# If photons don't have mass, why do their paths bend in a gravitational field?

1. Jul 19, 2010

### Naty1

If photons don't have mass, why do their paths "bend" in a gravitational field?

This is question #8 in the FAQ and the answer provided is this:
I'm trying to understand the last sentence.

I must be having a mental block: why would thinking of "relativistic mass" cause identical geodesics? Is this statement saying light of all frequencies follows the same geodesics?
(edit: that part seems ok)

If a given region of spacetime has some initial curvature, then as photons of different energy (or relativistic mass) pass that region should they not cause a slight change in the curvature .....and I therefore the geodesics for photons of different energy would be slightly different...??

Last edited: Jul 20, 2010
2. Jul 19, 2010

### NanakiXIII

Re: If photons don't have mass, why do their paths "bend" in a gravitational field?

EDIT: Ignore this post, I was wrong.

This may not be a definitive answer (and it may not even be correct, I'm by no means an expert on GR), but wouldn't it be rather strange if a particle, photon or otherwise, could affect its own geodesic? Suppose you have something traveling in plain flat space. If that particle's energy could affect its own geodesic, that would mean it might not travel in a straight line, even though space is flat. In classical terms, it would be exerting a force upon itself.

Last edited: Jul 20, 2010
3. Jul 19, 2010

### starthaus

Re: If photons don't have mass, why do their paths "bend" in a gravitational field?

In fact, charged particles do exactly this through radiating em energy, photons don't since they have zero charge.

4. Jul 19, 2010

### NanakiXIII

Re: If photons don't have mass, why do their paths "bend" in a gravitational field?

Fair enough, so taking into account any equivalent gravitational wave Brehmsstrahlung there might be some effect. However, besides the fact that the amount of radiation is likely to be utterly negligible, it is probably also somewhat beyond the scope of the FAQ that was quoted.

5. Jul 19, 2010

### starthaus

Re: If photons don't have mass, why do their paths "bend" in a gravitational field?

I don't think you paid enough attention, the photons have 0 charge, therefore the effact is null.

6. Jul 20, 2010

### atyy

Re: If photons don't have mass, why do their paths "bend" in a gravitational field?

Yes. In calculating the bending of light in the solar system, or in gravitational lensing, the curvature caused by the light is ignored, because it is very small compared to the curvature caused by massive bodies like the sun or the star that is bending the light. However, spacetime curvature caused by light is predicted by Einstein's theory - as solutions of the combined Einstein-Maxwell equations.

7. Jul 20, 2010

### NanakiXIII

Re: If photons don't have mass, why do their paths "bend" in a gravitational field?

You misinterpreted my post. I understand there is no electromagnetic Brehmsstrahlung, I was considering the possibility of an equivalent process involving gravitational waves. I don't know if such exists, it's just a thought.

After getting some sleep I realize, however, that my first post doesn't make any sense. Of course photons of different energy follow different geodesics, in principle. However, like atyy points out, the photons are considered to be test particles, i.e. their effect on spacetime is neglected, compared to the bodies that bend their paths.

Last edited: Jul 20, 2010
8. Jul 20, 2010

### TCS

Re: If photons don't have mass, why do their paths "bend" in a gravitational field?

Photons bend becasue the are traveling through bent spacetime.
No force acts on them.

Space is expanding, which means that it is hyperbolic with respect to time and that parrallel lines diverge as they move through time. Accordingly, straight lines in space are like helixes.

The amount of the expansion of a volume of a region of space varies by the amount of mass density within that region of space. Since some regions of space have greater mass densities than their neighbors, they are less expanded than their neighbor regions, and staright lines that move through them will appear to bend, since the radius of the helix (staright line) is smaller in denser regions of space.

Last edited: Jul 20, 2010
9. Jul 20, 2010

### Naty1

Re: If photons don't have mass, why do their paths "bend" in a gravitational field?

I know this has been discussed before.....

ok here is one, which I missed earlier this year .

In post #2 bccrowell says in responding to this quote :
There's nothing wrong with this.

but then in post #4 says in responding to this quote:
No. General relativity is a geometrical theory.

This is because they follow the same geodesic.)

In post #16 bccrowell states:

There are other interesting examples in the referenced thread....such that gravitational lensing doesn't produce rainbows, which I believe is accurate, and the equivalence principle..shining two laser beams of different frequency across an elevator..both beams will bend in the same curve....follow the same geodesic as viewed from the outside...these two examples convince me all light follows the same geodesic....

(ok, I think I understand this one,see next post)

Last edited: Jul 20, 2010
10. Jul 20, 2010

### Naty1

Re: If photons don't have mass, why do their paths "bend" in a gravitational field?

I'm now thinking this part of the original FAQ reply (from my post #1) is correct. The reason is that photons with higher energies experience a greater gravitational attraction and that enables them to follow the same geodesic as a lower energy photon which experiences somewhat less gravitational attraction.

It's the mass portion of that last sentence that I still don't understand.

11. Jul 20, 2010

### TCS

Re: If photons don't have mass, why do their paths "bend" in a gravitational field?

There is no gravitational attraction. A geodesic is a straight line.

12. Jul 20, 2010

### Naty1

Re: If photons don't have mass, why do their paths "bend" in a gravitational field?

Utterly incorrect.
There IS positively attracton; a geodesic is in general CURVED. It is straight ONLY when gravity is absent....as in Eucledian flat planes.

See redshfit and blue shift and gravitational lensing and the equivalence princple as illustrated by laser beams in an elevator...
see here http://en.wikipedia.org/wiki/Geodesic

PS your earlier post is quite wrong, except for the first two sentences....I mention that not to pick or be mean but because if no one says anything you never find out....

Last edited: Jul 20, 2010
13. Jul 20, 2010

### NanakiXIII

Re: If photons don't have mass, why do their paths "bend" in a gravitational field?

What TCS probably meant is that there isn't a force in the Newtonian way. A geodesic is a generalization of the concept of a straight line - geodesics are the straight lines of curved spaces. Objects simply follow these geodesics, like they follow "actual" straight lines in flat space. So there is no attraction, there is only curved space.

14. Jul 20, 2010

### TCS

Re: If photons don't have mass, why do their paths "bend" in a gravitational field?

If you transform a geodesic into a euclidian coordinate syste, then the resulting line will be curved. However, a geodesic is straight in Minkowski space. General relativity changes slope of the transformed line for bound energy, but the line is still straight.

momentum can't change unless a force is applied and no force is applied.

Last edited: Jul 20, 2010
15. Jul 20, 2010

### Naty1

Re: If photons don't have mass, why do their paths "bend" in a gravitational field?

Nana: Post #13 is correct....but very different from what TCS posted.

In post # 12 if there is not attraction and there is a straight line geodesic, that indicates a region of space with zero gravitational potential...a gravity free zone.

16. Jul 24, 2010

### Chaos' lil bro Order

Re: If photons don't have mass, why do their paths "bend" in a gravitational field?

Well, if a photon always moves in a straight line geodesic on the substrate of space, then if a great mass or energy of sufficient size, acts upon this space substrate, nearby photons will be bent. Make no mistake about it though, its space that bends, the photons merely follow what they think is a straight line in space, even though we observers can see that their path i s bent.

17. Jul 24, 2010

### Chaos' lil bro Order

Re: If photons don't have mass, why do their paths "bend" in a gravitational field?

I don't think its possible to gave a gravity free zone. Even Lagrangian points experience near nil gravity, but gravity nonetheless, just cancelled out to minutia.