Is the classical calculation of the sun bending light wrong?

[Lazarus]

It appears that the calculoation of the amount of bending of light passing the sun uses the same calculation that is used for a comet passing the sun..

 

If that is the case there is a problem. The comet accelerates then decelerates while the light maintians a constant velocity. That means it takes longer for the light to pass the sun than it would if it could be accelerated in the forward direction.

 

By allowing for the constant velocity of light the result should match the Special Relativity calculation.

 

Does this reaoning make sense?

[Strange]

It appears that the calculoation of the amount of bending of light passing the sun uses the same calculation that is used for a comet passing the sun..

 

It depends what calculations you are referring to. If you were to use General Relativity to calculate both, then you would get the right answer for both.

 

However, in the case of a comet, you could get an accurate enough result by using Newton's law of gravity. But if you use this for light, you get a result that is half the correct value.

 

If that is the case there is a problem. The comet accelerates then decelerates while the light maintians a constant velocity. That means it takes longer for the light to pass the sun than it would if it could be accelerated in the forward direction.

 

The changing energy of the light is seen in changing frequency rather than speed.

[Lazarus]

Thank yuou for the reply.

 

But still. doesn't it take longer for the light to pass the sun than the clascal fomula would expect?

[Strange]

What do you mean by the "classical" formula? If you mean Newton's formula then, yes it gives the wrong result.

 

General Relativity gives the right result (this was one of the first tests of GR).

[swansont]

There's the Shapiro delay, which comes from relativity, and is experimentally confirmed.

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

 

AFAIK this has no effect on the angle of bending

[Lazarus]

Strange said:

What do you mean by the "classical" formula? If you mean Newton's formula then, yes it gives the wrong result.

 

Reply:

My typing and spelling is certainly not dependable and I am bad about proofreader. Mea culpa.

 

The whole point is that if the classical calculcation is incorrect, a correct calculation accounting for the costant speed of light should give a correct answer.

[Strange]

The whole point is that if the classical calculcation is incorrect, a correct calculation accounting for the costant speed of light should give a correct answer.

 

Yes. GR gives the correct result.

[swansont]

Strange said:

What do you mean by the "classical" formula? If you mean Newton's formula then, yes it gives the wrong result.

 

Reply:

My typing and spelling is certainly not dependable and I am bad about proofreader. Mea culpa.

 

The whole point is that if the classical calculcation is incorrect, a correct calculation accounting for the costant speed of light should give a correct answer.

 

You still need to clarify what you mean by classical. GR is a classical theory, in the sense that it is not based on QM.

[Lazarus]

Swansont said:

What do you mean by the "classical" formula? If you mean Newton's formula then, yes it gives the wrong result.

 

Reply:

Take Newton's rules add the requirement that light must travel at a constant velocity. That iis all you need to conclude that light will take a different path by the sun than the equation for a comet passing the sun would generate.

[Strange]

Take Newton's rules add the requirement that light must travel at a constant velocity. That iis all you need to conclude that light will take a different path by the sun than the equation for a comet passing the sun would generate.

 

No. Newton's equation gives you the wrong result.

 

GR gives you the right result.

Edited September 29, 2014 by Strange

[elfmotat]

Swansont said:

What do you mean by the "classical" formula? If you mean Newton's formula then, yes it gives the wrong result.

 

Reply:

Take Newton's rules add the requirement that light must travel at a constant velocity. That iis all you need to conclude that light will take a different path by the sun than the equation for a comet passing the sun would generate.

 

I don't think you understand. That's exactly how the calculations were done - using Newtonian gravity and the fact that light always travels at c, you get a prediction that is 1/2 of what it should be. This is because Newtonian gravity does not give accurate predictions when you're considering objects moving at or near c, or when the gravitational field is very strong. You need GR in those cases. GR gives the correct result: twice the Newtonian prediction.

[Lazarus]

Strange said:

No. Newton's equation gives you the wrong result.

 

GR gives you the right result.

 

Reply:

 

There is no question about SR giving good results. The mathematical solution is wondefu and elegantl.

It is the interpetation that is the "strange" part.

 

The reason the "Newtonian" result is incorrect is that the wrong equation is being used.

It does not take in to account that light will not be accelerated in the forward direction.

[elfmotat]

Lazarus, you're under the impression that when the calculations using Newtonian gravity were done, they neglected to include the fact that light always travels at c. I don't know where you got this silly idea from, but it's completely untrue.

[Lazarus]

elfmotat said:

Posted Today, 01:34 PM

Lazarus, you're under the impression that when the calculations using Newtonian gravity were done, they neglected to include the fact that light always travels at c. I don't know where you got this silly idea from, but it's completely untrue.

 

---------------------------------

 

Reply:

That is the answer that I wanted. Everything I could find talked about the same equations that would be used for a comet.

 

Would you kindly point to a description of the calculation incorperating the velocity of light?

 

All I could find were things like: a = 2GM/rc^2 which is smilar to the equation for a comet but doesn't say anthing about the light not accelerating.

 

 

α=2GMrc2

 

Read more: http://www.physicsforums.com

[Strange]

There is no question about SR giving good results.

 

GR, not SR.

Would you kindly point to a description of the calculation incorperating the velocity of light?

 

http://lacosmo.com/DeflectionOfLight/index.html

[Lazarus]

Thank you for the reference but that is the Relativistic calaculation, not the "classical Newtonian" calculation that gives the wrong answer.

[elfmotat]

How about this: http://www.iisc.ernet.in/currsci/apr102005/1155.pdf

 

The first part shows the Newtonian calculation.

[Lazarus]

How about this: http://www.iisc.ernet.in/currsci/apr102005/1155.pdf

 

The first part shows the Newtonian calculation.

 

 

Reply:

That article is great.

 

I can see why the path of a photon cannot be the same as the path of a comet.

The comet compensates for the latent energy change by changing its speed.

The photon can't compensate fhe same way so changes its energy by changing

its wave length.

 

The comet follows the equal area in equal time rule but the photon doesn't so

its path is different.

 

Wave theory says that accounts for the additional bending. I don't fully understand

why so i need to do some research.

 

I appreciate all the help.

[swansont]

Swansont said:

What do you mean by the "classical" formula? If you mean Newton's formula then, yes it gives the wrong result.

 

Reply:

Take Newton's rules add the requirement that light must travel at a constant velocity. That iis all you need to conclude that light will take a different path by the sun than the equation for a comet passing the sun would generate.

 

Strange said that, not me. (This is the kind of confusion that using the quote function tends to avoid)

[Lazarus]

 

Strange said that, not me. (This is the kind of confusion that using the quote function tends to avoid)

 

Sorry about that. I probably can make mistakes usng the quote function.

 

Thinking abut it, havent you guys just taught me that the bending can calculated

correctly classically by puting together Newton's Laws, the constant speed of

light and the consevation of energy?

[swansont]

 

Thinking abut it, havent you guys just taught me that the bending can calculated

correctly classically by puting together Newton's Laws, the constant speed of

light and the consevation of energy?

 

I can see four distinct places that tell you Newton gives the wrong answer, so no.

 

Newtonian gravity already has a constant speed of light in it, in a way. The speed is infinite, but it will be infinite in all frames. There is no accelerating toward or away from the object.

 

(edit: post-morning-caffeine, I realize this is not correct. Gravity has infinite speed, not light, and those speeds are linked in relativity but not in a Newtonian approach)

 

I have no idea what you get with Newtonian gravity combined with a finite and invariant speed of light. I can't say that you can construct a self-consistent model with that combination.

[Strange]

 

Thinking abut it, havent you guys just taught me that the bending can calculated

correctly classically by puting together Newton's Laws, the constant speed of

light and the consevation of energy?

 

The paper that was linked earlier gets the right result by adding the pure Newtonian calculation to the effect of gravity on the wave front combined with constant speed. This (as I understand it from a quick read) is, for purely geometric reasons, equivalent to the red-shift (and therefore curvature of space-time) in GR and hence produces the same result. This is an intriguing view (especially when applied to particles, which have an inherent wave-nature) but I don't know if it has any deeper significance.

[elfmotat]

I have no idea what you get with Newtonian gravity combined with a finite and invariant speed of light. I can't say that you can construct a self-consistent model with that combination.

 

I can think of a few ways to do it. One way would be with a metric theory with the field equation:

 

[math]\nabla^2 h_{00} = \frac{8 \pi G}{c^2} \rho [/math]

 

where [math]g_{\mu \nu} = \eta_{\mu \nu} + h_{\mu \nu}[/math]. The field equation has no time derivatives in it, so the speed of gravity remains infinite just like Newtonian gravity. (But this is irrelevant for the OP's problem since the gravitational field of the Sun is assumed to be static.) For a spherical body like the sun, the metric in spherical coordinates would be:

 

[math]ds^2=-c^2 \left (1-\frac{2GM}{c^2 r} \right ) dt^2 +dr^2 +r^2 d \Omega^2[/math]

 

Plugging that into geodesic equation, the equations of motion are equivalent to those for Newtonian gravity. But now you can use the fact that ds² = 0 for photons to calculate their trajectories, so it's Newtonian gravity + constant speed of light.

Edited October 1, 2014 by elfmotat

[Lazarus]

In the article that elfmotat pointed out, C, S, Unnikrishnan said “the identification of the gravitational deflection of light as the crucial test of general relativity, in contrast to the gravitational redshift, does not seem defendable.”

 

Unless his mathematics is wrong the bending of light passing the sun is not evidence that time dilation is a valid interpretation of the equations of Relativity.

[elfmotat]

In the article that elfmotat pointed out, C, S, Unnikrishnan said “the identification of the gravitational deflection of light as the crucial test of general relativity, in contrast to the gravitational redshift, does not seem defendable.”

 

Unless his mathematics is wrong the bending of light passing the sun is not evidence that time dilation is a valid interpretation of the equations of Relativity.

 

I don't even know what you're trying to say. Where did we mention anything about time dilation? What about the cherry-picked quote you just gave makes you think it has anything whatsoever to do with interpretations of time dilatation?