogen ... ;
- predicting the Casimir effect ... ;
- understanding the origin of Van der Waals forces ... ;
- interpretation of the Aharonov-Bohm effect ... ;
- explaining Compton scattering ... ; and
- predicting the spectrum of noise in electrical circuits ... .

It is this latter effect that concerns us here. ... We predict that the measured spectrum in Josephson junction experiments must exhibit a cutoff at the critical frequency nu_c ... [ corresponding to the currently observed Dark Energy density 0.73 x critical density = 0.73 x 5.3 GeV/m^3 = 3.9 GeV/m^3 ]... If not, the corresponding vacuum energy density would exceed the currently measured dark energy density of the universe. ... The energy associated with the computed cutoff frequency nu_c ...[ about 1.7 x 10^12 Hz ]...

coincides with current experimental estimates of neutrino masses. .. It is likely that the Josephson junction experiment only measures the photonic part of the vacuum fluctuations, since this experiment is purely based on electromagnetic interaction. ...

If it is possible to increase the maximum frequency by a factor of about 3, then this experiment could provide valuable information on the nature of dark energy. ...

If the frequency cutoff is observed, it could be used to determine the fraction ... of dark energy density that is produced by electromagnetic processes ...

Finally, we conjecture that it will be interesting to re-analyze experimentally observed 1/f noise in electrical circuits under the hypothesis that it could be a possible manifestation of suppressed zero-point fluctuations. ... Our simple theoretical considerations show that 1/f noise arises naturally if bosonic vacuum fluctuations are suppressed by fermionic ones. ...".

AS TO THE ISSUE OF LORENTZ INVARIANCE OF A CUTOFF at higher energies than have yet been observed in Josephson Junction fluctuations, my view is that you need to have ALL the forces (gravity, color, weak, and QED) to get cancellations that give a cosmological constant near zero, and when you get energetic enough to introduce neutrinos, you are effectively bringing in the weak force that is felt by the neutrinos so that you begin to change the equation (or introduce a cut-off) at that energy. Since the cut-off is due to introduction of weak force effects (and probably NOT a simple hard-line energy/frequency cut-off, which could violate Lorentz symmetry) it probably is a cut-off regulated by the gauge symmetry of the weak force. As Lubos Motl said in an spr post : "... cutoffs ...[can be]... Lorentz invariant ... the gauge symmetries: the regulators must be of specific kind to preserve these kinds of symmetry - but they almost always preserve Lorentz symmetry. ...", so the cut-off due to the phasing in of the weak force probably does not violate Lorentz symmetry. As you go to higher and higher energies, you introduce more and more forces, etc, and in the high-energy limit of D4-D5-E6-E7-E8 VoDou Physics there are cancellations due to subtle supersymmetry. AS TO EXPERIMENTAL RESULTS, Beck and Mackey say: 1 - the critical density in our universe now is about 5 GeV/m^3 2 - it is made up of Dark Energy : Dark Matter : Ordinary Matter in a ratio DE : DM : OM = 73 : 23 : 4 3 - the density of the various types of stuff in our universe now is DE = about 4 GeV/m^3 DM = about 1 GeV/m^3 OM = about 0.2 GeV/m^3 4 - the density of vacuum fluctuations already observed in Josephson Junctions is about 0.062 GeV/m^3 which is for frequencies up to about 6 x 10^11 Hz 5 - the radiation density (for photons) varies with frequency as the 4th power of the frequency, i.e., as ( pi h / c^3 ) nu^4 6 - if Josephson Junction frequencies were to be experimentally realized up to 2 x 10^12 Hz, then, if the photon vacuum fluctuation energy density formula were to continue to hold, the vacuum energy density would be seen to be 0.062 x (20/6)^4 = = about 7 GeV/m^3 which exceeds the total critical density of our universe now 7 - to avoid such a divergence being physically realized, neutrinos should appear in the vacuum at frequencies high enough that E = h nu exceeds their mass of about 8 x 10^(-3) eV, or at frequencies over about 1.7 x 10^12 Hz 8 - if Josephson Junctions could be developed to see vacuum fluctuation frequencies up to 10^12 Hz, and if the photon equation were to hold there, then the obseved vacuum fluctuation density would be about 0.5 GeV/m^3 which is well over the 0.2 GeV/m^3 Ordinary Matter energy density which means that DE and/or DM COMPONENTS WOULD BE SEEN IN VACUUM FLUCTUATIONS IN JOSEPHSON JUNCTIONS THAT GO UP TO 10^12 HZ FREQUENCY As to the experimental question: HOW TO DESIGN A 10^12 HZ JOSEPHSON JUNCTION ? A PhysicsWeb article by Belle Dume at http://physicsweb.org/article/news/8/6/17 describes the Beck and Mackey paper, saying "... In 1982, Roger Koch and colleagues, then at the University of California at Berkeley and the Lawrence Berkeley Laboratory, performed an experiment in which they measured the frequency spectrum of current fluctuations in Josephson junctions. Their system was cooled to millikelvin temperatures so that thermal vibrations were reduced to a minimum, leaving only zero-point quantum fluctuations. ...". So, our junction must be cooled to a few millikelvin, which was done back in 1982, which means that the next question is how to find a junction sensitive to terahertz fluctuations. Here are a couple of relevant references: According to a paper by at http://www.iop.org/EJ/abstract/0953-2048/15/12/309 Terahertz frequency metrology based on high-Tc Josephson junctions J Chen1, H Horiguchi1, H B Wang1, K Nakajima1, T Yamashita2 and P H Wu3 1 Research Institute of Electrical Communication, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan 2 New Industry Creation Hatchery Center, Tohoku University, 04 Aza-aoba, Aramaki, Aoba-ku, Sendai 980-8579, Japan 3 Department of Electronic Science and Engineering, University of Nanjing, Nanjing 210093, People's Republic of China Received 1 July 2002 Published 22 November 2002: "... Using YBa2Cu3O7/MgO bicrystal Josephson junctions operating between 6-77 K, we have studied their responses to monochromatic electromagnetic radiation from 50 GHz to 4.25 THz. We have obtained direct detections for radiation at 70 K from 50 GHz to 760 GHz and at 40 K from 300 GHz to 3.1 THz. ...". Some details of how to make such things were outlined at http://fy.chalmers.se/~tarasov/e1109m_draft.htm by E. Stepantsov a,b, M. Tarasov a,c, A.Kalabukhov a,d, T. Lindströoem a, Z. Ivanov a, T. Claeson a a MINA, Chalmers University of Technology and Göteborg University, GothenburgGöteborg, SE-41296, Sweden b Institute of Crystallography, Leninsky Prosp 59, Moscow 117333, Russia c Institute of Radio Engineering and Electronics, Mokhovaya 11, Moscow 101999, Russia d Department of Physics, Moscow State University, 119899 Moscow, Russia dated August 2001 "... Submicron YBCO bicrystal Josephson junctions and devices for high frequency applications were designed, fabricated and experimentally studied. The key elements of these devices are bicrystal sapphire substrates. ... A technological process based on deep ultraviolet photolithography using a hard carbon mask was developed for the fabrication of 0.4-0.6 mm wide Josephson junctions. ... These junctions were used as Josephson detectors and spectrometers at frequencies up to 1.5 THz ...". As to the possibility of using arrays of Josephson junctions, here is a relevant article: A paper entitled Averaged Equations for Distributed Josephson Junction Arrays at http://www.physics.gatech.edu/mbennett/dist2003.pdf by Matthew Bennett and Kurt Wiesenfeld says: "... The Kirchhoff limit is valid provided the size of the system is small compared to the wavelength of the electromagnetic radiation. As it happens, the twin technological goals of generating higher operating frequencies ... and larger output powers (and thus more junctions) both work against this limit. ... To take an example, an array operating at 300 GHz - not a particularly high frequency for Josephson junctions - corresponds to a wavelength of 0.4 millimeters when the index of refraction is 2.5; for a typical spacing of 10 micrometers, this is about the same size as an array of about 40 junctions - not a particularly large number for Josephson arrays ... at higher frequencies the current in the wire is not necessarily spatially uniform, so the wire becomes a significant dynamical entity which couples the junctions along its length. ... we model the wire as a lossless transmission line ... ... The resonant case is especially revealing, and leads to significant physical insight into achieving attracting synchronized dynamics. The tighter the clusters, the more likely it is that phase locked solutions appear. ... There are also hints that distributed arrays exhibit fundamentally different phenomena than their lumped counterparts. In one case, experiments on distributed Josephson arrays reported evidence of super-radiance ...". Here is picture that I have in my mind for building a Josepson Junction device for exploring vacuum fluctuations: Consider the nested tori and linked circles of a Clifford-Hopf 3-sphere fibration. This picture

shows one torus, so imagine a lot of tori nested as in this picture

These pictures

show that for any given torus in the nesting the circles are interlinked similarly to 24-cell paths. Let each circle be a superconducting wire carrying some current, and let all the circles be embedded in an insulator so that the whole thing has characteristics of a lot of Josephson Junctions and then play with various magnetic field configurations and then watch what happens.

[[ 2009 addendum -

In their paperHigher order Josephson effectsarXiv 0808.1892 Roman V. Buniy and Thomas W. Kephart said: "... Gaussian linking of superconducting loops containing Josephson junctions with enclosed magnetic fields give rise to interference shifts in the phase that modulates the current carried through the loop, proportional to the magnitude of the enclosed flux. We generalize these results tohigher order linking of a superconducting loop with several magnetic solenoids, and show there may beinterference shifts proportional to the product of two or more fluxes. ... The simplest example is a Borromean ring arrangement ...... where the semiclassical path corresponds to one ring, which has higher order linking with two flux tubes carrying fluxes PHI_1 and PHI_2, which make up the other two rings. We found the phase shift in this system is ...[ proportional to the product PHI_1 PHI_2 ]... Higher order cases were explored in ...[ hep-th/0611335 and hep-th/0611336 ]... and shown to be related to commutator algebras of homotopy generators of the configuration space R3 \ { T1 u T2 } , where T1 and T2 are the tubes containing the fluxes. ... The same general logic can be applied to systems of superconductors, Josephson junctions, and magnetic fluxes where the Josephson effect can arise ...". ]]

In order to get up to the terahertz energy level you might have to fabricate the thing on sub-millmeter scales, which should be fun. When you get down to micron - nanometer scales, you get to scales of subcellular biological structures such as microtubules and centrioles (this picture

shows centriole structure), so maybe evolution has already built some related stuff into our cells, and maybe this stuff is on the borderline between conventional semiconductor/superconductor fabrication and biological growth of structures.

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