Wednesday, May 04, 2005

Is the integral of zero always zero?

On May 4, 2005, at 10:01 AM, Jack Sarfatti wrote:

On May 3, 2005, at 10:14 PM, wrote:

Jack Sarfatti wrote:

You are beating a dead horse. They haven't done it because they don't know how. That is good enough. It's a solved problem in GR.

So it's a solved problem in GR but it is not yet solved in Yilmaz? Fine.

Which means that Yilmaz has a lousy theory.

It may simply mean that the problem is not yet solved in Yilmaz.

They have had since 1958 to do it, or at least since 1974. It's a dead subject. Let sleeping dogs lie.

It clearly means that and that clearly implies that orthodox GR is the superior theory - that works.

Or merely that GR is currently in a superior state of formal and computational development, which I think may be true.

"May"? "may"? Oh, you are too precious with your dainty hesitant "may". It's OBVIOUSLY true!

I don't think anyone is claiming that GR doesn't "work". I fully realize that leading theoreticians who use it to solve real problems insist that it now works really well for them, both heuristically and computationally
At the same time, there is nothing wrong with comparing orthodox GR to alternatives -- as Clifford Will, for example, did very systematically in his PhD thesis and in various published works.

Of course, there is nothing wrong when it is done well with precision as opposed to dainty dancing around the topic without actually solving anything.

The interesting thing about Yilmaz is that it is basically a conventional field theory against a flat kinematic background, in which respect it has certain similarities to spin-2 graviton models of the Gupta-Feynman type, and also to Rosen's bimetric model.

All the more reason to reject it! GR is a NON-PERTURBATIVE emergent c-number vacuum ODLRO effective field theory. So if what you say is true Yilmaz theory has no chance of being useful. It's a complete misunderstanding of the nature of the problem. It's like trying to explain superconductivity with the normal Fermi surface ground state x = 0 as the starting point for a perturbation theory.

y = e^(1/x) Stepfunction(-x) = SUM of infinity of Feynman diagrams of a certain class in the false vacuum

Is the NON-PERTURBATIVE "BCS"(Nambu-Jona Lasino) basic formula that applies generally here.

What you propose is perturbation theory around x = 0, which is obvious nonsense.

y ~ |Vacuum ODLRO|

x ~ density of states per unit energy at Fermi surface of false vacuum x interaction first order perturbation theory matrix element between the virtual fermion-antifermion pair that forms the Vacuum ODLRO condensate in the inflation phase transition

This says you cannot do what Yilmaz proposes in principle!

Lim y as x -> 0- = 0

Lim y as x -> 0+ -> +infinity

That's WHY you cannot do it!

I think it also has a close relationship to the tetrad/gauge field model for standard GR, which it has been shown by B&G and Hestenes) can be interpreted as a bimetric theory.

Too vague. Does not convey useful information. Justify with an example.

The key here of course is the final resolution of the energy problem, which many outside the orthodox establishment (particularly in the Russian school) still consider to be an important internal conceptual problem of GR. BTW, can you give me a citation for an accurate *fully interactive* computational GR solution of the two-body problem *without constraints*?

I am not a librarian. Do Google.

The fact is that none of the top drawer people in that field bother with it - and for good reason.

Well, first off they simply deny that there is an "energy problem" in GR, as if the question was finally settled by Einstein's 1918 papers on the subject.

I suspect Penrose is correct in this view.

Sorry, but, for whatever it's worth, I for one don't buy it.

You are not Roger Penrose, so that is completely understandable. He is only, perhaps the greatest living mathematical physicist, Professor at Oxford, FRS Knighted by The Queen. Why should we care what he thinks? ;-)
Hawking agrees with him on this. So does Martin Rees. So does Kip Thorne, John Wheeler .... What is the betting odds that these chaps are wrong and an amateur with a Masters in Chemistry has seen deeper into this question than they have? What are the odds? Of course, if you had a real argument that would be different. But you don't.

One famous attempt to paper over this "non-problem" was the specious table-pounding argument found in MTW Chapter 20, which I understand even you have now abandoned.

No, I have not abandoned it. It's on the back burner until I have the time to ponder the issue afresh. I think the nonlocality of the gravity energy is simply from the multiply connected topology of closed non-exact forms! That is, the idea of "flux without flux" in which you get a non-vanishing flux integral of dB on the outer closed surface even though technically dB = 0 between the inner and outer non-bounding cycles that only together form a boundary for Stoke's theorem

||*C over boundary = |||d*C over interior of boundary

I suspect that is the essence of the gravity nonlocal energy problem.

i.e. ||d*C in interior of non-bounding OUTER cycle for ||*C =/= 0 even though d*C = 0 in that interior

where d*C = pure local vacuum gravity energy density

i.e. 3-form?

d*C ~ (c^4/8piG)/\zpfguv

= 0 in ordinary non-exotic classical vacuum where /\zpf = 0, which is the case in MTW.

C = 1-form

and we ignore the inner non-bounding cycle isolating a topological defect in the local Vacuum ODLRO order parameter Psi where |Psi| -> 0 at the Goldstone argPsi phase singularity (e.g. Sir Michael Berry's papers)

Bu^a = Bu(LpP^a/ih) operating on argPsi = substratum non-trivial part of Einstein-Cartan DYNAMICAL tetrad

Bu = Bu^a(Xa/Lp)operating on argPsi = substratum torsion potential from locally gauging T4 -> Diff(4) GCT Xu'^u

This is not Shipov's torsion from locally gauging O(1,3) to ...?

i.e. locally gauging T4xO(1,3) to Diff(10)? or Diff(4)x?(6)

eu^a = Iu^a + Bu^a

guv(curved space-time) = (Iu^a + Bu^a)(flat space-time)ab(Iv^b + Bv^b)

Forget about Yilmaz's field potential. Forget about the Freud identity. Just look at Yilmaz's field equations:

G_uv = K (T_uv + t_uv)

which differ from the Einstein-Hilbert equations only by the addition of a small tensor vacuum term t_uv to the RHS.

That's meaningless until t_uv is DEFINED.

It is DEFINED in Yilmaz's papers. He gives an explicit expression for it, based on his tensor potential and based on the exponential definition of the physical metric.

Prove it. Your words are too vague. Show the math. Remember what Ibison said last night about the inadequacy of the exponential metric.

Actually t_uv is determined by

1) the Bianchi identities;

2) the Freud identity; and

3) Newtonian correspondence (in the slow motion limit).

Prove this. Show the math.

If you cannot create it, you do not understand it. Write it down explicitly! It's a complicated expression in the derivatives of the potential phi:

What is "phi"? Who ordered that?

Where is the physical definition of phi? This formula is unintelligible as it stands out of context. There is no "phi" in 1916 GR. You are not allowed to stick it in without explanation and justification. That is not how to do theoretical physics. Also there are TWO phis here, one with indices the other without. This is completely unacceptable balderdash as it stands.

For the slow motion limit, phi --> phi_0^0 (all other terms vanish) and this becomes

Aside from the fact that we have no idea what these "phis" mean. Your math here is completely unintelligible.

What's 0 alpha & beta? Why does first term on RHS of first equation vanish. Think what you are saying here. It's total nonsense.

SLOW MOTION LIMIT in GR means u = v = 0 that's not what you wrote at all! Paul this is hardly competent. Really!

The point is that his t_uv is *unambiguously determined* in terms of phi, and vice versa,
based on the two "marble" identities and Newtonian correspondence conditions, contrary to
what you suggest.

Meaningless. Unacceptable.

"Tensor potential" of what? The words are meaningless.

It's like a classical field potential, except that it's a second-rank tensor quantity.

What is "It's like"? Meaningless. Unacceptable. This is BAD PHYSICS! At least the way you present it.

Do you have a problem with that? If so, what exactly is your problem?

Paul, having studied with Hans Bethe as my a one-on-one tutor at Cornell 1960, I would be embarrassed to bring such a goofy lame incoherent not-even-wrong argument to him, were he still alive. This is not acceptable.

In 1958 Yilmaz was talking about a *scalar potential*. Is that the latest Yilmaz paper anyone at
GR-17 knows about?

In "Towards a Field Theory of Gravitation" (Nuovo Cimento 107B, 941 (1992)), he is talking
about a tensor potential phi_u^v that reduces to 1 x phi_0^0 in the Newtonian slow-motion limit.

If you wrote down the actual math it might be obvious why g0i is not possible in that model.

It's a second rank tensor potential. It's a tensor field that describes a physical field that is closely
analogous to an electromagnetic field, and which is thus fundamentally different in Yilmaz's model
from an "inertial field" of fictitious forces.

Meaningless. Not acceptable. Why not stick in green cheese and the kitchen sink?

The formal expression Yilmaz gives in 1992 for the exponential form of the metric (p 948)

This is also meaningless under the quantities on the RHS are physically defined, explained and justified.

Rotation terms would be g0i, i = 1,2,3

logguv = lognuv + 2(phi - 2phi~)uv ?

Meaning what exactly?

There is no motivation for this goofy formal trick. This is BAD THEORETICAL PHYSICS.


I have some business to attend to.

On May 4, 2005, at 1:04 PM, Jack Sarfatti wrote:

It's a second rank tensor potential. It's a tensor field that describes a physical field that is closely
analogous to an electromagnetic field, and which is thus fundamentally different in Yilmaz's model
from an "inertial field" of fictitious forces.

The formal expression Yilmaz gives in 1992 for the exponential form of the metric (p 948)

gives the required form for t_uv consistent with the Bianchi and Freud identities together with
Newtonian correspondence conditions.

Why? How? Prove it.

Is the eta factor supposed to be the flat Minkowski metric?

guv = (Minkowski)uv e^PHIuv is that the idea?

It requires justification

guv = eu^a(Minkowski)abev^v

(Minkowski)uv = Iu^a(Minkowski)abIv^b

guv = (Minkowski)uv e^PHIuv = Iu^a(Minkowski)abIv^be^PHIuv

e^PHIuv = 1uv + Yuv

guv = (Minkowski)uv e^PHIuv = Iu^a(Minkowski)abIv^b + Iu^a(Minkowski)abIv^bYuv

{Minkowski(e^PHI - 1)}uv = Bu^a(Minkowski)abIv^b + Iu^a(Minkowski)abBv^b + Bu^a(Minkowski)abBv^b

So I see no advantage here. This is very clumsy, unwieldy. It's not even a conformal dilation.

*When PHIuv = 0, then Bu^a = 0. But there is NO PHYSICAL MEANING to PHIuv in contrast to Bu^a!

This exponential form of the metric as an expression in the potential phi is supposed to be exact for a
broad class of problems in the tensor version of the theory.


For example, PROVE the equation

And define the several kinds of "phi" before you do. Note that this is not an SBS Landau-Ginzburg Vacuum ODLRO type expression that one might expect here.

He does not get this by direct solution of what he calls a "complicated set of non-linear differential
equations". He gets this from what he considers an analog for the matter tensor tau_uv


What Top Hat did this White Rabbit pop out of? -- In what parallel universe of the multiverse?

What is the relation of the phi with indices to the phi without indices.

This is totally gobbledygook. I have no idea what it means? I see no motivation. No necessity for this obscure excess baggage, which is less with more.

... adhoc obscurities deleted

Here's an excerpt from the 1992 Nuovo Cimento paper (p 948):

Gibberish. Adding obscurity to turgidity.

What you cannot create you do not understand.

Just throwing this Laputonian scribble at me is worthless. Obviously you do not understand it. You cannot explain what it means in your own words. You cannot pass Feynman's litmus test here.

The burden of proof is on you to show the bottom line. When I looked at the Yilmaz papers some time ago they were unintelligible, obscure and badly written in contrast to MTW - a paragon of clarity.

I agree that they could be better written, and some of the arguments presented by Yilmaz definitely need to be rationalized and reformulated. Some are even confused and defective (e.g. his confused argument about free fall in Section 3.2 of the 1992 paper).

If he can't get free fall right - then the whole thing is obviously worthless.

But I still think Yilmaz's overall take on the energy problem -- referring back to the classic debates between Einstein and Lorentz, Levi-Civita, Schroedinger, Bauer, and Laue -- is essentially correct:  there really is a vacuum energy conundrum in Einstein GR,

There really isn't. You are wrong. When /\zpf = 0 then tuv(vacuum) = 0 even though the total energy seen asymptotically is not zero. That is, a "zero local energy density" required by EEP integrates to a non-zero total energy integrated "Poynting Flux" through the outer NON-BOUNDING closed surface in a multiply-connected Vacuum ODLRO space, i.e. Berry's "phase singularities" where |Vacuum ODLRO| = 0 in ordinary space like in a quantized vortex in superfluid helium.

Total vacuum gravity energy detected asymptotically with zero interior local energy density in the interior that has "holes" in it.

which I agree with Yilmaz was not satisfactorily resolved by Einstein's final definitive 1918 paper on the topic, notwithstanding all the bold dogmatic pronouncements of orthodoxy.

So you have a hopeless cause charging windmills.

Now we have a paper by Hestenes, referring back to papers by Moller, Rosen, and Babak & Grishchuk, which nowhere even mentions Yilmaz (although it does directly cite Freud's 1939 paper), which seems to support Yilmaz's position.

"Seems"? Not good enough. All this suggests is that there are a lot of confused theorists writing papers that no one will remember.

For the present purposes all that matters mathematically is that this represents a small tensor adjustment to the total stress-energy tensor on the RHS of the field equations.

Hogwash. Why SMALL? It's not always small. In my theory it's HUGE.We're not talking here about *your* theory. We are talking about Yilmaz vs. GR.

For the non-rotating SSS problem, the empirical predictions of Yilmaz's theory (with the added vacuum t_uv) hardly differ from those of the Einstein theory. This has been shown in mathematical detail in various published papers, and this as far as I know has not been refuted *or even disputed* by the likes of Misner et al.

Hogwash. When there is dark energy, you can forget Tuv (ordinary matter) completely. It is the perturbation! What you say here is completely false!

Most of precision cosmology anomalies are easily explained by the exotic vacuum equation

Guv + /\zpfguv = 0

You are dead wrong here.

Even in the strong field regime, I understand the deviations are not that great. However, in Yilmaz's model there are *no curvature singularities* that constitute hard "event horizons", as there are in the corresponding GR solutions for strongly gravitating SSS sources -- at least certainly not in the quasi-static regime.


Also I have an independent dynamics for t_uv(zpf) which Yilmaz/PV does not have!


OK? If you admit that, then you must reject Yilmaz's Ansatz as worthless.

It's as if Newton published

F = ma

without the independent law

F = GMm/r^2

Remember, I'm not insisting that Yilmaz's theory is actually correct. I'm simply questioning some of the arguments that have been been deployed to summarily throw it out of court -- which I consider to be logically defective if not entirely specious.

So far, from the evidence you have given, Yilmaz's theory is WORSE than even I expected. Maybe Mike Ibison can do a better job explaining what the physical motivation is, and what the set of phi mean? The cure is worse than the disease.

So given Yilmaz's equations,

G_uv = K (T_uv + t_uv),

I think the burden is on you and the GR-17 guys to show that the condition g_0i = 0 for all i ("no gravimagnetic terms") is a mathematical consequence of these equations, as applied to any rotating strongly gravitating object.

The burden is on you since you profess it.

But I don't really "profess it".

Then stop writing about it, since you cannot explain it in your own words showing that you do not understand it. I never claim to understand it.

The point is that if you are trying to claim that Yilmaz theory cannot handle rotating sources, or even that it can but it cannot consistently give you g_0i =/= 0 for such sources, then you need to show how this is rooted in the fundamental assumptions of the *most current version* of his theory. It is not enough simply to point out that so far no such solutions of Yilmaz's equations seem to be available.

Nonsense. As far as I am concerned Yilmaz does not have a coherent theory that is any challenge to orthodox plain vanilla 1916 GR. It is completely worthless unless Mike Ibison can show otherwise in a more competent way than you have done thus far.

But I agree that this strongly suggests at the very least some kind of difficulty with the application of Yilmaz's theory to rotating sources, which does raise interesting questions regarding Yilmaz vs.GR.

George Chapline's theory is the only contender I know of. Yilmaz's model was trashed long ago by the top people in the field.

No one of first rank in that field cares about the Yilmaz deviation.Exactly. So no one of "first rank" is going to support any investigations of the Yilmaz deviations. They may not even have read past the 1958 scalar potential version of his theory.

Too bad you cannot understand what Yilmaz did in 1974. It seems worthless to me at this point.

So what's your point? This seems completely circular to me. Why not stack up Yilmaz 1958 against Einstein 1907?

Because, there is Einstein 1916. That's why.

I say that orthodox GR is like the Titanic -- and you want to nail your colors to its mast.

That's extreme crack pottery. You are not helping your cause.

Orthodox 1916 GR is the most beautiful theory in physics and it is battle-tested.

They obviously all have looked at it and rejected it. MTW allude to it semi-politely.

Jack, they simply deny that there is an "energy problem" in GR. Like Penrose, they simply insist on the Einsteinian dogma that the energy-momentum of the gravitational vacuum is "non-localizable" because such energy-momentum can be produced or destroyed in any finite region by a *mere change of spacetime coordinates*.

I think I may have the beginning of the proper explanation for the nonlocality of gravity energy in terms of non-trivial cohomology/homology of the DeRahm integrals that requires Vacuum ODLRO inflation.

But even then there is a problem. Hence, for example, the sly and sneaky *ad hoc* imposition of "Galilean coordinates"(all g_uv, w = 0; the "line element of special relativity" (Pauli)) in the asymptotic region in order to fake sensible *global* conservation laws in GR!

That is simply a special case of

||C =/= 0 on outer non-bounding tetradic substratum 2-cycle even though the substratum 3-form dC ~ t_uv(vac)

The Cartan form structure must be in the antisymmetric tetradic substratum not in the symmetric geometrodynamic tensors.

Obviously, guv is bilinear in B = Budx^u = torsion potential connection in the tetradic substratum

(LC) involves first order partials of B i.e.

dB = Bu,vdx^u/\dx^v ~ (LC) geometrodynamic connection in curved space-time.

d^2B = Bu,v,w dx^u/\dx^v/\dx^w is the substratum torsion 3-form that corresponds to tidal curvature Ruvwl in the geometrodynamic picture and to Ruv, R & Tuv.

So this seems to work.

d^2 = 0 of course, but we really have

D = d + B

Yang-Mills covariant substratum exterior derivative and also "curvature without curvature" from non-trivial cohomology/homology groups in the Vacuum ODLRO order parameter space of emergent 1916 GR c-number effective field theory in the low-energy IR limit.

Of course, if you insist against all logic and common physical sense that there is no problem here, then you will also believe there is no need for a solution.

I am saying you are not equipped with the mathematical machinery to even ask the right question here.

"The Question is: What is The Question?" Wheeler

* Your naive notion that a zero local energy density cannot give a non-zero global integral is what is mathematically wrong! That is, the integral of a local zero need not be zero in a non-trivial topology. So that's your basic error in approaching the nonlocality of gravity energy problem.

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