Einsteins Vs Newtonian Solution

[vaibhavtewari]

hi,
I was going through the problem when light is bent by gravity. The Newtonian result is half of result obtained using Einsteins theory. Is this always true for some class of problems. I will be glad if someone can clarify.

 

[Dale]

The result is for the Schwarzschild solution in the weak-field limit.

 

[atyy]

The half result is not a result. It is an argument from the equivalence principle, which only gives the local bending. The global bending is given by how the local spacetimes are stitched together into a global spacetime. There is more than one theory which obeys the equivelence principle and is locally consistent with special relativity. All such theories give the same local bending. They differ in their global bending. The global bending in Nordstrom's second theory cancels out the local bending, while the global bending in GR adds to the local bending.

 

[Mueiz]

hi,
I was going through the problem when light is bent by gravity. The Newtonian result is half of result obtained using Einsteins theory. Is this always true for some class of problems. I will be glad if someone can clarify.

There are two cases:
1)Weak gravitational field and small spead:The Newtonian result is nearly equal to the result obtained using Einstein theory.
2)strong gravitational field or high speed :The Newtonian result does not equal that of Einstein .
The fact that the Newtonian result of light bending when passing near the surface of the sun is half of result obtained using GR has no significance on the relation between the two theories .. if the field is strong or the speed is high then the difference can be half , third or any number..

 

[Cleonis]

hi,
I was going through the problem when light is bent by gravity. The Newtonian result is half of result obtained using Einsteins theory. Is this always true for some class of problems.

In effect the half result arises only for light.
More generally, it arises only for entities traveling at the speed of light. That pretty much narrows it down to light.


By the way, the "Newtonian result" is actually ill defined. In terms of classical physics light is a propagating wave, and wave propagation is not affected by gravity.
The "Newtonian result" is for a particle with rest mass, moving at the speed of light. So it's a "thought result", rather than a defined physical prediction.


Around 1908 Einstein investigated an exploratory theory. That theory had gravitational time dilation, but no space curvature.
This exploratory theory was an implementation of the principle of equivalence. It implied the gravitational effect that was later, in the 1960's, confirmed by Pound and Rebka.

The 1908 theory didn't hit the nail on the head, but it was important, and its prediction of gravitational redshift has stood the test of time.

The 1908 exploratory theory also implied a curved path of light in a gravitational field. The amount of bending was the same as the "Newtonian result".

Later it became clear to Einstein that in addition to gravitational time dilation effect, there are spatial effects. The total of relativistic gravitational effects is what is called spacetime curvature.

For slow moving objects the time effect is predominant. For instance, the precession of the perihelion of Mercury has to do with the spatial relativistic effects. That gives you an idea how small the spatial effects is for planetary motion.

For entities moving at the speed of light the time effect and the spatial effect are on equal par, so to speak. That is why the final 1915 theory, the one we have today, predicts twice as much bending of light as the 1908 exploratory theory did.