bcc new advanced physics list
Paul, I suspect the key CLASSICAL argument against a LOCAL vacuum gravity stress-energy tensor different from Ruv itself in Einstein's vacuum field equation
Ruv = 0
goes something like this
1. If ordinary matter, radiation and near EM fields (all in Tuv) are locally present then Einstein's CLASSICAL local field equation
Guv = Ruv - (1/2)Rguv = - (8piG/c^4)Tuv
Can be written as
tuv(vac) + Tuv = 0
Where
tuv(vac) = (c^4/8piG)Guv = (String Tension)("Marble" Curvature)
i.e. in Einstein's colorful terms
tuv(Marble) + Tuv(Wood) = 0
End of story, simple solution.
2. Another aspect of the problem is to add new nonlinear terms like
t'uv(vac) =Lp^2 (c^4/8piG)RuwlsRv^w^l^s
to the field equation. I did not check BTW to see if that particular expression is a symmetric tensor. I am just trying to show the general idea.
3. Quantum aspect of the problem is that random zero point vacuum fluctuations of all physical quantum fields contribute to the "cosmological term"
/\zpfguv
that must be added to Einstein's field equations to get
Guv + /\zpfguv = - (String Tension)^-1Tuv
Note that Sakharov's
"Metric Elasticity" = (String Tension)^-1 = Space-Time Stiffness
The tighter the string tension the less elastic is the geometry.
/\zpf = exotic vacuum unified Dark Energy/Matter LOCAL field, which in large scale FRW regime is Einstein's "cosmological constant" but on smaller scale is a local inhomogeneous dynamic spin 0 field that stabilizes the spatially-extended "hidden variable" lepto-quarks against their explosive self-electric charge. The lepto-quarks obey a "micro-geon" quasi Kerr-Newmann metric with additional topological "handles" for the SU(2)xSU(3) charge generators in the extra space dimensions (i.e. Calabi-Yau spaces of M theory in "engineer's language" via "black hole - membrane" dualities). The lepto-quarks shrink from 10^-13 cm at low energy to 10^-18 cm for high energy large magnification Heisenberg microscope images because of the huge space warp from the strong G* ~ 10^40 G(Newton) zero point dark energy cores holding the explosive self-electric charge and the centrifugal & Coriolis inertial forces in equilibrium. All this is "IT" in the Bohm Pilot "BIT" Wave theory.
IT gets its marching orders from BIT (action)
BIT is warped by IT (reaction)
At a coarser purely IT level "Matter" emerges as micro-geons getting subsidiary "classical" marching orders from geometry.
The "geometry" is from the macro-quantum coherence, i.e.,
guv = (Minkowski)uv + (Metric Elasticity)(Modulation of Goldstone Vacuum Superfluid Phase)uv
/\zpf = (Planck Area*)^-1[1 - (Planck Volume)(Higgs Field)^2]
/\zpf = 0 is "classical" non-gravitating non-exotic vacuum.
/\zpf > 0 is w = -1 anti-gravity exotic vacuum "dark energy" with negative pressure and positive zero point energy density.
/\zpf < 0 is w = -1 gravitating exotic vacuum "dark matter" with positive pressure and negative zero point energy density.
Big clumps of w = -1 "dark matter" (e.g. dark galactic spheres) float in the Hubble flow like w ~ 0 for us distant observers.
Lp*^2 = G*h/c^3
Universal Regge slope of hadronic resonances on micro-scale is
G*/hc^5 in
J = (G*/hc^5)E^2 + Jo = n/2
Blackett Effect seen in many rotating astrophysical objects with anomalous magnetic dipole is reduced to
G^1/2m = e
(papers by Saul-Paul Sirag)
at large scale where G* ---> G.
Now Matt Visser's review paper has impractical perturbative quantum field theory formulae for both large-scale G(Newton) and cosmological constant /\.
However my model is better because it is intrinsically non-perturbative like the BCS theory is.
I have NON-PERTURBATIVE
Macro-Quantum Vacuum Coherence = (Higgs Field)e^i (Goldstone Phase)
Visser does not have that non-perturbative "More is different" (PW Anderson) "Vacuum Coherence" whose "generalized phase rigidity" is precisely "String Tension" (in Blackhole-Membrane Duality) = Sakharov's (Metric Elasticity)^-1.
I also explain how LOCAL MACRO PHYSICS emerges from quantum field theory whose entangled Fock space states are nonlocal. I also explain why post-inflationary early universe has low entropy from collapse of vacuum phase space volume hence how the cosmic irreversibility Arrow of Time is pointed. I also give a micro-QED dynamical instability for the large scale FRW "chaotic inflation field" of Linde et-al, which previously was only a useful "fudge factor" with no fundamental dynamics (according to Mike Turner at both March & April 2003 APS meetings).
On Tuesday, November 4, 2003, at 08:29 AM, Jack Sarfatti wrote:
On Monday, November 3, 2003, at 10:09 PM, Paul Zielinski wrote:
Jack Sarfatti wrote:
Paul
The MTW argument against Yilmaz is simply that one cannot make a local
classical vacuum pure gravity stress-energy density tensor from the
torsion-free non tensor connection without violating the equivalence
principle.
"But we have to be very careful about what we mean by "the equivalence principle".
There is the so-called "EEP"; there is Einstein's original "equivalence principle;" which
can be viewed as an interpretation of the "EEP"; and there is the alternative interpretation
of the "EEP" in terms of *inertial compensation* which rejects Einstein's fundamental
identification of gravitational and inertial fields."
What you need to do is spell out carefully all of these different versions in "formal" terms and in clear
operational terms to see if there is really any scientific difference of any importance. I do not understand
what you mean by "inertial compensation" above. I think the gravity force, i.e. the "fictitious" or "inertial" g-force i.e. the metric torsion-free connection for parallel transport in the original 1915 theory is LOCALLY equivalent to a
"gravity force". Whether or not that gravity force is "real" depends on whether or not there is a local tidal curvature differential in the g-force as described by the geodesic deviation equation between two neighboring timelike geodesic LIF free float observers. This curvature tensor tidal differential force cannot be eliminated locally.
All I mean effectively by "EEP" is the set of following "formal" statements.
1. There exist local tetrads ea^u(P) at point P such that
nab = ea^u(P)eb^v(P)guv(P)
2. The local symmetric torsion-free connection from first derivatives of the metric guv(P) can be set to zero locally at P.
This defines the distinction between LIFs on timelike geodesics and LNIF's on timelike non-geodesics both intersecting at same P.
Note timelike non-geodesics could not exist without electrical charge. Neither presumably could "light" hence no light cones hence nothing - not even null geodesics. This suggests in itself that gravity is an emergent collective effect primarily from electromagnetism and Heisenberg quantum uncertainty as
suggested by Sakharov's "metric elasticity."
Part of the confusion is that "curvature" = "field strength" in the modern fiber bundle picture of the spin 1 gauge forces.
The "connection" for parallel transport in the internal dimensions beyond space-time (or extra space dimensions of Kaluza-Klein et-al) is theYang-Mills "potential" like the EM 4-vector potential Au(P) in the U(1) EM simplest case.
On the other hand it is the metric, specifically goo(P) ~ (1 + 2U(Newton)/c^2) in weak field slow motion static spherically symmetric vacuum case outside M
where U(Newton) = -GM/r = Gravity potential energy per test particle from source mass M
leading to notion of gravity force as connection from Newton's 2nd law on test particle m
F = -m GradU(Newton)
F is locally eliminitable on the LIF timelike geodesics in curved space-time.
Tidal inhomogeneous differentials F(P+dP) - F(P) are not.
""EEP", as I understand it, merely requires that the net gravitational-inertial forces
acting on any test particle locally vanish in the free-fall frame, while tidal effects can
always be locally neglected."
This last statement needs clarification. It is strictly not true. It is only a "weak field" approximation
that the tidal effects are of order (L/r)^2 where r is the local scale of radius of curvature. MTW make
this approximate nature of the remark very clear when I read them. You have misinterpreted them
as making a much stronger statement and I think this is the root of the pseudo-problem you pose.
If Einstein was a bit confused on this in the early days, I don't know, it is of no real consequence
except in the history of the evolution of the idea.
"This can be consistently interpreted in at least two different ways: (1) as the consequence
of a (local) *fundamental physical identity* of gravitational and inertial fields (Einstein, Pauli);
or (2) as merely the result of inertial compensation of the separately existing gravitational
field (Eddington et al.) in conjunction with the natural attenuation of tidal effects within
arbitrarily small neighborhoods of spacetime.
Either way , the theory remains generally covariant, and a "weak" correspondence
relationship with SR holds -- locally measurable effects that locally discriminate between
the predictions of SR ("flat" spacetime) from those of GR ("curved" spacetime) can be
regarded as practically negligible in a sufficiently small neighborhood."
Yes, in the weak field limit, but not at a black hole, which Puthoff wrongly claims does not exist.
"I would argue that a "weak" correspondence relation is all that one can reasonably
demand of the re-interpreted theory. There is in reality no "flat" spacetime *anywhere*."
Fine, that's how I read MTW anyway. Also in my theory, globally flat space-time is intrinsically
dynamically unstable from quantum electrodynamics.
"Also, it is important to understand that none of this depends on the empirical correctness of
Yilmaz's particular theory vis a vis GR."
I find Yilmaz's idea completely obscure intuitively.
"For example, the alternative approach is taken in a number of bimetric theories that agree empirically with GR. These employ a "background" metric that accounts for inertial effects in conjunction with a separate (though commensurable)
"gravitational" metric that accounts for physical gravitation."
Very ugly. Less with more.
"In the alternative interpretation, I believe the way is open to consistently defining a true
gravitational field stress-energy density, which is fully localizable, and an inertially-compensated
*net effective* stress-energy density which corresponds to the force field that is actually
measured in an accelerated frame of reference."
Show me the math otherwise the words have no meaning to me.
"This means that Mach's principle is effectively abandoned -- along with his rather loony brand
of strict empiricism (remember, Mach flatly rejected the atomic theory)."
Mach's idea re-enters in the Holographic World where
Lp* = Lp^2/3(c/H)^1/3 = 1 fermi "now".
But this may have a fatal flaw since H is cosmic time dependent in the FRW regime.
The connection for parallel transport locally vanishes in
LIF's on timelike geodesics.
"Of course it does. But we can (at least locally) distinguish between the inertial and
the gravitational *components* of the canonical connection field (distinct contributions
to the net metric gradients). That comes right out of the differential geometry (also, see e.g.
Weinberg's "Gravitation and Cosmology")."
I think I said that above.
"The changes observed in net gravitational-inertial forces under acceleration of one's frame of
reference are then viewed not *merely* as an abstract mathematical property of the laws of GR
under certain class of spacetime coordinate transformations, but also as a *real physical effect*
arising from the interaction of ponderable matter with the physical vacuum (AKA "the luminiferous
aether").
The physical vacuum is not a void! It is the mother of all particles! The Urstoff!
Non-material, yet physical...
As I understand it, this is precisely the way the electromagnetic field is treated in GR when
observed in accelerated frames -- as inertially compensated. There is in canonical GR no
question of deriving EM forces from a geometrodynamic connection field, and so we are left
(in standard GR) with inertial forces derived from an *inertial* connection field that can physically
compensate the EM forces in the EM analog of free-fall.
Of course, we then no longer have "general relativity" in Einstein's sense, since we
do not have "strict" gravitational-inertial equivalence (gravitational and inertial fields
considered fundamentally indistinguishable).
Einstein's point may then be taken as this: the non-material aether is so inextricably bound up
with empty space, that the physical effects that result from interaction of ponderable matter
with the vacuum might as well be viewed as arising from a certain kind of geometry. We then
build accelerative effects into the kinematics of our theory. From this POV, we can always
decide as an alternative approach to investigate the properties of "empty" space as properties
of a physical entity -- the vacuum -- which is to be distinguished from a void. The "void"
of Einstein with its Riemannian geometry of spacetime manifolds then appears merely as the
shadow cast by a deeper reality -- the physics of the *physical vacuum* ("ghost of the departed
aether").
However, we do still have general covariance of the laws. The strength of the gravitational field
-- and, I would argue, its associated gravitational field stress-energy density -- is then no longer
dependent on one's frame of reference, and the true gravitational stress-energy should itself then
be represented by a tensor quantity (Diff(4) world-tensor).
What *is* dependent on one's frame of reference in this alternative interpretation is the *inertial
contribution* to the net forces experienced by massive bodies. Thus the inertial stress-energy
will then obviously NOT be represented by a tensor.
So we are talking about a (local) decomposition of the Christoffel connection into its inertial
(acceleration-dependent) and gravitational (acceleration-independent) parts.
In this view, for a single gravitating mass, the "true" gravitational field is the force field that is
observed in a frame at rest with respect to the source.
In the Einstein approach, in contrast, *all* frames of reference are on an equal physical footing
("general relativity") and there is no "true" gravitational force field -- any more than there is in SR a
true inertial frame in which clocks and rods assume their "actual" properties, or a "true" electric
or magnetic field considered separately.
If the connection is not zero at a point
then one is in a LNIF at that point feeling "weight" or "g-force" on a
timelike non-geodesic world line.
Of course. None of this is disturbed by the shift of interpretation, nor by the (local)
decomposition of the connection field into its inertial and gravitational parts.
We simply make a fundamental physical distinction between inertial and gravitational forces,
while fully recognizing the close mathematical analogy between them that was pointed out by
Einstein (both are derivable from metric-tensor fields) . In the alternative paradigm, we look for
the ground of this analogy at a deeper physical level, rather than basing it on some mystic
Galilean-Platonistic faith in the reality of the "forms" presented to us at first glance by tensor
analysis and differential geometry.
In the alternative ("neo-Lorentzian") paradigm, gravitation is a physical effect that depends
on the existence of gravitating matter and its time-dependent distribution in space. Inertial
"forces", on the other hand, are separate and distinct physical effects that do not depend on
the existence of material gravitational sources but only on the accelerative interaction of
ponderable matter with the physical vacuum (and not, *contra* Mach, with other material
objects)-- as I would assume any workable field theory of quantum gravity would predict.
While the curvature tensor tidal
force between two neighboring time-like LIF geodesic observers is
small in the weak field limit it is not locally zero in general and
cannot be eliminated exactly.
But there is the awkward question of the multipole effects experienced by spinning test-particles in
Riemannian gravitational fields -- which I understand do not scale down with spacetime volume as
do tidal effects.
And of course, there is also the closely related absolute character of "spacetime curvature", by
which I mean Riemannian curvature. It's either there or it isn't. Einstein was only able to save
his "general relativity" thesis by pretending that Riemann curvature has no direct empirical
meaning -- at least locally -- thus fixing all attention on the connection field as physically "real".
That now strikes me as a classic *ad hoc* stratagem in what Imre Lakatos might have called a
"degenerating problemshift".
These kinds of questions were thoroughly thrashed out between Einstein and von Laue in the early
1920s. I believe later Einstein quietly came to accept the fact that his concept of "general relativity" had
failed.
Which raises fundamental questions about the true character and status of special relativity, since
Einstein's "theory of relativity" program required both special *and* general relativity to succeed in
order to be fully vindicated.
One could try to make a local classical
vacuum stress-energy density tensor from contracted quadratic forms of
the 4th rank curvature tensor, but then one has a field equation like
Ruv - (1/2)Rguv + /\zpfguv + Quadratic Functional of Ruvwl =
8pi(G/c^4)Tuv(matter)
The problem then is to conserve the local currents.
Wouldn't it be easier to look first at the definitions of gravitational and inertial stress-energy densities
for "flat" fields?
What is the stress-energy density of the pure inertial field (no sources)? What are its mathematical
properties?
What is the acceleration-independent gravitational field stress-energy density in the far field ("asymptotically
flat" spacetime)? What are its mathematical properties?"
Z.
I will get back to you on last half later.
