Lord of The Ring Singularity
Most physicists do not understand the physics of General Relativity. They know how to do the math but do not have a clear idea of the operational meaning of the equations they solve. This is even more so in quantum theory. Part of the reason in the former is that as Einstein said it took him seven years to free himself from the Newtonian-Cartesian notion of the "immediate metrical meaning of coordinates". Also physicists, like Zielinski below, lapse into Newtonian modes of thought that the gravitational force field is an intrinsic objectively local real field independent of the measuring apparatus, which is not true. Only the local invariants of the matter-induced Ricci curvature appear to be intrinsic objectively local properties of the gravitational field. The fact that the Weyl conformal vacuum curvature is intrinsically nonlocal and is connected with the geometrodynamic entropy is profound and has to do with the "world hologram" i.e. the vacuum geometrodynamic field degrees of freedom are "surface" not "volume". The spacelike "volume" slices of the geometrodynamic field structure of the fabric of spacetime are analogous to the projected 3D images from a 2D hologram. That is the intrinsic geometrodynamic field is in 2 + 1 spacetime surrounding surfaces of the 3 + 1 spacetime. When you look at quantum properties of the geometrodynamic field you get "anyon" behavior with interpolating fractional quantum statistics that are coherent superpositions of fermions and bosons and are intrinsically supersymmetric.
That is, relative to a smooth vacuum ODLRO curved metric background, the elementary excitation quantum statistics derive from the fractional commutation rule
aa* + e^i@a*a = 1
@ = 0 fermions with Paul exclusion principle
@ = pi bosons with vacuum/ground state ODLRO spontaneous broken symmetries from emergence of a macroscopic eigenvalue of reduced micro-quantum density matrices that trigger macro-quantum single-valued local order parameters with long-range coherence and remote viewing retro-causal signal nonlocality violating the "perfect" no-cloning a quantum theorem.
@ can be anything in 2 + 1 space-time as shown by Frank Wilczek.
On Jul 29, 2006, at 10:10 PM, Jack Sarfatti wrote to Zielinski:
So you need to start from beginning. Remember you are starting from zero even negative credibility with outrageous claims that require a careful logical development with a minimum of handwaving and citing obscure references. You must create it on the spot here using the Feynman Method.
Z: I've already put considerable effort into explaining "my" points to you, and to others with the appropriate
credentials.
I have been very specific. I gave you a lecture on the equivalence principle that I repeat below. Respond in kind. Now it's your turn. Explain the ideas in your own words and math!
Z: Throwing down the GAUNTLET huh?
OK, at least now I have your attention.
On Jul 29, 2006, at 3:04 AM, Paul Zielinski wrote:
Jack Sarfatti wrote:
On Jul 28, 2006, at 5:10 PM, Paul Zielinski wrote:
Jack Sarfatti wrote:
Yes, you have not yet understood the equivalence principle.
Z: So you say, but our numerous exchanges revealed that you weren't aware of Einstein's own classic version of this principle, which is what I was referring to. I gave you the direct quotes from Einstein himself, but it didn't seem to make any difference.
And you are making outrageous claims that go against mainstream views in the field.
Z: It's called "affirming the weaker argument".
"Across the street they've nailed the curtains
They're getting ready for the feast
The phantom of the opera
A perfect image of a priest
They're spoon feeding Casanova
To get him to feel more assured
Then they'll kill him with self-confidence
After poisoning him with words"
Actually you are wrong about this as a matter of fact. Your GR clock seems to have stopped in the 1970s. In the US there were severe criticisms of the accounts given of the equivalence principle in MTW 1971-3. This was only fully cleared up by Wheeler in the mid-1990s when he co-authored "Gravitation and Inertia" with Ciufolini. But even Wheeler's remaining figleaf -- that you cannot measure tidal forces in an infinitesimal neighborhood of spacetime -- was blown away by the water droplet thought experiments in Ohanian and Ruffini.
You are comparing apples with oranges. You are making a category error. The direct simplest way to measure curvature, i.e. geodesic deviation is to use pairs of closely spaced geodesic test particles, each of which has zero g-force. The g-force in the connection field has little to do with the curvature. You can mock up the local g-force even in flat space-time. There is nothing objectively local about g-force. It is entirely an inertial force depending on arbitrary choice of local rest frame of the local detector. In contrast there are objective curvature invariants whose measurement is orthogonal to any g-force measurement. You, and others, simply garble "gravity field" as meaning "g-force" connection on Tuesdays, Thursdays and Saturdays and as meaning "curvature invariants" on the other days -- sloppy ill-posed questions.
The equivalence principle SAYS NOTHING ABOUT CURVATURE! The equivalence principle is only about g-force! The curvature is irrelevant.
In SSS field of ideal Earth, radial g-force is
g = - GM/r^2 ~ connection field in hovering LNIF
What does this mean? This is only the HOVERING FORCE per unit mass.
i.e. how much rocket thrust you need to apply radially inward to keep a fixed distance from surface of Earth in space.
This is locally indistinguishable from the inertial force, indeed it is ENTIRELY an inertial force. You get same local g in deep space by simply accelerating the rocket properly without any Earth M at all. Of course you will not have any tidal effect out there.
That the tidal conformal geodesic deviations there are ~ GM/c^2r^3 can also be measured "quasi locally" to be sure, but it is a completely irrelevant piece of information to the equivalence principle per se.
Z: There is also the issue of *spinning test particles*, which you seem to think has something to do with "locality".
The equivalence principle is only formulated as an APPROXIMATE principle for IDEAL UNCHARGED NOT SPINNING POINT TEST PARTICLES. When you use spinning gyroscopes as test particles then the gyroscope's precession detect gravimagnetic fields from the rotation of the source, e.g. Earth in NASA Einstein B. All this assumes zero torsion fields. If there are torsion fields and some quantum effects as well you will violate the approximate equivalence principle.
Z: Bottom line here is that no one now takes the idea of "general relativity" and "equivalence" as originally espoused by Einstein seriously. Fock and Synge have been vindicated. "General relativity" now means something completely different -- to the extent that anyone can actually explain what it is now supposed to mean.
More polemics Paul -- physics beyond what I said much more specifically than your will o' the wisp Laputan disquisitions.
Here you can see a picture by M. C. Escher. The mechanism of levitation was first guessed to be based on magnetism (see, for example, Swift, 1726) or rocketry (for example Adams, 1982), but in fact it is based on a principle of the superstring theory in quantum physics far too complicated to explain it here. The name of the city derives etymologically from "large reputation", that means "the very honourable city" (and not from the spanish "la puta", as some scientists assumed). The government is a representative anarchy, the economy is based on a liberal stalinism. There are approximately 120,000 persons living constantly in Laputa. About 17,000 of those citizens are of noble birth and have wings; the rest of the population is forced to visit the ground with ropes or helicopters. It is forbidden by law for the nobles to marry one of the other citizens or one of the people living on the face of earth. Legends say that Laputa was originally invented as a weapon for warfare, but this is certainly untrue, since the city is fragile and unable to take part in combat. In fact, it was invented to allow the king to visit all parts of his country together with his court without discomfort, since the king was expected to travel trough his land all the time. The only time Laputa was used in a war lead immediately to its destruction. 3,000 years after this event, Laputa was rebuilt by the Disney company as an amusement park.
There is a sad bittersweet story about a noble girl from Laputa falling in love with a man from the earth in over 7,000 verses by a gifted poet.
http://www.janthor.de/anycolor/c599.htm
Note that remark on "superstring theory" - hmm...
Laputa hoisted by its own superstring.
Z: This is not based on Einstein's popular writings. It's based on his published papers supplemented by other writings, such as private letters.
Show the evidence.
Z: We've already been through all this Jack. We have already debated all this at great length.
Irrelevant. Andy has not seen any of this. And yes, IMO you completely distorted the meaning of the texts. I have explained it properly. As usual you have made a mountain out of a molehill - a tempest in a teapot.
Z: Einstein's classic equivalence hypothesis was designed to *explain* weak equivalence -- not just restate it. Einstein's explanation of weak equivalence was the basis for his concept of "general relativity": that an inertial field seen by an accelerating observer is -- at least "locally" -- indistinguishable from a matter-produced gravitational field
AND SO IT IS!
Z: *in all physically meaningful respects*.
Strike that last Red Herring, thank you.
a,b,c are LIF coordinate indices raise and lower with Flat Metric,
u,v,w are COINCIDENT LNIF coordinate indices raise and lower with Curved Metric
You appended *in all physically meaningful respects* which is completely irrelevant for the mathematical formulation of the equivalence principle in such applications as:
1) (Curved Metric Field)uv = (Tetrad Field)u^a(Flat Metric Field)ab(Tetrad Field)v^b
2) (Connection Field)^abc = 0 for LIF(P)
Note LIF(P) =/= LIF(P')
when
P =/= P'
that is you need to choose different local geodesic coordinate patches for different events.
Another application is
3) The vacuum dark zero point energy-stress density tensor is ~ Lambda(Curved Metric Field)uv
4) Minimal gauge coupling of source "matter" to geometrodynamic field, i.e. replace ordinary derivatives by gauge covariant derivatives using the connection field as the "gauge potential".
The connection field is quadratic in the tetrads and their derivatives etc.
5) Let W^a^b be the spin-connection 1-form be
Wab = Wabudx^u
W = W^a^b&a&b
Let e be the tetrad field
The Levi-Civita connection field of Einstein's 1915 GR is
{vw,u } = evaew^bWabu
zero torsion is when
{vw,u} = {wv,u}
e = 1 + A
A = 0 in region of space-time makes it globally flat.
A = A^a&a
A^a = Au^adx^u = 1-form curved Einstein-Cartan tetrads in SUBSPACE
dA = (hG/c^3)d(Theta)/\d(Phi) = Area flux density 2-form =/= 0 with spatial point singularities
But the volume 3-form d^2A = 0, i.e. WORLD HOLOGRAM - primacy of the Area flux density
Theta & Phi are the projected inflation Higgs-type field's Goldstone phases of Hawking's "Mind of God" as it were in a manner of metaphorical speaking.
Quantum of Area = hG/c^3
When a non-bounding closed 2D surface surrounds a point topological defect in space, the single-valuedness of the inflation field's local vacuum ODLRO order parameter ensures that the integral dA is quantized just like the circulation is quantized for a line phase singularity in a superfluid. This explains the Hawking-Bekenstein rule for entropy S of a black hole
S/k ~ Area/(Planck Area)
I don't have the factor of 4.
Do not confound this subspace point topological defect with the geometrodynamic level curvature singularity.
Z: Yes you can get a GR -> SR correspondence principle out of this, but you cannot reduce this "equivalence hypothesis" -- and that's what it was, a hypothesis -- to a correspondence principle.
So what? Where's the physics? Solve a problem that is interesting with his bogus insight. Then I will be impressed.
Z: You try to paper all this over with your strained and artificial definitions of "locality" and "g-field", but in my view this doesn't work. Test body spin, for example, has no natural connection with "locality". Remember I have easy access to Einstein's Collected Writings in the original German and in English translation at the UCB Library. The translations were done by people like Stachel, who knows the German and also know Einstein's physics extremely well.
Do you read German? OK present your evidence. I say you are not correctly understanding what you are reading.
OK, let's look at it with a magnifying glass.
Z: Let's ... so?
So show us the texts.
Also you are looking at an English translation of his German that may not be accurate enough.
Z: Of course you can always argue this way when I give you a direct quote that conflicts with your preconceived ideas, but I don't think so Jack. Einstein was actually pretty up front about this. You need to check the original with a physicist whose native language is German to get the nuance. I can look at the German myself, but I tend to trust Stachel. But as to the equivalence principle, there is simply no question that What you mean by the 'equivalence principle' is not what Einstein meant by the 'equivalence principle'. That is your misunderstanding, not mine.
Prove, I mean justify your outrageous allegation. Where is the evidence?
Z: Fair question.
I explained this above.
Z: Look it's not as if I'm pushing a controversial thesis here. Einstein's classic version of the equivalence principle is well known and understood in the field. Most Ph D physicists I've talked to get heartburn when they are told that Einstein reverted to an ether in 1918. They never believe it. But I have the papers!
You need to say "generally covariant aether". Tensor calculus grew out of crystal physics with defects. In fact the aether is a SUPER SOLID in 4D maybe imbedded in hyperspace.
But I'll see if I can dig up some direct quotes for you.
Here is my first shot across your bow on the Equivalence Principle:
On Jul 28, 2006, at 9:27 PM, Jack Sarfatti wrote:
Franz Kafka, feeling like a cockroach under a magnifying glass focusing a blinding light, wakes up having been abducted by Gray cyborgs. He is in a closed room with no windows. He manages to undo the straps of the table bolted to the floor and he begins to float off the table. He holds on to one of the straps. Being a good physicist as well as story writer, Kafka knows instantly he is on a timelike geodesic out in space. Warp drive is the same experience the difference is that the Captain can control his ship's geodesic glide path to point in any direction and speed he likes without feeling any g-forces at all because no propellant is ejected in the maneuvers including sharp turns in space even instant U-turns. This is metric engineering the dark energy-matter envelope around the ship.
All forms of mass-energy density, pressures and stressed induce a real gravity field with a non-vanishing invariant curvature pattern. I mean ALL FORMS including virtual zero point quantum inside the vacuum, i.e. both repulsive dark energy and attractive dark matter are virtual exotic vacuum phenomena as distinguished from ordinary real matter of atoms, magnetohydrodynamic plasma, radiation, neutrinos - possible exotic particles. When you put a slab of dark energy near a slab of dark matter with equal and opposite zero point energy pressure you have a weightless geodesic warp drive and that's basically how the "saucers" fly.
Note how with anyonic fractional quantum statistics we switch from fermionic to bosonic and in between
http://www.astrosciences.info/WarpDrive_files/image024.jpg
Note in the above picture, the BLUE SHIFT is from the DARK ENERGY'S STRONG SHORT-RANGE REPULSIVE ZERO POINT INDUCED ANTIGRAVITY from bosonic positive zero point energy density with equal but opposite negative quantum pressure. The RED SHIFT is from the DARK MATTER'S ZERO POINT INDUCED STRONG SHORT-RANGE ATTRACTIVE GRAVITY from fermionic negative zero point energy density with equal but opposite positive pressure. The pressure is three times more powerful than is the energy density in Einstein’s field equations with the constitutive constraints on the vacuum from Lorentz invariance and the equivalence principle that are the two corner stones of Einstein’s theory of gravity as curved space-time. The alien ET saucer geodesically glides with zero g-force to the left in the above picture. That is the BLUE SHIFT is the STERN and the RED SHIFT is the BOW. Sudden zero g-force turns come from modulating the PHASE ARRAY MATRIX of a high Tc surface ANYONIC superconductor in the thin nanoengineered fuselage using a kind of Josephson effect. The ANYONIC control phase locks to the Goldstone phases of the coherent inflation field whose nonlocally coherent, but locally incoherent, component is the dark energy/matter.
Kafka manages to find a port hole cover. He opens it. To his horror he sees that the ship is falling toward the Sun! That explains why it's been getting hotter. He sees a control panel on the side of the table he had been strapped to. He pulls on the strap to get closer to it. In desperation he starts playing with a joystick and suddenly he is pulled to the table. He feels weight returning. The ship's normal impulse swivel rocket engines have been switched on. He plays with the stick and some of the knobs and finally through his psychic intuition he finds a setting in which the ship stands still relative to the distant Sun that fortunately is still as far away as Venus. Indeed looking in a different direction he can see the planet Venus. The zero point energy powered rocket engines must continually fire to keep the ship hovering at a fixed distance from the Sun and from Venus. This hovering fixed point is a non-geodesic path through spacetime. Having wiped the sweat off his brow, he sees a spigot on the table side and is able to get some sweet-tasting water that instantly gives him a sense of well-being and relaxation in addition to a feeling of great muscular strength and youthful vitality. At that moment three Grays enter the room. The delicate one in the middle who seems more feminine than the other two says to him telepathically without sound "That was nicely done Professor Kafka. We apologize for putting you under stress, but you were in no real danger. Would you like us to explain to you how our ship works." Kafka answers - thinking telepathically "Is The Pope Catholic?"
The Equivalence Principle
What Einstein meant, and what everyone in physics still means today, by the equivalence principle in simplest form is:
"There is no local way to distinguish a real gravity "force" from an inertial "fictitious" g-force."
Z: A key term here is "distinguish".
You have to carefully define "local" here, and what "fictitious" inertial forces are.
Z: Those too.
Step hard on the accelerator of a powerful sports car - you feel the "fictitious" inertial g-force. Stand still on the floor. You feel your weight - gravity "force."
Inertial forces are caused by the acceleration of the non- inertial rest frame of reference of the object feeling the inertial force. Note the counter-intuitive way of using "inertial forces" in "non-inertial frames."
Z: Your "inertial forces" are not the same as the "fictitious forces" of an "inertial field".
What's the difference? Use math here. Words not good enough.
I mean "connection field" for "inertial field". I see no PHYSICAL DIFFERENCE.
Z: You have to be very careful here not to get these two kinds of "forces" confused.
Prove there are two kinds. Show me an experiment that can distinguish the two - and don't say measure curvature.
There is only ONE KIND of g-force and it's not physically objective. It's a contingent artifact of an arbitrary choice.
Unfortunately that is what Murray Gell-Mann calls a contingent unfortunate "frozen accident of history." It's bad English. We should call them fictitious non- inertial forces in non-inertial rest frames, but physicists do not - perhaps to confuse the masses if one wants to get conspiratorial. Note when you sit in the rigid car you are at rest relative to the car. The car is your non-inertial rest frame.
Z: So why use this confusing term "inertial forces"? Why not use the more neutral "inertial resistance"?
Because a jillion text books use it. Also
m = inertial resistance in most books!
as in F = ma
so that's not good either.
Note that the word "inertial" roughly translates to "timelike geodesic".
Z: In GR inertial motion is *unforced* motion along spacetime geodesics. Everyone agrees on that.
Yes, you pay lip service to it, but do not apply it correctly. In Newtonian gravity the curved timelike geodesic is interpreted as the effect of a gravity force. But that is always relative to a non-inertial frame like surface of Earth. I use "inertial" and "noninertial" only in sense of pseudo-Riemannian geometry.
Given two point events in a 4D curved space- time. Imagine all possible neighboring paths, or world lines, connecting the same two points. The geodesic is the longest one among them in a space-time. This leads to the the relative time dilation of two twins.
Z: This doesn't account for the relativity of simultaneity.
Sure it does.
Z: You are skating over the paradox.
I am not.
Z: You have to look at the simultaneity maps between observer frames to really understand the problem -- not just at the proper times computed from the world lines.
You are confusing global special relativity with local general relativity. You do not have the luxury of global frames anymore when there is curvature. Operationally all we can do is locally compare the twins on their return to a common place at a common time. That's good enough.
The one who takes a non-geodesic between the two points will be younger than the one who takes the geodesic.
Z: True, but I think you are missing the point of the two-clock problem, which is that the reciprocal character of the
time dilation is not additive.
Show an experiment for that. If Richard Feynman heard you spout that "philofawzy" he would jump on the table, stomp on it, hiss like The Snake East of Eden at you and whip you a new traversable wormhole. That's what Feynman would do and did with similar pompous peers making silly statements with authority. See intro to one of the Feynman Lectures on Computation on such an incident in Cal Tech Student Cafeteria with hundreds of students watching Feynman lambast a fellow professor.
You cannot move off a geodesic unless a non-gravity force operates and when you do the induced "g-force" felt as "weight" is a reaction to that non-gravity force.
Z; It is only modeled as "weight" -- in certain observer frames.
It's not "modeled" it's "felt" it's "measured".
Therefore, in fact there is no such thing as a pure gravity force that could exist without a non-gravity force like an electric force on a charge.
Z: No, because such a force can have the effect of accelerating a test body relative to a source of the field -- which
in itself does not involve any "non-gravity force".
What is "such a force"? Define it with the math. You lapsed into Newtonian thinking! That's not a kosher move in the game!
In general relativity motion of a test particle on a timelike geodesic is g-force free. Only if you stick a charge on that test particle and switch on an EM field will that charge move to a time-like non-geodesic. If you make the system more complex and stick a detector in - the detector will show g-force only when the EM field is switched on. Or if you have a rocket, only when matter is ejected.
Dual to the above, jump off a high place (in imagination unless you are a University of California Chancellor stealing money from the students like ENRON execs from stockholders and employees - then by all means be my guest ;-)) you will feel weightless - the gravity force disappears.
Z: Again, definitions. All you can really say here without invoking Einsteinian assumptions is that the *net observed effect* of the field *and* of the observer's motion disappears *in this frame*.
More obscurantism. Now you know why Feynman said "Kick out the CARGO CULT philofawzers of pseudoscience!" (paraphrase)
Z: Of course if you ignore the observer's acceleration relative to the source, it appears that the gravitational field is no longer present -- but this is quite different from saying that the physical field itself has actually been "annihilated", locally or otherwise. Acceleration of the test body relative to the source is an *objective* physical criterion for distinguishing the two situations.
The above is excess verbiage. IT'S NOT WELL-POSED. Looking outside the "elevator" gives remote information - it's classical nonlocal. Also it's irrelevant because there is kinematic acceleration relative to source for both zero g-force geodesics and non-zero g-force non-geodesics. So that's an irrelevant Red Herring.
When the test particle is on a geodesic a little detector at rest relative to the test particle will show 'zero g-force" on the test particle. If the test particle is a little conscious computer on the space-craft it will squawk in a cold metallic voice "Hey Boss, I am weightless." Switch on rockets and weight returns. The acceleration relative to Earth is a RED HERRING!
"Local" is defined in terms of idealized non-rotating uncharged test particles.
Z: Why non-rotating? And what has "locality" to do with the rotation of a test body?
Rotation of the test particle makes the problem of its path more complicated. One can do it of course and then there is the issue of what is the signature of any torsion field. The rotation of the test particle is a gravimagnetic moment and if the source is rotating then there will be a coupling to the source gravimagnetic field that will look like a deviation from the equivalence principle for an ensemble beam of test particles are spinning in random directions. It's like a Stern-Gerlach experiment with a mu.B interaction - but without the quantum effect if the particles are classical.
Z: This is simply disguised "ad hocery" IMHO.
Too much philofawzy and conspiracy theorizing makes Zielinski a dull boy.
Paul, you did cheap trick magic. The real Sorceror does Magick without magic!
Uh Oh look who just dropped in
"You summoned me Master?"
http://www.enworld.org/Pozas/Pictures/Monsters/kobold_sorceror.jpg
See what happens Paul when you use the wrong formula, the wrong incantation! What did I tell you?
A test particle is acted upon but does not directly react back on the field it is detecting.
Z: OK.
"Local" here means using only ONE test particle.
Z: What is the connection between "locality" and the limitation to a single test particle?
That's obvious since the idealization is a POINT TEST PARTICLE.
Z: This seems completely *ad hoc* to me.
NO, it's the simplest NON-QUANTUM model. It strikes at the core of your not even wrong argument.
One litmus test of a real gravity field is NONLOCAL only done using a pair of test particles each in geodesic free fall close to each other.
Z: Why is this "non-local"? Can you explain what you mean here?
Yeah, the two point test particles are not at the same place at the same time!
They are not "coincident" they are "proximate".
This is a matter of Hausdorf topology.
Each test particle has a set of coordinate patches that do not mutually overlap!
This is a TOPOLOGICAL DISTINCTION.
Therefore, there is no overlap function, not transition function from one to the other without specifying both a path and a connection field along that path.
You didn't think of that did you Paul? Huh! Huh!
Z: Do you mean simply that it requires the use of more than one test-particle? Why exactly do you think
that is a "non-local" measurement?
Locally means a single test particle in above topological pre-metrical sense.
Z: Isn't a measurement performed with a single test body of finite size then also "non-local"?
YES! That's why WEYL vacuum conformal curvature is NONLOCAL!
Then it's a matter of your RESOLVING POWER OF INSTRUMENTS
Then you need to use WAVELETS and FRACTALS may arise!
Z: If not, why not?
You measure their relative acceleration toward or away from each other. That tells you a component of their curvature tensor.
Z: Right.
The gravity field is real only if that relative acceleration is there and not zero for all possible directions at every point in a spacetime region.
Z: OK, so you do make a physical distinction between a real gravitational field and a fictitious field -- which is precisely
what Einstein eliminated in order to get what he called "general relativity", conceived as an extension of the domain of
the 1905 relativity principle to arbitrary motion.
NO YOU GARBLED IT AGAIN! YOU MISSED THE IDEA!
The g-force is FICTITIOUS WHETHER OR NOT CURVATURE IS THERE!
Take the SSS solution outside Earth - for now 2M/r << 1
ds^2 = -(1 - 2M/r)dt^2 + (1 - 2M/r)^-1dr^2 + r^2(dtheta^2 + sin^2thetadphi^2)
here when you get
g ~ GM/r^2
That's how you must fire the rocket in space to keep hovering at fixed r.
This is a hovering non-geodesic LNIF made possible from the non-gravitational electrical forces of combustion ejecting propellant.
This is an inertial g-force felt as weight by the astronaut - just the right amount to keep him hovering. So he knows there is a real gravity curvature field there by inference looking at the Earth with light. He knows from GR theory that IF he did the tidal measurements with pairs of test particles he would find GM/c^2r^3 Weyl curvature components. These are local properties of course. But in a Ricci vacuum Ruv = R = 0 and the pure local gravity stress-energy density tensor ~ Guv = 0 yet there is a total energy globally in the gravity field. That total energy need not be conserved in GR. For example the total dark energy of our pocket universe of the Cosmic Landscape of the Megaverse is increasing.
http://www-conf.slac.stanford.edu/ssi/2005/lec_notes/Kolb1/kolb1new_Page_05_jpg.htm
The total radiation energy redshifts down as a^-1.
The total cold matter energy is constant.
The total vacuum zero point dark energy increases as a^3.
The universe is not time translation invariant. Therefore it's total energy is not conserved.
Note that dark energy makes Ricci curvature that then induces Weyl conformal vacuum curvature increasing entropy.
Z: Einsteinian "general relativity" really only works for a perfectly homogeneous gravitational field.
Once you impose the locality condition, you are talking about a very different animal. You are then only saying that in *certain qualified* respects, a gravitational field is identical in its physically observable effects to a field of fictitious forces.
NO - the g-force is completely identical to an inertial force in all important respects because I don't give a fig if the curvature is there or not as far as g-force is concerned. Curvature is an objective invariant, g-force is a contingent artifact. You cannot directly compare them. It's apples and oranges. Your theory is not even wrong ill-posed.
Z: Thus if you impose the locality restriction, you have lost Einstein's original concept of "general relativity", which requires
unconditional equivalence.
Show what difference this makes to experimental physics.
Z: However, it's even worse: you even lose it *locally* when the arguments of Ohanian and Ruffini are taken into account,
since in principle at least you can in GR measure tidal effects inside arbitrarily small neighborhoods. So your "locality"
condition is artificial and irrelevant.
No! Their criterion is irrelevant.
I. Do you have curvature?
2. Do you have g-force.
The two questions are conceptually orthogonal. They are logically independent.
OK it's very simple Paul. It's elementary differential calculus.
We are trying to INFER a real function f of a single real variable x with local measurements.
i) We measure f(xo) this is the metric field
ii) We measure df(xo)/dx this is the connection g-force field
iii) We measure d^2f(xo)/dx^2 this is the curvature field.
The equivalence principle is only about ii) it says nothing about iii).
The equivalence principle introduces another function F such that
Given df(xo)/dx =/= 0
F(df(xo)/dx) = 0
Also, if d^2f(xo)/dx^2 =/= 0
then
F(d^2f(xo)/dx^2) =/= 0
And if
d^2f(xo)/dx^2 = 0
then
F(d^2f(xo)/dx^2) =/= 0
that's all. The equivalence principle says a generalized F exists in the real world of 4D for the geometrodynamic field. It's an empirical principle.
That you can measure a curvature says nothing about the fact that locally the SUBJECTIVE g-force is 100% inertial independent of whether there is OBJECTIVE curvature or not.
z- After all, in GR the components of the Riemann tensor are defined at every point in spacetime, aren't they?
Yes for the RICCI CURVATURE. It's an issue for the Weyl conformal curvature that carries the geometrodynamic entropy in the surface modes.
There is no g-force in the above curvature measurement gedankenexperiment.
Z: But you are artificially separating one type of effect ("g-forces") of the presence of a gravitational field from another
("tidal forces").
NO YOU ARE ARTIFICIALLY CONFLATING THEM! Never the twain shall meet. You do not understand the key idea of Einstein's theory. There is no hope for you Paul. Climb to the top of a very tall ladder and fall off. Take a dive Paul!
Z: In reality they are both properties of a single physical field.
NO! Curvature is an objective invariant of the geometrodynamic field, g-force is not. g-force is contingent on arbitrary choice of motions of an LOCAL total experimental arrangement. (Bohr).
Z: It is simply that the non-tidal "g-forces" can be canceled by inertial effects in certain frames, leading to a local mockup of gravity-free conditions.
You are trying to force Einstein's discovery back into Newton's coffin. It won't work Paul. It's UGLY. It's an ABOMINATION. You are an ABORTIONIST of a GREAT LIVING IDEA!
Z: But this is simply a matter of observer-motion-dependent appearances. The physical field does not go out of existence; it is simply compensated.
When any field is zero classically, it's still there. Zero is number. You are confused about the meaning of "the field is zero". It's still there in the virtual quanta. "Zero" is not same as "Void".
Paul what you say is physically meaningless until you:
1) write an equation
2) show how to separately measure the "physical field" and the "compensating field" otherwise it's JUNK PHYSICS in Sharon Weinberger's sense of "Imaginary Weapons" p. 137 (if I recall correctly)
Z: I am arguing that this is the only fully consistent way to interpret the 1916 theory, once you go to general gravitational
fields which are not globally physically equivalent to inertial fields. Because you then have essential physical distinctions
between the two types of field.
NOT EVEN WRONG IMO.
Does it lead you do say there are no black hole horizons?
If so then it becomes physics. It will be tested and found wrong.
Z: What you are doing here is taking a position between two stools: you are positioning yourself half-way between the
original Einsteinian idea of equivalence, and the inertial compensation model, but artificially splitting the g-field, which is
inertially compensatable, from the tidal field, which is not. But these are really two aspects of the same integral
physical field, the gravitational field. A matter-produced g-field
There is no such thing Paul as a "matter-produced "g-force" field. There is only the objective matter produced 4th rank homogeneous tensor curvature field that you can construct local invariants from.
You cannot make objective invariants out of the non-tensor inhomogeneous connection field.
g-force is subjective, i.e. depends on arbitrary choice of local non-geodesic rest LNIF for the measurement of g-force.
There is no objective way to split the g-force into an objective inertial tensor field + a subjective compensating field
- in the case of zero torsion.
When you go beyond 1915 GR you do have a tensor torsion field added to the non-tensor connection field.
Z: is not the same physically as an inertial field of fictitious forces because a matter-produced
g-field is not fictitious.
I repeat: There is no such thing as a matter produced g-force field.
Define your terms here. You are being sloppy. This is bogus junk physics.
Show the math.
Z: Only an "inertial field" is fictitious,
Write the formula for the "inertial field". What is it?
Z: since it can be switched on or off simply by changing the motion of an observer. Also, different observers see different inertial fields; while all observers see the same physical g-field.
Define "g-field" - what is it?
Write the formula for "g-field".
As mentioned above, the only way you feel a gravity force locally equivalent to an inertial g-force is if the test object is pushed off the free float geodesic path in the curved spacetime by some non-gravity force.
Z: If you switch on a physical g-field, the test object is "pushed" by the field.
Is that N-rays or orgone rays?
Stop Paul. You are going off the deep end.
OK show me a gedankenexperiment defining what it means operationally. How do you tell an engineer to build the switch for the "physical g-field"?
Write the formula for it.
Z: You can see the object accelerating towards the source. Such an observable effect has nothing to do with the operation of non-gravitational forces.
Irrelevant. Dopper radar shows that kind of kinematic acceleration for both geodesic and non-geodesic motionm.
Z: So what is the significance of "feelings" here? Are visual observations of the effects of a gravitational field on test
bodies relative to sources no good here?
Look Paul all you can say is that when you fire a rocket jet in space in order to keep a fixed distance from a black hole for example, you know there is also a curvature field there. If there were no curvature field there, then you would accelerate away from the black hole when you fired the rocket no matter how hard you fired it. But when there is curvature there is a critical thrust that keeps you hovering. That's a contingent subjective criterion.
When you write grr = (1 - 2M/r)^-1
that's only for those HOVERING ROCKETS in space.
That gives Newton's g-field
g = -GM/r^2
ONLY FOR THEM!
g is 100% inertial!
i.e. from the ejection of propellant.
Z: What is this, gravitational physics on e-pills?
Yes. No such thing as "gravity force" apart from the reaction force to electric and other internal symmetry local gauge forces inducing non-geodesic motions of test charges.
This is done by electrical forces pushing on our feet when we stand in reaction to us pushing down on the ground. We are pushed off the natural geodesic path in the curved spacetime and that's why we feel weight - it's locally same as stomping on the accelerator of a Jaguar. The surface of the Earth is our local noninertial rest frame (LNIF).
Now there are a lot of deeper aspects of this having to do with the local gauging of the global symmetry of translations of source objects giving a compensating "connection" for parallel transport of oriented test particles that is essentially the inertial g-force in LNIFs. One way to tell if you are in a real gravity field is if you have to fire a rocket in space to keep at a fixed distance from the object. If you switch the rocket off you are weightless. That is, gravity fields emerge from the breakdown of the global homogeneity of the action of the source object, The gravity field in a sense restores the lost homogeneity symmetry by adding new geometrodynamic degrees of freedom to the action in addition to the degrees of freedom of the original source object.
Z: Homogeneous gravitational fields *look* like inertial fields,
Show me a source that makes a homogeneous gravity field - I mean globally exactly.
Every field looks homogeneous on a small enough scale.
That is for hovering LNIF special choice only
g = - GM/r^2
if r = ro + r'
when
r'/ro << 1
g looks uniform in a small neighborhood of ro from Taylor series
1/r^2 = 1/(ro + r')^2 ~ 1/ro^2(1 + 2r'/ro + ...) ~ (1/ro^2)(1 - 2r'/ro + ...)
g = - GM/r^2 ~ -GM/ro^2 + 2GMr'/ro^3 + ...
The first term on RHS is the approximate homogeneous HOVERING g-field.
THE HOVERING OBSERVER CONSTRAINT is a choice of INHOMOGENOUS PART OF THE FIELD.
IT'S NOT INTRINSICALLY GEOMETRODYNAMIC.
Z: but are still objective
False.
Z: and can be defined independently of the motion of any observer. Inertial fields, on the other hand, depend entirely on the motion of an observer, and different observers can see different inertial fields. Einstein's card trick was to pretend that this distinction does not exist,
Einstein was correct and you are not even wrong.
Z: and to treat the combined inertial-gravitational g-field as observer-dependent. But this is simply not the case. That is why modern treatments insist on the distinction between "non-permanent" and "permanent" fields, even in the case of a perfectly homogeneous field which while it does *appear* to go away globally in free-fall frames, doesn't actually -- neither globally nor locally.
Tangential issue.
