Do photons obey the 1/r^2 gravity law?

[HomogenousCow]

We don't discuss metaphysics here, I have no idea where you got that part about "2 electric fields and six magnetic fields".

 

[K^2]

Trajectories, that's all that matters, to me at least. What I wanted is something concrete I can relate to classical mechanics so I can compare it with upper limits given for estimation of photon mass. I was hoping someone would spill some numbers related to photon gravity field, but I'm just as happy with those equations given by PeterDonis and pervect related to light bending. All that so I can keep my understanding that photons actually do have intrinsic mass.

My second post in this thread.

If you pretend that photons are particles traveling at speed c having a mass p/c, and you are looking at "acceleration" due to gravity in perpendicular direction, you'll only be a factor of 2 off.

Which is consistent with factor of 2 you get from pervect's equation in the limit v->c.

But this is light following gravitational field of a spherical body. There is an exact solution for that in GR. That's a much simpler problem than photon generating gravity.

 

[andrien]

If you pretend that photons are particles traveling at speed c having a mass p/c, and you are looking at "acceleration" due to gravity in perpendicular direction, you'll only be a factor of 2 off.

are you talking about the deflection of light which is twice as large as compared to Newtonian theory?

 

[Barry_G]

My second post in this thread.

Which is consistent with factor of 2 you get from pervect's equation in the limit v->c.

I know you said that, I especially like how you defined mass, and I like that factor of two because I think I might be able to explain it, but you gave no links nor did you respond to my question about it. Ok, so where do you see factor of two? More specifically, what value do you take for momentum since it varies according to wavelength, and what equations are you comparing?

 

[K^2]

If you only look at the deflection angle, which is the best way to go about it, you can drop the mass. In classical theory it doesn't matter, and in GR, it means something completely different.

So method one. Take a particle of arbitrary mass m (you can take limit m->0 in the end, as it doesn't matter) and shoot it past, say, a star of mass M. You fire it originally distance b from radial, and infinitely far away the particle's initial velocity (hyperbolic excess velocity) is c. You compute classic trajectory, and observe the particle leave the star with the same distance b from radial, same velocity c, but heading in a slightly different direction, making angle θ with original.

$$\theta = sin^{-1}\left(2\sqrt{\frac{GM^2}{GM^2+b^2 v^4}}\right)$$

This is general formula that works for any v, so you can take v->c. It can be derived from formualae on this page by keeping in mind that b*v_∞ = v(r)*r at closest approach r = -a(1-e) due to conservation of angular momentum. Note, also, that what I'm calling θ is the deflection angle. The angle in the article is angle between asymptotes. Hence the inverse sine instead of inverse cosine and the factor of 2. In the limit bv² >> GM and v->c, the deflection angle is small, and the above simplifies to the following.

$$\theta = \frac{2GM}{bc^2}$$

Method two. You find a null-geodesic that corresponds to the parameter b above. It also yields you an angle, some θ'. I am not going to point to derivation of that, because it involves Christoffel Symbols of Schwarzschild Metric. But the result is given in this article on Gravitational Lensing. Note that what I call b they call r.

$$\theta = \frac{4GM}{bc^2}$$

Both of these describe a "photon". First method describes it in classical approximation, second under GR. The difference in the deflection angle is exactly factor of 2.

This lead to one of the original tests of GR described on this page. The deflection of the light from the stars due to gravity of the Sun can be measured, and does, in fact agree with GR rather than the classical result.

However, because the difference in deflection between GR and classical result is by a constant factor, it can be said that influence on the gravity on light does drop as 1/r as it does in classical theory. In fact, both formulae give deflection as 1/r from distance to the star.

And that was my original point. I just didn't expect to have to explain it in that much detail in the GR section of this forum.

 

[andrien]

here is a link in which both Newtonian result and prediction of einstein theory is given.Calculation is discussed also
http://www.mathpages.com/rr/s6-03/6-03.htm

 

[swle]

here is a link in which both Newtonian result and prediction of einstein theory is given.Calculation is discussed also
http://www.mathpages.com/rr/s6-03/6-03.htm

Thank-you andrien, that is a really interesting link - who is Kevin Brown?

 

[andrien]

Thank-you andrien, that is a really interesting link - who is Kevin Brown?

A man,who just does not want to reveal himself.
http://www.numericana.com/fame/