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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.

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- Thread starter vaibhavtewari
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- #1

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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.

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

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atyy

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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:

2)

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..

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Cleonis

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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 travelling at the speed of light. That pretty much narrows it down to

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

For slow moving objects the time effect is predominant. For instance, the precession of the perihelion of Mercury has to do with the

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.

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