Foundations of General Relativity, Torsion & Zero Point Energy

Paul

I am leaving for UK in a few days and probably will not have time for
this till August.
I am meeting Alex in Dublin at GR 17. So keep up discussion with Alex.

Paul I think there are TWO different energy problems here. The one Alex
is doing asks a different question from the one I am addressing. Asking
about a TOTAL Pu in an asympototically flat space-time from a pure
gravity field localized geon is what requires the pseudo-tensor and
nonlocality of the energy of the pure gravity field (unless Alex has a
new way to look at it) and is different from Einstein's field equation
which can always be written as

tuv(pure gravity) + Tuv(matter) = 0

Where in GR 1916

Tuv^;v = 0

tuv^'v = 0

tuv(pure gravity) = (c^4/8piG)Guv

tuv(pure gravity) = 0 when /\zpf = 0 in ALL frames geodesic LIF and
non-geodesic LNIF as Wheeler says explicitly.

This is different from the above Pu(total) problem related to gravity waves.

SEPARATELY - a degenerate case for non-exotic vacuum without torsion
et-al where /\zpf = 0.

The Question is: "What is The Question?" (Wheeler)


On Jul 6, 2004, at 12:39 PM, wrote:



Jack Sarfatti wrote:



On Jul 5, 2004, at 7:54 PM, Paul Zielinski wrote:


Jack Sarfatti wrote:

I don't see anything in Eddington that contradicts my position!

Spell it out - type the words you think inconsistent with what I am
saying?

PZ: OK, let's look at what he says:

From p.39-41 of "Mathematical Theory of Relativity" (1923):

17. The Principle of Equivalence.

AE (Arthur Eddington): In § 15 we have stated the laws of motion of
undisturbed material particles and of
light-pulses in a form independent of the coordinates chosen.


JS: Of course.


AE: Since a great deal
will depend upon the truth of these laws it is desirable to consider
what justification
there is for believing them to be both accurate and universal. Three
courses are open:

(a) It will be shown in Chapters IV and VI that these laws follow
rigorously from a
more fundamental discussion of the nature of matter and of
electromagnetic fields;
that is to say, the hypotheses underlying them may be pushed a stage
further back.

(b) The track of a moving particle or light-pulse under specified
initial conditions is
unique, and it does not seem to be possible to specify any unique
tracks in terms
of intervals only other than those given by equations (15.7) and (15.8).


JS: Fine


AE: (c) We may arrive at these laws by induction from experiment.


JS: Indeed.


AE: If we rely solely on experimental evidence we cannot claim
exactness for the laws.


JS: Sure


PZ: OK, this is the first point. Experiments alone cannot prove the
validity of the laws of GR,
including the equivalence principle.


JS: So what? This is the case for ALL physics theories about anything.
Physics, unlike math, cannot "prove."
Physics is completely pragmatic tested by observation and experiment
and technology spin-off. Our most
cherished philosophical preconceptions are most frequently found to be
worthless by the progress of science.

PZ: True. So why is Eddington reminding his readership of this here if
it is so completely redundant?

JS: Ask Saul-Paul. AE wrote this a very long time ago and I guess the
book is semi-popular?

PZ: Answer: Because he fears his readers may be taking the Equivalence
Principle too seriously, perhaps
forgetting in their excitement that it is really just a tentative
inductive hypothesis and that we should not
assume or even expect its universal validity in curved spacetime.

JS: You just lost me. The equivalence principle makes no sense in
globally flat space-time where there is no gravity. Mathematically the
local form of the equivalence principle is simply the tetrad map between
coincident LIFs and LNIFs at approximately the same point event P. An
astronaut in space makes such a tetrad switch by turning conventional
rockets on or off - qualitatively different from ZPF warp drive!

JS: Universally the case for all physical theories.

PZ: Not so easy for entrenched principles, because they can function as
"a priori synthetic propositions".
Try and refute the thermodynamic "no perpetual motion devices" principle
with a single experiment.
Try and convince anyone you've seen a talking horse, even if you have.

JS: Replace "talking horse" by "flying saucer" and "paranormal events."

PZ: So there are some subtleties here. Eddington obviously feels that
it is too early to crown Einstein
equivalence as an entrenched principle of physics, and even suggests
that it is not in fact universally
valid.

JS: I know of no physical idea that is universally valid.


AE: Belief in the perfect accuracy of
(15.7) and (15.8) can only be justified on the theoretical grounds (a)
or (b).


JS: No physicist "believes" in the "perfect accuracy" of ANY theoretical
idea! If this is what your argument is based on, it is spurious.

Pz: From an epistemic standpoint, yes. But this is Eddington, not me.
This is what *Eddington's* position is based on.

JS: AE could be wrong too. He wrote this in the early days.

PZ: I seem to recall that he was once one of the two -- maybe three --
people in the world who
were actually thought to understand general relativity ca. 1919?

JS: So like a journalist! :-)

PZ: His point here is that the equivalence principle is *no exception*
and has no privileged a priori
or entrenched status.

JS: Who would disagree with that?

PZ: Of course, entrenchment of normative principles in physics is not
really an epistemic matter.

However, it still occurs, and sceitnists proceed *as if* such
principles are "proved".

JS: But "scientists" should not. :-)


PZ: Jack, I think you may have read too much Hume. :-)

JS: Mea Culpa

PZ: But the more
important consideration is the universality, rather than the accuracy,
of the experimental laws;
we have to guard against a spurious generalisation extended to
conditions intrinsically
dissimilar from those for which the laws have been established
observationally.

JS: Again this is Philosophy of Science 101 for all scientific theories.


Obviously!


PZ: So we have to guard against spurious generalization to all posible
physical conditions
of these laws.

Einstein proposed gravitational-inertial equivalence as an absolute
fundamental principle, based on what
almost amounted to an *ontological identification*, for the purposes
of physics, of gravitational with
inertial fields.

JS: So Al was over-enthusiastic when he was creating his theory.


PZ: This was the cornerstone for his entire theory of gravitation and
this cast a huge spell over physics
for half a century and more.cYou don't seem to acknowledge this. He
really believed that it *had* to be true. Because "the good Lord
doesn't play tricks". It was all just too beautiful to be false.

JS: It's not "false" in its proper context domain of validity. All
theoretical physics is heuristics!

PZ: Eddington was here acting as a counterweight to the immense
charismatic authority and scientific
reputation of Einstein.

JS: Fine, but this is psychology, sociology, anthropology and politics
of physicists not physics.


AE: We derived (15.7) [the geodesic law] from the equations (15.5)
which describe the observed
behaviour of a particle moving under no field of force.

JS: Yes, that is a classical equation for an idealized point test
particle - an approximation with a limited domain of validity.

PZ: Right. But GR takes this as fundamental, since it guarantees
general covariance of the laws of motion,
and also the complete fundamental relativity of the *observed*
appearance of such motion regardless of the
frame from which it is viewed. Otherwise you pick out a preferred
frame of reference in which inertial motion looks straight as well as
*being in fact actually straight*.

JS: Remember there are preferred frames at the level of SOLUTIONS. There
are no preferred frames at the level of the local tensor-spinor field
equations. The Hubble flow in which the cosmic black body radiation is
isotropic to 10^-5 is such a preferred global frame in FRW cosmology.
It's practical for interstellar and intergalactic navigation. One can
get an absolute fix via local measurements only on "when" relative to
Big Bang and "how fast" coming out of the star gate where no Earth
person has gone before. You may not know "where," but definitely you
know "when" and this includes time travel to the past if the wormhole is
old enough. The wormhole is sustained by dark energy density's negative
quantum ZPF pressure.

PZ: Eotvos equivalence makes this shift *possible*; the equivalence
principle renders it *necessary*, as I understand Einstein's thinking.
We assume that the result holds in all circumstances.

JS: No, not at all. First of all we assume no torsion and no other
geometrodynamic field from locally gauging the full 15 parameter
conformal space-time symmetry group. Einstein's 1916 GR only works if it
is sufficient to only locally gauge the 4-parameter translation
sub-group of the conformal group whose infinitesimal generators are the
total momenergy Pu. The issue is, what is the connection field for
parallel transport? Second, we ignore micro-quantum ZPF corrections and
issues of extended spatial "string" structure and the breakdown of the
passive point test particle approximation.

Everything depends upon the physical nature of the tetrads that are the
local compensating gauge force fields of the relevant continuous
symmetry groups. The tetrads are for gravity what the vector potential
Au is for electromagnetism. Also hyperspace effects? Supersymmetry?


PZ: The risky point in the generalisation is not in introducing a
field of force, because
that may be due to an attitude of mind of which the particle has no
cognizance. The risk is in
passing from regions of the world where Galilean coordinates (x, y, z,
t) are possible to
intrinsically dissimilar regions where no such coordinates exist-from
flat space-time to space-time
which is not flat. So he is saying that the extension of the domain of
applicability of the geodesic condition

Int ds stationary

to curved spacetime is hypothetical.

JS: I don't know what he is saying. It's too vague. Modern differential
geometry of charts and atlases handles all this.

The geodesic principle here is simply the classical action principle for
a passive point test particle of invariant mass m whose action
differential dS is

dS = mc^2ds/c = mcds

ds^2 = guv(P)dx^udx^v

in curved or flat space-time. There is no direct back-reaction on the
geometrodynamic field. Of course in warp drive there is! You can no
longer think in terms of test particles when you metric engineer
reactionless warp drive.

PZ: I mean he is saying that the exact applicability of the principle
is hypothetical with respect to
curved regions of spacetime (in the presence of gravitational fields).

JS: This does not strike me as important. Everything is hypothetical
ultimately.

"The risky point in the generalisation is not in introducing a field
of force... The risk is in passing from
regions of the world where Galilean coordinates (x, y, z, t) are
possible to intrinsically dissimilar regions
where no such coordinates exist -- *from flat space-time to space-time
which is not flat*."

PZ: What I read him as saying here is that we cannot assume that the
effect of a gravititational field can be
exhaustively determined in terms of geodesic motion in a connection
field, since Riemann curvature
may also itself have direct local physical effects on the motion of a
test particle -- and that is a matter
for experiment to decide.

JS: NO for a point test particle. YES for a spatially-extended structure
if the detectors are sensitive enough.


The Principle of Equivalence asserts the legitimacy of this
generalisation.

JS: Vague.

PZ: He is saying that if one fails, then so does the other. The logic
is clear.
In other words, the principle of equivalence depends criticially on
the unrestricted applicability
of the geodesic law to curved spacetime -- and thus extension of its
own applicability to
general spacetime is itself hypothetical.

JS: I don't see how this is useful for solving the problems I am
interested in i.e. nature of the dark energy and how to properly metric
engineer space-time for industrial expansion into space.


....


PZ: In other words, in Eddington's view, there is nothing *a priori*
compelling about this principle.

This is trite. So what? That is so for ALL theories!
Some principles are a lot more equal than others. Some are taken more
seriously than others, and are
harder to dislodge.

Do you really think the great Eddington is just blowing hot air here?
Filling up white space? Repeating the
painfully obvious?

JS: So it appears yes.

PZ: Or are you missing something?

JS: Always possible, but I see no evidence for that.

...

PZ: So there is a subset of phenomena for which the equivalence
principle holds good -- but there
may be other phenomena for which equivalence breaks down. We cannot
say in advance.

JS: No one disputes that.

PZ: OK.

...

The equivalence principle would be violated, and the pure geometric
model of geodesic motion in curved
spacetime would then unravel.

Jack, it is becoming obvious that you do not understand Einstein's
actual theory. You seem to be working
with a gutted-out version, which is a stripped-down formal-empirical
system -- a husk. I suppose that is
why you do not see why these issues are even relevant.

JS: They are not relevant to any of the problems I am interested in. Or,
if they are, you have not shown me how.
Eddington's book was in the early days and it is quaint interesting to
historians, but I do not see how it is relevant? Of course, I could be
wrong but the burden of proof is on you.

PZ: But Einstein himself certainly believed them to be relevant to the
validity of his theory. That is why he insisted on the complete
reduction of the gravitational field to a connection field, which does
indeed completely cancel at at some point in every LIF.

JS: This is correct given the provisos above. I see no reason to give
that idea up within it's proper empirical context i.e. set of useful
approximations.

PZ: The modern view is quite different. Clearly there must be some
phenomena of this kind which discriminate between a flat world and a
curved world; otherwise we could have no knowledge of world-curvature.

JS: Ditto.

PZ: For these the Principle of Equivalence breaks down.

JS: Depends on what "breaks down" means.

PZ: He means it would then no longer hold as Einstein originally stated it.

JS: For passive point test particles there is no problem of consistency.
The existence of tidal tensors in no way invalidates the equivalence
principle for the non-tensor "g-force" connection field (at least in
absence of torsion et-al). Measurements of the g-force in a LNIF and the
tidal stretch-squeezes in ANY frame LIF or LNIF are not at all dependent
on each other. There is no conflict at all. It's up to you to show in a
particular case how I might be wrong in my last remark.

I have said that the equivalence principle says nothing about
stretch-squeeze tidal effects measured by pairs of point test particles
on neighboring timelike geodesics, it only speaks to g-force effects on
one point test particle NOT on a timelike geodesic! So it's apples and
oranges!

PZ: And of course all of this is an approximate model!

JS: Of course.

PZ: *You* say that, but that was not *Einstein's* position.

JS: I am not prepared to debate the historical accuracy of what you just
said. I will leave that to experts in the history of the evolution of
Einstein's informal language about how to understand his equations.

PZ: Yours was not the reasoning behind the Einstein stress-energy
pseudotensor, which assumes
exact universal Einstein equivalence as a fundamental principle. That
is why Einstein was led
to this pseudo-tensor definition, and why he hung onto it tenaciously
despite all its problems.

JS: Again Einstein was asking a question about a global Pu from a
localized region of matter free curvature, i.e. a geon. The problem is
relevant to gravity waves coming from multipole wobbles of the geon
quadrupole and higher. This is my memory of it - I need to do some work
on that.

PZ: From your POV, this must all be a total mystery. In which case I
cannot imagine why you put
so much emphasis on the MTW p 456 et seq. argument against a tensorial
gravitational stress-
energy, an argument which is based squarely on precisely this
Einsteinian premise.

JS: The way I understand MTW there is simply

1. In ordinary vacuum /\zpf = 0 then there is a local stress-energy
density tensor for the pure gravity field and it is exactly ZERO because
Guv = 0. This includes EVERYTHING both far field and near field.

2. If you have a localized wobbling geon surrounded by flat space-time
and you are interested in the gravity waves coming from it, you need a
GLOBAL Pu in that flat asymptotic boundary region that is an integral
over the space of the geon and its integrand is obviously NOT the zero
tensor I defined in 1! That is the problem. The problem then is to
separate out near-field and far-field dynamical degrees of freedom of
the pure geometrodynamic field and one way of doing that is using that
pseudo-tensor technique.

tuv(Geon in /\zpf = 0 vacuum) = tuv(Near Field) + tuv(Far Field) = 0

Something like that.

PZ: A good example would be local tidal forces, which are finite down to
a point. Another example
would be quadrupole effects on spinning test particles, which do not
diminsh with the relative
spacetime scale of the particle or the experimental apparatus.
CORRECTION: Here I should have written "... are measurable down to a
point".

JS: This has nothing to do with the equivalence principle that is making
an assertion at a different level, but is consistent with what you just
said because

Ruvwl(LNIFP) = Eu^a Ev^b Ew^c El^d Rabcd(LIFP)

Where R is the stretch-squeeze tidal tensor


PZ: Then how do you account for the position taken in Ciufolini & Wheeler?

I quote:

"In general relativity, the content and meaning of the strong
equivalence prin*ciple is that in a sufficiently
small neighborhood of any spacetime event, in a local freely falling
frame, *no gravitational effects are
observable*." - C&W, p17

JS: The key phrase you block from your consciousness there is "in a
sufficiently small neighborhood" i.e. below the radar of your
stretch-squeeze measuring instruments and not so small that you may
encounter quantum foam ZPF, which may not even exist BTW.

JS:In contrast, the g-force is the symmetric connection field that
vanishes on a timelike geodesic! There is no problem here! Astronauts
are weightless all the time on their free orbits round the Earth.
Switching on a rocket motor is a Eu^a(P)!

PZ: "I see no ships!"

JS: Heads up.

....

This is all in Einstein 1907 and many of his later writings. And
that's also the entire basis for the geometric
model of the gravitato-inertial field.

JS: Citing Einstein in 1907 is NOT fair.

....

Wheeler fully acknowledges the undeniable fact that the Riemann
curvature tensor cannot
be made zero anywhere in spacetime by a mere coorinate transformation.

PZ: But here's what he says in Ciufolini & Wheeler:

"In general relativity, the content and meaning of the strong
equivalence prin*ciple is that in a sufficiently
small neighborhood of any spacetime event, in a local freely falling
frame, *no gravitational effects are
observable*."

"Here, neigh*borhood means neighborhood in space and time. Therefore,
one might formulate the medium
strong equivalence principle, or Einstein equivalence principle, in
the following form: for every spacetime
event (then excluding singularities), for any experimental apparatus,
with some limiting accuracy, there
exists a neighborhood, in space and time, of the event, and infinitely
many local freely falling frames, such
that for every nongravitational phenomenon the differ*ence between the
measurements performed (assuming
that the smallness of the spacetime neighborhood does not affect the
experimental accuracy) and the
theoretical results predicted by special relativity (including the
Minkowskian character of the geometry) is
less than the limiting accuracy and therefore un*detectable in the
neighborhood"

"In other words, in the spacetime neighborhood considered, in a freely
falling frame all the nongravitational
laws of physics agree with the laws of special relativity (including
the Minkowskian character of spacetime),
apart from a small difference due to the gravitational field that is;
however, unmeasurable with the given
experimental accuracy."

"We might formulate the very strong equivalence principle in a similar
way."

-- Ciufolini & Wheeler, Ch 2, pp 16- 17

JS: This is what I have been saying.

PZ: So what C&W are doing here is replacing Einstein's original version
of the equivalence principle -- which literally identified gravitational
with inertial fields -- with a weaker operational version which holds
that within a sufficiently small neighborhood of spacetime, tidal *and
any other effects* which might locally be used to empirically
distinguish a true gravity field from an inertial field within a some
limited spacetime neighborhood will *always* become operationally
negligible when the neighborhood is made sufficiently small.

This rather desperate defense is immediately defeated by Ohanian &
Ruffini's counterexample of the ratio of
transverse deformations of a water droplet, which simply does not
diminish in this manner, but rather approaches a *finite empirically
determinable limit* when the neighborhood is contracted to zero, under
the influence of local tidal forces.

JS: There is no contradiction. The water droplet is no longer a POINT
test particle. It has EXTENDED STRUCTURE and of course the tidal tensor
stretch squeeze is a LOCAL FIELD. The point here however is that the
POINT center of mass of the water droplet will free float along a
timelike geodesic although its rotational/vibrational motion about that
center may depend on the stretch-squeeze field? There is no basic
contradiction here!

..

PZ: It is clear that C&W are trying to pretend here that this is not
really the case, and that their version of "Einstein equivalence" is
somehow defensible in some weaker operational form -- taking the
restrictive model of a pair of test particles, or a gravitometer, as a
cue.But as I have previously argued -- quite accurately, I think -- this
is mere cardboard-cutout. Jus' sayin' it don't make it so.

JS: I think I just showed the error in your argument?

PZ: Now let us revisit the argument in MTW (p 456-7):

JAW: "No gammas, no gravitational field; no gravitational field, no
gravitational stress-energy" (MTW p 457)

JS: Yes exactly! That is tuv(Pure Gravity, /\zpf = 0, NEAR + FAR
overlap) = 0 because Guv = 0 in that case and

tuv = (c^4/8piG)Guv

Assumes no torsion field, no micro-quantum ZPF, no other exotic field
contributions to the connection field.


PZ: That is, at at least some spacetime point in any LIF, the g-field
must *entirely disappear* -- that is, be
*completely annihilated* -- because the "gammas" all cancel.

JS: To violate this would mean astronauts around Earth not weightless
with rockets off.

"Jack Sarfatti" wrote in message
. com...
Paul
snip "discussions" with himself

In summery:

Jack S. is proposing to connect a wire from one ear to his other ear to
connect the two ZPFs and then wait until a bolt of energy is generated and
goes across the wire, degaussing his gray matter, which has been fouled by
60 cycle powerlines.

The effect would be greater if he used more coils of wire round his head, 20
should do, and had two small antennas going OUT from each ear about 2 feet
each to maximize the probability of ZPF occurrence. Of course he will have
to keep it on all the time, some magnets would help.


(#3 reply edited 7-5-04, 10:29 PST, Change history, added OUT, added
magnets, and powerline stuff etc)

"Jack Sarfatti" wrote in message
. com...
Paul
snip "discussions" with himself

In summery:

Jack S. is proposing to connect a wire from one ear to his other ear to
connect the two ZPFs and then wait until a bolt of energy is generated and
goes across the wire, degaussing his gray matter, which has been fouled by
60 cycle powerlines.

The effect would be greater if he used more coils of wire round his head, 20
should do, and had two small antennas going OUT from each ear about 2 feet
each to maximize the probability of ZPF occurrence. Of course he will have
to keep it on all the time, some magnets would help.


(#3 reply edited 7-5-04, 10:29 PST, Change history, added OUT, added
magnets, and powerline stuff etc)