
#1
Dec2012, 05:58 AM

P: 492

Could someone explain to me what specifically distinguishes Einsteins more advanced treatment of gravity over Newtons? Here’s what I (think I) know. Newton described gravity as a “force” of attraction between two bodies or masses. That force was given by the G constant times the two masses divided by the square of the radius between the two masses. The force of gravity was then modeled as a corresponding acceleration vector between the bodies. The classical Lagrangian using the principal of least action reproduces newtons same equations of motion, but instead of assuming a” force of attraction” between the two bodies, models the relation between the two masses as a minimized “path.”
Now we get to Einstein. Einstein eschewed the idea of attraction and instead saw gravity as a process whereby objectmasses moved along a physically illdefined but mathematically compelling “geodesic” which traced out a complex curved spacetime in the vicinity of massive bodies. Mathematically the curving of this spacetime and the geodesics that arise from it are found through the continuous redefinition of the local coordinate axis due to the local mass energy density of the system in question. This value is given by the stressenergy tensor. The particular “shape,” then, of the local coordinate axis is given by the Einstein tensor. The value of each of these tensors rely on each other in real time so as to make the equations nonlinear. Do I have this right? Anyway, my question is what is it about the Reimenian geometric approach of GR that gives it it’s advantage over the classical model, which works well enough for everyday modeling that we can use it solely to send people to the moon and back? Is the answer in the nonlinearity of the solutions, that the motions of the bodies are continuously updated in real time. Is it that GR incorporates energy and pressure into the stressenergy tensor whereas Newtons equations just include mass? Does it have something to do with the geometrical approach over a force of attraction approach? Also, I’ve read that it has something to do with the Taylor series expansion, where the higher order terms give you something that the lower terms don’t, which is where you get Newton’s equations? Finally, where does one want to go through the ordeal of using GR to model a system where Newton won’t work. The places I’m familiar with are black holes, GPS, the eclipse thing, and the precession of Mercury. But why and how does this give us a better solution here. Thanks. 



#2
Dec2012, 07:00 AM

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#3
Dec2012, 07:03 AM

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#4
Dec2012, 11:44 AM

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Newton vs EinsteinWith other words: physics does not answer such "why"questions. 



#5
Dec2012, 12:00 PM

PF Gold
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#6
Dec2012, 12:18 PM

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#7
Dec2012, 01:32 PM

PF Gold
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#8
Dec2012, 02:19 PM

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But you're right. That is getting a bit off topic. 



#9
Dec2112, 12:54 AM

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#10
Dec2112, 02:10 AM

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#11
Dec2112, 02:14 AM

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I think at the fundamental level the big difference between GR and Newton is that GR is basically a theory of massless selfinteracting spin2 (wrt the Lorentz group) particles, while the Newtonian theory is a theory of massless nonselfinteracting spin0 (wrt the homogeneous part of the Galilei group: rotations and boosts) particles. All the other properties should be consequences of this, I would say.




#12
Dec2112, 12:35 PM

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You mean massive particles in Newtonian gravity. And the way you formulated your sentence makes people think of quantum field theory, which has nothing to do with Newtonian gravity.




#13
Dec2112, 04:08 PM

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No, i mean massless particles; i regard the newton potential as a massless galileiscalar field. What one basically does is to take the nonrel. and weak field limit of the EinsteinHilbert action. That such a theory would be nonrenormalizible is clear, as GR is nonren. Maybe the word particle is a bit deceiving; i m not sure to which extent one can regard such a theory as an effective (quantum) field theory and interpret the excitations of the fields as particles. So if that's what you mean, i fully agree :)




#14
Dec2212, 03:18 PM

P: 5,634

A perhaps minor point:
Dircpool : When I think of Einstein's gravitational theory, I now think 'geometry of spacetime has physical consequences' and especially 'cosmology'. For example, ....Geometric circumstances create real particles e.g. Hawking radiation at BH horizon and Unruh radiation caused by acceleration or felt by an accelerated observer. So it seems that expansion of geometry itself, especially inflation, can produce matter! ....How about horizons in general, as Hubble, Event, and Black Hole for examples...the geometric solutions are amazing..Schwarszschild, Rindler, etc, ....And how about the fact that in an isotropic and homogeneous universe, geometry, leads to an unstable cosmos.....expanding or contracting but not static. Where would we be with Hubble's observational finding of not only expansion but accelerated expansion without the underling theory of Einstein..... ...and gravitational time dilation and gravitational redshift.... I've never read about NewtonCartan gravity mentioned by Dalespam....is it nonrelativistic.....must be, right??......anyway , I suspect EFE go way beyond what would be suggested by a non relativistic theory. 



#15
Dec2312, 12:30 AM

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#16
Dec2312, 06:23 AM

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#17
Dec2312, 06:29 AM

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What SR can't handle is the fact that spacetime is curved. With the usual timeslicing, space, as well as spacetime, is curved. Light bending (and I think Mercury's perihelion advance as well) can in particular be attributed to the purely spatial part of spacetime curvature. In particular the PPN parameter gamma has to be nonzero to explain observed light deflection results. ((PPN : http://en.wikipedia.org/w/index.php?...ldid=523184874). Gamma is a measure of spacecurvature  and light bending isn't senstive to the other PPN parameters, just gamma. According to wiki, current measurments place gamma equal to it's predictedbyGR value of 1 within an error of about +/ 25 parts per million. 



#18
Dec2312, 07:02 AM

P: 5,634

Pervect: Thanks or the PPN link posted above.
I never saw all that nor discussions in a link within that article: If so, we are back to the questions that have been discussed, but not answered, in these forums previously: Why does ANY of our man made math seem to describe the world around us? Why does some math work but not others? The only possible answer I have seen so far that registered with me is the possibility that if there is a multiverse and maybe our 'other' math would apply there. What I still find incredible is that 'Einstein intuition' seems to have allowed him to pick an 'off the shelf' math that is SO close overall and perhaps virtually perfect on large scales. And Diracpool may be asking in the future about a more accurate theory of 'quantum gravity'..... 


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