Spacetime, gravitational force

[Hernik]

Hi.

If Newtons theory of gravity was changed - so that gravity is considered to propagate at the speed of light AND not only masses but all energy feels and radiates gravitational attraction - would the predictions then be identical to the ones of Einsteins generel relativity?'

Thanks, Henrik

 

[tiny-tim]

Hi Henrik!

No, the speed of light makes almost no difference.

Obviously, it's essential in considering gravity waves, but for motion of a body under gravity, we usually use the static solutions of general relativity anyway.

For example, the static GR field round a star is the Scharwzschild/Kerr solution, and that's the one we use to calculate eg the precession of the perihelion of Mercury, and all the other tests of GR.

Since those tests do not involve energy or the speed of light, adding them to Newtonian gravity cannot make it agree with GR.

 

[haushofer]

I think the speed of light does make a difference. A Newtonian spacetime is obtained by letting c --> oo in GR, which changes the causal structure of spacetime drastically.

 

[Naty1]

Hello Hernick:
Tiny Tim provides one correct answer...

It's not simple to describe:

I think it's correct to say that Newton's formulation does NOT recognize the variable nature of space and time...even with your assumed changes...but if you include the variable nature of space and time AND what you said in your post, energy, then the only way to do that is via the tensor formulation Einstein developed...so you can't simply change a few ingredients and get an "identical" set of predictions. An analogous explanation, I think, is that Newton worked in three dimensions; GR requires four dimensions (3 space plus one time)

(If these are wrong I'm sure someone will chastise me!)

Here are a few insights from Wikipedia:

General relativity reduces to Newtonian gravity in the limit of small potential and low velocities, so Newton's law of gravitation is often said to be the low-gravity limit of general relativity.

Newton's Theory of Gravitation requires that the gravitational force be transmitted instantaneously. Given the classical assumptions of the nature of space and time before the development of General Relativity, a significant propagation delay in gravity leads to unstable planetary and stellar orbits.

The observed fact that the gravitational mass and the inertial mass is the same for all objects is unexplained within Newton's Theories. ... they did not and do not explain the equivalence of the behavior of various masses under the influence of gravity, independent of the quantities of matter involved

.

http://en.wikipedia.org/wiki/Newtonian_gravity

 

[harrylin]

Hi.

If Newtons theory of gravity was changed - so that gravity is considered to propagate at the speed of light AND not only masses but all energy feels and radiates gravitational attraction - would the predictions then be identical to the ones of Einsteins generel relativity?'

Thanks, Henrik

An aspect that others have not mentioned: general relativity includes the prediction of special relativity, which has no effects of gravitation but still differs considerably from Newton's mechanics.
So, even if you would perfectly correct all effects of gravitation in Newton's theory, you would still not obtain general relativity.

 

[Hernik]

Thank you all. I'll have to try to comprehend the mathematics I'm afraid in order to really understand this.

harrylin: Can it be explained i words how special relativity is predicted from generel relativity (or shall I have to await my improved insight into the mysteries of complicated geometry, sigh :-)

 

[K^2]

Hi.

If Newtons theory of gravity was changed - so that gravity is considered to propagate at the speed of light AND not only masses but all energy feels and radiates gravitational attraction - would the predictions then be identical to the ones of Einsteins generel relativity?'

Thanks, Henrik

If you do that, and also take into account special relativity, you'd get something that's equivalent to linearized gravity. Basically, electromagnetism, but your two fields are gravitational and gravitomagnetic, with mass/energy being source of the former, and moving mass/energy the source of the later.

However, this only works as a good approximation for relatively light bodies. Even for something as light as planet Earth, you'd be able to measure a difference. Linearized gravity fails to describe dynamics of massive super-dense objects such as neutron stars and black holes. It is not without uses, however. Linearized gravity is second-quantizable, which allows for some simple toy-models of quantum gravity.

 

[harrylin]

[..] harrylin: Can it be explained i words how special relativity is predicted from generel relativity (or shall I have to await my improved insight into the mysteries of complicated geometry, sigh :-)

I'm not sure to say it correctly (someone else may improve on this), but basically, the space time equations of special relativity are modified by the effects of gravitation in GRT (experts tend to speak of "curved space-time" because it makes the linear equations of special relativity non-linear).
What you ask is simply the inverse: removing the effects of gravitation one obtains again what they call "flat space-time": the special relativity equations which are without deformations, so that space has everywhere the same properties.

Those equations are still significantly different from Newtonian equations (effects as length contraction, time dilation, dynamic mass increase, nothing can go faster than light; special relativity is a topic on its own).

For example:

In general relativity, the speed of light is locally measured to be equal to the constant c, but as seen from Earth it is actually less near the Sun. The light waves coming from a star thus slow down when they pass near the Sun and bend towards it - this is also called gravitational lensing, because the space near a heavy body acts just like a lens.

In special relativity it is much simpler: light speed is a universal constant. As a consequence, light waves in special relativity can not bend when they travel in free space from a star to the Earth.

Cheers,
Harald

 

[Hernik]

I see. I get the part about flat spacetime and how special relativity depends on it. Thanks again.

- henrik