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On Aug 7, 2011, at 1:20 PM, Paul Zielinski wrote:

There no is question that Kibble, building on the work of Utiyama, did this formally in his 1961 paper. There is no point in denying that. But there is a trick here, having something to do I suspect with the construction of the covariant derivative.


Show us. The covariant derivative is the choice of the connection field that you keep confounding with the gauge transformations because you have not gone through the algebra of the local gauging program with sufficient attention to detail.

I'm not sure why you think this Jack. The gauge field of any gauge theory is essentially a connection field.

You are having trouble parsing my sentences again.

I am?

What don't you get in my

"The covariant derivative is the choice of the connection field that you keep confounding with the gauge transformations"

Let's be explicit about this in the simplest U1 EM case.

This better be good. :-)

Using Cartan's elegant short and sweet notation

Local gauging global U1 to U1(x) induces the connection 1-form A when you require minimal coupling which means

d -->  D = d + A

for now I suppress coupling strengths to keep the math simples

In classical U1 gauge theory the "connection 1-form A" is only really "induced" in the sense that it is mathematically constructed to compensate for the spurious effects of locally gauging a group of "rigid" phase transformations on the partial derivatives d.

That's what I said.

I'm not sure whether it was ever specified by Weyl, London, or the others whether such "gauge transformations"  of the phase were passive or active.

Irrelevant - makes no difference to the physical reality out there. All detectors connected by a gauge transformation in GR must be locally coincident. An active gauge transformation does not take you from Earth to the Stars. That seems to be part of your misconception. You seem to think that an active gauge transformation is a real physical displacement over a perhaps cosmological distance. For that we need a stable wormhole.

So we're back to square one.

Speak for yourself.

Recall that Weyl's original scale factor was regarded as being purely mathematical in character, and yet he hoped to pull out unified EM theory like a rabbit out of a hat! This is all aside from the fact the it didn't work for other reasons.

It's the extension of the Lagrangian density of the input source field that is the physics - not the redundant gauge transformations.

That is, one starts with a Lagrangian density L(psi, psi,u) that is invariant under the global U1

because of the derivatives in the parameters of the group U1(x)  ~ e^iQ@(x) we need the A and this gives a new Lagrangian density

Yes because passive phase transformations don't have any physical meaning. But if that's the case, why would locally gauged phase transformations be compensated by a *physical* field?

Why bother to argue at all? Why not just say, "Abracadabra"?


This idea eludes you. The physics is to keep the total dynamical action integral invariant under the larger local group and the only way to do that is to introduce a compensating gauge potential - a Cartan 1-form that in general is not closed.

That is, given the compensating gauge potential A Cartan 1-form, it's exterior derivative 2-form

F = dA =/= 0

note that

A = AIdx^I

I indices of the Poincare group of 1905 SR for internal symmetries in extra dimensions beyond spacetime

F = FIJdx^I/\dx^J

in U1 EM

FIJ = AI,J - AJ,I = - FJI

in Yang-Mills SU2(weak flavor gauge force), SU3(strong color gauge force) it's

FIJ^a = AI,J^a - AJ,I^a + C^abcA^bIAcJ

where a, b, c are the internal (flavor, color) charge indices

[Qb,Qc] = C^abcQa   Lie algebra for charges Qa

a non-closed A 1-form is topologically different from a closed 1-form C = df

A single-valued gauge transformation can never take you from a C to an A - for that you need the Kleinert singular transformations that create and destroy topological defects.

In the case of GR

A = AI(LIF)dx^I = Au(LNIF)dx^u

AI(LIF) = (tetrad)I^uAu(LNIF)

etc

LIF & LNIF are locally coincident

i.e. their separations small compared to local radii of spacetime curvature

LIF is the "inertial frame" objects at rest in it are weightless zero g-force as in Baron Muchhausen's cannonball ride

http:// http://movieclips.com/KSYA-the-adventures-of-baron-munchausen-movie-the-cannonball-ride/


LNIF can be rotating about its center of mass that is still on a timelike geodesic

objects clamped to rotating frame feel inward centripetal reaction force akin to "weight"

e.g. artificial gravity on space-station

http://www.youtube.com/watch?v=q3oHmVhviO8

or it can have translational acceleration from a non-gravity force like a rocket engine firing

http://www.bbc.co.uk/news/science-environment-12573491


and the static LNIF is





It only makes sense from my POV if you specify *active* phase transformations and attach concrete physical meaning to relative phases at spacelike separation.

The idea is that the phases at spacelike separated events are independent because of the local gauging of the group.

Here "phases" are the conjugate variables for the Lie algebra generators of the Lie group.

For example in the Bohm-Aharonov effect the phase shift of the electron's quantum wave function connecting two events is the path-dependent integral of AIdx^I - not the best example because that path is timelike for a real electron. Therefore, there is no unique meaning to the relative phase between any two separated points in the general case unless A is exact

i.e. if A = df

f = 0-form

then the path integral of A is independent of path because of generalized Stokes theorem.

That's the only case where you can define your relative phase.

Now I suppose formally we can use a spacelike path - interesting question.

I think this may be the "original sin" of gauge theory.

Not even wrong in my opinion.

L'(phi, phi,u A) whose global action integral is now gauge invariant under the bigger local group U1(x) with subgroup U1.

Fine.

All local physical observables must be gauge invariant.

So mathematically you need the connection field A to ensure this.

That's what I said.

The 1-1 non-singular topology conserving redundant gauge transformations that do not change any physical reality out there, but simply represent raw data collected by different sets of detectors are

A --->  A' = A + df

where f is a nonsingular 0-form

It's one thing to say that the gauge transformations have no physical meaning, and quite another to say that they leave all local observables invariant.

So what?

In the context of gauge gravity, why can't the connection A be interpreted as simply compensating for the artifacts associated with frame acceleration?

That's what I have been trying to put across to you. The 16 tetrad components connect locally coincident non-accelerating inertial frames with accelerating/rotating non-inertial ones.

Wouldn't that be more direct and natural?

Yes, that's what I have been saying.

Using d^2 = 0 in the absence of singularities (see Kleinert's multi-valued extension where in effect d^2 =/= 0 i.e. a real topodynamical change from mass-energy-stress currrent densities)

F = dA --->  F' = dA' = dA + d^2f = dA = F

so F' = F is a gauge invariant.

OK, but gauge theory interprets A as a *physical field*. It is not treated as a mere connection field.

Correct.

If the gauge transformations have no physical significance, why should compensation of the effects of such transformations on the Lagrangian to restore local gauge invariance give rise to a *physical* field, as opposed to a mere mathematical artifice, which is what a connection really is?

The gauge transformations in GR do have physical meaning, but they do not change the dynamics of the gravity field. Each locally coincident LIF and LNIF makes measurements of the gravity field, e.g. the 4th rank curvature tensor and the theory allows them to construct local gauge invariants from them just like in special relativity.

The gauge transformations connect the shadows on the wall of Plato's Cave for the same Eternal Form Invariant Idea of Objective Reality Out There.

The set of all non-singular f's is the gauge orbit of all physically equivalent solutions that look different to different sets of locally coincident detectors, but the theory allows each set to compute the gauge invariant F's - defining objective reality out there.

Start there, have not read the rest of what you wrote because we are not yet off home plate.

Jack, I feel that you are missing the point here. I have no problem with the mathematical procedure of locally gauging U1 -> U1(x) and then introducing the connection field A to compensate, ensuring local gauge invariance. My problem is with the precise mathematical and physical interpretations of A, and how they are justified.

I have made that very clear in the case of GR where all local frames are coincident detectors solving Einstein's hole paradox.

1) Lorentz group SO1,3 is LIF(Alice) <---> LIF(Bob)

2) T4(x) is LNIF(Carol) <---> LNIF(Ted)

3) Tetrads are all four combinations:

LIF(Alice) <---> LNIF(Ted)

LIF(Alice) <---> LNIF(Carol)

LIF(Bob) <---> LNIF(Ted)

LIF(Bob) <---> LNIF(Carol)

However, in contrast, in the case of internal symmetries A's meaning is in the quantum Bohm-Aharonov effect fringe shifts, but unlike GR there is no direct physical meaning to different "frames" connected by internal gauge transformations that I know of for Bob, Carol, Ted and Alice. Maybe Nick Herbert can think of one? ;-)

Aug 07

It's Utiyama not Umezawa

Posted by: JackSarfatti |
Tagged in: Untagged 

On Aug 7, 2011, at 1:20 PM, Paul Zielinski wrote:

There no is question that Kibble, building on the work of Utiyama, did this formally in his 1961 paper. There is no point in denying that. But there is a trick here, having something to do I suspect with the construction of the covariant derivative.

Show us. The covariant derivative is the choice of the connection field that you keep confounding with the gauge transformations because you have not gone through the algebra of the local gauging program with sufficient attention to detail.

The connection is never a tensor relative to the gauge group transformations.

The gauge covariant curl of the non-tensor connection is the physical tensor field.

A gauge transformation never morphs a zero tensor into a non-zero tensor. You are still confused about that.

Gauge transformations are single-valued 1-1 reversible non-singular redundant defining an equivalence class of solutions all with the same topology, homotopy, homology etc. They are merely Plato's shadows of the real Idea in The Cave.

What you are groping for, like the blinded Cyclops trashing about, is Hagen Kleinert's multi-valued singular topology-changing transformations.

Curvature changes are the creation and destruction of disclination topological defects in the 4D world crystal lattice of quantum gravity. Torsion changes are creation and destruction of dislocation topological defects in the same.

The two convert into each other as shown in detail by Hagen Kleinert.

So mass-energy-stress current densities are sources and sinks for these defects that are like Landau's "elementary excitations" and no doubt you can make an S-matrix theory of their collisions, mergers, splittings etc.

I mean quanta of curvature and torsion.

We've been here before. The criticisms of Kibble's use of passive coordinate displacements made by Hehl et al, are well known. Hehl in particular starts with active diffeomorphisms and ends up with precisely the same Einstein-Cartan type theory.

You are confused. The distinction you are looking for has nothing to do with "active" & "passive" single-valued diffeomorphisms, but with the topology-changing singular multivalued transformations of Hagen Kleinert - those only happened pumped by changes in mass-energy stress current densities.

Kibble's method works formally, but I suspect that Hehl's gauge theoretic argument is logically and mathematically sound whereas Kibble's is not -- although it may look OK on the surface.

Prove it.

On 8/7/2011 9:15 AM, Jack Sarfatti wrote:

If localizing the group T4 of coordinate displacements just yields a larger class of coordinate transformations, then why doesn't the same apply to the Poincare group?

It does. Umezawa localized Lorentz group got curvature declinations but put in GCT by hand. Kibble did whole Poincare got torsion + curvature.

Utiyama?

Yes, thanks
Aug 07
I have yet to catch up on Jim's latest. However, looking at Sciama 1969 using full tensor formalism I can see why Jim has not been able to adapt it to his experiment. However, the teleparallel approach e.g. Waldyr Rodrigues Jr & Hagen Kleinert (independently) offers a promise of a more exact model with the nonlinear effects of gravity. Jim's current model does not seem to have the important nonlinearities in the strong field case.
Recasting Einstein's 1916 GR in the teleparallel case where you can express curvature in terms of an effective torsion field (W. Rodrigues Jr & H. Kleinert - independent works) is more useful because the torsion field equations are more like Maxwell's equations in form. More precisely, they are highly nonlinear Yang-Mills equations in form reflecting the strong gravity field nonlinear self-interaction, e.g. geons analog to glueballs in the SU3 QM chromodynamics case.
Basically Jim has the linear
F = dA  Cartan 2-form
A = Cartan 1-form
for his "Sciama" gravidynamic field "vector potential", the more exact equation from GR in the torsion formulation (a different gauge from the traditional curvature form as shown by Hagen Kleinert) is non-Abelian i.e. the nonlinear in A
F = DA = dA + A/A  Cartan 2-form "field tensor"
DF = 0  (Faraday "EMF" induction + no gravimagnetic monopole torsion analog) Cartan 3-form
dual to Cartan 1-form in 3D + 1 spacetime
D*F = *J  Cartan 3-form dual to e.g. **J = J 1-form in 4D spacetime
D*J = 0 local conservation of the "torsion current densities" gauge equivalent to s

From: "jfwoodward@juno.com" <jfwoodward@juno.com>
To: iksnileiz@gmail.com
Sent: Sun, August 7, 2011 1:00:27 AM
Subject: Re: What Sciama means by the "origin of inertia"

Paul,
Responses below.
---------- Original Message ----------
From: Paul Zielinski <iksnileiz@gmail.com>
Subject: Re: What Sciama means by the "origin of inertia"
Date: Sat, 06 Aug 2011 18:55:35 -0700
On 8/6/2011 1:22 PM, jfwoodward@juno.com wrote:
> I think I can be more helpful, though, by taking up where Jack said he "lost" me several emails ago.  He asserted that the definition of inertial mass, in concert with the definition championed by Frank Wilczek in his Physics Today articles, lectures, and book, should be m = E/c^2, or, as Wilczek calls it, Einstein's "second law" (the first being E = mc^2).
PZ: Don't we need to distinguish here between rest mass, which is truly
dynamical, and the relativist inertial mass, which includes an
additional contribution of purely kinematical origin?
JW: No, at least not as far as the inertial mass of a region of space(time) containing arbitrary non-gravitational energies is concerned.  Rest mass is just one of a number of different types of energy.  For example, the region might contain electromagnetic radiation with some energy E that contributes mass m = E/c^2 to the total mass in the region.  Wilczek's point when he first talked about this around 2000 was that the gluons in nucleons are zero rest mass, yet they make up almost all of the inertial mass of the nucleons.
JS: Exactly. I agree with Woodward on this.
JW:  There is an important caveat to be added to this definition: E does NOT include gravitational potential energies.  Why?  Because the Einstein Equivalence Principle (EEP) prohibits the "localization" of gravitational [potential] energy.
PZ: I would go further and argue that strictly speaking 1916 GR does not allow any physically plausible definition of gravitational energy, since  even globally such energy is a frame-dependent quantity, unless restrictive boundary conditions are  imposed at infinity on an *ad hoc* basis. Even then the invariance is only approximate.
JW: Well, since then is has become accepted to include energy in gravity waves as contributing to local energy (but with the caveat in MTW that you have to average over several wavelengths to avoid localization problems). 
JS: This washes out any "near field" effect that must be generally less than a single wavelength if I recall correctly? The near field has extra polarizations not found in the far field in the zero rest mass case both for spin 1 and spin 2 waves. So the gravity wave near field has 5 polarizations, the EM near field has 3 and for both only two propagate on-mass-shell to the far field "infinity."
JW: But localization of gravitational potential energy is strictly prohibited for the reasons I mentioned.  This does not mean, however, that the total scalar gravitational potential must either be zero or undefined.  It means that, like the vacuum speed of light in electrodynamics, the total scalar potential must be a locally measured invariant.  In fact, to get everything to work as it does, it has to be equal to c^2.
JS: This I am as yet not able to grasp - and it is an essential step in Jim's connection with his experiments. If he gets agreement with data then the fault is mine.
PZ: But the EEP definitely rules out an even approximately GCT- invariant localized stress-energy density, as you say.
JS: Not so sure about that in the torsion reformulation? -  Ask Rodrigues and Kleinert (they are not collaborating on this - don't get me wrong, i don't mean to imply that. The question then is, is the Yang-Mills field energy also nonlocal because of the self-interaction nonlinearities?
JW: Yes. Why?  Because if gravitational potential energy is localizable, accelerated reference frames can be distinguished from gravity fields,
JS: I would like to see a detailed proof of that. Reference?
PZ: Theoretically yes, but not empirically. All you need is a theoretic distinction between frame acceleration and a gravitational spacetime  "warp". The effects observed in observer reference frames can still remain empirically indistinguishable.
JS: Z's remark here strikes me as a malapropism ill-posed not even wrong garbling curvature (geodesic deviation) with LNIF covariant off-geodesic g-force (aka "weight") acceleration - not a proper problem.
JW: I'm not sure I get exactly what you are trying to say here. 
JS: That makes two of us. ;-) Z is lapsing into his meta-theoretic philofawzical angels & aliens dancing on pins Laputan mode again. :-)
 "As I see it, if gravitational potential energies are treated the same way as other non-gravitational energies are, and contribute to m through E in m = E/c^2, then local observers making local measurements can always distinguish in practice (with sufficienly accurate apparatus) between accelerated frames and gravity fields."
Did PZ write the above or JW?  I would like to see how one can make such a distinction that violates EEP where it is understood that "gravity field" means g-force felt in a LNIF not curvature.
JW? and the geometrization of gravity field in general relativity fails.  (This was shown by Carl Brans in 1962.)
PZ: Can you explain to us what this means? The EEP simply asserts that the coordinate and geometric contributions to the LC connection field  mutually cancel at some spacetime point in any local free fall frame.
JS: PZ is fundamentally confused in the above statement.
Newton's first law of mechanical motion = geodesic equation
Most generally this is for a test particle coordinate x^u
D^2x^u/ds^2 = 0
this means the physical covariant tensor acceleration of the test particle vanishes in every locally coincident frame inertial or non-inertial
where ds = proper time differential along the test particle's world line (classical no QM here)
Unfolding this to
d^2x^u/ds^2 + (connection)^uvw(dx^v/ds)(dx^w/ds) = 0
What is this connection field?
In the formalism of differential geometry the space is anholonomic, i.e. dragging tensor/spinor fields is path dependent. This is like irreversible thermodynamics with memory hysteresis where the entropy and other thermodynamic functions are not conservative state functions but are path dependent in the relevant parameter space. Similarly for dissipative mechanical systems with friction.
However, this does not help with the physical meaning of the connection in General Relativity. The physical meaning of the connection is the g-force effect in local non-inertial frames LNIF's.
Connection field =/= 0 only in a LNIF
all of the inertial pseudo-forces are encoded in the components of the connection field.
this includes Newton's gravity force, which is simply the static LNIF g-force in the SSS metric in the simplest case.
In Einstein's GR the actual formula including gravity time dilation is (in SSS case for source mass M, test particle mass m)
FNewton/m = -(GM/r^2)(1 - 2GM/c^2r)^-1/2  ~ {connection}^rtt ~ quantum Unruh temperature of ambient blackbody real photons
r > 2GM/c^2
Contrary to Z's confused remark above the connection field vanishes in the LIF so that Newton's second law there is simply
d^2x^u/ds^2 = 0
there is no cancellation of two "forces" in the LIF.
Indeed, such a formal cancellation is in the LNIF not the LIF.
PZ: But even if a theoretic distinction is drawn between frame acceleration and the locally observed non-tidal effects of an actual
gravity field, one can still represent actual gravitation (as opposed to frame acceleration) with the coordinate-covariant partial derivatives of  the g_uv metric!
JS: Meaningless sentence above to my mind.
JW: Bran's paper is among the references that I think I left in the attachment to the first version of this email.  So you can no doubt track it down on line.  Stripping away all of the subtleties, the argument goes that if local gravitational potential energy contributes to E along with other non-gravitational sources, then the mass of an electrically charged object will differ from the same object in an accelerating reference frame.  As a result, the charge to mass ratio will depend on the presence of local gravity fields (due to "spectator" matter in the lingo of that day).  Charge to mass ratios are locally determinable.
JS: OK, I get what Jim is saying. However, the charge to mass ratio certainly depends on the velocity of the charge, i.e.
e/m = (e/mo)(1 - (v/c)^2)^1/2
JW: A simpler way to make a local discrimination of this sort is simply to let an object fall and make a dent in the floor.  If the EEP is true, the dents will be identical.  If spectator matter changes the mass of the test object through its gravitational potential energy, the dents will not be the same.
JS: Any actual experiments?
JWMach's principle -- at least as I define it -- ties all of this together.  Mach's principle contains two physical assertions.  One is that the "origin" of inertial reaction forces is the gravitational action of chiefly distant "matter".
PZ: I suppose that's "Machian" -- in Einstein's sense of the term --  depending on what you mean by "matter".
JS: Here I agree with PZ. I find Jim's above formulation of Mach's principle as uncomfortably vague needing mathematical form.
"Well, it's a metahistorical speculation, but I'd guess that physicists of the earlier 20th century would say everything that gravitates is "matter".  I think that was the clear intent of Einstein in his 1905 paper where he stated his "second" law: m = E/c^2."
not sure who wrote the above
JW:  As Jack notes, "matter", defined as everything that gravitates, means a lot more than it did in the 1950s when the serious debate over Mach got started.
PZ: OK, but Mach had quite specific reasons for referring the rotation of Newton's bucket to ponderable matter -- stuff that can be directly observed.
JW: Yes, Mach's "philosophy" made him suspicious of things that could not be directly sensed.  And he was suspicious of relativity theory.  But I'm not really interested in what Mach thought about Mach's principle.  It's Einstein's conceptualization of it -- up to the mid-'20s anyway -- that's of interest.  That's caught in The Meaning of Relativity, roughly pages 99 - 116 if memory serves.
PZ: You seem to be leaving the Machian reservation here.
JW: The second assertion is that the "origin" of inertial mass is the action of gravity.  This follows from the first version of Mach's principle -- the gravitational origin of inertial reaction force -- in a simple way.
JS: OK if I understand this. It's false in the light of modern physics i.e. quantum chromodynamics for the strong force of hadron masses and the Higg's mechanism for the weak force for lepton and quark masses. I mean rest masses.
PZ: But I don't understand. In a globally flat spacetime, according to GR you still get an inertial reaction to being pushed off a geodesic, but since the Riemann tensor is everywhere zero, there is no gravity. In which case how can you argue that in GR such inertia is gravitational in origin?
JS: Finally a Gold Star for PZ. Finally he gets a bull's eye right on the target. ;-)
JW: Globally flat Minkowski spacetime is an idealization that has no corresponding actuality.  Inertial structure in such a spacetime is simply assumed.  Assuming that such a spacetime could possibly exist is perfectly reasonable given our experience.  But just because we can imagine it doesn't mean that it could really exist.  The fact of our existence is that space is (at the cosmic scale) globally flat, and it is NOT empty.  Given that reality, the question is: do inertial reaction forces arise from some intrinsic property of the things that have inertia, or are they caused by the action of a field due to the other stuff in the reality?  The Sciama and Nordvedt calculations that I've mentioned both say that gravity causes inertial reaction forces.  In Sciama's calculation (one page), it is a direct force.  In Nordtvedt's PPN calculation (two pages), it is a "linear accelerative frame dragging" effect.  Either way, distant stuff there produces a gravitational force here which turns out, like gravity, to be "fictitious" in the eyes of most mechanics.
JS: Einstein and Infeld modeled test particles as singularities in the metric field guv. I forget if they did it as singularities in the curvature tensor field Ruvwl? If the latter, they missed black holes. But suppose you can do such a thing. Then you are forced to the Bohm hidden variable model of quantum reality.
Indeed, the Heisenberg uncertainty principle must change to
&x ~ h/&p + (quantum of area)&p/h
PZ: I seem to recall that Einstein initially believed that according to his 1916 theory, if all gravitating matter were removed from spacetime, there would be no such thing as inertia. That is, until de Sitter set him straight.
JW: Yes, deSitter showed that his field equations had asymptotically empty solutions with inertial structure.  The problem, of course, is that his equations are those of a local field theory. 
JS: In fact, the de Sitter solution is our future universe, but not our past universe. This explains the Arrow of Time that Sean Carroll could not explain and wrote a whole book coming to the conclusion that he could not explain it. The d Sitter solution has the constant dark energy density / (Einstein's cosmological constant) as the inverse future asymptotic area of our future event horizon.
We know that this area is a thermodynamic entropy (Bekenstein --> Hawking --> Unruh) and is also a computer (Seth Lloyd, MIT).
If the universe is a hologram then the area of our future de Sitter horizon is the total thermodynamic entropy of our observable universe sandwiched between our past and future horizons (Tamara David PhD 2003 University New Sourh Wales). That area is one Planck pixel at inflation and it saturates to about 10^123 pixels explaining the Arrow of Time trivially. The future de Sitter horizon is then Mach's "distant matter" and all interior bulk physical fields are hologram images in the Wheeler-Feynman --> Hoyle-Narlikar --> Cramer --> Aharonov post-selected "Destiny" retrocausal "back from the future" sense. Remember our future horizon is an observer dependent spherical shell of Planck thickness surrounding us completely in a kind of bubble whose entropy/area increases from 1 Planck pixel to 10^123 pixels in finite conformal time (infinite proper time). We get nearer to it as we get farther away from our past particle horizon.
JW: And in addition to solutions that satisfy Mach's principle (as I am defining it at least), there are other solutions that are manifestly anti-Machian.  The Godel rotating universe is the customary solution to bring up in this connection.  But just because equations have "unphysical" solutions doesn't mean that they should be rejected out of hand.
It turns out to be easy to show -- at least in the vector approximation of GRT -- that inertial reaction forces arise from the gravitational action of chiefly distant matter.
JS: I would like to see that in full detail.
PZ: Which does seem to imply that there is no such thing as inertia in a spacetime that is empty of gravitational sources.
JW: Yes and no.  I take it to imply that in our universe, which is not empty, that inertial reaction forces are gravitational. 
JS: I don't understand how Jim means "inertial reaction forces". As I explained in another note, by that term I mean only for a LNIF's rest frame that
(connection field)^itt = (external non-gravity force)^i/m = g-force measured in the LNIF as weight
i = x,y,z
this is explained by Hawking in (see attachement 2)
PW: And this fits, as I have argued, with the EEP, the principle of relativity, and Newtonian mechanics (especially the third law).  But no, Einstein's equations admit solutions where this is not true -- the anti-Machian solutions.
PZ: If this is your position, how do you answer de Sitter?
JW: I think I've already done this above.
That is what Sciama did back in 1953 (as part of his doctoral work with Paul Dirac). Now Sciama's calculation can be criticized on a number of grounds (and has been over the years).  But this is a case where the simplifying assumptions that Sciama made did not compromise the result he obtained.  As recounted in the beginning of the attached derivation (and one of the appendixes to MP+ME), the condition that must hold if inertial reaction forces are caused by gravity is that the total scalar gravitational potential MUST be equal to the square of the speed of light.
PZ: OK so this is a *necessary* condition?
JS: I reiterate I do not understand the meaning of that move in the game. Remember also Maxwell's
c^2 = (electrical permittivityxmagnetic permeabiity)^-1
both for virtual particles inside the vacuum and real particles outside the vacuum making real objects in the quaint Victorian sense of both Mach and Einstein.
PZ: Yes, but with the added condition that, like the vacuum speed of light, it must be a locally measured invariant.
JS: Not in a material where like the translation group, the Lorentz group is spontaneously broken for interior measurements (e.g. Cerenkov effect) though not for external measurements of the material object as a whole.
JW: And if this is to be true everywhere and everywhen -- so that Newton's third law is also universally true -- then phi must be a locally measured invariant like c.  Note that if this is true, then the non-localizability condition of the EEP follows automatically.
JS: I don't yet understand the physical meaning of this "phi" as Rabi said of Pauli's neutrino "Who ordered that?" ;-)
"But the so-called "non-localizability" theorem is based on the frame *dependence* of the vacuum energy density."
Who wrote that? I suppose it's JW.
PZ: If phi is proportional to the vacuum energy density, then I would have thought the conclusion would be the exact opposite -- you need an *invariant* stress-energy density. Or am I missing something?
JW: Perhaps I am missing something.  The non-localizability prohibition of the EEP, as I understand it, is not based on vacuum energy density (which in classical GR without dark energy is zero), it is based on Bran's argument about the action of spectator matter (where he, by the way, corrected an incorrect argument by Einstein in 1921).
JS: Yes, I agree with JW on that point.
JW: By the way, should you want the frame dragging equivalent of Sciama's calculation, Nordtvedt did all but the last step in the PPN formalism in 1988. ... Now, the non-localizability of gravitational potential energy [EEP], the locally measured invariance of phi, and the fact that phi equals c^2, all different facets of the same jewel, have serious consequences for the origin of inertial mass.  Take the Sarfatti/Wilczek/Cambier assertion about the "origin" of inertial mass, expressed through Einstein's second law:
             m = E/c^2
where E is the total NON-GRAVITATIONAL energy in some local region of spacetime, m the inertial mass possessed by that energy, and c the vacuum speed of light.  By the way, I am NOT trying to pick a fight here.  This is a special relativity definition.  But when we allow for general relativity, we know that c^2 is identically equal to phi via the argument above.  So we can replace c^2 with phi and do a little rearranging to get:
              E = m phi
JS: But Maxwell tells us therefore that
E = m/(electrical permittivity x magnetic permeability)
Hence in a metamaterial with only one of the factors negative, we get a negative energy E < 0.
We can even get E as a complex number.
JW: Now, if the inertial mass m is the same as the gravitational mass as the equivalence principle tells us it is, then this simple equation tells us that the non-gravitational energy of the stuff in our region of spacetime is just its total gravitational potential energy. 
JS: This is a stretch and probably spurious. It's not clear that there is such a thing as total gravity potential energy in Einstein's GR in the most general case.
In the SSS case gtt = 1 + 2Newton's potential energy per unit test particle/c^2
but when we have terms like git, i = x,y,z or t, theta, phi etc the simple model JW uses gets more problematical.
Also if gravity is an emergent low energy large scale c-number Glauber state Higgs-Goldstone vacuum effective field theory, there is no reason to try to explain micro-quantum physics rest masses of elementary particles with it. That's like trying to explain atoms with the elasticity tensor! Rather, it's the other way round. JW seems to be putting the cart before the horse?
PZ: In other words, the "origin" of non-gravitational energy is in the gravitational interaction of stuff with chiefly distant matter.  Note that this doesn't work if the non-localizability prescription of the EEP is abandoned (and with it, the geometrizability of the gravitational field of general relativity).
PZ: I'd like to see Brans' 1962 argument.
JW: If memory serves, it is included in Dicke's Benjamin reprint book called "Experimental Relativity" published in the mid-'60s.
PZ: This looks like a *non sequitur* to me. Another possilbe suspicion is that it's a tautology.
JS: Z thinks everything is a tautology because he talks in circles much of the time. ;-)
PZ: But I don't think it is.  It's analogous to saying that the EP works because "fictitious" forces [inertial reaction forces] and gravity forces both have the same properties. 
JS: Yes. However, I would not use the word "reaction" I would only use "inertial pseudo-forces" i.e. contingent artifacts of the free choice of the LNIF.
PZ: Well, it then seems a reasonable inference that they may have the same properties because they are all the same force.  [That, in a sense, is a version of Mach's principle.]  One needs to do calculations to make sure that this is the case.  But is the inference a non-sequitir?
JS: Not even wrong - my opinion.
JW: If you read through the derivation attached, you will find that E = m phi (expressed as densities) is the formulation of Mach's principle that allows you to "separate variables" to recover Mach effects in the relativistic Newtonian order approximation to GRT.  So Mach effects really are general relativistic effects -- but much larger than the effects usually attributed to GRT.  :-)
JS: I don't understand JW's last remark.
PZ: Of course an obvious question is, how does this explain the local isotropy of inertia? Gravitational interactions between masses
strengthen the closer they get. A "Machian" interaction with distant matter would have to behave in the exact opposite matter, or
else local sources would destroy the isotropy of inertia. How does your model account for this?
JW: The simple answer has two parts.  One is that made by Sciama.  Inertial reaction forces come from the gravitomagnetic vector potential in the c^-1 dA/dt term in the gravitoelectric field equation.  When the source currents are integrated over in his manner, the r dependence of this term is 1/r, not 1/r^2.  This makes the dominant contribution due to the distant matter.  The other issue you raise is the "tensor mass" business.  Cocconi and Salpeter suggested this in 1959 (in the Mach's principle debate of the day).  Not too long thereafter, Dicke and Peebles showed that as long as there is only one long range tensor field, these sort of things can be absorbed into the metric leaving isotropy intact.  This was in connection with the Hughes-Drever experiments performed at the time.  The paper is also in the Benjamin reprint that I mentioned above.
Best,
Jim
JW: For those interested:  A lab update.  I've succeeded in confirming John's "decline effect" prediction.  The peak voltage in the runs done the other day were about 530 counts, as opposed to 575 counts for the 1 uN result obtained a couple of months ago.  More telling is the stack accelerometer result: 580 versus 700 counts.  Now, i suppose you can do a scaling calculation with these numbers.  But I wouldn't.  Having scratched a lot of itches, it's time to move on to Bruce's dual resonance matcher.  That's first up next trip.  I've also got a stack in preparation using the new crystals.  It probably won't get run next trip.  But perhaps the trip after.
>
> May you all have a good weekend,
>
> Jim
>
>
on the Blog. We did not realize there was a problem that is now supposedly fixed on http://stardrive.org
Aug 07
OK if you do the teleparallism
localize the full Poincare group.

The spin connection 1-form gets an extra piece K the contortion

A' = A(T4) + K(SO1.3)

Define the curvature 2-form

R' = DA' + A'/\A'

Teleparallelism means

R' = 0

Obviously then the old Einstein curvature F can be expressed in terms of the contortion tensor (relative to GCT of GR) and

T = K/\e =/= 0

because de + A/\e = 0

We now have a true Yang-Mills theory where

the first set of "Maxwell" equations is

D'T = 0 = torsion analogs of Faraday induction and no magnetic monopoles - but for the gravity field

where

D' = d + A + K

the source equations (analog of Ampere's and Gauss's laws) are

D'*T = *J

local conservation of torsion currents

D*J = 0

as Waldyr Rodrigues says this is all equivalent to Einstein's GR

Hagen Kleinert also says you can either use the torsion or the curvature in the teleparallel sense.

Since Woodward needs the EM analogy, this is more rigorous and perhaps can be applied to his experiment.

Note the Yang-Mills Lagrangian torsion density is ~ (1/4)Tr{T/\*T} - it's a non-Abelian gauge theory for gravity.


From:
Jack Sarfatti <sarfatti@pacbell.net>
To: Paul Zielinski <iksnileiz@gmail.com>

Sent: Sat, August 6, 2011 9:41:27 PM
Subject: Re: What Sciama means by the "origin of inertia" & Woodward's Interstellar Star Ship Time-Space Solution


"So where's the beef Jack? Where is the cash value here? What is the motivation for locally gauging T4 to get GCTs? What do we really gain by going from the plain vanilla 1916 formalism to the gauge gravity model? Isn't it just the same old wine in different mathematical bottles? I mean aside from the advantages of the tetrad formalism for dealing with angular momentum."

The local gauge principle with minimal coupling allows one to infer the extended Lagrangian of the original source field + the induced gauge force field. It is basically Einstein's locality principle. Observers that are spacelike separated can orient their detectors independently without changing the physics. Remember this is all classical - no quantum entanglement at this stage.

In general

Local gauging induces a connection 1-form A

This gives a covariant exterior derivative

D = d + A

the "field" F (in GR it's curvature, when A is the spin-connection)

F = DA = dA + A/\A

The torsion is

T = De

where e = the set of 4 tetrads

In analogy with U1 electromagnetism

DF = 0 (a kind of Bianchi identity)

D*F = *J   this equation in tetrad notation maps to Einstein's Guv + kTuv = 0

See Rovelli Ch. 2

D*J = 0 is local conservation of stress-energy current densities in the case of T4(x) GR.

Similarly if there is torsion.

To get both torsion and curvature as independent dynamical fields we need to localize the entire Poincare group not just its T4 subgroup.
Aug 07

Zielinski strikes back! :-)

Posted by: JackSarfatti |
Tagged in: Untagged 

The comments program on Joomla does not work so if anyone wants to comment send it directly to me at adastra1@me.com

On Aug 6, 2011, at 6:12 PM, Paul Zielinski wrote:
Sent: Sat, August 6, 2011 3:47:20 PM
Subject: Re: What Sciama means by the "origin of inertia" & Woodward's Interstellar Star Ship Time-Space Solution
It's all Zielinski's fault! :-)
Now that I read Sciama 1952 & 1969 I understand what Sciama means by "origin of inertia". He simply means deriving the geodesic structure of the entire spacetime history. Geodesics describe the universal (independent of rest mass) zero g-force "inertial motion" of neutral test particles - the very beginning of Sciama's 1952 paper. Sciama never claims to be able to derive the rest mass of the electron to be 10^-27 grams for example.
OK.
Let me explain how Mach's Principle is irrelevant in the modern local gauge theory.
Einstein's 1916 GR is simply 1905 SR when the rigid 4 parameter translation group T4 is locally gauged to T4(x).
Passive T4(x) gives you GCTs, active T4(x) gives you curved geometry. Right?
Wrong. There is no physical difference at all. You are confusing active with dynamical.
See Rovelli Ch 2 he explains that active & passive are simply two ways of looking at the same thing - the main thing are the gauge orbits (all solutions of field equations connected by elements of the gauge group are physically identical - gauge freedom is redundancy in the physical description explained e.g. by Dirac - it's also the solution of the Einstein hole problem).
active T4(x) does not change tensor fields.
You are looking for Kleinert's "multi-valued gauge transformations" - there it's the singularities that represent new physical differences. The T4(x) gauge transformations are not singular. All the solutions they connect are different representations of the same invariant dynamical configuration of fields as seen by different sets of detectors.
These are the general coordinate transformation which are gauge transformations just like in electromagnetism.rt But coordinate transformations can't change the intrinsic geometry!

Exactly.
If you're starting with a flat Minkowski spacetime, how can locally gaugiing passive T4 -> T4(x) give you the curved geometry of GR?
It doesn't. You misunderstand. The localization of the group is NOT the same as the gauge transformations. The tetrads e^I are induced by the local gauging T4 --> T4(x). They are gauge invariants under the GCT gauge transformations.
You got things garbled.
e^I (LIF) = e^Iue^u(LNIF)
the T4(x) gauge transformation is the GCT
e^Iu' = Xu'^ue^Iu
this is all in Rovelli Ch 2 very clearly explained.
All solutions of the field equations connected by local gauge transformation represent the same physical space-time! The same physics.
True if you're talking about passive T4. But then why not just go straight to Diff(R^4)? Why do we need to locally gauge passive T4 anyway? What does it add to the usual approach?

All the solutions are on the same gauge orbit correspond to what different sets of detectors measure when each is in an arbitrary world line that does not need to be a timelike geodesic. They can be in rocket ships in space firing their engines. See Rovelli Ch 2 Quantum Gravity free online.
OK.
The four LIF Cartan tetrad 1-forms and their six spin-connection 1-forms are induced by the local gauging and restore the symmetry to the enlarged system of matter + gravity. It's very beautiful and same idea as in the other electromagnetic - weak - strong forces. This is a real conceptual unification. The local gauge principle is simply Einstein's locality i.e. no signals outside the light cone. All of this ignores quantum theory entanglement of course - it's classical. With signal locality there is no conflict with quantum theory - what Abner Shimony calls "passion at a distance."
What this appears to boil down to is cancelling the physical manifestations of intrinsic curvature with GCTs -- which is just a "fancy shmancy" restatement of Einstein equivalence.

In the plain vanilla 1916 formalism the LC connection field locally cancels in free fall. Same thing. Same wine in different mathematical bottles.
The equivalence principle simply means universal minimal coupling of the gravity field tetrads to all the prior matter fields.
No it has to mean more than that if local gauging is to make theoretic sense Jack. How can one restore geometric symmetry by applying a GCT? Locally or otherwise?
Mathematically at least this is nonsense.

I have no idea what your sentences here mean. I never wrote that a GCT restores the symmetry. You got things garbled again. Its the induced tetrads e^I for the geodesic LIFs that restores the symmetry to the original matter field with the new gauge force connection in the larger configuration space. These induced tetrads are GAUGE INVARIANT "scalars" under the GCT gauge transformations.
That said, it's all "interior bulk physics" in the sense of the hologram virtual universe conjecture where we are retrocausal computations of the VALIS computer (see Seth Lloyd on event horizons as computers) at the future edge of time - the dark energy de Sitter future horizon. This brings back a super-strong Mach's principle using the ideas of Wheeler-Feynman -> Hoyle-Narlikar -> Cramer's transaction -> Aharonov's Destiny Vector. But this is really speculative. Will say no more about it here.
Far out.

For example, to couple the electromagnetic vector potential AI(LIF) from 1905 SR to 1916 GR with the 16 tetrad components (gravity field LNIF)
Au(LNIF) = eu^I(tetrad)AI(LIF)
For the Dirac spinor electron the universal EEP minimal coupling of say the electron to gravity is
Du(LNIF) = eu^IPI(LIF) + (Spin Connection)u^I^JPIJ(LIF)
=  generally covariant partial derivative matrix operator on the spinor Psi multi-component column vector
there are 24 spin connection components connecting the LIF to the coincident LNIF in accord with the EEP.

OK. Spin connection is a kind of covariant derivative.

Where PIJ is the appropriate matrix representation of the 6-parameter Lorentz group's Lie algebra acting on the spinor quantized field operator & PI are the Lie algebra of T4 (energy-momentum) together they are the Lie algebra of the Poincare group that form the global symmetries of 1905 SR.
OK this all seems to work formally, but why?
Local gauge principle.

Aug 07

It's all Zielinski's fault! :-)

Posted by: JackSarfatti |
Tagged in: Untagged 

 


Sent: Sat, August 6, 2011 3:47:20 PM
Subject: Re: What Sciama means by the "origin of inertia" & Woodward's Interstellar Star Ship Time-Space Solution


Now that I read Sciama 1952 & 1969 I understand what Sciama means by "origin of inertia". He simply means deriving the geodesic structure of the entire spacetime history. Geodesics describe the universal (independent of rest mass) zero g-force "inertial motion" of neutral test particles - the very beginning of Sciama's 1952 paper. Sciama never claims to be able to derive the rest mass of the electron to be 10^-27 grams for example.
Let me explain how Mach's Principle is irrelevant in the modern local gauge theory.
Einstein's 1916 GR is simply 1905 SR when the rigid 4 parameter translation group T4 is locally gauged to T4(x). These are the general coordinate transformations, which are gauge transformations just like in electromagnetism. All solutions of the field equations connected by local gauge transformation represent the same physical space-time! The same physics. All the solutions are on the same gauge orbit correspond to what different sets of detectors measure when each is in an arbitrary world line that does not need to be a timelike geodesic. They can be in rocket ships in space firing their engines. See Rovelli Ch 2 Quantum Gravity free online.

The four LIF Cartan tetrad 1-forms and their six spin-connection 1-forms are induced by the local gauging and restore the symmetry to the enlarged system of matter + gravity. It's very beautiful and same idea as in the other electromagnetic - weak - strong forces. This is a real conceptual unification. The local gauge principle is simply Einstein's locality i.e. no signals outside the light cone. All of this ignores quantum theory entanglement of course - it's classical. With signal locality there is no conflict with quantum theory - what Abner Shimony calls "passion at a distance."

The equivalence principle simply means universal minimal coupling of the gravity field tetrads to all the prior matter fields.

That said, it's all "interior bulk physics" in the sense of the hologram virtual universe conjecture where we are retrocausal computations of the VALIS computer (see Seth Lloyd on event horizons as computers) at the future edge of time - the dark energy de Sitter future horizon. This brings back a super-strong Mach's principle using the ideas of Wheeler-Feynman -> Hoyle-Narlikar -> Cramer's transaction -> Aharonov's Destiny Vector. But this is really speculative. Will say no more about it here.

For example, to couple the electromagnetic vector potential AI(LIF) from 1905 SR to 1916 GR with the 16 tetrad components (gravity field LNIF)

Au(LNIF) = eu^I(tetrad)AI(LIF)

For the Dirac spinor electron the universal EEP minimal coupling of say the electron to gravity is

Du(LNIF) = eu^IPI(LIF) + (Spin Connection)u^I^JPIJ(LIF)

=  generally covariant partial derivative matrix operator on the spinor Psi multi-component column vector

There are 24 spin connection components connecting the LIF to the coincident LNIF in accord with the EEP.

Where PIJ is the appropriate matrix representation of the 6-parameter Lorentz group Lie algebra acting on the spinor quantized field operator & PI are the Lie algebra of T4 (energy-momentum) together they are the Lie algebra of the Poincare group that form the global symmetries of 1905 SR.

From: "jfwoodward@juno.com" <jfwoodward@juno.com>
To: iksnileiz@gmail.com
Subject: Re: What Sciama means by the "origin of inertia"

Folks,
I've been trying to keep up with the conversation since being in transit here and there for the last day or two.  I'd like to try to facilitate things in two ways.  One is to provide (attached) a stripped down version of "Flux Capacitors and the Origin of Inertia" that only has the formal derivation of Mach effects so that all of the math is there, without other stuff, to be evaluated.  As an aside, I should mention that this has been through peer review.  Foundations of Physics requests suggested referees.  I volunteered six names (and suggested that the ms be sent to all of them).  Were I to break confidence and tell you the names I submitted, you would likely instantly recognize at least two or three, and some of you would recognize four or five.  In addition, a number of you have been through this derivation for yourselves.  And I took it to Ron Crowley and Stephen Goode (both excellent general relativists) before publishing it.

I think I can be more helpful, though, by taking up where Jack said he "lost" me several emails ago.  He asserted that the definition of inertial mass, in concert with the definition championed by Frank Wilczek in his Physics Today articles, lectures, and book, should be m = E/c^2, or, as Wilczek calls it, Einstein's "second law" (the first being E = mc^2).  There is an important caveat to be added to this definition: E does NOT include gravitational potential energies.  Why?  Because the Einstein Equivalence Principle (EEP) prohibits the "localization" of gravitational [potential] energy.  Why?  Because if gravitational potential energy is localizable, accelerated reference frames can be distinguished from gravity fields, and the geometrization of gravity field in general relativity fails.  (This was shown by Carl Brans in 1962.)


Mach's principle -- at least as I define it -- ties all of this together.  Mach's principle contains two physical assertions.  One is that the "origin" of inertial reaction forces is the gravitational action of chiefly distant "matter".  As Jack notes, "matter", defined as everything that gravitates, means a lot more than it did in the 1950s when the serious debate over Mach got started.
The second assertion is that the "origin" of inertial mass is the action of gravity.  This follows from the first version of Mach's principle -- the gravitational origin of inertial reaction force -- in a simple way.


[Jack interjects: please define how you mean "inertial mass" - what is that? Is the rest mass of the electron 10^-27 grams "inertial mass"? Do you mean to say that one needs Mach's principle to compute that number?

Also define what you mean by "inertial reaction force" in terms of the equations.

Here is what I mean:

For a weightless zero g-force massive test particle on a timelike geodesic (curvature is irrelevant) Newton's first law of mechanical motion in any local frame of reference is

d^2x^u/ds^2 + {Levi-Civita Connection}^uvw(dx^v/ds)(dx^w/ds) = 0            geodesic equation has no inertial mass m in it at all!

The second term on LHS is zero in a LIF it's only non-zero in a LNIF locally coincident with the LIF (Sciama's "rest frame" of the test particle)

Do you mean the 2nd term on the LHS is the inertial reaction force?
That's not what I mean by the same term. What I mean is this:
             
Use Newton's 2nd Law of mechanical motion

d^2x^u/ds^2 + {Levi-Civita Connection}^uvw(dx^v/ds)(dx^w/ds) = F^u/m

where F^u is an applied translational non-gravity force e.g. for a charge q

F^u = qF^uv(dx^v/ds)

Fuv - EM field tensor  - neglecting Dirac's radiation reaction "jerk" (third order partial differential equation with future light cone nonlocal solutions - Wheeler-Feyman future absorber/Cramer transaction)

The rest mass m of the test particle appears in Newton's second law but not in Newton's first law! 
In the LNIF "rest frame" of the test particle m,q in this case under the action of the external non-gravity force F^u

d^2x^i/ds^2 = 0 , i = 1,2,3 (space axes)

dx^i/ds = 0  Therefore

{Levi-Civita Connection}^i00 = F^i/m
i = 1,2,3

For example, for us standing on surface of Earth, the quantum electrical reaction force pushing us off a timelike geodesic of the Earth's total mass M is the term F^i/m. The weight shown by standing on a scale is simply F^i ]

It turns out to be easy to show -- at least in the vector approximation of GRT -- that inertial reaction forces arise from the gravitational action of chiefly distant matter.
[JS: Perhaps you show this in your attachment I have not read yet. I am very concerned about what the "vector approximation to GRT" means because of John Norton's paper on the subject. But maybe - final test is experiment and you have experimental data.]

That is what Sciama did back in 1953 (as part of his doctoral work with Paul Dirac). Now Sciama's calculation can be criticized on a number of grounds (and has been over the years).  But this is a case where the simplifying assumptions that Sciama made did not compromise the result he obtained.  As recounted in the beginning of the attached derivation (and one of the appendixes to MP+ME), the condition that must hold if inertial reaction forces are caused by gravity is that the total scalar gravitational potential MUST be equal to the square of the speed of light. 

[JS: This is something I yet do not understand. The whole idea of the scalar potential is questionable. In Einstein's GR the scalar potential of Newton is subsumed in the metric tensor field guv for static LNIF test particle observers in the simplest case of a spherical static source mass M.]

And if this is to be true everywhere and everywhen -- so that Newton's third law is also universally true -- then phi must be a locally measured invariant like c. 

[JS; Very dubious in the light of modern precision cosmology since our universe is accelerating from dark energy's anti-gravity field never anticipated by Sciama.]

Note that if this is true, then the non-localizability condition of the EEP follows automatically.  By the way, should you want the frame dragging equivalent of Sciama's calculation, Nordtvedt did all but the last step in the PPN formalism in 1988.

Now, the non-localizability of gravitational potential energy [EEP], the locally measured invariance of phi, and the fact that phi equals c^2, all different facets of the same jewel, have serious consequences for the origin of inertial mass.  Take the Sarfatti/Wilczek/Cambier assertion about the "origin" of inertial mass, expressed through Einstein's second law:

            m = E/c^2

where E is the total NON-GRAVITATIONAL energy in some local region of spacetime, m the inertial mass possessed by that energy, and c the vacuum speed of light.  By the way, I am NOT trying to pick a fight here.  This is a special relativity definition.  But when we allow for general relativity, we know that c^2 is identically equal to phi via the argument above.  So we can replace c^2 with phi and do a little rearranging to get:

            E = m phi


[JS: I don't understand this either yet. What about Maxwell's discovery that c^2 = (electrical permittivity x magnetic permeability)^-1 ?]

Now, if the inertial mass m is the same as the gravitational mass as the equivalence principle tells us it is, then this simple equation tells us that the non-gravitational energy of the stuff in our region of spacetime is just its total gravitational potential energy.  In other words, the "origin" of non-gravitational energy is in the gravitational interaction of stuff with cheifly distant matter.  Note that this doesn't work if the non-localizability prescription of the EEP is abandoned (and with it, the geometrizability of the gravitational field of general relativity).

If you read through the derivation attached, you will find that E = m phi (expressed as densities) is the formulation of Mach's principle that allows you to "separate variables" to recover Mach effects in the relativistic Newtonian order approximation to GRT.  So Mach effects really are general relativistic effects -- but much larger than the effects usually attributed to GRT.  :-)

For those interested:  A lab update.  I've succeeded in confirming John's "decline effect" prediction.  The peak voltage in the runs done the other day were about 530 counts, as opposed to 575 counts for the 1 uN result obtained a couple of months ago.  More telling is the stack accelerometer result: 580 versus 700 counts.  Now, i suppose you can do a scaling calculation with these numbers.  But I wouldn't.  Having scratched a lot of itches, it's time to move on to Bruce's dual resonance matcher.  That's first up next trip.  I've also got a stack in preparation using the new crystals.  It probably won't get run next trip.  But perhaps the trip after.

May you all have a good weekend,

Jim
Aug 06

Discussion with Paul Murad 8-5-11

Posted by: JackSarfatti |
Tagged in: Untagged 
See pdf uploaded to Advanced Propulsion
Aug 05

Feynman's Cal Tech Lectures on Gravity

Posted by: JackSarfatti |
Tagged in: Untagged 

On Aug 5, 2011, at 2:30 PM, Paul Zielinski wrote:

I think for one that this was Feynman's general view of the real physical meaning of Einstein's 1916 theory of gravity.


Feynman in his lectures on gravitation builds Einstein's GR from his diagrams starting with a non-dynamical globally flat background like what I just used in the tetrad Fourier transforms ---> convolutions for products in the universal minimal coupling of gravity to all matter fields.

As I recall Feynman found the same kind of non-analytic phase transition as one sees in BCS theory of superconductivity.

That is, in order to get the complete classical theory

Guv + kTuv = 0

he had to sum an infinite series of I think tree diagrams - those with loops being quantum gravity corrections - as I recall.

In effect this may be a model for the inflation vacuum phase transition when gravity comes into being as a collective mode in a kind of bootstrap. The false vacuum having no tensor gravity at all just zero rest mass leptons, quarks and internal symmetry gauge bosons.
Aug 05

The never-ending story with Zielinski 8-5-11

Posted by: JackSarfatti |
Tagged in: Untagged 

On Aug 5, 2011, at 1:55 PM, Paul Zielinski wrote:

Einstein's theory of gravity aside, we can always choose a curved geometry to formulate physics.

This is false. You can choose curvilinear coordinates, but the tensor curvature Ruvwl will still be zero if it was initially.

There is no mathematical or empirical reason to prevent us from doing so as a matter of convention (as argued in detail by Poincare and others). Then free test objects will *not* move along geodesics.The actual physics, however, will be the same regardless. The law of inertia will still hold.

Another false statement. The geodesic equation is a tensor equation.

D^2x^u/ds^2 = 0

the covariant derivative of a tensor is still a tensor.

One way of looking at Einstein's theory is that the geodesics are simply deformed to agree with the inertial effects of a gravitational field produced by matter.

If you mean by that vague sentence

Guv + kTuv = 0

then I agree.

Again if you use equations instead of words when possible, you are less likely to be misunderstood.


From that POV, Einstein's curved spacetime is simply an abstract geometric model for gravity, with no more explanatory
content than Ptolemy's epicycles.


Epicycles were good for its time. However, I disagree with your opinion. Depends what you mean by explanation.

Then the real physical content of the Einstein-Hilbert field equations is simply that the presence of  gravitating matter THERE alters the local conditions of inertial motion HERE

Wait a minute

Guv + kTuv = 0

means matter here bends spacetime here - it's a local equation.

Of course the solutions involve Green's function propagators (with boundary conditions) so indeed matter here will bend spacetime there, but that requires more information than only the local dynamical field equations.

This is true in all local field theories not just Einstein's.

-- and that this is simply modeled mathematically in terms of a  curved spacetime geometry, treated as a pseudo-Riemannian manifold, where it is stipulated that  the local Ricci curvature (and the coupled  Weyl curvature outside the sources of the field) is determined by the matter distribution.

Now it is true, that if you use the graviphoton spin 1 vector gravity tetrad fields instead of the spin 2 metric tensor fields (the latter's graviton is composite from the former of course) that the four Cartan tetrad 1-forms e^I  (LIF basis) describe the Sciama "origin of inertial motion" as geometrodynamic fields on a formally globally flat Minkowski background.

That Minkowski background cannot not be detected globally only locally (EEP). Background independence is obeyed because the tetrad components couple universally and minimally to all non-gravity matter source and force fields. Therefore, all the usual gravity time distortions of the classic GR tests and beyond are obeyed.

But, for example, you can make a globally flat Fourier decomposition of e^I(x) into plane waves like in ordinary classical/quantum field theory, but the universal minimal coupling of EEP will give complicated convolution integrals.

For example, given the EM vector potential A^I in a LIF, it transforms to a locally coincident LNIF as

A^u(x) = e^uI(x)A^I(x)

Formally then, the Fourier transform of A^u(x) in the fictitious non-dynamical Minkowski background (with trivial global topology for now) is the convolution integral of AI(k,f) with e^uI(k,f).


http://www-structmed.cimr.cam.ac.uk/Course/Convolution/convolution.html


At least it's another way of looking at this. And who now believes that the gravitational field is literally reducible to curved Riemannian geometry?

Depends what you mean by "literal" - your meta-theoretical concerns are usually too vague for me.

spin 2 tensor gravitons may be composite entangled pairs of spin 1 gravi-photons (not same as Maxwell's photons).

In addition spin 1 vector particles are entangled pairs of Weyl 2-component spinors ---> twistors (Penrose) indeed the Bell states of IT FROM BIT quantum information theory pop up here - quantum teleportation and all that.

But if all that is true there should be spin 0 (Dicke) as well as spin 1 gravity fields in addition to the spin 2 gravity fields. Perhaps the spin 0 and spin 1 gravitons get rest mass from a Higgs mechanism and are confined to short distances?


See the Penrose & Rindler book.

On 8/5/2011 11:18 AM, JACK SARFATTI wrote:

First of all this word "inertia" is bandied about too loosely causing much of the confusion. It has at least different meanings in relativity.

Meaning # 1  Origin of inertia in one of Sciama's senses is trying to explain why test particles move on geodesics.
i.e. zero g-force free-float "weightless" "inertial motion" universal independent of the rest masses m of the test particles.

This is essentially trying to explain Newton's first law of mechanical motion generalized to curved space-time. Einstein with Infeld actually proved the geodesic rule from his nonlinear field equations

Ruv + 8piGTuv/c^4 = 0

modeling the test particle as a singularity in the 4th rank curvature tensor Ruvwl field if I remember correctly off the top of my head.

The Einstein-Infeld calculation is purely local not needing Mach's Principle.

Mach's Principle is archaic and quaint referring to "distant matter" that makes no real sense at all in modern precision cosmology since the 1990's because the only kind of "matter" Mach knew about is only 4% of all the gravitating stuff in the universe!

Woodward refers to the distant matter in "causal contact" with his local flux capacitor space drive prototype device that he actually has running in his lab much to his engineering credit. On the other hand, the situation seems to be like cold fusion and high-frequency-gravity-wave propulsion & Podkletnov type allegations discussed at the JASON meeting I attended a few years ago at General Atomics in La Jolla - hard to replicate by independent parties.

Woodward is not clear what he means by "causal contact" at times he seems to mean only the past light cone out to the "particle horizon" of the flux capacitor, but this contradicts the key assumption in his eq (44) that the universe as a constant density of "distant matter" if by that he means what Mach meant the "distant stars" - there is great ambiguity here and his equations rest on very shaky ground.

Keep in mind Tamara Davis's diagram



At other times Woodward alludes to Wheeler-Feynman and of course Sciama worked with Hoyle who developed the Wheeler-Feynman classical retrocausal ideas to quantum theory and cosmology. This brings in the future light cone of his device reaching to our future event horizon - hence John Cramer's "transactions" and Yakir Aharonov's "destiny" (post-selection final boundary condition) and even 't Hooft-Susskind's hologram conjecture.

Meaning #2 of "inertia" as resistance to non-gravity forces pushing the test particle of rest mass m off its timelike geodesic determined locally by source stress-energy density tensors Tuv(non-gravity fields). No need for Mach's Principle here.
So this is essentially F = ma Newton's 2nd law of mechanical motion of test particles generalized to curved spacetime.

The computation of the rest masses m of ordinary matter (real on mass shell in sense of quantum field theory's Feynman propagators) does not require gravity or Mach's principle, but is explained quantitatively for hadrons by Franck Wilczek's quantum chromodynamic supercomputer computations using the Higgs field couplings to the quarks in the input to the program.

What Sciama means by the "origin of inertia" is really the origin of the universal geodesic inertial motion of neutral test particles. He does not mean that Mach's principle is needed to explain why or how the rest mass of the electron is ~ 10^-27 grams or the rest mass of the proton is ~ 10^-24 grams - that is not a gravity physics problem needing the cosmological scale Mach's Principle.


Subject: What Sciama means by the "origin of inertia"

He does not at all mean the computation of the rest masses m of the elementary particles. He simply means the geodesic structure of the curved spacetime - the LIFs (Local Inertial Frames) with zero g force. By "inertial properties of matter" he means neutral point test particles moving along geodesics - the generalized Newton first law of motion in curved spacetime. His language is ambiguous, but in context it's clear he is not thinking of how much acceleration one gets when applying a non-gravity force to a test particle pushing it off its subluminal timelike geodesic in possibly curved spacetime. Sciama is not thinking of Newton's 2nd law of motion in this 1952 paper only the first law.  In other words his problem here is "why do neutral test particles follow geodesics" - a metaphysical quest for sufficient reason for what most of us accept pragmatically because it works. Note that his Maxwell vector model here is only meant as a rough qualitative toy model. Sciama is doing what Zielinski tried to do. That is, here Sciama is using Newton's picture where gravity is a real force that is canceled out by the rest of the universe in the free float geodesic motion. It's Rube Goldberg and is not necessary as Einstein's curved spacetime picture is better, more elegant, in my opinion. Also what is "distant matter"? When is it as well as where is it. Remember 1952 was the Dark Age of primitive cosmology. Sciama's ideas are now quaint and obsolete in the light of the 1998 discovery of dark energy - not to mention dark matter as well. On the other hand the gravity effect of the universe as a whole sounds like Wheeler- Feynman's future universe quantum influence functional as developed by Hoyle and Narlikar. The analogy to Wheeler-Feynman is not perfect because the future total absorber was the emitter of Cramer's advanced waves needed to complete a "transaction" for the emission of a photon. This is a retrocausal explanation for the manifestly non-geodesic motion "jerk" of Dirac's radiation reaction. Hoyle and Narlikar (1995 Rev Mod Phys) show that our future de Sitter horizon is the Wheeler-Feynman total absorber explaining why there is an Arrow of Time at least on the cosmological scale i.e. why we age as the universe expands and indeed is now accelerating for several billion years since the turning point.