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

[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.

In general relativity, gravitation is a manifestation of the curvature of spacetime. The motion of all objects is affected by this curvature, regardless of whether they have mass or not. Light follows geodesic paths in spacetime, which are straight lines in flat spacetime, and curved paths in curved spacetime.

Note that by "mass" above I mean "invariant mass" as discussed in post #6 above, because it is the invariant mass that is zero for a photon. If you prefer to think in terms of "relativistic mass" (which is related to energy via E = m_relc²), note that all photons follow the same geodesics, regardless of their energy.

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...??
(edit: No they are not..had to think about this; so it's just the "relativistic mass" that's now confusing me.

 

[NanakiXIII]

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.

 

[starthaus]

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.

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

 

[NanakiXIII]

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

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.

 

[starthaus]

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.

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

 

[atyy]

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 geodesic for photons of different energy would be slightly different...??

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.

 

[NanakiXIII]

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

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.

 

[TCS]

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.

 

[Naty1]

I know this has been discussed before...

ok here is one, which I missed earlier this year .
https://www.physicsforums.com/showthread.php?t=391798&highlight=light+in+a+gravitational+field



In post #2 bccrowell says in responding to this quote :

Then more energetic light should be more affected by gravity than less energetic light, like in the way a heavier object is more affected by the Earth than a lighter object.

There's nothing wrong with this.

but then in post #4 says in responding to this quote:

I kind of understand your examples but also kind of... not. For example, I have learned that photons are affected by gravity by gravitational redshift and bending. Would then blue light be more bent than red light?

No. General relativity is a geometrical theory.

This is because they follow the same geodesic.)



In post #16 bccrowell states:

I'm claiming that there's nothing in any of this beyond freshman relativity. If you keep the number of photons constant while increasing the frequency, you get more mass-energy. A greater mass-energy means proportionately stronger gravitational interactions.

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)

 

[Naty1]

note that all photons follow the same geodesics, regardless of their energy.

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.

 

[TCS]

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.

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

 

[Naty1]

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

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...

 

[NanakiXIII]

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.

 

[TCS]

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

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.

 

[Naty1]

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.

 

[Chaos' lil bro Order]

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.

 

[Chaos' lil bro Order]

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.

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