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: "This email address is being protected from spambots. You need JavaScript enabled to view it. " <This email address is being protected from spambots. You need JavaScript enabled to view it. >
To:This email address is being protected from spambots. You need JavaScript enabled to view it.
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 <This email address is being protected from spambots. You need JavaScript enabled to view it. >
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,This email address is being protected from spambots. You need JavaScript enabled to view it. 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?
JW: 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".
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
>
>
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: "
To:
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 <
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,
> 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?
JW: 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".
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.
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> May you all have a good weekend,
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> Jim
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