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, iksnileiz@earthlink.net 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 prin­ciple 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 prin­ciple is that in a sufficiently
small neighborhood of any spacetime event, in a local freely falling frame, *no gravitational effects are
observable*."   

"Here, neigh­borhood 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 differ­ence 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 un­detectable 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.