Question regarding the qualitative difference between General Relativi

[Herbascious J]

I have a question regarding the qualitative difference between General Relativity and classical Newtonian gravity. I understand this difference in theory (warped space-time as opposed to a force operating in flat space). However, I read an article (taken with a grain of salt) which claimed that the fundamental difference, quantitatively, between the two theories rested on the idea, proposed by Einstein, that the energy of gravity, created a gravitational effect in and of itself. In GR because gravity itself creates gravity it has a mild compounding effect, however very slight. The article I read claimed that if this one attribute of the theory (gravitational energy having an additional gravitational effect) was removed the theory of GR, it would reduce perfectly to Newton, from a quantitative point of view. Meaning, each theory predicted identical results. The article claimed without this subtle effect in GR, the orbits of Mercury, etc. would be indistinguishable from Newtonian predictions. Does anyone know if this is true? I am sorry I don't have a reference to the article. Thank you for the any input.

-Slightly Confused

 

[Bill_K]

The article I read claimed that if this one attribute of the theory (gravitational energy having an additional gravitational effect) was removed the theory of GR would reduce perfectly to Newton, from a quantitative point of view. Meaning, each theory predicted identical results.

No, the theories are different in more ways than one. Qualitatively as well as quantitatively. Newtonian gravity, for example, does not know about Special Relativity. That is, it does not know that c is a limiting velocity and therefore does not correctly predict the interaction between objects moving at relativistic speeds.

Also it fails to predict the existence of gravitational waves.

 

[Herbascious J]

Hi Bill,
Thank you for the prompt response! So, just for my understanding, then the orbit of mercury is different from classical gravity for more reasons than the one described above? Trying to work it out in my head. Thanks!

 

[WannabeNewton]

I have a question regarding the qualitative difference between General Relativity and classical Newtonian gravity. I understand this difference in theory (warped space-time as opposed to a force operating in flat space).

This is not really the difference between the two. You can formulate Newtonian gravity using the notion of gravity as a manifestation of space-time geometry and curvature as well and the distinction you pointed out is completely dissolved.

Does anyone know if this is true? I am sorry I don't have a reference to the article. Thank you for the any input.

-Slightly Confused

It's hard to judge anything without a proper article reference because people don't paraphrase articles properly due to their own misconceptions when reading; direct quotes are always better in this context. Regardless, what was stated is most definitely not the full story behind the difference between GR and Newtonian gravity. For one thing, in Newtonian gravity the matter field in the field equations is just the mass density (scalar field) whereas in GR it is the energy-momentum tensor (2-tensor field) and even in the regime of linearized gravity this leads to physical effects predicted by GR that are absent from Newtonian gravity such as frame dragging; furthermore, GR is a relativistic field theory whereas Newtonian gravity is not and again in the linearized regime one can derive a wave equation from the Einstein equation hence predicting gravitational waves, something that is absent from Newtonian gravity.

 

[Herbascious J]

I see, thank you! Much better, I think the article was not a proper representation of GR. Cheers!