Roger Penrose's diagram for Minkowski Space-Time of Special Relativity - Prelude to Einstein's General Relativity of Gravity

From my book Star Gate under construction (following Hawking & Ellis "The Large Scale Structure of Space-Time", Cambridge.

The intrinsic space-time geometry is only in the non-gravity force-free geodesic structure. There is no objective intrinsic gravity force in Einstein's theory of gravity. There is such an objective gravity force in Newton's older theory. Einstein eliminates Newton's pure gravity force acting at a distance replacing it with local variable curvature, i.e. geodesic deviations of neighboring passive test particles. Any attempt to restore Newton's gravity in Einstein's theory as another valid way of interpreting Einstein's theory is crackpot, inconsistent and displays a fundamental lack of understanding of what John Archibald Wheeler called "Einstein's Vision." Non-geodesics have no fundamental relation to the intrinsic geometry of spacetime. You cannot have non-geodesic paths of test particles without a non-gravity force like the long-range electromagnetic force. You cannot "pull g's" i.e. feel "weight" without a non-gravity force pushing you off a timelike geodesic inside the local light cone.

Geodesics are the straightest EXTREMAL paths in curved space-time.

Note that timelike geodesics are the longest paths in experienced proper time along them in the sense of the action principle of particle mechanics from the calculus of variations, i.e. neighboring bundle of paths with same starting and ending points. Virtual nongeodesic paths without non-gravity forces in this sense are quantum gravity zero point vacuum fluctuations in the Feynman path integral expression for the quantum amplitude of a classical geodesic path. Spacelike geodesics are the shortest straightest paths outside the light cone. Null geodesics have zero length. Real on-mass-shell faster than light tachyons do not exist in globally flat quantum field theories. They signal a vacuum instability as in the Higgs mechanism for the macro-quantum coherent origin of inertia and gravity as curvature. The Haisch-Puthoff model for the origin of inertia and gravity from random locally incoherent electromagnetic zero point fluctuations is wrong IMO.

A useful local nongeodesic "LNIF" frame in curved spacetime is the HOVERING non-geodesic "shell frame" at a fixed distance from a source. However such a frame does not always exist, e.g. inside the black hole null surface event horizon one-way membrane trapped surfaces containing null geodesics. Misunderstanding the contingent nature of the this admittedly useful frame, when it exists, leads one to delusionary ideas that, for example, with the SSS source M

g = GM/r^2

is an objective gravity force even in Einstein's GR. That is not true at all. That formula simply tells you how much rocket thrust you need in space to keep at a fixed distance from the source. It also tells you your weight per mass if you stand on a rigid surface of circumference 2pir encircling mass M.

The "Hilbert error" claim that there are no SSS event horizons is also crackpot IMO.

1. Globally flat Minkowski space-time
The metric in Cartesian coordinates is (c = 1)

ds^2 = -(dx^4)^2 + (dx^1)^2+ (dx^2)^2 + (dx^3)^2

Here the geodesics of maximal proper time are

x^a(affine parameter) = b^a(affine parameter) + c^a

Theorem: any two points in globally flat spacetime are connected by a unique geodesic.
Proof needs fancy formal stuff about exponential map of tangent space to manifold. See Hawking & Ellis for details.

Use the global coordinate transformation to spherical polar coordinates

x^4 = t
x^3 = rcostheta
x^2 = rsinthetacosphi
x^3 = rsinthetasinphi

theta is latitude on celestial sphere centered at r = 0
phi is longitude

Do the differential calculus with product rule to get

ds^2 = - dt^2 + dr^2 + r^2[(dtheta)^2 + sin^2theta(dphi)^2]

There is a non-physical coordinate singularity at r = 0 where the two angles theta & phi are undefined.

Theta ranges from 0 to pi, phi from 0 to 2pi, r from zero to infinity.

The choice of r = 0 in this unstable pre-inflationary pre Big Bang globally flat false vacuum is arbitrary here of course.

2. Wheeler-Feynman type of trick

Use the past to future retarded and future to past advanced light cone radial "null coordinates"

v = t + r i.e. advanced destiny wave back from the future (retro-causal future light cone)

w = t - r i.e. retarded history wave toward the future (past light cone)

Both v & w range from -infinity to + infinity

the GLOBAL FRAME INVARIANT metric field is then

ds^2 = -dudv - (1/4)(v - w)^2[(dtheta)^2 + sin^2theta(dphi)^2]

note that [(dtheta)^2 + sin^2theta(dphi)^2] describes a unit 2D spherical surface S2. Every "point" in the t-r plane is actually an S2 with radius r.

The v = constant, w = constant hypersurfaces are made from light cone null geodesics. Their intersection is a sphere

i.e. all the tangent vectors inside those hypersurfaces are null because no dv^2 & dw^2 terms.

v(w),av(w),bn^a^b = 0

,a is ordinary partial derivative

Penrose diagram for globally flat Minkowski spacetime to make infinity finite.

v = tanp

w = tanq

both p & q range from - pi/2 to + pi/2

Therefore, algebra & trig give

ds^2 = sec^2p sec^2q{-dpdq + (1/4)sin^2(p - q)[(dtheta)^2 + sin^2theta(dphi)^2]}

There exists a conformal map to

ds*^2 = -4dpdq + sin^2(p - q)[(dtheta)^2 + sin^2theta(dphi)^2]

i.e.

ds^2 = (1/4)sec^2(t' + r')sec^2(t' - r')ds*^2

Where we define

t' = p + q

r' = p - q

t' + r' ranges from -pi to pi

t' - r' ranges from -pi to pi

r' > 0

Therefore, algebra demands

ds*^2 = - (dt')^2 + (dr')^2 + sin^2r'[(dtheta)^2 + sin^2theta(dphi)^2]

which is LOCALLY a piece of the Einstein static universe.

Thus the WHOLE OF GLOBALLY FLAT MINKOWSKI SPACE-TIME is given by the FINITE REGION

t' + r' ranges from -pi to pi

t' - r' ranges from -pi to pi

r' > 0

of

ds^2 = (1/4)sec^2(t' + r')sec^2(t' - r')ds*^2

The original coordinates t & r are in

2t = tan[(1/2)(t'+r')] + tan[(1/2)(t'-r')]

2r = tan[(1/2)(t'+r')] - tan[(1/2)(t'-r')]


Suppress theta & phi, then the 1 + 1 string analog Einstein universe is globally equivalent to the unit circle S1, i.e. x^2 + y^2 = 1 imbedded in ANYONIC quantum well 2 + 1 Minkowski with

ds^2 = - dt^2 + dx^2 + dy^2

Note we really mean (ds)^2, (dt)^2 etc.

The full 4D Einstein static universe with his original cosmological constant /\ is the unit S^3

x^2 + y^2 + z^2 + w^2 = 1

imbedded in Kaluza-Klein 5D hyperspace

ds^2 = - dt^2 + dx^2 + dy^2 + dz^2 + dw^2

"One therefore has the situation: the whole of Minkowski space-time is conformal to the region

t' + r' ranges from -pi to pi

t' - r' ranges from -pi to pi

r' > 0

of the Einstein static universe, that is the shaded region of Fig 14. The boundary of this region may therefore be thought of as representing the conformal structure of infinity of Minkowski spacetime. It consists of the null surfaces p = +pi/2 labeled I^+ and q = -pi/2 labeled I^-, together with the points (p = pi/2,q = pi/2) (labeled i^+), (p = pi/2,q = - pi/2) (labeled i^0) and (p = -pi/2,q = -pi/2) (labeled i^-). Any future directed timelike geodesic in Minkowski space approaches i^+(i^-) for large positive (negative) values of its affine parameter, so one can regard any timelike geodesic as originating at i^- and finishing at i^+. Similarly one can regard null geodesics as originating at I^- and ending on I^+, while spacelike geodesics both originate and end at i^0. Thus one may regard i^+ and i^- as representing future and past timelike infinity, I^+ and I^- as representing future and past null infinity, and i^0 as representing spacelike infinity. (However nongeodesics do not obey these rules; e.g. nongeodesic timelike curves may start on I^- and end on I^+.) Since any Cauchy surface intersects all timelike and null geodesics, it is clear it will appear as a cross-section of the space everywhere reaching the boundary at i^0. One can also represent the conformal structure at infinity by drawing a diagram of the (t',r') plane. Each point of this diagram represents a sphere S2 and radial null geodesics are represented as lines at +- pi/4. In fact, the structure of infinity of any spherically symmetric spacetime can be represented by a diagram of this sort, which we call a Penrose diagram. On such diagrams, we shall represent infinity by single lines, the origin of polar coordinates by dotted lines, and irremovable singularities of the metric by double lines. ... Finally, ... one can obtain spaces locally identical to (Minkowski) but with different large scale topological properties by identifying points which are equivalent under a discrete isometry without fixed point ..." 5.1 Hawking and Ellis.


http://content.answers.com/main/content/wp/en/thumb/7/7c/180px-Penrose.PNG

Anyons, Weyl Curvature & Arrow of Time

1. The Weyl curvature tensor is zero in 2 + 1 spacetime.
2. Therefore, the gravity entropy is zero there. There is only a Ricci tensor.
3. In the World Hologram, the anyonic 2 + 1 spacetime boundary of 3 + 1 space-time is more fundamental.
4. The 2 + 1 space-time can only have zero gravity entropy if Penrose is right.
This suggests the the initial singularity is 2 + 1 space-time with zero-entropy in order to have the correct Arrow of Time.
5. Note that the dark energy and dark matter as zero point energy of negative and positive pressures respectively on larger and short scales respectively are virtual sources of zero entropy Ricci tensor.


This mathematical concept becomes useful in the physics of two-dimensional systems such as sheets of graphite or the quantum Hall effect. In space of three dimensions (or more), elementary particles have tightly constrained quantum numbers and, in particular, are restricted to being fermions or bosons. In two-dimensional systems, however, quasiparticles are observed whose quantum states range continuously between fermionic and bosonic, taking on any quantum value in between. Frank Wilczek coined the term "anyons" in 1982 to describe such particles.
Let's say we have two identical particles on a plane. If we interchange both particles so that each particle travels counterclockwise for half a cycle around the center of both particles, the wave function of the system changes by a factor of eiθ where θ is an angle which only depends upon the type of particle in question. If θ is zero, we have a boson and if θ is π we have a fermion. For any other value, we have an anyon. If we have two particles a and b, which may or may not be identical, then their mutual statistics is the change in the phase factor, which is picked up after particle b is rotated counterclockwise around particle a for one full cycle. The mutual statistics may be completely unrelated to the interchange angle between two identical particles.
http://en.wikipedia.org/wiki/Anyon

Weyl curvature hypothesis
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This article or section is in need of attention from an expert on the subject.
Please help recruit one, or improve this page yourself if you can. See discussion page for details.
This article concerns Roger Penrose's 1979 Weyl curvature hypothesis, which would justify spatial homogeneity and isotropy of the observable part of the Universe in the Big Bang model. A different article discusses Weyl's postulate, which is an assumption relating to separation of space and time in the Big Bang model.
The Weyl curvature hypothesis, which arises in the application of Albert Einstein's general theory of relativity to physical cosmology, was introduced by the British mathematician and theoretical physicist Sir Roger Penrose in an article in 1979 [1] in an attempt to provide explanations for two of the most fundamental issues in physics. On the one hand one would like to account for a Universe which on its largest observational scales appears remarkably spatially homogeneous and isotropic in its physical properties (and so can be described by a simple Friedmann-Lemaître model), on the other hand there is the deep question on the origin of the second law of thermodynamics.
Penrose suggests that the resolution of both of these problems is rooted in a concept of the entropy content of gravitational fields. Near the initial cosmological singularity (the Big Bang), he proposes, the entropy content of the cosmological gravitational field was extremely low (compared to what it theoretically could have been), and started rising monotonically thereafter. This process manifested itself e.g. in the formation of structure through the clumping of matter to form galaxies and clusters of galaxies. Penrose associates the initial low entropy content of the Universe with the effective vanishing of the Weyl curvature tensor of the cosmological gravitational field near the Big Bang. From then on, he proposes, its dynamical influence gradually increased, thus being responsible for an overall increase in the amount of entropy in the Universe, and so inducing a cosmological arrow of time.
The Weyl curvature represents such gravitational effects as tidal fields and gravitational radiation. Mathematical treatments of Penrose's ideas on the Weyl curvature hypothesis have been given in the context of isotropic initial cosmological singularities e.g. in the articles [2] ,[3] ,[4] ,[5]. Penrose views the Weyl curvature hypothesis as a physically more credible alternative to cosmic inflation (a hypothetical phase of accelerated expansion in the early life of the Universe) in order to account for the presently observed almost spatial homogeneity and isotropy of our Universe [6].
http://en.wikipedia.org/wiki/Weyl_curvature_hypothesis

Weyl tensor
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In differential geometry, the Weyl curvature tensor, named after Hermann Weyl, is the traceless component of the Riemann curvature tensor. In other words, it is a tensor that has the same symmetries as the Riemann curvature tensor with the extra condition that its Ricci curvature must vanish.
In dimensions 2 and 3 the Weyl curvature tensor vanishes identically. In dimensions ≥ 4, the Weyl curvature is generally nonzero.
The Weyl tensor can be obtained from the full curvature tensor by subtracting out various traces. This is most easily done by writing the Riemann tensor as a (0,4) valent tensor (by contracting with the metric). The (0,4) valent Weyl tensor is then



where n is the dimension of the manifold, g is the metric, R is the Riemann tensor, Ric is the Ricci tensor, s is the scalar curvature, and hOk denotes the Kulkarni-Nomizu product of two symmetric (0,2) tensors:










The ordinary (1,3) valent Weyl tensor is then given by contracting the above with the inverse of the metric.
The Weyl tensor has the special property that it is invariant under conformal changes to the metric. That is, if g′ = f g for some positive scalar function then the (1,3) valent Weyl tensor satisfies W′ = W. For this reason the Weyl tensor is also called the conformal tensor. It follows that a necessary condition for a Riemannian manifold to be conformally flat is that the Weyl tensor vanish. It turns out that in dimensions ≥ 4 this condition is sufficient as well. In dimension 3 the vanishing of the Cotton tensor is a necessary and sufficient condition for the Riemannian manifold being conformally flat.
The Weyl tensor is given in components by



where Rabcd is the Riemann tensor, Rab is the Ricci tensor, R is the Ricci scalar (the scalar curvature) and [] refers to the antisymmetric part.
[edit]

Wikipedia articles on physics by Chris Hillman who works with John Baez
Critique of Yilmaz theory I agree 100% with Chris Hillman on
Yilmaz theory of gravitation
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The Yilmaz theory of gravitation is an attempt by Huseyin Yilmaz and a handful of coworkers to formulate a classical field theory of gravitation which closely mimics general relativity in weak-field conditions, but in which event horizons cannot appear.
(Orthographic caveat: in Turkish, Yilmaz's name is properly written Hüseyin Yılmaz; we will avoid this spelling because English-speaking readers are likely to misread the ı as i, which could cause technical difficulties. The spelling we use is the one Yilmaz adopts in the arXiv.)
Yilmaz's work has been sharply criticized on various grounds, including the claims that
his proposed field equation is ill-defined,
the two desiderata above are incompatible (event horizons can occur in weak field situations according to gtr, in the case of a supermassive black hole).
Yilmaz vigorously disputes these criticisms. Nonetheless, apart from Yilmaz's own papers, the theory has apparently received no attention in the research literature, apart from two critical papers. Yilmaz claims that his critics have misunderstood him, but it has been suggested that his papers are too murky in crucial places to admit a single clear interpretation. Yilmaz's credibility has also been badly damaged by what appear to be serious misstatements about general relativity.
It is well known that naive attempts to quantize general relativity along the same lines which lead from Maxwell's classical field theory of electromagnetism to quantum electrodynamics fail, and that it has proven very difficult to construct a theory of quantum gravity which goes over to general relativity in an appropriate limit. Yilmaz has claimed that, in contrast, his theory is in some sense 'compatible with quantum mechanics'. He even suggests that it might be an alternative to superstring theory. These claims have apparently been given no credence by physicists other than Yilmaz and a handful of his coworkers.
Yilmaz has offered several descriptions of the alleged field equation for his 'theory', which his critics feel are neither entirely consistent with each other nor well-defined. To understand one of the most basic criticisms of Yilmaz's work, one needs to be familiar with
the statement of the Einstein field equation,
the distinction between coordinate dependent and coordinate independent quantities,
well known facts concerning integration in curved spacetimes,
well known facts concerning gravitational energy-momentum pseudotensors in general relativity.
With this background in hand, one can say that Yilmaz apparently wishes to keep the left hand side of the Einstein field equation (namely the Einstein tensor, which is well defined for any Lorentzian manifold, independent of general relativity) but to modify the right hand side, the stress-energy tensor, by adding a kind of gravitational contribution. According to Yilmaz's critics, this additional term is not well-defined, and cannot be made well defined.
Yilmaz has apparently failed to produce a convincing proposal for an observational or experimental test of his theory, and it would appear that no astronomers have contemplated any attempts to test his ideas. On the other hand, astronomers are very interested indeed in testing theoretically solid competitors of general relativity; see Category:Tests of general relativity.
http://en.wikipedia.org/w/index.php?title=Yilmaz_theory_of_gravitation&oldid=45631271
Polarizable vacuum
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In theoretical physics, particularly fringe physics, polarizable vacuum (PV) refers to a proposal by Harold Puthoff, which has been various characterized as
an attempt to reformulate general relativity in terms of a purely formal analogy with the propagation of light through an optical medium,
an attempt to replace general relativity with a scalar theory of gravitation featuring formal analogies with Maxwell's theory of electromagnetism,
an attempt to unify gravitation and electromagnetism in a theory of electrogravity,
an attempt to provide a physical mechanism for how spacetime gets curved in general relativity, which suggests (to Puthoff) the possibility of "metric engineering" for such purposes as spacecraft propulsion (see Breakthrough Propulsion Physics Program).
Puthoff himself has apparently offered various characterizations of his proposal, which has not been accepted in mainstream physics.
Contents [hide]
1 Related work
2 Puthoff's claims
3 A unified field theory?
4 External links
5 References

Related work

Antecedents of PV and more recent related proposals include the following:
A proposal in 1921 by H. A. Wilson to reduce gravitation to electromagnetism by pursuing the formal analogy between "light bending" in metric theories of gravitation and propagation of light through an optical medium having a spatially varying refractive index. Wilson's approach to a unified field theory is not considered viable today.
An attempt (roughly 1960-1970) by Robert Dicke and Fernando de Felice to resurrect and improve Wilson's idea of an optical analogue of gravitational effects. If interpreted conservatively as an attempt to provide an alternative approach to gtr, rather than as work toward a theory unifying electromagnetism and gravitation, this is not an unreasonable approach, although most likely of rather limited utility.
The 1967 proposal of Andrei Sakharov that gravitation might arise from underlying quantum field theory effects, in a manner somewhat analogous to the way that the (simple) classical theory of elasticity arises from (complicated) particle physics. This work is generally regarded as mainstream and not entirely implausible, but highly speculative, and most physicists seem to feel that little progress has been made.

My work is along the lines of Sakharov 1967.
In a series of papers, Bernard Haisch and Alfonso Rueda have proposed that the inertia of massive objects arises as a "electromagnetic reaction force", due to interaction with the so-called zero point field. According to mainstream physics, their claims rest upon incorrect computations using quantum field theory.
I agree with Hillman's assessment here.
Recent work, motivated in large part by the discoveries of the Unruh effect, Hawking radiation, and black hole thermodynamics, to work out a complete theory of physical analogues such as optical black holes. This is not work toward a unified field theory, but in another sense can be regarded as work towards an even more ambitious unification, in which some of the most famous effects usually ascribed to general relativity (but actually common to many metric theories of gravitation) would be seen as essentially thermodynamical effects, not specifically gravitational effects. This work has excited great interest because it might enable experimental verification of the basic concept of Hawking radiation, which is widely regarded as one of the most revolutionary proposals in twentieth century physics, but which in its gravitational incarnation seems to be impossible to verify in experiments in earthly laboratories.

Uh Oh
The 1999 proposal by Keith Watt and Charles W. Misner of a scalar theory of gravitation which postulates a stratified conformally flat metric of the form

, given with respect to a Cartesian chart, where φ satisfies a certain partial differential equation which reduces in a vacuum region to the flat spacetime wave equation

. This is a "toy theory", not a fully fledged theory of gravitation, since as Watt and Misner pointed out, while this theory does have the correct Newtonian limit, it disagrees with the result of certain observations.

Puthoff's claims

Disputed science:
Polarizable vacuum
Disciplines:
physics
Core tenets:
Gravitation can be described via a scalar theory of gravitation, using a stratified conformally flat metric, in which the field equation arises from the notion that the vacuum behaves like a optical polarizable medium.
Year proposed:
* 1998
Original proponents:
Harold Puthoff, Bernard Haisch
Current proponents:
ditto
In essence, Puthoff proposes that the presence of mass alters the electric permittivity and the magnetic permeability of flat spacetime, εo and μo respectively by multiplying them by a scalar function, K:
εo→ε = Kεo, μo→μ = Kμo
Puthoff argues that this will affect the lengths of rulers made of ordinary matter, so that (he argues), in the presence of a gravitational field, the spacetime metric of Minkowski spacetime is replaced by



where κ2 = K is the so-called "dialetric constant of the vacuum". This is a "diagonal" metric given in terms of a Cartesian chart and having the same stratified conformally flat form in the Watt-Misner theory of gravitation. However, according to Puthoff, κ must satisfy a field equation which differs from the field equation of the Watt-Misner theory. In the case of a static spherically symmetric vacuum, this reduces to



which happens to agree with the analogous situation in the Watt-Misner theory. This yields the asymptotically flat solution



The resulting Lorentzian spacetime has the same weak-field limit (and the same far-field) as the Schwarzschild vacuum solution in general relativity, and it satisfies three of the four classical tests of relativistic gravitation (redshift, deflection of light, precession of the perihelion of Mercury) to within the limit of observational accuracy. However, it yields a different prediction for the inspiral of test particles due to gravitational radiation.
However, requiring stratified-conformally flat metrics rules out the possibility of recovering the weak-field Kerr metric, and is certainly inconsistent with the claim that PV can give a general "approximation" of gtr. In particular, this theory exhibits no frame-dragging effects.

This explains why Puthoff has not been able to describe a rotating source in PV theory.

Also, the effect of gravitational radiation on test particles differs profoundly between scalar theories and tensor theories of gravitation such as general relativity. LIGO is not intended primarily as a test ruling out scalar theories, but is widely expected to do so as a side benefit once it detects unambiguous gravitational wave signals exhibiting the characteristics expected in general relativity.
Ibison has considered a "cosmological solution" of PV, analogous to the Friedmann dust solution (with flat orthogonal hyperslices) in general relativity, and argues that this model is inconsistent with various observational and theoretical constraints. He also finds a rate of inspiral disagreeing with observation, but apparently his result disagrees with that of Watt and Misner (who studied the same Lorentzian manifold in the context of their own scalar theory of gravitation).
It is widely appreciated in physics that, contrary to Puthoff's claims, no scalar theory of gravitation can reproduce all of general relativity's successes. It might be noted that De Felice uses constitutive relations to obtain a susceptability tensor which lives in spatial hyperslices; this provides extra degrees of freedom which help make up for the degree of freedom lacking in PV (and other scalar theories).

A unified field theory?

Ibison feels that Puthoff has never claimed to provide a unified field theory which combines gravitation and electromagnetism. However, Puthoff has coauthored papers with Bernard Haisch which apparently do make this claim, and Puthoff's other papers apparently fail to explicitly disavow any such intention.
In any case, whether or not Puthoff intends any such claim, mainstream physicists agree that PV is
not viable as a unification of gravitation and electromagnetism
not a "reformulation" of general relativity,
not a viable theory of gravitation, since it violates observational and theoretical requirements.
In addition, while this point is presumably moot, Puthoff's arguments for his field equations are highly suspect.

I agree with Hillman's assessment of Puthoff's PV theory 100%.

External links

H. E. Puthoff, M. Ibison, Polarizable Vacuum "Metric Engineering" Approach to GR-Type Effects, MITRE Conference, McLean, VA, May 8, 2003. From the website of EarthTech, a company founded by Puthoff.

References

Visser, Matt (2005). Analog Gravity. Living Reviews in Relativity. Retrieved on 2006-06-02.
Ibison, M. (2003). "Investigation of the polarizable vacuum cosmology." 2003.
Watt, Keith; and Misner, Charles (1999). "Relativistic Scalar Gravity: A Laboratory for Numerical Relativity." 10 Oct 1999.
Puthoff, H. E. (2002). "Polarizable-Vacuum (PV) representation of general relativity". Found. of Phys. 32: 927-943. arXiv eprint
de Felice, F. (1971). "On the gravitational field acting as an optical medium". General Relativity and Gravitation 2: 347-.
Dicke, R. H. (1957). "Gravitation without a principle of equivalence". Reviews of Modern Physics 29: 363-376.
Wilson, H. A. (1921). "An electromagnetic theory of gravitation". Physical Review 17: 54-59.
http://en.wikipedia.org/w/index.php?title=Polarizable_vacuum&oldid=56603531
Stochastic electrodynamics
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In theoretical physics, Stochastic electrodynamics (SED) refers to a more or less controversial theory which posits that the interaction of elementary particles with the vacuum radiation field, or zero point field, is ultimately responsible for various familiar quantum phenonmena.
SED has been developed by a number of physicists; their contributions can generally be characterized as speculative proposals within mainstream physics, but widely popularized work by Haisch and Rueda (especially as portrayed in various cranky websites) is often considered fringe science.
Contents [hide]
1 Brief history
2 Nature of SED
3 The work of Haisch and Rueda
4 Internet culture
5 See also
6 External links
7 References

Brief history

Stochastic electrodynamics is usually credited to Timothy H. Boyer, but builds upon the notions of stochastic optics proposed by T. W. Marshall and the notion of induced gravity proposed by Andrei Sakharov. Boyer's ideas have been further developed by L. de la Pena and A. M. Cetto, who introduced linear stochastic electrodyamics (LSED).
This work is generally regarded as more or less mainstream physics. However, starting in about 1984, Bernard Haisch and Alfonso Rueda, sometimes joined by Harold E. Puthoff, have championed the notion the inertia of a massive object arises via an electromagnetic reaction force via interaction with the so-called zero point field. This builds upon a much earlier proposal by Walther Nernst, but is highly controversial; even more controversial is their proposal that this putative effect can be used for spacecraft propulsion and might even explain the UFO phenomenon.

I agree with Puthoff and Haisch that UFOs are real and need explaining. I do not agree with their explanation.

Nature of SED

The zero point field can be thought of, roughly speaking, as a superposition of electromagnetic waves with random frequencies, phases and directions, with a distribution proportional to the cube of frequency, up to a cutoff frequency on the order of the reciprocal of the Planck time. Planck's constant then appears as a kind of typical amplitude for quantum fluctuations in the zero point field.
The original motivation for SED is that it seeks to provide a local realist foundation for various mysterious effects of quantum field theory, including
Casimir force
van der Waals forces,
diamagnetism
cavity effects
Unruh effect
radiative corrections in the theory of the quantum harmonic oscillator
More controversially, Haisch and Rueda have tried to use SED to provide explanations for the phenomena of
inertia
gravitation

The work of Haisch and Rueda

According to Haisch and Rueda, inertia arises as an electromagnetic drag force on accelerating particles, produced by interaction with the zero-point field. In their 1998 Ann. Phys. paper (see citations), they speak of a "Rindler flux", presumably meaning the Unruh effect, and claim to have computed a nonzero "z.p.f. momentum". This computation rests upon their claim to compute a nonzero "z.p.f. Poynting vector", but according to Bill Unruh this computation is incorrect.
Haisch and Rueda also claim that gravitation arises from an electromagnetic induced dipole shielding similar to the Van der Waals force. They claim to explain the equality of gravitational and inertial mass, which is assumed but not derived in general relativity, and they claim to compute thereby the value of the Planck constant from the gravitational constant, or vice versa.
Haisch and Rueda claim that the structure of atoms arises from a thermal equilibrium between between a particle in a potential well and the zero point field. They claim that this resolves the radiation paradox of the Bohr model, a well known shortcoming of that model. This paradox states that an orbiting classical electron will quickly radiate all its energy away and collapse into the nucleus, which is in drastic disagreement with observation. According to Haisch and Rueda, however, in their theory, each orbiting electron absorbs exactly as much energy from the zero-point field as it radiates. They claim that the absorption and re-emission by the electrons in an atom preserves both the frequency distribution and isotropic random phase character of the zero-point field. They suggest an this intuitive picture: the electron is constantly trying to collapse into the nucleus but is blown off course by "gusts" from the background field and so maintains a stable orbit.
Haisch and Rueda claim that the Heisenberg uncertainty principle also arises from interaction of particles with the zero-point field, which, they say, randomly changes the position and velocity of every particle.
These claims are vigorously disputed by other physicists.
The Haisch/Rueda version of SED appears to incorrectly predict no deflection of light in a gravitational field. Their theory also appears to predict an enormous value for the cosmological constant. Haisch and Rueda propose to solve this problem by assuming that the zero-point field does not itself have gravitational mass; rather, they say, the gravitational mass of a massive object is created by the interaction between this object and the zero-point field. Issues which they have apparently not yet addressed include the homogeneous and isotropic nature of their notion of the zero point field.

Of course this is a serious error in the Haisch-Puthoff theory as the discovery of dark energy accelerating the universe proves. Tensor GCT covariance and equivalence principle imply that virtual quanta gravitate if spin 1/2 and anti-gravitate if spin 1. This follows from w = -1 (neglecting boundary effects) and quantum statistics in 3 + 1 space-time. What happens for anyons in 2 + 1 spacetime in quantum wells with fractional statistics is an interesting question I am thinking about. The world hologram idea is that 2 + 1 space-time is more fundamental than 3 + 1 spacetime.

Internet culture

The proposals of Haisch and Rueda have been eagerly promoted at many websites by new energy fans, who hope that the notion of zero point energy might ultimately provide no cost "energy from the vacuum", thereby solving many current problems in contemporary human society. Others claim that the work of Haisch, Rueda, and Puthoff holds out hope of developing an "inertial-less drive" (see Dean drive) which can be used to enable humans to visit far distant regions of the universe. According to a newstory which appeared in the Washington Post, a paper by Haisch played a key role in the bizarre story of the life-changing encounter of Joe Firmage with a (possibly imaginary) "luminous being".

Yes, this is a true story.

See also

Casimir effect
Polarizable vacuum
Rindler coordinates
Unruh effect
Vacuum energy
Zero-point energy
Andrei Sakharov
Bernard Haisch
Harold E. Puthoff

External links

California Institute for Physics and Astrophysics, a fringe physics organization founded by Bernard Haisch
The CEO from Cyberspace: Joe Firmage, a master of the Universe at 28, Wants to Defy Gravity and Visit the Far Corners Of His Realm, by Joel Achenbach, Washington Post, March 31, 1999, from the anticult website of Rick Ross
H. E. Puthoff, Quantum Vacuum Fluctuations: A New Rosetta Stone of Physics? from Lambert Dolphin's website; Dolphin has claimed that the speed of light has measurably decreased during the past 300 years, that special relativity is incorrect, has promoted the claims of Tom Van Flandern, and so on

References

Marshall, T. W. (1963). "TITLE NEEDED". Proc. Roy. Soc. A: 475.
Sakharov, A. D. (1968). "Vacuum Quantum Fluctuations in Curved Space and the Theory of Gravitation". Sov. Phys. Doklady: 1040.
Boyer, Timothy H. (1975). "Random electrodynamics: The theory of classical electrodynamics with classical electromagnetic zero-point radiation". Phys. Rev.: 790-808.
Boyer, T. H. (1980). "A Brief Survey of Stochastic Electrodynamics". Foundations of Radiation Theory and Quantum Electrodynamics. ISBN 0306402777
Boyer, Timothy H. (1985). "The Classical Vacuum". Scientific American. online version from PADRAK, the website of Patrick Bailey, who publishes New Energy News in Salt Lake City, UT, and who promotes a cranky theory of "plasmoids", which he says "contradict theories about gravity and 'mass' "
Milonni, Peter W. (1994). The Quantum Vacuum: An introduction to quantum electrodynamics. San Diego: Academic Press. ISBN 0-124-98080-5.
Haisch, B.; Rueda, A.; and Puthoff, H. E. (1994). "Inertia as a zero-point-field Lorentz force". Phys. Rev. A: 678-694. on-line version from Haisch's website
de la Pena, L.; and Cetto, A. M. (1996). The Quantum Dice: An Introduction to Stochastic Electrodynamics. Dordrecht: Kluwer. ISBN 0792338189. amazon page
Rueda, Alfonso; and Haisch, Bernard (1998). "Contribution to inertial mass by reaction of the vacuum to accelerated motion". Found. Phys.: 1057-1108. physics/9802030
Rueda, Alfonso, and Haisch, Bernard (2005). "Gravity and the Quantum Vacuum Inertia Hypothesis". Ann. Phys.: 479-498. gr-qc/0504061
de la Pena, L.; and Cetto, A. M. (2005). "Contribution from stochastic electrodynamics to the understanding of quantum mechanics." 4 Jan 2005., a review paper
See Stochastic_electrodynamics/Bibliography for more research papers.

http://en.wikipedia.org/w/index.php?title=Stochastic_electrodynamics&oldid=56907094

to be continued

Conceptual Breakthrough Today in Emergent Gravity from Inflation

On Aug 17, 2006, at 5:45 PM, Jack Sarfatti wrote:

The effective coupling of the World Hologram Coherent Vacuum Goldstone Phases to the fabric of spacetime requires the following conditions

1. The cosmological constant /\ =/= 0. When /\ = 0 you cannot have curved spacetime at all in my theory. That is, there is no emergent Einstein gravitational field in that case.

2. When Planck's quantum of action h is zero there is no gravitational field because the gravitational field is an emergent macroquantum effect just like the superfluid flow hydrodynamic field.

3. When Newton's G is zero there is no gravity field - hardly surprising.

4. When the vacuum speed of light c is infinite there is no local Einstein curved spacetime gravity field. In that case we have the pre-special relativity Galilean group with absolute simultaneity.

Note I can extend to string theory with extra Calabi-Yau 6 space-dimensions easily as I did in the first archive paper. For now I want to keep it simple in a toy model "hydrogen atom" model. This simply means more Goldstone phases i.e. more real components to the inflation vacuum ODLRO field.

What about quantum gravity? Einstein's smooth classical guv curved metric field is simply an emergent property of the vacuum ODLRO order parameter, i.e. the inflation field. There are off-mass shell zero point quantum vacuum fluctuations in this Bose-Einstein condensate of course. Look at liquid helium where ~90% of the total density at absolute zero is zero point. That's why helium remains a liquid near absolute zero. Thermal excitations are real on-mass-shell "normal fluid" i.e. ordinary matter if thermal equilibrium, which our universe is not in.

The false vacuum is when the intensity of the inflation field vanishes - so this is globally flat special relativistic space-time with spin 1/2 & spin 1 virtual quanta for sure. Maybe spin 0, but it is not clear if there are some spin 2 quanta? Also spin 3/2 quanta? In any case this would be in the false vacuum.

Now, the issue is what is the inflation field really made out of? It is a macro-quantum vacuum condensate of virtual quanta - what virtual quanta? The condensate is a reservoir of virtual quanta popping out of and into the condensate. The virtual quanta density is essentially /\ ~ dark energy density.

Now in 1916 GR /\ is really constant. However, when we go beyond 1916 GR and stick in torsion fields then /\ becomes a local scalar variable field and at small scales /\ < 0 is dark matter! Both dark energy /\ > 0 and dark matter /\ < 0 on different scales are the absolute zero temperature zero point fluctuations into and out of the vacuum condensate.

Since Einstein's guv c-number field is bottom -> up emergent it's stupid to quantize it top -> down. Whilst "classical" gravity waves exist to be found in LISA & LIGO in my theory the idea of the spin 2 nonlinear graviton on a smooth curved space-time non-rigid dynamical background seems not likely to exist.


On Aug 17, 2006, at 3:12 PM, Jack Sarfatti wrote:

http://arxiv.org/abs/gr-qc/0608086
On Aug 17, 2006, at 2:32 PM, Jack Sarfatti wrote:


OK this is the final version.

I finally solved a problem bugging me for months.

e = I + A

A is the intrinsic curved part of the contracted tetrad scalar local objective frame-invariant.

e is dimensionless.

What I need is a dimensionless coupling

e = I + ?A

I finally got it only just now!

? = (Quantum of Area)(Lambda Cosmic Landscape "Curvature)

= hG/\/c^3

when /\ = 0 you get nothing, i.e. only global SR

when G = 0 you get nothing

when h = 0 "

when c --> infinity "

That's all good physics.

Michio Kaku's Type IV Advanced ET Time Traveling Masters of Hyperspace

On Aug 16, 2006, at 11:03 PM, Anna wrote:

"Yes, providing that we allow matter to claim spirituality. For some reason, many people think that matter is at best a dead wood to knock on it. I see matter as a manifestation of consciousness.
Anna"

The physical world consists of mental pilot quantum waves BIT and material particles and fields IT.

IT gets its marching orders from BIT via David Bohm's "quantum potential" for particles and the super-potential for classical electromagnetic fields and other force fields.

There is still no consciousness there.

You only get MORE IS DIFFERENT inner consciousness with "qualia" when the IT backreacts directly on the BIT mind field. This requires a huge number of particles to Bose-Einstein condense into the same quantum state. This collapse of phase space lowers the entropy of the conscious system. The conscious system is a self-organizing hologram that adapts to its environment. It is an open system far from the heat death of thermal equilibrium and it has signal nonlocality, i.e. spooky telepathic retro-causal entanglement action at a distance that we see in "remote viewing" and other paranormal phenomena. When the coherent phases of the conscious system locks into the coherent substratum of the fabric of curved spacetime, i.e. the world hologram, then we have the Type IV (Michio Kaku) Q Star Trek VALIS (PK Dick) Starmaker (Stapledon) metric engineering (H. Puthoff) direct conscious control of the local space-time geometry (Skinwalker) that allows the weightless geodesic warp drive of the alien ET flying saucer time travel (future to past) that Colonel Phillip Corso described as mentally controlled by brain waves.

General MacArthur, General Marshall, General Twining and other top military men from WWII already allegedly knew of some of this - also apparently James Jesus Angleton of the CIA.

http://www.authorhouse.com/BookStore/ItemDetail.aspx?bookid=23999

Einstein's gravity field emerges from the coherent Goldstone phases of the vacuum Higgs inflation field.

Given a p-form P and an q-form Q

P/\Q is a p + q form

P/\Q = (-1)^(pq) Q/\P

d(P/\Q) = (dP)/\Q + (-1)^pP/\(dQ)

Let O be a 0-form and I be a 1-form

O/\I = (-1)^(0x1)I/\O = I/\0

d(O/\I) = dO/\I + (-1)^0O/\dI = dO/\I + O/\dI

d^2 = 0

Let Theta & Phi be Goldstone phase 0-forms of the vacuum ODLRO inflation field.

Define the 1-form

A = Theta/\dPhi - dTheta/\Phi

d(Theta/\dPhi) = dTheta/\dPhi + Theta/\d^2Phi = dTheta/\dPhi

d(dTheta/\Phi) = d^2(Theta)/\Phi - dTheta/\dPhi = -dTheta/\dPhi

Therefore, the 2-form is

dA = +2dTheta/\dPhi

Let eu^a be a set of Einstein-Cartan sub-geometrodynamic tetrad field components. The O(1,3) indices a,b,c... are raised and lowered with the globally flat constant Minkowski metric nab. The GCT Diff(4) indices are raised and lowered with the locally curvilinear GCT metric guv. Einstein's local principle of equivalence is formally here for a point event E

guv(E) = eu^a(E)nabev^b(E)

The 4 GCT 1-form tetrad fields are

e^a = eu^adx^u

Form the contracted O(1,3) scalar

e = e^a&a

&a is a basis of vector fields in flat tangent space.

Ansatz

e = 1 + A

1 is the constant unit scalar

When there is no real gravity curvature field

A = 0 identically in the region of events {E}.

A = Theta/\dPhi - dTheta/\Phi

Au^a = Lp(Theta/\dPhi - dTheta/\Phi)u^a

Lp = (hG/c^3)^1/2

dA = 2(dTheta)/\(dPhi) = (dA)uv^adx^u/\dx^v&a

(dA)uv^a = 2Lp^2(dTheta/\dPhi)uv^a

A topological 3D space point defect (world line in 4D spacetime) in the macro-quantum "More is different" vacuum ODLRO local order parameter inflation field from a spontaneously broken continuous symmetry has Theta & Phi undefined.

The integral of dA around a closed surface that surrounds that point defect is quantized in order to keep the local order parameter single valued.

Therefore

Integral of dA on a closed surface with no boundary that is itself not a boundary ~ (Integer)Lp^2, i.e. Hawking-Bekenstein black hole entropy rule of 1 c-bit per Planck quantum of area and t'Hooft-Susskind world hologram rolled into one formula.

Note, if there was only one Goldstone phase Theta instead of 2 the situation would be like
1. Superfluid helium
2. Superconductor
3. Self-trapped laser filaments in nonlinear optics.

The topological defects would be string vortex lines, i.e. world sheets in 4D spacetime.
The surrounding surface would be a non-bounding 1D loop without boundary enclosing a vortex line, and the corresponding loop integral would be quantized as integer h/m for a neutral superfluid, or h/2e magnetic flux quantum for a superconductor.

VORTEX PROPELLANTLESS PROPULSION?

On Aug 6, 2006, at 4:21 AM, Waldyr A. Rodrigues Jr. wrote:

1) I said the universe is boring in the sense that it used the same basic idea many times. UFOS do not need an exotic topological manifold to "fly".
Well if you can prove that it will be very interesting of course. I disagree. I think Stargates are real and they are exotic topologies. I could be wrong of course so let's see your proof of this. I mean your model. Also your new theory without blackhole event horizons presumably must explain all the data - a daunting task.
Also, as you know I have been investigating paranormal phenomena (almost as main activity) for more than 30 years.

Yes, of course.
You cannot leave out our "brane" in a "material" state, even if you are on board of a UFO.
I don't understand the above sentence. You mean "branes" or "brains"? :-)
2) I know very well that gravitational field is described by QFT by a spin 2 field.
Of course.
The interacting tetrad fields are equivalent to a spin 2 field when some conditions are fulfilled.
My idea here is that the SUBSPACE tetrad fields when quantized should be spin 1. It is then obvious that they are vector quantum field theories in flat Minkowski tangent fiber space to curved space-time base space of the tangent bundle. Since Einstein's geometrodynamic field forming EMERGENT curved base space is bilinear in the spin 1 tetrads we know from the quantum rules for adding spins

1 + 1 = 2, or 1, or 0

That is the basic Einstein geometrodynamic quanta have spin 2 - the conventional ones, but also spin 1 and spin 0 fields!

You can think of the spin 2 geometrodynamic quantum as an Einstein-Podolsky-Rosen pair correlated state like in a BCS superconductor - but the SUBSPACE tetrad quanta are also bosons I suppose. The spin 1 boson tetrad fields are also 2-qubit Penrose SPINOR fermion entangled states. Therefore the Einstein geometrodynamic field is a 4 qubit entangled string.

IT FROM BIT!

It is now obvious that TETRAD SUBSPACE is a truly flat space-time quantum field theory in the tangent fiber sense and that it is obviously MAXWELLIAN and RENORMALIZABLE.

It also suggests additional "anti-gravity" spin 1 quantum gravity vector fields and spin 0 scalar fields.

If A is curved invariant tetrad scalar field in FLAT SUBSPACE

F = dA ~ dTheta/\dPhi ~ SUBSPACE Maxwellian Field Tensor

Theta & Phi Goldstone phases of vacuum ODLRO inflation field

This is World Hologram Ansatz

F = Loop Quantum Gravity Area Flux Density Field

dF = 0

d*F = *J

d&J = 0

for U(1) group

You can make this Yang-Mills trivially by introducing 3 and 8 additional internal dimensions respectively and

D = d + A/
for SU(2) and SU(3)

When it is described by a single 1-form potential A, the field is generated by the Ricci operator (which is an exterior product of two Dirac operators D^D) applied to that potential G=(D^D)A, and the resulting field is of spin 2 if some conditions are fulfilled. Note that the electromagnetic field F is generated from a potential 1-form A’ using only one time the Dirac operator by F=DA’…

3) The tetrads are mathematical objects that are sections a principal bundle called the frame bundle. Each member of a given tetrad is also a section of a vector bundle called the cotangent bundle.

Tetrads are not flat or curved. These wordings concerning these objects are sheer nonsense. Flat or curve refers to properties of a connection.

I disagree.

In my theory, the local frame independent scalar invariant e formed from the 4 tetrads e^a is

e = 1 + A

When A = 0 the emergent geometrodynamic field given by the EQUIVALENCE PRINCIPLE

guv = eu^a(MINKOWSKI METRIC)abev^b

has intrinsic geodesic deviation AKA "curvature".

When A = 0 the emergent space-time is globally flat.

I explicitly showed that you can interpret the gravitational field in Einstein’s theory as fields in the Faraday sense living in Minkowski spacetime or as generating an effective Lorentzian spacetime (with non null Riemann curvature tensor and null torsion)
I don't understand how it can simultaneously be Minkowski and yet have curvature? That seems a contradiction. In my theory I have TWO levels.

1. DIRAC SUBSTRATUM (or "SUBSPACE")RENORMALIZABLE FLAT SPIN 1 TETRAD LEVEL "square root" of EMERGENT GEOMETRODYNAMIC FIELD.

2. Einstein emergent SPIN 2 CURVED GEOMETRODYNAMIC FIELD. Also possibly spin 1 & spin 0 effects in the zero point quantum "dark energy/matter" fluctuations on the smooth c-number vacuum ODLRO "condensate" (SUPERSOLID) non-rigid dynamical background.
or an effective teleparallel spacetime (with null Riemann curvature and non null torsion tensor). Of course, other possibilities exist. I can (and already done more than 20 years ago) describe the gravitational filed in a geometry with a non null non metricity tensor. Which geometry to use? The one it is more convenient. This is exactly what Poincaré said in his book Hypothesis and Science (read by Einstein…) a long long time ago.

Eventually it is time for more people to read Poincaré.

I will try to do so in Paris next month.
4) Another comment. Of course, since Cartan it is well known that the equations satisfied by the tetrads have some similaritiy to Maxwell equations.
I discovered that independently as I do not read much literature.
However, what are the currents J_a? Here only intuitive ideas are of no help. You need a Lagrangian. In my theory there is one. The interesting aspect of that Lagrangian is that besides the Yangs-Mills and gauge fixing terms there is an auto-interacting term involving the vorticities of the tetrads.
Yes, I am well aware of that intuitively.
Kiehn already verified that these objects are important for all known solutions of the Einstein equations, although he did not discovered how to write a Lagrangian.

I observe moreover that for the electromagnetic field the majority of solutions that you found in textbooks have null vorticity A’^DA’.
However many of the extraordinary solutions (sub and super c) that I found in 95 have non zero vorticities…
Yes, this is important. So this is how you get SUPERLUMINAL WARP DRIVE?
5) Last comment. My theory explains all known experimental facts described by GR. Moreover, in it there are fidedigne conservation laws, which is not the case of GR. You do not need exotic topologies to explain data associated to what people call “black-holes” and also as I already said you do not need such topologies to travel fast…. More on this and on “Hilbert error” some of these days.

Please hurry. :-)


-----Mensagem original-----
De: Jack Sarfatti [mailto:sarfatti@pacbell.net]
Enviada em: sábado, 5 de agosto de 2006 22:29
Para: Sarfatti_Physics_Seminars
Assunto: Waldyr Rodrigues responds on "Hilbert's Error" & my objections



On Aug 5, 2006, at 5:07 PM, Waldyr A. Rodrigues Jr. wrote:


> 1) Universe eventually is really boring.


But UFOS prove that the universe, i.e. MEGAVERSE of parallel pocket

universes is not boring. My God Waldyr, if I thought we lived in a

boring universe I would have given up this infernal physics nonsense!

> What can I do?

Remember that Brazilian Army General you took me and Fred Alan Wolf

to see in 1984 and he showed us the bent metal from the kids in the

Amazon who had been zapped by UFOs like Uri Geller - right? Well

that's hardly a boring universe - eh?


George Chapline Jr agrees with you that there is no time travel.

> My theory seems to indicate that nature has used a good idea many

> times … I recall that now it is Einstein’s equations that are put

> in Maxwell-like form and I already showed that Dirac equation can

> be written as a Maxwell equation (see. e.g., Maxwell-Dirac

> Equivalence of the First and Second Kinds and the Seiberg-Witten

> Equations on Minkowski Spacetime, International Journal of

> Mathematics and Mathematical Sciences 2003, 2707-2734 (2003), RP

> 61/02 IMECC-UNICAMP, math-phys/0212034. MR2004136 )


But Maxwell's first rank tensor equations are spin 1 quantum fields

and Einstein's second rank tensor equations are spin 2 which is why

you have universal attraction for positive masses as shown by Feynman

for example. But of course on tetrad level what you say is perfectly

obvious. I said it before you in fact! The tetrads are spin 1 and

they live in flat Minkowski space - but it's only local tangent fiber

space so Einstein's curved spacetime is still needed globally with

wormhole topologies. I get your theory in essence trivially in a few

lines without all that math in your paper.


e = 1 + A at SUBSPACE spin 1 tetrad level "square root" of Einstein

geometrodynamic level.


F = dA is analog of Maxwell field tensor


dF = 0 Faraday's law & no magnetic monopoles law


d*F = *J Ampere's law and Gauss's law in SUBSPACE


d*J = 0 local conservation


There you have it.


Now we do nonlinear map to Einstein's 1915 geometrodynamics using the


EQUIVALENCE PRINCIPLE


guv(CURVED) = eu^a(FLAT)abev^b


The local scalar invariant is


ds^2 = guvdx^udx^v


The torsion 2-form is


T = De = 0 in 1915 GR


D = d + S/

S is spin connection 1-form local scalar invariant


S = S^a^b&a&b


S^a^b = - S^b^a


S^a^b = Su^a^bdx^u


The Riemann curvature 2-form is


R = DS


The Einstein-Hilbert Action Density is


~ R/\e/\e


The vacuum Euler-Lagrange field equation is


R/\e = 0


Note that


D(R/\e) = DR/\e + R/\De = 0


DR/\e + R/\T = 0


if torsion T is not zero, then


DR =/= 0


When T = 0


then


DR = 0

>


> 2) There is not a single evidence for nontrivial topologies until now.


UFOs are such evidence. Blackhole data are such evidence.

> But do not get boring. There are other ways to travel fast in our

> big universe which do not implies the existence of exotic topologies….


So you say there are warp drives but no stargates?

> 3) Moreover, my theory can be formulated in topological spaces

> different form R^4 with some small changes if experimental evidence

> shows up. However this is not necessary at present time.

>

> 3) The “evidence” for black holes can be easily simulated in my

> theory. Beckwith as many other physicists always forget to say that

> the experimental evidence is also compatible with alternative

> explanations and with other theories. By the way, many know only a

> single theory and do not even have imagination to develop

> alternative theories with different ontologies, yet mathematically

> equivalent to some standard one.

>

> 4) I will discuss ‘Hilbert error’ in another paper. I studied a

> lot the issue in the last few weeks.


Is there one or not?

>

> -----Mensagem original-----

> De: Jack Sarfatti [mailto:sarfatti@pacbell.net]

> Enviada em: sábado, 5 de agosto de 2006 20:28

> Para: Sarfatti_Physics_Seminars

> Assunto: I don't agree with Waldyr's new paper

>

>

> Look at the Conclusion attached. No black holes, no non-trivial

> toplogy, no time travel - in fact a boring humdrum universe Waldyr

> has constructed. As Andy Beckwith showed there is evidence for

> black holes so that Waldyr's "correct math" is of no physical

> interest. I will learn some of the differential forms and Clifford

> bundle techniques from it.

>

>

> Also I suspect the claims that David Hilbert made an error in

> Schwarzschild solution are most likely bogus. I can't prove that

> right now - only my instinct.

>

>

> On Aug 5, 2006, at 2:53 PM, Jack Sarfatti wrote:

>

>

>

>

> bcc



On Aug 5, 2006, at 5:55 PM, Jack Sarfatti wrote:


> Delusional metanoids are very "logical" Paul. :-)

> You have constructed a Rube Goldberg skyscraper on shaky ground.

> In fact on a swamp.

> It's not even wrong Paul.

> You cannot construct a local frame invariant scalar field from the

> non-tensor connection field. Therefore it has no objective

> footprints as it were.

> You can do it for any tensor field like the metric field and the

> curvature field.

> That you cannot do it for any connection field even in internal

> symmetries like EM is called gauge freedom Paul!

>

> The GR connection field {uvw} is analogous to the EM vector

> potential Au.

>

> Both are 1-forms i.e. the spin-connection underlying {uvw} is Sab

> where

>

> S^a^b = Su^a^bdx^u = - S^b^a SPIN 2

>

> compare to

>

> A = Audx^u in U(1) EM SPIN 1

>

> & Yang-Mills

>

> A^a = Au^adx^u SPIN 1

>

> where a is internal fiber index of SU(2) or SU(3)

>

> a = 1,2,3 for SU(2) weak radioactivity force

>

> a = 1,2,3,4,5,6,7,8 for SU(3) sub-nuclear force

>

> The Bohm-Aharonov effect is that the loop integrals of the

> connection 1-form A are quantum phase observables and when the

> "charged" source order parameter is single-valued those loop

> integrals are quantized and are non-zero around line vortex defects

> in the phase of the order parameter. In those cases the closed loop

> has no boundary but is itself not a boundary of an area because of

> the enclosed phase singularity.

>

> Because of the equivalence principle you cannot do this the same

> way on this spin 2 tensor geometrodynamical level.

>

> All that Waldyr et-al has rediscovered is that you do have a

> Minkowski field theory at the tetrad level. That's already in my

> archive paper and it's in my book Super Cosmos!

>

> The tetrads are "square roots" of the metric tensor that is spin 2

> as a NONRENORMALIZABLE quantum field. Therefore, the tetrads as

> quantum fields are spin 1 renormalizable and they only have the

> FLAT MINKOWSKI METRIC nab - but this is like Star Trek "subspace" -

> I have that alluded to already in my first page of Super Cosmos.

>

> The local frame-invariant scalar invariant contraction of the 4

> tetrad fields e^a is

>

> e = 1 + A = e^a&a

>

> A is the truly intrinsic curved part of the subspace tetrad field

>

> dA ~ d(Theta)/\d(Phi) ~ analog of EM field is what I call the

> subspace area flux density.

>

> This is actually the key idea in loop quantum gravity in much

> simpler more physical form.

>

> Quantization of magnetic flux in loops in EM becomes quantization

> of areas on closed non-bounding surfaces that enclose the point

> singularity of the two vacuum Goldstone phases of the single valued

> ODLRO parameter in subspace geometrodynamics where we associate 1 c-

> bit per quantum of area.

>

> Theta and Phi are Goldstone phases associated with the Higgsian

> type vacuum ODLRO coherent inflation field whose random residue is

> either anti-gravitating negative pressure dark energy or

> gravitating positive pressure dark matter. This has a point defect

> with quantized area consistent with Bekenstein-Hawking black hole

> entropy and t'Hooft-Susskind world hologram. Event horizons are

> here to stay Paul and any theory like Waldyr's and those who say

> Hilbert made an error are wrong physically even if their math is

> not "nonsense"! As Feynman said a beautiful math theory is murdered

> by an ugly fact. Here is my beautiful physical idea:

>

> (Quantum of Area)^-1 = |Vacuum ODLRO Condensate|^2 + /
>

> /\ > 0 is dark energy exotic vacuum state

>

> /\ < 0 is dark matter exotic vacuum state - no on-mass-shell exotic

> particles in LHC.

Gravity Force in Newton & Einstein
In other words Paul

In Newton's gravity theory you can explain the weightlessness felt by that freely-falling object as an objective g-force

g = - GradV(Newton)

cancelled by the object's local rest frame fall.

to get

g' = 0 for the object in the object's local rest frame, which in Newton's theory

is NON-INERTIAL because Newton's geodesics for his first law are straight lines without acceleration.

That is you have

Objective g-force - Inertial force = 0 on the parabolic path of the cannon ball for the vertical component because

Einstein's geodesic = Newton's non-geodesic.

But in Einstein's theory the geodesic g-force is zero from the equivalence principle.

There is no objective g-force at all like there is in Newton's theory. Newton's objective g-force in flat Euclidean space with absolute time is replaced by a free-float geodesic in curved space-time! The only "g-force" is felt on a non-geodesic in curved space-time caused by a non-gravity force! You have never understood General Relativity Paul. Your whole short career in relativity has been predicated on attempting to force inappropriate concepts of the earlier smaller theory on the later covering theory - a basic error.
On the formal aspects of Einstein's equivalence principle

i.e. with Einstein-Cartan tetrad fields eu^a

guv = eu^a(Minkowski Flat)abev^b

Define the local frame invariant

e = eu^adx^u&a

e = 1 + L

L is the curved tetrad local invariant

L^a are L's 4 tetrads that Waldyr got all hot and bothered about because he did not like my index-free notation above. This is a symbolic compact notation and is a very useful piece of "mathematical nonsense."

Define the spin connection 1-forms

W^a^b = W^a^budx^u

Or W = W^a^b&a&b

Define symbolically

D = d + W/\ exterior covariant derivative for T4 local gauging

The torsion field 2-form is

T = De = 0 by definition of this limited 1915 GR theory.

i.e.

dL is a 2-form.

In my theory

(Quantum of Area)^1/2dL is the area flux density 2-form A

dL = 2(Quantum of Area)^1/2d@/\d&

where

d(@/\d&) = d@/\d&

d((d@)/\&) = -d@/\d&

Therefore

L ~ @/\d& - d@/\&

is a non-closed 1-form.

This is essentially the World Hologram Ansatz

@ and & are two effective Goldstone phases in 4D space-time projected out of a larger set in hyperspace.

T = de + W/\e = dL + W/\(1 + L) = 0

since d1 = 0

The curvature 2-form is

R = DW

Bianchi identities are

DR = 0

To make a partial analogy with Maxwell's electromagnetism

W is like A

R is like F

dF = 0 is Faraday's law and no magnetic monopoles

But now the analogy breaks down. In Maxwell's theory

d*F = *J are the source Ampere's law and Gauss's law.

d^2*F = d*J = 0 is local current density conservation

The false analogy would be

D*R = *J

but that is not Einstein's source equation.

Rather the Einstein-Hilbert geometrodynamical action density is ~ the 4-form

~ R/\e/\e

The Euler-Lagrange field equation is then for this vacuum case

R/\e = 0 ---> Ruv = 0

D(R/\e) = DR/\e + (-1)^2R/\De = 0

Since zero torsion De = 0

DR = 0

But in general

DR/\e + R/\T = 0



On Aug 2, 2006, at 6:37 PM, Jack Sarfatti wrote:


On Aug 2, 2006, at 5:24 PM, Paul Zielinski wrote:

All the math you need to understand this is F = ma. Jack, you are making things much too complicated.

Einstein said "Physics should be as simple as possible, but not simpler than is possible." Your last remark on "F = ma" is simpler than is possible.

The covariant "F = ma" is the local frame-independent NON-GEODESIC equation

x^u;s;s = F^u/m

in the coincident LNIF

In the coincident LIF x^u;s;s ---> x^u,s,s

However in the REST LNIF (c = 1) of the test particle

{i00} ~ F^i/m is the g-force/mass reaction to the non-gravity force F^i

i = 1,2,3


You are the one making extraordinary claims here Paul not me.

Whereas I think the thesis that an observer-dependent inertial field is the same as an objective physical g-field caused by the presence of matter is, if taken seriously, an extraordinary claim that needs to be justified.

Your statement above is not even wrong. There is no "objective physical g-field" caused by the presence of matter! Therefore, your whole thesis is bogus. You have misunderstood the equivalence principle and Einstein's vision. You have not been able to get outside of Newton's prison. For you it is a prison.

Look Paul you can REPRESENT Einstein's metric field for small M/r (G = c = 1 convention) above Earth's surface as

ds^2 = -(1 - 2M/r)dt^2 + (1 - 2M/r)^-1dr^2 + r^2d(angle)^2

This is only for local LNIF HOVERING NON-GEODESIC OBSERVERS.

When you stand on Earth you are such an observer!

When you get at Earth's surface

g = -M/r^2

that comes from the connection field {uvw} in this hovering LNIF REPRESENTATION

{i00} = -F^i(electric)/m = g

Your "weight" W = m{i00} is the reaction inertial force to the classical electric forces + quantum exchange Pauli Exclusion Principle potentials from the atomic electrons in the ground.

You have compensation only in the HOVERING rest LNIF

g-force + non-gravity force = 0

Actually Bernie Haisch got that part right in one of his wrong "ZPF Origin of Inertia" papers.

In contrast on a geodesic, logically independent of curvature, g-force = 0, i.e. people on geodesics are in free float i.e. weightless whether there is curvature or not! When the curvature gets strong every one feels it whether on geodesics or not! That's the physical meaning of curvature as a tensor field.

In short, there is no such thing as an objective gravity force created by matter in Einstein's geometrodynamics although there is in Newton's theory of gravity. Quantum field theorists speak loosely in a Newtonian way of gravity as a force. This is one reason that "quantum gravity" is muddled.

You can think that way in Newton's theory but not in Einstein's. That is because the two theories have different concepts of "geodesics". Newton's geodesic assumes implicitly flat space-time. Therefore a parabolic path must be caused by an objective g-force in Newton's picture. You are stuck in the 17th Century Paul.

Breakdown of analogy of gravity to electromagnetism

All local gauge theories come from localizing a rigid global symmetry of a physical dynamical action.

The compensating gauge potential field restoring the symmetry by adding additional dynamical degrees of freedom is a connection field for parallel transport. It is not a tensor relative to the gauge group.

The tensor "force" is the curvature of the connection.

Einstein's universal gravity comes from localizing the 4D translational symmetry of ALL physical actions. Translational symmetries are generated by energy-momentum. The equivalence principle breaks the usual Noether theorem connecting symmetry to conservation laws. All forms of energy-momentum including the virtual zero point vacuum quanta are gravity charges. This is why dark energy accelerates the expansion of space in our pocket universe of the megaverse of parallel worlds on the populated cosmic landscape of chaotic eternal inflation of sprouting baby pocket universes. It is also essentially how flying saucers work. The direct role of virtual zero point quanta in gravity is very different from its indirect role in internal symmetry gauge forces where it is indirect like in Casimir force and in the Lamb shift for example. The difference is the equivalence principle that adds a qualitative new feature to the physics making the gravity field non-renormalizable in top-down quantization. This is because the gravity field is bottom-up emergent from the renormalizable internal symmetry quantum fields forming the pre-inflationary false vacuum.

If you think "gravity field" think tensor curvature geodesic deviation on pairs of neutral test particle in same breath as tensor electromagnetic Lorentz force field on a single test particle. Do not think the 100% inertial g-force AKA "weight" because that is a connection field with gauge freedom exactly like the electromagnetic 4-potential that includes the Coulomb potential. Newton's potential is part of the metric field at the next level up from the connection Levi-Civita field. Therefore, the simplistic formal analogy of V(Newton) = -GM/r to V(Coulomb) = Q/r is very deceptive indeed - a Siren that has sunk Zielinski's ship!

Note raw alleged evidence for flying saucers on video.
http://www.hbccufo.org/modules.php?name=News&file=article&sid=4597
http://www.youtube.com/watch?v=Z7jrmkeU78I&mode=related&search=ufo





On Aug 1, 2006, at 11:54 PM, Jack Sarfatti wrote:

change

It's also confusing because gravity really is a force in Newton's theory, though not in Einstein's. Einstein eliminates gravity as an intrinsic force like electromagnetic force replacing gravity force.

to

It's also confusing because gravity really is a force in Newton's theory, though not in Einstein's. Einstein eliminates gravity as an intrinsic force like electromagnetic force replacing g-force with curved space-time.

Note the "curvature" in internal fiber space is the gauge "force". Therefore, the correct analogy between gravity and electromagnetism

space-time curvature analogous to electromagnetic force
i.e.

d^2(x^u - x'^u)/ds^2 = R^uvwl(dx^v/ds)(dx'^w/ds)(x^l - x'^l) gravity tidal acceleration for a pair of geodesic test particles

(This local frame-independent tensor equation can be calculated in either a LIF or a coincident LNIF)

is properly compared to the electromagnetic Lorentz force tensor equation

d^2x^u/ds^2 = (e/m)F^uvdx^v/ds for a single test particle with charge to mass ratio e/m.

In the language of Cartan's differential forms for space-time gravity for zero torsion limit

R = DW

R = curvature 2-form

W = spin-connection 1-form

D = d + W/\ = covariant exterior derivative

/\ = exterior multiplication

For general internal symmetry Yang-Mills fields (EM as trivial Abelian case)

D = d + A/
A = 4-potential connection 1-form

F = DA = Yang-Mills curvature 2-form ---> Yang-Mills 'force field" analog to Lorentz force eq.

Both

DR = D^2W = 0 (Gravity) and DF = D^2A = 0 (Yang Mills) analog of Faraday's law & no magnetic monopoles

also

D*W = *J source eq. D*F = *J (Yang-Mills) source eq.

Here the analogy breaks down from the equivalence principle.

The Gravity source equation is a 4-form equation because W is a 1-form and *W is a 3-form. So *J is a 4-form.
J is 0-form local scalar.

With tetrad indices this is

D*Wab = *Jab

that maps to

Guv = kTuv

Local conservation of matter source stress-energy current density is from

D^2*Wab = D*Jab = 0

i.e. Tuv(Matter)^;v = 0

In contrast for Yang-Mills fields

D*F = *J is a 3-form eq. analog of Ampere's law and Gauss's law.

D*J = 0 local conservation of electrical current densities.

Understanding "Gravity Force"
bcc
In a nut shell Zielinski makes the common amateur error of pushing the superficial analogy of Newton's gravity potential -GM/r with Coulomb's electrical potential Q/r too far. See details below.

Franz Kafka, feeling like a cockroach under a magnifying glass focusing a blinding light, wakes up having been abducted by Gray cyborgs. He is in a closed room with no windows. He manages to undo the straps of the table bolted to the floor and he begins to float off the table. He holds on to one of the straps. Being a good physicist as well as story writer, Kafka knows instantly he is on a timelike geodesic out in space. Warp drive is the same experience the difference is that the Captain can control his ship's geodesic glide path to point in any direction and speed he likes without feeling any g-forces at all because no propellant is ejected in the maneuvers including sharp turns in space even instant U-turns. This is metric engineering the dark energy-matter envelope around the ship.

Kafka manages to find a port hole cover. He opens it. To his horror he sees that the ship is falling toward the Sun! That explains why it's been getting hotter. He sees a control panel on the side of the table he had been strapped to. He pulls on the strap to get closer to it. In desperation he starts playing with a joystick and suddenly he is pulled to the table. He feels weight returning. The ship's normal impulse swivel rocket engines have been switched on. He plays with the stick and some of the knobs and finally through his psychic intuition he finds a setting in which the ship stands still relative to the distant Sun that fortunately is still as far away as Venus. Indeed looking in a different direction he can see the planet Venus. The zero point energy powered rocket engines must continually fire to keep the ship hovering at a fixed distance from the Sun and from Venus. This hovering fixed point is a non-geodesic path through spacetime. Having wiped the sweat off his brow, he sees a spigot on the table side and is able to get some sweet-tasting water that instantly gives him a sense of well-being and relaxation in addition to a feeling of great muscular strength and youthful vitality. At that moment three Grays enter the room. The delicate one in the middle who seems more feminine than the other two says to him telepathically without sound "That was nicely done Professor Kafka. We apologize for putting you under stress, but you were in no real danger. Would you like us to explain to you how our ship works." Kafka answers - thinking telepathically "Is The Pope Catholic?"

On Aug 1, 2006, at 3:23 PM, Paul Zielinski wrote:

Jack Sarfatti wrote:

Paul you are fundamentally wrong. I need to run now. More later tonite.
You are not the only one confused by this. It's subtle. There is no intrinsic gravity force. It's an inertial force created by nongravity forces pushing test particles off geodesics.

Yes it is very confusing owing to the nature of the GR terminology, but I can assure you I'm not the one who is
confused here.

It's also confusing because gravity really is a force in Newton's theory, though not in Einstein's. Einstein eliminates gravity as an intrinsic force like electromagnetic force replacing g-force with curved space-time.

Note the "curvature" in internal fiber space is the gauge "force". Therefore, the correct analogy between gravity and electromagnetism

space-time curvature analogous to electromagnetic force
i.e.

d^2(x^u - x'^u)/ds^2 = R^uvwl(dx^v/ds)(dx'^w/ds)(x^l - x'^l) gravity tidal acceleration for a pair of geodesic test particles

(This local frame-independent tensor equation can be calculated in either a LIF or a coincident LNIF)

is properly compared to the electromagnetic Lorentz force tensor equation

d^2x^u/ds^2 = (e/m)F^uvdx^v/ds for a single test particle with charge to mass ratio e/m.

In the language of Cartan's differential forms for space-time gravity for zero torsion limit

R = DW

R = curvature 2-form

W = spin-connection 1-form

D = d + W/\ = covariant exterior derivative

/\ = exterior multiplication

For general internal symmetry Yang-Mills fields (EM as trivial Abelian case)

D = d + A/
A = 4-potential connection 1-form

F = DA = Yang-Mills curvature 2-form ---> Yang-Mills 'force field" analog to Lorentz force eq.

Both

DR = D^2W = 0 (Gravity) and DF = D^2A = 0 (Yang Mills) analog of Faraday's law & no magnetic monopoles

also

D*W = *J source eq. D*F = *J (Yang-Mills) source eq.

Here the analogy breaks down from the equivalence principle.

The Gravity source equation is a 4-form equation because W is a 1-form and *W is a 3-form. So *J is a 4-form.
J is 0-form local scalar.

With tetrad indices this is

D*Wab = *Jab

that maps to

Guv = kTuv

Local conservation of matter source stress-energy current density is from

D^2*Wab = D*Jab = 0

i.e. Tuv(Matter)^;v = 0

In contrast for Yang-Mills fields

D*F = *J is a 3-form eq. analog of Ampere's law and Gauss's law.

D*J = 0 local conservation of electrical current densities.

The equivalence principle is profound and many-faceted. There are deep similarities but also profound differences between the internal symmetry (extra dimensions of space) gauge theories and the space-time gauge theory of GR - the key difference is the equivalence principle.

The geodesic in Newton's theory is a straight line in Euclidean 3D space decoupled from 1D time at constant speed, no acceleration. Global inertial frames cover the entire space.

A test object falls freely to Earth. In Newton's theory the surface of earth is approximated as a GLOBAL INERTIAL FRAME. The parabolic trajectory of the test object is explained as a real gravity force in the Earth as an inertial frame. Einstein turns this upside down - PARADIGM SHIFT! The Earth is now a LOCAL NON-INERTIAL FRAME i.e. no global frames and the geodesic is completely different. The Einsteinian geodesic is in curved 4D space-time it can be a precessing ellipse in 3D space with accelerations relative to Earth frame at a focus. There is no pure gravity force on the test object because by definition real forces push test objects off geodesics.

Of course in both Newton's and Einstein's theories an observer on the freely-falling test object is weightless. However, the explanation for this invariant fact under morphing between the theories is very different.

Your error Paul is that you are trying to force Newton's explanation on Einstein's theory. It doesn't work! Apples and Oranges.

Any g-force is 100% an inertial reaction force in the local rest non-inertial frame of the test object generated by a non-gravity force (for all practical purposes an electromagnetic force).

Let's take some examples.

In globally flat empty space-time the metric is that of special relativity c = 1

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

This formula is an INERTIAL REPRESENTATION of invariant ds^2 for tiny inertial observer-detectors on timelike geodesics. In this case the timelike geodesics are Newtonian to a good approximation.

Obviously the Levi-Civita connection field (whose special combination is g-force) is globally zero in this inertial representation because the first partial derivatives of the constant metric components vanish. Obviously the geodesic deviation curvature tensor components vanish also. Note two kinds of geodesic deviation - Ricci components for a cloud of GEODESIC TEST OBJECTS and WEYL CONFORMAL TIDAL STRETCH-SQUEEZE (e.g. gravity waves). The pure gravity vacuum field without dark energy and torsion is 100% Weyl tensor. See Penrose "Road to Reality" for more details on that distinction.

However, we can still do a GCT (General Coordinate Transformation) on our flat metric to get

ds^2 = guvdx^udx^v

Now we will get a non-vanishing connection field!

What does this mean?

It means we are now in a LOCALLY VARIABLE NON-INERTIAL NON-GEODESIC REPRESENTATION.

Paul one of your errors is thinking only FORMALLY without thinking of the OPERATION MEANING of the GCT. What we have here is a NETWORK WEB of tiny NON-GEODESIC OBSERVERS firing their rocket engines arbitrarily. Not one of these observers could get on a non-geodesic were it not for the electromagnetic force. We can neglect consideration weak-strong forces here for all practical purposes since they are short range and we are at macro-range here.

Now compute the geodesic deviation - what is it? All components STILL ZERO. The curvature is zero!

How do the local non-geodesic observers do the experiment? -They can use tiny water drops if you like. The drop will not change shape. Better to use a dust cloud so as not to correct for surface tension.

Next in isotropic radial coordinate (that Hal Puthoff confounds with Schwarzschild radial coordinate in his wrong PV gravity theory in Eric Davis's USAF "Teleportation" study) in weak slow test particle speed limit, with UNIVERSAL Newtonian gravity potential energy V per unit test particle mass with a SSS (Static Spherically Symmetric) SOURCE:

ds^2 ~ (1 + 2V)dt^2 - (1 - 2V)[dx^2 + dy^2 + dz^2]

In Hal Puthoff's PV theory replace (1 + 2V) by e^2V

But this too is a representation in terms of HOVERING local non-inertial observers firing their rocket engines just so such that they all experience WEIGHT/MASS = UNIVERSAL "g-force" (loose terminology)

gi ~ - dV/dxi

ds^2 = [(1 - 2m/4r*)/(1 + 2m/4r*)]^2dt^2 - (1 + 2m/4r*)^4(dr*^2 + r*^2dAngle^2)

Note to get to usual Schwarzshild non-inertial representation use

r = r*(1 + 2m/4r*)^2

ds^2 = (1 - 2m/r)dt^2 - (1 - 2m/r)^-1dr^2 + r^2dAngle^2

really only for 2m/r < 1

Then V = - m/r

Area of concentric sphere about center of symmetry is 4pir^2

V is dimensionless in these units

g ~ -m/r^2 ~ 1/Length

However, now when they use tiny dust cloud of geodesic nanobots with transceivers to central computer they get in empty space the Weyl conformal curvature components C of the form (loosely speaking)

C ~ m/r^3 ~ 1/Area

Now here is the crucial point - in first case of globally flat space-time you can MOCK up the g-field to look just like the second case, but you will not find geodesic deviation i.e. you will find C = 0.

THIS DOES NOT VIOLATE EQUIVALENCE PRINCIPLE IT CONFIRMS IT.

LOCALLY all g-force measurements are same in both cases. Only when you do a completely different kind of measurement can you tell that there is a source in second case and none in first case. In both cases the local observers are in NON-INERTIAL REPRESENTATIONS!

Another point Paul is that you cannot think in the Newtonian manner, as you do, that

g-force = objective intrinsic tensor g-force - compensating local frame-dependent g-force

such that

g-force = 0 in a Local Inertial Frame coincident with test object on geodesic.

Note that the geodesic equation for test object is in frame-invariant form

D^2x^u/ds^2 = 0

In the REST LIF of the test object this is simply

d^2x^u/ds^2 = 0

g-force (100% inertial) is only registered in the rest frame of the test object when it is OFF-GEODESIC i.e. a different equation

D^2x^u/ds^2 = F^u(non-gravity)/M(test object)

In the object's now local non-inertial frame

d^2x&u/ds^2 = 0 as before, but now

g-inertial force (AKA "weight") ~ Connection Field^i00 ~ F^i(non-gravity)/M(test object)

i = 1,2,3 space components.


You are confusing a coordinate transformation of a given geodesic trajectory with an actual change from
one geodesic trajectory to another. Even in standard GR there is at least a *mathematical* distinction between
the two cases.

No I am not.

Changes in observer motion alone cannot change the geodesic trajectory of any freely falling body;

Of course.

while a changing gravitational field can.

Of course.

In GR, frame acceleration simply changes the *coordinate representation* of a geodesic.

Correct, and that's consistent with what I do above.

Suppose the test object is charged in an electric field, then in a local LIF, NO LONGER A REST FRAME of the test object

d^2x^u/ds^2 = F^u/M =/= 0.

connection field zero in that momentary LIF.


In addition, it should be intuitively obvious that there are two separate components to the Einstein g-field, one
physical and frame-independent, and the other subjective and frame-dependent.

You are wrong. Your intuition is no good here. That is proved by the fact you have not been able to formulate your intuition here mathematically in many years and you will never be able to do so because it is impossible. You are forcing Newton's world picture into Einstein's incompatible world picture - never mind that they give same answers to a good approximation in many ordinary situations.

Let's suppose there is a material source
located at some point, generating a static gravitational field of some kind, and we are observing this in a frame of
reference that is stationary with respect to the source. Now transform into a frame of reference that is accelerating
away from the source. If, keeping that frame of reference fixed, we suddenly remove the source to infinity, both the
tidal and the physical part of the g-field vanish, leaving only the inertial field. This shows immediately the physical
link between tidal curvature and the objective physical part of the g-field. In GR, there is also a corresponding
mathematical link between the two properties (tidal and g-field) of the curved metric. This also shows that the
distinction between the inertial and gravitational components of the combined g-field is *physically meaningful*
(since one component causally depends on the matter distribution, while the other does not).

What I am doing here is treating the objective physical g-field just like, say, an electrostatic field.

Yes, I know you are and that is an error!

The problem is that we have a metric field guv ~ Newton's potential

Einstein's connection ~ gradients of Newton's potential

Einstein's curvature ~ gradients of gradients of Newton's potential

Your analogy to electrostatics is naive, superficial and completely wrong. It's what all amateurs do!

V(Newton) ~ -GM/r

V(Coulomb) ~ - Q/r

However, in Maxwell EM field theory

V(Coulomb) & Vector Potential A form the CONNECTION FIELD in internal S1 fiber space!

This is where your analogy profoundly breaks down and your entire thesis is not even wrong!

To take your analogy to it's absurd conclusion:

Einstein's metric would be a space-time connection since Newton's potential is part of it!

Now you can also see your error also in the Reissner-Nordstrom geometry with a charge on the SSS source where

(1 - 2m/r) is replaced by (1 - 2m/r + Q^2/r^2)

If we were to use your false analogy this should be, by your faulty intuition,

(1 + 2V(Gravity) +2 V(Coulomb) ) = (1 - 2m/r + Q/r)

The point is that in Maxwell's local gauge theory of the electromagnetic field, the Coulomb potential is the timelike part of a 4-potential connection field in internal symmetry space. Think fiber bundles.

But you cannot think of Newton's potential as part of the space-time connection field!

The difference is the equivalence principle. There is no equivalence principle for the EM force (not allowing Kaluza-Klein theory here).

Note that the gauge freedom of the connection fields is GCT in the case of the space-time connection.

Gauge transformations of EM/Yang-Mills connection fields are INHOMOGENEOUS just like space-time connection.

So in Einstein's GR gravity you have 3 levels

Metric (Newton's potential in weak field limit) tensor with local invariant ds^2

Connection (g-force) non-tensor NO local invariants! (barring tensor torsion of course)

Curvature tensor with local invariants.

There is also the 4 subspace level of tetrads where the metric is symmetric bilinear in the tetrads.

Curved tetrad is from local gauging of T4 - zero torsion.

Then in my emergent gravity theory the tetrads come from variations in the World Hologram Goldstone Phases of the Higgsian type Vacuum ODLRO inflation field. So this is a 5th level.

But in Maxwell & Yang-Mills local gaugings of internal U(1em), SU(2 weak) & SU(3 strong)

NO METRIC LEVEL!

The Coulomb potential is part of the CONNECTION

The tensor FIELD CURVATURE gives the electrostatic force that you FALSELY compare with g-force.

It should now be obvious why your entire thesis is PROFOUNDLY NOT-EVEN-WRONG.

Paul you have made a very common naive error made by many amateurs trying to make FREE ENERGY MACHINES and explain UFO saucer propulsion.

I am not reading the stuff below based on your false analogy of gravity to electrostatics.

Another way to see it is that

EM, Weak, Strong are renormalizable SPIN 1 theories.

Gravity is unrenormalizable SPIN 2 - but that gets into quantum field theory complications

The apparent net
effect of the electrostatic field on the motion of a charged particle depends on the observer's frame of reference,
because in certain observer frames the effects of the electrostatic field are compensated by the effects of frame
acceleration. Of course that doesn't mean that the electrostatic field itself is actually changing -- it is simply being
offset, as viewed from a given frame of reference, by an inertial field (of fictitious forces). Clearly in this case
the electrostatic and inertial fields are "apples and oranges", even in 100% orthodox textbook GR.

The situation is exactly the same for gravitational fields in GR, in the model I am proposing. The electrostatic example
clearly shows that such an "inertial compensation" interpretation of GR is feasible as a physical model.

This is why quantum fluctuations are in creative tension with classical equivalence since they are non-geodesic from the Bohm quantum potential which mimics electrical forces in a sense. The intrinsic gravity field is the relationship among the geodesics - hence curvature as "geodesic deviation". That you can write the connection field as a smooth field is relative to a set of detectors like hovering detections in standard REP is deceptive causing your confusion. But it has no scalar invariants i.e. is not a tensor field.

Jack, it is you who is confused here. The "forces" that are felt when you push a freely falling body off a geodesic
have nothing to do with *fictitious forces*. In GR this is simply a form of inertial resistance, which *appears* in
certain frames as inertia, while it *appears* in certain other frames as weight. This equally apparent character of
inertia and weight is what Einstein hoped would give him his "general relativity" and explain the equality of
gravitational and inertial mass. But when you look at his final 1916 theory, you immediately see that geodesics are
defined in a full covariant and completely objective manner, and frame transformations have the effect of changing
only the coordinate representation of geodesics, and not the actual geodesics themselves. So the most natural
interpretation of the 1916 formalism is the inertial compensation model I am proposing, which is however inconsistent
with Einstein's original concept of "general relativity".

It's just that in my model, the combined gravitational-inertial field of Einstein has a separate and distinct objective
component that is causally tied to the source(s) of the field. Eliminate the sources -- in a fixed frame of reference --
and you automatically eliminate both the tidal effects *and* the effects of the physical observer-independent part of the
g-field. Thus both the tidal and physical g-fields are causally related to the source of the actual physical
gravitational field. What is left after you remove the source while keeping the reference frame fixed is the pure inertial
part of Einstein's field.

This is like

F(x,y) = X(x) + Y(y)

So these two components really are apples and oranges, even in GR. In this respect GR is actually not significantly
different from Newtonian theory, despite all the hype. Strange, but true.

This is tricky and deep.

It is tricky.

Z.


On Aug 1, 2006, at 12:07 AM, Paul Zielinski wrote:

Jack Sarfatti wrote:

> Z: One aspect of this field is the action of so-called "g- forces" that act on
> test bodies;


WRONG. The g-force is NOT a property of the the gravitational field!

OK, then here is the nub of our disagreement.

I'm saying that there is an irreducible frame-independent component of the combined
g-field that is directly linked to curvature. I am saying that if you remove the sources
of the gravitational field, in a fixed observer frame, then this physical g-field
component goes to zero, along with the tidal forces, while the inertial g-field
component is unaltered.

The g-force is a property of non-gravity forces that create non- geodesic paths!

I say this only applies to the frame-dependent part (inertial part) of the combined
g-field.

Pure gravity is all geodesic paths.
Curvature is a property of geodesics.
There is no such thing as pure gravity force in GR.

Yes there is. That's the whole point.