Debate on GR

bcc

No closure yet. ;-)

On Thursday, January 8, 2004, at 02:52 PM, Paul Zielinski wrote:

Jack Sarfatti wrote:

I am trying to get some closure on this debate of at least 2 years that
has been interesting in that it has deepened my heuristic understanding
of Einstein's magnificent achievement and of the "cheap" attempts to
replace it as in Hal Puthoff's "PV" approach to "metric engineering"
(exotic UFO warp drive). I support a lot of Hal's scientific work BTW,
but not this particular item.

PZ: Let's be clear that I also view Einstein's theory as a magnificent
achievement, even
if the position I have been arguing here is eventually vindicated.

It is certainly a beautiful theory. A little too beautiful, perhaps.

JS: Not possible IMHO.

PZ: The question in my POV is, from the standpoint of gravitational
*physics*, is it the
proper point of departure for heuristic development of a viable theory
of quantum
gravity? And, does classic GR, with its Einsteinian "equivalence
principle", faithfully
reflect the true nature of physical gravitation?

JS: In my opinion it does. There is no problem with Einstein's original
idea of the equivalence principle i.e.
The non-tensor g-force is locally equivalent to an inertial force. This
is always true, independent of the local tensor curvature at the same
"point".
Also, the g-force can be locally eliminated by switching the test
particle from a non-geodesic LNIF to a geodesic LIF that is "coincident"
with it at the same "point".

Paul Zielinski is concerned with distinguishing artificial gravity with
real gravity.

PZ: In relation to a dialectical examination of the true character of
Einstein's equivalence
hypothesis and its implications for the energy-momentum content of the
permanent
gravitational field.

JS: I think I have solved all that - at least to my satisfaction.
Einstein's ideas have survived your critique IMHO.

The latter, would only happen when the local 4th rank
curvature tensor did not vanish. Paul seems to think there is a
logical contradiction in the foundations of Einstein's thinking that is
glossed over in MTW (1973) "Gravitation". I do not think Paul is
correct here.

PZ: I have been arguing that there is an interpretive inconsistency in
the MTW treatment.

JS: I fail to see there is any problem here once it is clear that the
"total experimental arrangements" (Niels Bohr) for measuring "gravity
force" (g-force) on a single test particle in a non-geodesic LNIF and,
in contrast, for measuring "local tensor curvature" at 4th rank level
(relative tidal acceleration between two geodesic test particles each
with ZERO g-force) are "incompatible" or "complementary" in Bohr's
sense, there is no longer any conceptual problem at all here! It is
curious that Bohr's "quantum measurement" ideas work as well for General
Relativity as they do for Quantum Theory. This may be a clue for the
correct theory of quantum gravity. Note my claim that Einstein's GR is
a MACRO-QUANTUM theory based upon "Vacuum Coherence" missing in most
approaches although not in Chapline's and Volovik's independent approaches.

PZ: I am saying that the MTW "committee" apply both a modern
interpretation, in which
the question of non-vanishing Riemann curvature is taken seriously as a
mark of
inequivalence between inertial and permanent gravitational fields, and
also the classic
Einsteinian interpretation, in which it is not -- all depending on the
context.

JS: That distinction has absolutely no impact on Einstein's local
equivalence principle as I define it above.

PZ: From the standpoint of interpretive consistency, it is a chimerical
mish-mash.

JS: I do not think so at all.

The relevant form of Einstein's equivalence principle is that:

I. A "point" test particle on a time-like non-geodesic world line has a
"weight" or "g-force" proportional to the 3rd-rank non-tensor
connection field for parallel transport. Make the test particle jump to
a time-like geodesic (neutralize the charge) and the g-force vanishes.
In this sense, gravity is locally equivalent to an accelerating frame
dependent "inertial force".

PZ: Yes, this is the local translational aspect.

This is also true in Newtonian theory -- but the Newtonian
*interpretation* is of course
very different.

The point here is that the GR inertial and gravitational *forces* can
cancel at a
point without cancellation of the entire gravitational field together
with its physical
energy content.

JS: Your last sentence seems to garble things.

The TOTAL g-force IS an inertial force not just a tensor piece of it. It
does not "cancel" an inertial force. This may be the root of your confusion?

The LNIF connection field is of the form

g-force = Indexed coeffcient (Third rank tensor + inhomogeneous term)
with summation convention, i.e. big sum of terms

Apply the local tetrad transformation to get

(g-force) in LIF = 0

The gravity force is the TOTAL SUM of the tensor part and the
inhomogeneous part.

It is an error to think that the inhomogeneous part is the "inertial force".

g-force = inertial force is local EEP

The 4th rank curvature tensor is irrelevant at this level.

In math terms

g-force per test particle mass = d^2x^u/ds^2 = (^u|vw)(dx^u/ds)(dx^w/ds)


(^u|vw) = tensor + non-tensor

u,v,w are LNIF indices

a,b,c are LIF indices at SAME point event P

Use the tetrads to switch from LNIF to LIF

i.e. eu^aeb^vec^w(^u|vw) = (^a|bc) = 0

The tensor piece cancels the non-tensor piece in the LIF

But when you take partial derivatives of the connection to get curvature
you cannot maintain this clean separation.
You have missed this mathematical fact IMHO.

You cannot consistently think of the tensor part of the connection field
as the "real gravity" with the non-tensor part as the "fake gravity".


PZ: A good model for this is the rest-frame behavior of a charged
particle freely moving in
a *pure* electrostatic field, as treated in standard GR, which is there
interpreted as
*inertial compensation*: the net apparent translational forces on the
particle vanish in
this frame, but the *electrostatic field* does not.

JS: I do not understand what you just wrote. I think it is wrong. The
rest frame of the charge here is an LNIF on a timelike non-geodesic with
a net g-force, or "weight", on the charge from the local EM field that
is equal and opposite to the electrostatic reaction force from the
charge on the EM field (or equivalently on the distant charges making
the EM field). That is, the total momentum of charge and EM field is
conserved. There is no "free float" weightlessness in the LNIF rest
frame of the charge.

Off the top of my head (I could be making a mistake?):

I think you need to use for the point test particle something like

P = p - (e/c)A = 0 by definition in the LNIF "rest frame".

with

DP/ds = Dp/ds - (e/c)DA/ds = 0

in the rest LNIF

where D/ds is a covariant proper time derivative?

Your example is wrong IMHO. A tiny strain gauge on the charge in the
electrostatic field shows a "weight". The non-geodesic time-like motion
depends on e/m. In no way could the electrostatic force on a charge be
confused with a gravity force. There is no "universality". Your example
is equivalent to us standing on the surface of the Earth. We have no net
charge, but there are induced electric and magnetic multi-pole forces on
neutral bodies that have a similar effect as in your less complex example.

Of course there are approximations here, e.g. "point particle", "world
line" that break down in quantum gravity, also lack of a torsion-spin
coupling.

PZ: Yes. Here we are at the least ignoring local rotational effects.

JS: Note that there is no way to put a test particle on a non-geodesic
without an electric charge in an external EM field. Neglect weak and
strong charges for simplicity for now.

PZ: OK.

JS: Note that I is independent on the contingency that the 4th rank
curvature tensor vanishes or does not vanish on the world line of the
single test particle.

Therefore, the decomposition suggested by Zielinski

PZ: ?!

JS: guv = guv(artificial) + guv(real)

makes no physical sense at all IMHO.

PZ: I agree this makes no physical sense. However, I NEVER SUGGESTED ANY
SUCH THING.

JS: I am pretty sure I can produce e-mails from you with that equation?

PZ: I am NOT proposing a linear decomposition of the unified g_uv of
this sort; I am
proposing a linear decomposition of the GRADIENTS g_uv, w of the metric
components g_uv with respect to the coordinates x_u ONLY.

JS: OK even for the gradients the distinction is no good at the next
curvature level. BTW I seem to remember
you also wrote the split at the metric level. Perhaps it was a typo.

PZ: Neither do bimetric theories entail any such decomposition: they
define two separate
metrics, a "deformable" physical metric g_uv, and a "transformable"
kinematical
metric gamma_uv over a flat background manifold.

JS: Angels dancing on the head of a pin IMHO.

PZL So your

guv = guv(artificial) + guv(real)

is a straw man of your own invention.

Jack, you will at least have to clear up this basic confusion if you
want real closure
of the debate!

JS: I handled the gradients above.

II. Measurement of the local 4th rank curvature tensor, outside the
regime of quantum gravity, uses the time-like geodesic motion of a pair
of neighboring test particles each feeling ZERO g-force, according to
Einstein's "geodesic deviation equation" for stretch-strain relative
tidal accelerations.

PZ: This a merely an assertion. In fact it is, strictly speaking, false.
The correct version
is:

"... Measurement of the local 4th rank curvature tensor, outside the
regime of
quantum gravity, CAN USE the time-like geodesic motion of a pair of
neighboring
test particles..."

This is a very important detail. This is explained at length in Ohanian
& Ruffini,
"Gravitation and Spacetime", Sec 1.9.

You do not HAVE to use a pair of test particles.

JS: I do not have immediate access to 1.9. What is the relevant quote?
Any valid alternative cannot contradict the method with a pair of test
particles.

This measurement on a pair of test particles is
completely independent of the measurement of g-force on a single test
particle.

PZ: Yes.

JS: Indeed, the two kinds of measurement are "incompatible" in the sense of
Bohr's principle of complementarity.

PZ: OK, I have to agree that you seem to be injecting Bohrian
complementarity into this
discussion of GR.

This is a very serious issue IMO. In my POV it is a license for
*semantical incoherence*.
It reduces all discussion of interpretation of a formal-empirical
framework in terms of
concrete models to a matter of subjective preference ("personal belief"
-- W. Heisenberg).
It encourages equivocacy and pedagogical caprice.

This attitude represents a troglodyte theory of science that is no
longer taken seriously amongst
professional philosophers of science. From my POV it betrays a serious
lack of understanding
of the epistemologically essential role that concrete physical models --
and the semantic integrity
of such models -- pay in scientific explanation, empirical prediction,
and heuristic development.

It is what is fundamentally wrong with so-called "modern physics", IMHO.

Ironically, the born-again realist Einstein later himself emphatically
rejected this "pseudo-
positivist" approach. And as you know, Jack, the late-Einsteinian
neo-realist torch was later
taken up by David Bohm.

So Jack, where do you really stand on all of this? Are you now finally
unmasked as a
Copenhagenist?

JS: Not really, only on Tuesdays, Thursdays and Sundays. ;-)
I am a pragmatist. If the shoe fits, wear it.

III. What about the nonlocality of energy and momenta of the pure
gravity field? This has to do with the issue of gravity waves. You need
to split the near field from the far field. You need to define a global
flux integral over a space-like slice for total Pu (also Muv for
angular momentum), for example, using an "effective" non-tensor for
ONLY the far field dynamical degrees of freedom!

PZ: The point is that moving matter exchanges energy-momentum with the
field. It
can do this in the standard theory by gravitational radiation.

JS: What "moving matter"? Take a gravity wave detector in the Hubble
flow for example.

PZ: A gravitational pulse propagates through the vacuum in a lawful manner.

JS: Wait! An EM wave propagates relative to a fixed space-time geometry
in Special Relativity.
A gravity wave IS wiggly space-time geometry. So what is the reference
frame for the wiggles?
You need to split the degrees of freedom of gravity into propagating and
non-propagating pieces.

PZ: It carries
energy momentum. Yet, according to the canonical theory, while it is in
flight, we
cannot say exactly where the energy-momentum carried by the pulse is. It is,
strictly speaking, everywhere and nowhere.

At the same time, we are told that the pulse propagates at two separate
speeds;
one (the propagation speed of the curvature component) is objective,
while the other
(the propagation speed of the gradient component) is frame-dependent.

My take on all this is that "modern physicists" are so punch-drunk with
Alice-in-
Wonderland quantum mechanics that they are now ready to swallow just about
anything. You could almost convince them that the moon is made of green
cheese
if some Copenhagenist techno-priest says so.

What energy-momentum conservation principles apply to the matter-field
system?
There is no sensible answer to this basic physical question in orthodox
GR. This is
a real problem: Einstein himself saw this, and so did Schrodinger,
Bauer, and Laue,
among others, in the early days of GR.

JS: What do you mean? In orthodox GR

Tuv^;v = 0


PZ: Even Roger Penrose wrote a whole article on this a few years ago in
"Philosophy of
Vacuum" ("The Mass of the Classical Vacuum"). Even Penrose understands
that this
is a serious problem in orthodox GR.

JS: Do you have that digital? Please send it to me ASAP. Thanks.

PZ: Now we have Lee Smolin chasing his tail trying to find "quasi-local"
conserved
quantities in GR. All such efforts are doomed IMO for the reasons I have
been arguing:
there is a fundamental problem with the Einstein equivalence hypothesis.

The solution of this problem, I am arguing, must go to the roots of
Einstein's
"relativistic" thinking. It will require a radical deconstruction of the
early Einsteinian
philosophy -- of the depth undertaken, ironically, by none other than
Einstein himself,
starting in the early 1920s.

WILL THE REAL ALBERT EINSTEIN PLEASE STAND UP?

JS: Note that the elimination of dynamical degrees of freedom of the
electromagnetic field by Wheeler and Feynman, extended to the gravity
field by Hoyle and Narlikar, only applies to the far field on the light
cone not to the near field off the light cone!

PZ: OK.

JS: What about Freud's identity as in Yilmaz's theory? It is not relevant
because it attempts to replace curved space-time covariant divergences
by global flat space-time ordinary divergences.

PZ: The Freud theorems (Freud decomposition and Freud identity) are purely
mathematical propositions that are true for all geometrodynamic theories of
the GR type. These do not depend on specific versions of the RHS of the
field equations.

JS: Agreed. Nothing I said contradicts that.

PZ: From my POV there are serious questions regarding Einstein's
unphysical use of
covariant divergences, and this is part of the problem.

JS: "The Question is: What is The Question?" Wheeler

It is useful in
treating gravity waves in asymptotic flat space-times, but it is not
more than that. Yilmaz is mistaken to try to elevate it as a basis for
a new theory.

PZ: But Yilmaz doesn't do that, Jack. He simply uses "it" as a
mathematical *point of
departure* for an alternative development and interpretation of GR. You have
simply not understood his argument.

JS: A delicate distinction. ;-)

PZ: IMO this is no different from Bohm's use of a trivial decomposition
of the
Schrodinger wave function as a *point of departure* for his neo-realist
interpretation
of QM.

JS: No comparison IMHO, but that is another long story.

PZ: Or do you now have a problem with that? Was Bohm "mistaken to try to
elevate
it as a basis for a new theory"? In your current opinion?

JS: Loaded question based on a false comparison IMHO.

There is a local stress-energy density covariant tensor for the pure
gravity field, it is simply

tuv(Gravity) = [(Witten's String Tension)/(QED dimensionless
coupling)]Guv(Einstein)

PZ: That is not phenomenological GR! There is no "string tension" in GR!
There is no
"QED dimensionless coupling" in GR!

JS: You are wrong. It is there, but hidden because many theoretical
physicists today are really "elegant tailors" more into the gloss of
fashion than substance. They are too quick to take G = h = c = k = 1 and
thereby miss some deep connection a bit under the surface of
phenomenological GR. I am offering a constructive theory like Lorentz
and Fitzgerald but for GR in the sense of Sakharov and PW Anderson's
"More is different". I am offering a "kinetic theory" to Einstein's 1915
"thermodynamics". Einstein always was interested in doing that.

PZ: You are arguing all over the shop!

JS: I am asking you to scratch the surface. There is a deeper insight of
Einstein's GR as an emergent MACRO-QUANTUM coherent vacuum theory.

PZ: In any case, if there are such things in a deeper theory, and your
statement above

JS: tuv(Gravity) = [(Witten's String Tension)/(QED dimensionless
coupling)]Guv(Einstein)

PZ: is valid, then by correspondence this tensor tuv(Gravity) should
show up at the
macro-level -- which supports my argument.

How do you answer this?

JS: Exotic vacuum dark energy + dark matter add up to Omega ~ 0.96 with
our kind of matter a mere Omega ~ 0.04.
This is IMHO a crucial fact and test of my Vacuum Coherence theory of
Einstein's gravity. I do not think the recent Blanchard argument that
dark energy is a mirage will hold up. I agree with Martin Rees on that.


Guv(Einstein) = Ruv - (1/2)Rguv

In the non-exotic vacuum Guv = 0 exactly.

PZ: Yes, because R_uv = 0 and R = 0. But we still have the Weyl
components of Ruvwl
to play with.

JS: Note that if you try to write

tuv(Gravity) = tuv(Gravity)near-field +tuv(Gravity)far-field

the two terms on the RHS are not covariant tensors separately.

PZ: In orthodox GR.

JS: This may have been part of the confusion.

PZ: What "confusion"? You are unwittingly supporting the Yilmaz thesis
by correspondence!

Perhaps this is the "confusion"?

This has nothing to do with near-field vs. far-field. There are NO
less-than-global *exactly*
frame-independent vacuum energy-momentum densities *anywhere* in
orthodox GR.

JS: Straw Man. The generally covariant vacuum stress-energy density
tensor is

tuv(vacuum gravity) = [(String Tension)/(QED coupling)]Guv(Einstein)

-- ZERO in non-exotic vacuum, i.e. no dark energy and no dark matter in
the small region around P.

In exotic vacua with positive zero point energy pressure (attractive
dark matter Omega ~ 0.3) and negative zero point energy pressure
(repulsive dark energy Omega ~ 0.7)

tuv(Gravity) = - (Witten String Tension)/(QED dimensionless
coupling)/\zpfguv

/\zpf = (Loop Gravity Area Quantum)^-1[(Loop Gravity Area
Quantum)^3/2|Vacuum Coherence|^2 - 1]

Witten String Tension = hc/(Loop Gravity Area Quantum)

The discrete stringy link "edge" in a spin network is dual to the Loop
Gravity Area Quantum) ~ Bekenstein BIT.

guv = Einstein's Special Relativity Metric + (Loop Gravity Area
Quantum)(Phase of Vacuum Coherence)(,u,v)

where passive general coordinate transformations at a fixed event P
emerge from local gauge transformations on the Goldstone Phase of the
Vacuum Coherence field.

PZ: Ah hah! So this is indeed closely analogous to the Feynman spin-2
case, where
he gets macro-covariance from the micro- gauge invariance of the underlying
quantum field.

JS: No! because my decomposition is NON-PERTURBATIVE. The second term on
RHS is NOT SMALL compared to first.

PZ: This does NOT give you Einstein equivalence in the correspondence model!
That's the point I have been trying to get over to you.

Read Feynman!

JS: False comparison IMHO.

PZ: The viability of Einstein equivalence, the unified g_uv, and the
entire Riemannian
manifold model, is all simply contingent on the symmetries of the
underlying quantum
field -- in your case a virtual BEC. But the same Feynmanian arguments
apply.

This was all laid out by Feynman in his "Lectures on Gravitation". He
thought that the
success of the Einstein geometric model was the result of a mere
mathematical
"coincidence".

JS: You only get GR by summing an infinite number of Feynman diagrams of
certain topological class. This is non-perturbative like in BCS theory.

PZ: So you are in fact unwittingly supporting my "Venutian" (Feynman
1963) position by
correspondence!

Or so it seems to me.

JS: ,u is ordinary partial derivative.

PSI = |Vacuum Coherence|e^i(Goldstone Phase of Vacuum Coherence)

Higgs Field = |Vacuum Coherence|

Curvature comes from stringy "vortex core" topological defects in the
U(1) order parameter PSI as shown by Hagen Kleinert.

More specifically curvature from disclination defects and torsion from
dislocation defects in 4D "world crystal" lattice, whose discrete
symmetry groups inside the unit cell on scale (Loop Gravity Area
Quantum) are different vacuum phases.

This theory can be extended to hyperspace with supersymmetry matrix
dimensions of M-theory in which gauge force charges are reduced to
Kaluza-Klein geometrodynamics.

PZ: This all looks very interesting. The only problem I have with it so
far -- within the
limits of my current comprehension -- is your stubborn insistence on
Einstein
equivalence at the macro-level, which does not IMHO seem to be supported by
any reasonable correspondence model that is based on your virtual
BEC/Goldstone
phase theory of gravity.

JS: Sure it is. One can get the tetrads and hence vanishing connection
field in LIFs.
Indeed Hagen Kleinert works all that out in detail.

PZ: Neither can it be.

Z.