Waiting for Ehlers' paper
Stingray
I solicited a copy of Ehlers J: Examples of Newtonian Limits of Relativistic Spacetimes, Class. Quantum Grav. 14 (1997), A119 but I have not got still.
Still I can do some preliminary comments (remember that I didn’t read still Ehlers work) and all is based in my survey of last days.
Ehlers' work appears to be mainly focused to cosmological models.
It appears that his work has not been very popular for the construction of post-Newtonian models.
When I mean the recovering of Newton gravity from GR, I mean a consistent derivation of the full Newtonian model. Of course, one can obtain the “correct” Newton equation for trajectories in coordinate time
d^2 x / dt^2 = – “time-time connection”
but the physical metric corresponds to curved spacetime g = nu(SR) + gamma.
Often, one takes formally the c--> infinite in the obtaining of coordinate time, but one maintains c finite in the nu metric.
Generally, one argues for the derivation of “correct” Newtonian equation
a = – grad (phy)
from the “geodesic” equation
a + “time-time connection” = 0
and, therefore, the covariant derivatives does not commute, this implies that one cannot use ordinary derivatives in this regime.
If one want that covariant derivative exactly coincides with ordinary derivatives then one obtain that bodies are unaffected by gravity.
If one works all of this in detail for a Schwarzschild metric, one obtains either a pure flat spacetime with zero affine connections and zero Rieman curvature tensor, or usual GR “linear” gravitation on curved spacetime and c finite. Newtonian theory is a theory of gravity in flat spacetime and c --> infinite.
I don’t see how Ehlers’ work can modify this maintaining intact the basic structure of GR.
Stingray said:
Please read my reference. Newtonian gravity can be recovered as a formal c->infinity limit without any ad hoc procedures (at least for asymptotically flat spacetimes).
As said I didn’t read paper yet, but I have found others interesting related works. It is interesting that other author refers to same Ehlers’ work like the “c--> infinite” limit and carefully emphasize the
“”. This suggests to me that Ehlers is performing not the real limit after of all, only some formal "reparametrization". Of course, i am not sure of thyis because didn't read the article.
Yet Ehlers use at least (I didn’t read the paper) an
ad hoc assumption: asymptotically flat spacetime. Not only is
ad hoc, moreover, it is unphysical. In the basis of experimental evidence and analysis from Penrose or Misner:
“
universe is not an island of matter surrounded by emptiness”.
Perhaps other better work imposing on the curvature tensor an
ad hoc condition "prohibiting rotational holonomy" can permit us obtain Newton gravity in a “consistent” manner, but I doubt like one can obtain curved “geodesic” motion with a zero Christoffel. All attempts that I know until now are mixed approaches with flat structure plus a Newtonian potential = non-flat spacetime such as the world lines of test bodies follow the true non-flat metric. If the true metric is flat there is no gravitation, only pure free motion.
I unknown if Ehlers’ paper deals with solar system problem, but all works that I am seeing are focusing to cosmological issues, where one may expect deviations from pure Newtonian gravity and therefore the fact one does not obtain exactly Newtonian theory is not a problem, it is a virtue.
I think that GR clearly states that gravitation is curvature as was said by Einstein. By curvature I do not mean exclusively the Riemann curvature tensor, since that Christoffel symbols are another form of defining curvature.
Your distinction between “curvature” or “connection” regarding the true origin of gravity is not applicable to my non-technical work
http://www.canonicalscience.com/stringcriticism.pdf
Because I mean that in pure Newtonian theory, both vanish.
I think that Carlip know very well that there is no complete derivation of Newtonian theory from GR and that there are problems still unsolved. The cite that I quoted
“general relativity very nearly reproduces the infinite-propagation-speed Newtonian predictions. ”
is best understood in their surrounds
For weak fields, however, one can describe the theory in a sort of Newtonian language. In that case, though, one finds that the "force" in GR is not quite central---it does not point directly towards the source of the gravitational field---and that it depends on velocities as well as positions. The net result is that the effect of propagation delay is almost exactly cancelled; general relativity very nearly reproduces the infinite-propagation-speed Newtonian predictions.
It signifies that is not clear if GR can describe solar system dynamics due to aberration and other issues. There is no consensus if GR is compatible with experimental data or no. I think that
no, as said many standard “proofs” and “verifications” are misleading. For example, the famous recent claim of measure of gravity speed may be seen like misleading (was not measure of that). Recent Carlip's paper in aberration of celestial bodies is, unfortunately, full of failures, and finally he agrees that interpretations of others using instantaneous interaction (for example canonical gravitodynamics) are consistent with experimental absence of aberration.
But he is not demonstrating that absence of aberration is consistent with GR.
As said I didn’t not post here what are the errors of Carlip’s papers (in fact, one would need several pages in a paper for a detailed following), but I put an "indicator".
One cannot demonstrate a thing if begins assuming that thing in the form of a hidden assumption.
Therefore, one needs a theory of gravity with next requirements:
1) A theory giving exactly the Newtonian limit in a flat Euclidean space and absolute time. “Cartan-like” covariant “reformulations” are not that.
2) A theory for gravity on a flat spacetime. Unless one can measure curved spacetime, all our experimental evidence is for flat space and time.
3) A theory explaining usual Solar system tests: perihelion, radar delay, redshift, etc.
4) A theory explaining other tests, e.g. binary stars, but without appeal to unobserved gravitational waves, etc.
5) A theory where gravity speed is infinite. The model cannot violate SR but may, at the same time, fits experimental orbiting and astronomical data on BH, binary stars, aberration, etc.
6) A theory departing from GR at extragalactic regimes explaining data and empirical laws (e.g. TF one) without ad hoc assumptions like unobserved dark matter and fine tuning with two-three parameters.
7) A theory unified with EM.
8) A theory that can be satisfactorily quantized from first principles.
9) Solving of most hard problems of cosmology: inflation, cosmological dark matter (90%!), cosmological constant, etc.
At least twenty-five alternative theories to Einstein GR have been investigated from the 60’s. I cannot say that I have solved all those problems already (I don’t studied 9 still) but already said that things I have already obtained.
The research is very young but very, very promising.
(giving you a pat in the back). I just read the first line in the last posts from you cause your paranoic being doesn't deserve the atention, i do believe that Chronon and all others guys have more importants things that reading your things. I think the most people here enters for sakes of curiosity (y tú solo haces el ridículo) and for this we use to read the new posts. There is not respect from you trying to convince everybody about a thing that has not been published nor being reviewed by experts, and saying that everybody here and almost everybody in the world is bad when is the case you never haven't proven, all the time you just talk about your "theoy" (it is not a real theory), but never talked about what really is it. Regards Juanito.
