# Can Chromatic Aberration arise from Gravitational Lensing?

1. Feb 3, 2010

### JessicaNY

I've been puzzled by this. If light of different frequencies (like ultra violet to infra-red) would experience different refraction angles in the presence of a powerful gravity field. I understand that light has zero rest mass but has effective mass given the fact it's in motion.

What I'm figuring is it's frequency (I'm only guessing here) may yield a greater effective mass (eg, the ultra-violet over the infra-red) and that the two rays may refract at a slightly different angle due this?

I'm a bit confused due to my knowledge of Newtonian vectors, and I only have a basic understanding of Relativity. Could someone explain this to me thanks, also is there a research paper about this thanks.

2. Feb 3, 2010

### atyy

Usually the bending of light is treated by having it move on a "straight line in curved spacetime", where the spacetime curvature is produced by the total mass-energy in the universe. In principle, the light should be included in the total mass-energy, in which case we don't have to use this approximation of light moving on a straight line. I don't know the answer to your question in the full theory, but in the approximation of light moving on a straight line, the path of light is independent of its frequency.

3. Feb 3, 2010

### gonegahgah

I understand that chromatic aberration does occur to light passing around the sun but that this is removed as it is considered to be caused by the chromosphere of the sun rather than by the space-time curvature. Interpret as you like.

4. Feb 3, 2010

### bcrowell

Staff Emeritus
An object's motion in a gravitational field doesn't depend on its mass, so even though photons of different frequencies have energies that are equivalent to different amounts of mass, we wouldn't expect this to affect their motions, by analogy with the case of material objects.

When light disperses in a physical medium like a prism, the different amounts of refraction relate to the different speeds of light with different frequencies. So the question you're asking is equivalent to the question of whether light waves have the same speed in vacuum regardless of frequency. Special relativity claims that they do, and if experimental evidence to the contrary came along, it would show that special relativity was only an approximation.

For a description of experimental tests of this, see subsection 2.4.1 of this: http://www.lightandmatter.com/html_books/genrel/ch02/ch02.html#Section2.4 [Broken]

Last edited by a moderator: May 4, 2017
5. Feb 3, 2010

### Nabeshin

As bcrowell notes, you can't use newtonian gravity to try and explain gravitational lensing; you need the full theory of general relativity. And indeed, when one does the calculation one can show that deflection angle is independent of any properties of the incident photons.

6. Feb 10, 2010

### LouieHussey

Can chromatic aberration arise from gravitational lensing?

Jessica, it is true that the energy, and therefore the effective mass, of photons is a function of their frequency, but, as pointed out elsewhere in these replies, the rate of fall in a gravitational field is independent of mass. Do you recall the famous experiment that Galileo is said to have performed, in which he dropped two different weights from the Leaning Tower of Pisa to prove that they fell at the same rate? He released them at the same time, and they both hit the ground at the same time. The reason the rate of fall is independent of mass is that inertial mass and gravitational mass are exactly proportional. Although the heaver mass has more gravitational force (more weight) pulling it to the ground, it also has more inertia, and it takes more force to accelerate it at a given rate. The amount of additional force is just enough to overcome the additional inertia, therefore it accelerates at the same rate as the lighter weight. This is true of both rest mass and effective mass.