# Why does light bend under Newton's law?

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We know that light does bend around a mass under the General Theory of Relativity, but why does light also bend under Newton's Law? and how is it calculated?

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I won't go through it carefully now, but the key observation is that the acceleration on an object due to gravity is independent of the mass of that object. So, we have

$a = \frac{GM}{r}$,

where $M$ is the mass of the star or other massive body you are thinking about. Going through the calculation, which involves a little calculus, you get half the value predicted by general relativity.

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I do understand the equivalence of acceleration and gravity under the General Relativity, but this equivalence did not exist in the Newtonian physics, there must be another reason why light bends under Newton's law.

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I do understand the equivalence of acceleration and gravity under the General Relativity, but this equivalence did not exist in the Newtonian physics, there must be another reason why light bends under Newton's law.

The acceleration due to gravity in Newtonian gravity is independent of the mass of the "test particle". This is the point.

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I do not question what you are saying, but I do not understand it. Would you be able to give me some hint where I could read more about it?

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You can find a derivation here (opens PDF).

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Many thanks for this, I am absolutely delighted by this.

I won't go through it carefully now, but the key observation is that the acceleration on an object due to gravity is independent of the mass of that object. So, we have

$a = \frac{GM}{r}$,

where $M$ is the mass of the star or other massive body you are thinking about. Going through the calculation, which involves a little calculus, you get half the value predicted by general relativity.

The r should be squared.

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The r should be squared.

Sorry yes, it is the potential that is not squared.

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Also, Newtonian gravity can be represented as time curvature with the following metric:

$ds^2=-\left ( 1-\frac{2M}{r} \right )dt^2 + dr^2+r^2 d \Omega^2$

This is just the Schwarzschild metric without any spacial curvature. So, essentially light is still affected by Newtonian gravity, but it's not affected as much as it is in the "correct" theory of General Relativity.

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Also, Newtonian gravity can be represented as time curvature with the following metric:

$ds^2=-\left ( 1-\frac{2M}{r} \right )dt^2 + dr^2+r^2 d \Omega^2$

This is just the Schwarzschild metric without any spacial curvature. So, essentially light is still affected by Newtonian gravity, but it's not affected as much as it is in the "correct" theory of General Relativity.

I am sure what you are saying is correct, but without notations I do not understand it.

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We know that light does bend around a mass under the General Theory of Relativity, but why does light also bend under Newton's Law? and how is it calculated?

Bending in Newtonian theory uses tricks, because Newtonian theory is only valid for low velocities and does not really apply to relativistic particles such as photons. Start with the Newtonian potential energy

$V = - \frac{GMm}{r}$

and use the trick $m = p/c$ by substituting the speed of light on the Newtonian momentum $p=mv$ (it is a trick because this expression is only valid for speeds much smaller than c and because for a photon m=0)

$V = - \frac{GMp}{rc}$

This potential can be now used in the Newtonian equation of motion

$\frac{dp}{dt} = \frac{\partial}{\partial r} \frac{GMp}{rc} = - \frac{GMp}{r^2c}$

but gives one-half of the observed bending. Then the second trick consists on multiplying the Newtonian bending by a factor 2.

Using a relativistic theory one obtains the correct bending and without any trick.

Edited by juanrga
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We know that light does bend around a mass under the General Theory of Relativity, but why does light also bend under Newton's Law? and how is it calculated?

just because.101

Force is mass acceleration and curvature is equal and opposite reaction to inertial pressure differential.

Mathematical calculations based on curvature are alphanumeric images of force.

Images are easily misinterpreted; especially by zealots.

Light (energy) bends toward lower quantum pressure the same way sound (energy) bends towards lower baryonic pressure.

How do you calculate what happens as sound encounters the event horizon of a supersonic cyclone?

Can you imagine the eye of a baryonic vortex condensed to a singular quantum point up?

peace

ron

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just because.101

Force is mass acceleration and curvature is equal and opposite reaction to inertial pressure differential.

Mathematical calculations based on curvature are alphanumeric images of force.

Images are easily misinterpreted; especially by zealots.

Light (energy) bends toward lower quantum pressure the same way sound (energy) bends towards lower baryonic pressure.

How do you calculate what happens as sound encounters the event horizon of a supersonic cyclone?

Can you imagine the eye of a baryonic vortex condensed to a singular quantum point up?

peace

ron

That might be the most meaningless nonsense I've ever read in a single post.

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That might be the most meaningless nonsense I've ever read in a single post.

def: hush

There is never need to brag about willful ignorance. I can no more make trolls understand basic physics than I can make a creationist understand evolution.

Relative equivalence is not quite the same as is. Force is inertial differential. Curvature is not force.

Please cite the first word that escapes your limited comprehension of self evident and stop insulting your self.

ItS

peace

r~

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That might be the most meaningless nonsense I've ever read in a single post.

Agreed.

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!

Moderator Note

OK, that's enough sniping, and that's enough hijacking. (A mention of quantum pressure in a thread on gravity is a tell-tale sign that one has strayed from the mainstream)

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truth is not a hijack

Force is inertial pressure differential. Curvature is not.

peace

ron

!

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