| |
 |
|
|
Science Forum Index » Mathematics Forum » Energy of Gravity Vacuum
Page 1 of 1
|
| Author |
Message |
| Jack Sarfatti |
 Posted: Fri Dec 19, 2003 10:46 pm |
|
|
|
Guest
|
bcc
On Friday, December 19, 2003, at 02:45 PM, Paul Zielinski wrote:
Jack Sarfatti wrote:
bcc
On Friday, December 19, 2003, at 11:47 AM, Paul Zielinski wrote:
Jack Sarfatti wrote:
On Wednesday, December 17, 2003, at 06:38 PM, Paul Zielinski wrote:
Jack Sarfatti wrote:
Part III
On Monday, December 15, 2003, at 04:27 PM, Paul Zielinski wrote:
PZ: Why make it look superficially as if the physical effects
of
acceleration do not mark off inertial frames if
in fact they do?
You cannot throw away differential geometry.
JS: Huh?
Standard GR has a difference between LIFs and LNIF's, it's simply
that the local field equations do not depend on the difference.
It's tensors all the way Jose.
PZ: The point is that general covariance alone is not actual general
relativity -- although it can look superficially like general
relativity in a formally general covariant theory.
....
PZ: Einstein wished to extend the special principle of relativity
into
a general theory in which the inertial
frames were not marked off as physically special.
JS: Obviously.
PZ: This is not at all obvious. And it turns out it didn't actually
work, since there
is in fact no Einsteinian strict equivalence.
JS: I do not understand why you keep saying this? I am not sure where
the miscommunication is.
The g-force is locally equivalent to an inertial force. The LOCAL
g-force on a "point" test particle vanishes when
that test particle is a LIF on a time-like geodesic. Ignoring torsion
and non-metricity of course.
PZ: So, Jack, is this really what you think Einstein meant by "equivalence"?
That the net translational forces on a test particle vanish in free fall?
Isn't this also trivially true in Newtonian physics?
JS: Sure, they have that in common. Newtonian gravity is a limiting case of
Einstein gravity, which has a richer mathematical structure and additional
physical predictions like event horizons and gravimagnetism for example.
There is an excellent article in "Physics Meets Philosophy at the Planck
Scale"
by "Steven Weinstein" "Naive Quantum Gravity" that demolishes basis for
Yilmaz & Puthoff's "really a flat background spacetime".
In contrast, the "curvature tensor" local relative tidal acceleration
on two geodesic test particles does not vanish in the limit that the
separation shrinks to "zero" (neglecting Lp effect) need not vanish
even though the g-force on each test particle does vanish. That's it.
PZ: That's what? Einstein equivalence? Or do you mean that's all one can
really say?
JS: The latter. All you can say is:
1. No g-force on timelike geodesics (for non rotating extended systems)
in Einstein gravity as well as Newton's (The painter on the falling
ladder Einstein story and floating astronauts.)
2. Test for local curvature via timelike geodesic deviation in relative
tidal acceleration of TWO test particles each with zero g-force.
3. What to do in LNIF say on surface of Earth is more complicated since
one must correct for electrical reaction forces to get a pure
gravity curvature measurement.
4. Special relativity works to good approximation in LIFs for all
non-gravity "forces" i.e. mainly electrical-magnetic & light.
PZ: This is all just as true in Newtonian theory. Nothing specifically
"Einsteinian"
about it.
JS: Correct, until you look for post-Newtonian effects including
gravimagnetism, bending of light with factor of 2 not found in Newton. Also
Grad^2V(stuff") = 4piGrho(1 + 3w)
w = 0 in Newton
w = Pressure/Energy Density of "stuff"
Also gravity waves not found in Newton's math.
PZ: Einstein's idea of extending the special principle of relativity,
and what is wrong
with this, is explained very clearly in Roberto Torretti's highly
regarded "Relativity
and Geometry" (Dover 1996):
"While Einstein's description of his strong Principle of
Equivalence... as 'a
natural extrapolation of one of the most universal empirical
statements of physics'
is not unjustified, his original presentation of it as a
generalization of the Relativity
Principle is completely misleading. The physical equivalence of
reference frames
at rest in a homogeneous gravitational field and uniformly accelerated
frames
does not obliterate the physical inequivalence between the latter and
inertial
frames... It simply entails that a reference frame at rest in a
gravitational field
cannot be inertial."
JS: What does "obliterate" mean?
PZ: The same as Landau & Lifshitz's "annihilate". That is at the core of
Einstein's
idea: that the *entire physical reality* of the gravitational field goes
out of existence
in an LIF.
JS: Only in the approximate heuristic correspondence sense of Wheeler,
MTW obviously.
PZ: Apparently you are having a very hard time understanding what all
these people are
worried about.
JS: Yes. It's a non-problem.
Of course Einstein knew there is a
physical difference between LIF's and LNIF's
mutually coincident at same "point" event P.
PZ. Then how do you think Einstein could imagine that he was extending
the Relativity
Principle to accelerated frames?
JS: I see no problem here? Where is the conflict?
General coordinate transformations that are local at P are
not identical to global Lorentz and translational transformations.
Tensors of the general local coordinate transformations include
the accelerated frames missing in the global Lorentz symmetry
group of special relativity.
Tensors of the global Poincare group are not the same as local LNIF GR
tensors.
One can use the local tetrad map to go from LNIF GR tensors to LIF local
Lorentz sub-group tensors.
Note that they are not global translation group tensors anymore. The
global translational group is
locally gauged to get the guv LNIF metric field of the base space.
All laws of physics (in GR forgetting quantum theory) are LOCAL tensor
laws with respect to the
given base space group Diff(4) and the given tangent fiber group O(1,3).
The tetrad maps between
base space and tangent fiber. EEP is formally in that LOCAL map. All
this neglects Lp^2 = hG/c^3 effects.
LIF observers are
weightless, LNIF observers feel weight from non-gravity
electrical reaction forces putting them off a geodesic world line
through P. The point is that there is a local tetrad map eu^a(P) and
inverse from
LIF to LNIF in which the local geometrodynamic field equation has
"same" form
PZ: But that in itself does not extend the Relativity Principle as
Einstein thought.
That's Torretti's point.
JS: I do not understand what you just said. I do not see why it is
important for anything interesting? Give examples. It's too abstract and
vague with no context for my mind.
i,e,
tuv("Marble" Geometry) + Tuv("Wood" Matter) = 0 in LNIF at P
tab ("Marble" Geometry) + Tab("Wood" Matter) = 0 in LNIF at SAME P
t..(Geometry) = (String Tension)G..(Einstein)
G..(Einstein) = R..(Ricci) - (1/2)R(Ricci)g..
gab = Minkowski LIF metric at P
guv = LNIF metric at same P
t..(Geometry) = 0 in ALL FRAMES
in non-exotic vacuum where /\zpf = 0
corresponding to a large critical VACUUM COHERENCE BTW
http://qedcorp.com/APS/EmergentGravity.pdf
PZ: Fine. Who disagrees with this?
JS: The Question is: Who is even aware of this new way to look at what
was thought was understood.
Who agrees with
/\zpf = Lp^-2(Lp^2|Vacuum Coherence|^2 - 1) ?
I would say none of the Pundits are thinking this way at all.
"Vacuum Coherence"? Who ordered that? they would say at least today.
Also "String Tension" in an Einstein gravity formula?
They would scratch their heads. "Huh?"
Yes, a local frame "at rest" in a gravity field is LNIF.
PZ: And then you experience the *true* strength of the real
gravitational force.
JS: Nonsense. What is this "true"? Means nothing in this context.
G-force is a frame dependent
quantity. Definitely it is "physically real" and very "measurable". But
it is purely contingent.
The way you use "true" here is not physically important IMHO.
Whenever
there is a g-force you are in a LNIF.
PZ: Again, the term "g-force" is ambiguous, since it ignores the
distinction between
inertial and gravitational effects.
JS: This is your basic illusion here. There is no such distinction!
G-force is a single point test particle property contingent on
electrical reaction forces!
G-force + electrical rection force = 0
In free float
electrical reaction force = 0
Tidal curvature is a relationship between a PAIR of point test particles
EACH in FREE FALL with zero G-Force on each.
It's GEODESIC DEVIATION. So it's apples and oranges at different levels
with different operational procedures to define the concepts.
You can split the connection field into a tensor part and a non-tensor
part, but that is I think not a unique split. It changes as the LNIF
changes.
And in LIF
tensor part + nontensor part = 0.
PZ: You can get "g-forces" without any gravitational fields.
JS: Obviously. So what? First ask HOW do you measure the tidal curvature
tensor using TWO test particles each feeling a G-FORCE?
YOU HAVE NOT ASKED THE RIGHT QUESTION!
You measure components of the Ruvwl curvature tensor using PAIRS of
point test particles EACH with ZERO G-Force on them!
That is you first ELIMINATE G-Force on your PAIR and THEN measure CURVATURE.
I mean that's the direct procedure, the simplest.
If there are G-Forces on them it's a more complicated procedure.
The geodesic deviation equation has no ELECTRICAL-MAGNETIC FORCES in it.
That adds "noise" to the "signal". As a practical matter however we need
an analysis of that. I have not seen one. Have you?
But it is clear to me Paul that you did not think this far operationally
and therefore I think your "idea" is not sound, it not self-consistent,
is not well-posed. There is no "there" there as far as I can understand
your obsession on all this?
The interesting idea here is that you use TWO test particles, each
feeling ZERO g-force, to measure
their intrinsic curvature relative tidal acceleration if one is there.
PZ: You don't need two test bodies. You can use a water droplet.
JS: That counts as "two".
PZ: You can use all
kinds of simple devices to measure Riemann curvature -- some of which do NOT
scale down in sensitivity to curvature with the size of the "neighborhood".
JS: Give examples of last remark? I do not understand it.
PZ: So even the MTW "EEP" is in trouble.
JS: Justify with examples. Otherwise I don't believe what you say.
PZ: "Far from generalizing the Principle of Relativity, [the
equivalence principle]
drastically alters its meaning and restricts its scope."
("Relativity and Geometry", Section 5.2 pp 135-136 )
JS: Much Ado About Nothing IMHO.
PZ: : Because you don't understand Einstein equivalence -- which is OK,
since it's
wrong!
JS: You are correct that I do not understand what you think it is you
are understanding. ;-)
PZ: But don't try and tell me that this "strict equivalence" was not the
core of Einstein's
theory. It was.
JS: I do not know. Even if Einstein early on overstated something
informally so what? That happens all the time.
PZ: And here is Ohanian and Ruffini:
"Unfortunately, Einstein's statement [Einstein (1916)] has often been
generalized
to sweeping assertions about all laws of physics about all laws of
physics being
the same in a laboratory freely falling in a gravitational field and
in another
laboratory far away from any field... "
JS: O & R do not say Einstein did that. BTW Hal Puthoff does do that in
his PV "Tables" on K.
OR: "Such generalizations are unwarranted since...
even quite simple devices will signal the presence of a true
gravitational field by
their sensitivity to tidal forces and will therefore permit us to
discriminate between
a gravitational field and the pseudo-force of acceleration."
JS: Exactly what I have said all along.
PZ: You have not said that there are tidal measurement devices that are
scale-
insensitive.
JS: It's obvious.
PZ: The point is that we can always tell the difference between a
gravitational
field and an inertial field essentially everywhere in an accelerated frame,
and the magnitude of the measured effects does not necessarily scale down
with spacetime volume.
JS: This is purely a semantic issue
on how to use informal language precisely and clearly.
There is no new physics here. Einstein understood all this.
PZ: Of course he knew about Riemann curvature and tidal forces. But he
did not consider them essential to the definition of "the gravitational
field".
That's the point.
JS: Again you never are clear enough here what you mean by "field"?
G-Force or tidal acceleration?
PZ: Why do you think all these authors -- including your old buddy Dick
Feynman --
have made such a song and dance about this if there is no issue here?
JS: What did Feynman say that you think applies here?
"This statement [of the Einstein equivalence principle] is true only
in a limited sense.
Gravitation and acceleration are equivalent only as far as the
translational motion
of point particles is concerned... If the rotational degrees of
freedom of the motion
of the masses are taken into consideration, then the equivalence
fails."
JS: Of course, I have repeatedly said the same thing.
PZ: OK. So then you agree with me that Einsteinian strict equivalence,
as I have
defined it,
JS: Yes you set up a Straw Man.
PZ: is untenable, and with Ohanian and Ruffini that the "EEP" as
formulated by Wheeler is not actually empirically valid?
JS: I need to read the exact Wheeler statement.
PZ: "Gravitation and Spacetime", Second Edition (Norton (1995), Section
1.9)
JS: I do not have a copy here in lobby of Bay Club.
PZ: So there is at this point no physical reason to take Einstein's
belief in the "complete
physical equivalence" of gravitational and inertial fields seriously,
except in the sense
of a *limited heuristic analogy*.
JS: Depends what one means by vague "complete".
PZ: Einstein meant *complete*. That means: NO fundamental physical
distinction
between gravitational and inertial fields, PERIOD.
One and the same.
JS: If you mean by "field" "G-FORCE", then YES no fundamental difference
LOCALLY!
If you mean by "field" "tidal curvature" , then NO there is a
fundamental difference LOCALLY!
This is not a big deal.
"Everyone" understands
what OR say and agrees with it. It's all in MTW.
PZ: That you can *always* operationally discriminate between a physical
gravitational field and an inertial force, no matter how small the
neighborhood?
JS: Here you garble "tidal curvature" with G-Force.
PZ: *z- Where?
The how can this "EEP" support the argument on p 476 that the physical
stress-
energy of the gravitational field *must* vanish at at least one point in
an LIF, because
the connections ("gammas") also vanish at the same point?
JS: This is a logically independent problem from what we were just
discussing.
I showed a tensor for that which is zero in non-exotic vacuum , but is
NOT zero in the exotic vacuum.
Classical GR does not have quantum idea of "exotic vacuum". That is NEW
PHYSICS.
PZ: Which is what I have been arguing for at least a year.
JS: No one ever disagreed with that. You have been very obscure about
this getting it mixed up with the Yilmaz
issue.
PZ: It is directly related to the Yilmaz issue.
You have now agreed (and you say you always did agree) that the
gravitational
field is fundamentally different from a "fictitious" inertial field.
JS: NO! Because I never know what you mean by "field"? Sometimes you
mean "G-Force"
and sometimes you seem to mean "CURVATURE".
PZ: Now, I ask you again:
(1) Does the vacuum stress-energy of the gravitational field self-gravitate?
JS: In my definition YES.
My definition is
tuv(vacuum gravity = (String Tension)Guv(Einstein) = -(String
Tension)/\zpfguv
The only vacuum recognized in CLASSICAL GR is non-exotic where /\zpf = 0.
"Dark energy" (i.e. /\zpf > 0) and "dark matter" (i,e. /\zpf < 0) exotic
vacua not known to Einstein or
to anyone before 2002! This is REALLY NEW PHYSICS.
PZ: (2) Does the vacuum stress-energy of the inertial field self-gravitate?
JS: Meaningless question unless you show me the formula for it.
PZ: (3) Is the vacuum stress-energy of the inertial field even defined?
If not, why
not?
JS: I don't think it is. Maybe it is in Yilmaz's theory. You tell me.
PZ: By "self-gravitate" I mean "act as its own source".
JS: In GR ALL stress-energy density is its own source!
Every important idea in physics is a "limited heuristic analogy"
IMHO. There are no absolute truths in science.
PZ: OK, in the context of discovery.
But need we concern ourselves with dreams of snakes biting tails in order to
understand the ring structure of benzene?
JS: Ring structure is itself a concept of limited utility and
meaningfulness.
PZ: If so, then there is no reason to expect inertial forces to
contribute to or alter the physical
stress-energy of the gravitational field, and thus no deep reason to
demand that this
physical stress-energy density be annihilated *anywhere* in an LIF --
contrary to the bold
Einsteinian assertions of Charles Misner et al.
JS: This does not follow logically from what was said before.
PZ: OK -- then are you now saying that there *is* a deep reason to
expect inertial forces to
contribute to or alter the physical stress-energy of the gravitational
field?
JS: No, I am saying I see NO deep reason to try to build gravity
stress-energy from G-Forces at all!
Apparently Yilmaz does? I don't do it that way at all!
Again my formula is very different from that. It is
tuv(Geometry) = (String Tension)Guv(Einstein) = -(String Tension)/\zpfguv
PZ: Which is it? It has to be one or the other.
JS: NO there is NO deep reason IMHO.
Indeed, I show that when quantum zero point energy is included in the
exotic w = -1 vacua of both "dark energy"
and "dark matter" as LOCAL fields, which in FRW case limit to
Einstein's "Cosmological Constant" that
tuv(Marble Geometry Vacuum) = - tuv(Exotic Vacuum)
tuv(Exotic Vacuum) = (String Tension)/\zpfguv
/\zpf = 0 in non-exotic vacuum
/\zpf > 0 repulsive dark energy exotic vacuum
/\zpf < 0 attractive dark matter exotic vacuum
/\zpf = Lp^-2[Lp^3|Vacuum Coherence|^2 - 1]
guv = (Minkowski)uv + du,v + dv,u
du = Lp^2(arg Vacuum Coherence),u
,u = ordinary partial derivative
Lp^2 = hG/c^2 = 1 Bekenstein "BIT" on surface of Susskind's
"World Hologram" that has the 3D projection image that is ordinary
uncompactified space.
When Vacuum Coherence = 0 we have globally flat Minkowski space-time,
but with a huge cosmological constant. This is unstable and is why we
have inflation IMHO.
PZ: Interesting, but this does not answer the question I posed, which
is: Does the
stress-energy of the pure inertial field, with no matter sources (if it
is even defined)
self-gravitate, i.e., itself act as a source of the gravitational field?
JS: "stress energy of the pure inertial field" has no meaning to me
unless you can produce a
GR formula for it.
PZ: I don't see a clear answer to this question in what you wrote above.
Z.
* /\zpf = 0 is like Lenny Susskind's supersymmetry limit where the
vacua on the
"Landscape" of "Megalopolis" (Francis Ford Coppola's new movie) do not
depend on the "moduli" of the extra hyperspace dimensions of Calabi-Yau. |
|
|
| Back to top |
|
| |
|
Page 1 of 1
All times are GMT - 5 Hours
The time now is Sun Jul 27, 2008 3:50 am
|
|
