High Frequency Photons: More Mass, More Bend?

[mdeng]

TL;DR Summary

gravitational rainbow effects

Since high frequency photons have more relativistic mass, should we expect them to bend more than lower frequency lights when traveling through a gravitational field, thus produce a rainbow effect? But we don't seem to experience rainbow effects with star light.

 

[Orodruin]

should we expect them to bend more than lower frequency lights when traveling through a gravitational field

No. There are many issues with your question. Just to mention a couple:

- Relativistic mass is essentially nothing but a different name for energy. Its has fallen out of use in most of the physics community.
- You cannot use relativistic mass and just insert it into Newtonian gravitation formulae. Newtonian gravity is not compatible with relativity.
- Even if you could use Newtonian gravitation and relativistic mass, you should not expect high frequency photons to bend more. Even in classical mechanics with Newtonian gravity, the motion of a test particle in a gravitational field does not depend on the mass of the test particle.

 

[mdeng]

Thanks. But what's behind the statement of "even light can't escape the gravitational pull of a black hole", is it not due to photons having mass therefore are subject to the pull?

 

[Dale]

Thanks. But what's behind the statement of "even light can't escape the gravitational pull of a black hole", is it not due to photons having mass therefore are subject to the pull?

No. Even in Newtonian gravity you could have massless objects affected by gravity.

But in GR the reason light cannot escape a black hole is because there are no null geodesics going away from the singularity inside the horizon

 

[mdeng]

Oh, I also realized my ignorance in my question because, as another post said, "If you shoot two rocks past the Earth, one more massive than the other, with the same initial positions and velocities, they will both follow identical trajectories. By analogy, the same should be true for two photons of different energies which are shot with the same initial positions and velocities (the velocities have to be the same in this case because they're both photons)."

 

[Orodruin]

Thanks. But what's behind the statement of "even light can't escape the gravitational pull of a black hole", is it not due to photons having mass therefore are subject to the pull?

No. That is a very popularized statement and as all popularized statements should be taken with a gallon of salt. The reason light cannot escape a black hole is the way that spacetime curves around it.

 

[OmCheeto]

hmmm... I seem to recall that "light" generates a gravitational field because although it doesn't have mass, it does have momentum. So if we were to take a light beam and shoot it past a star, that light beam should tug on that star. And that tugging should be seen reciprocally by the light beam. Otherwise, it seems to violate Newton's law of action and reaction.

Now if two light beams with different frequencies were to take that journey, it seems the answer to the OP's question would be yes.

I can forewarn you that if your answer includes the word "tensor" I will not understand it. I spent about a week trying to figure out what those are, but I could find no clear examples.

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ps. Just notice the [A] level marker. Ok to call on Drakkith to let me know that this is so far over my head that even the simplest explanation will be beyond the wildest dreams of my comprehension.

 

[PAllen]

hmmm... I seem to recall that "light" generates a gravitational field because although it doesn't have mass, it does have momentum. So if we were to take a light beam and shoot it past a star, that light beam should tug on that star. And that tugging should be seen reciprocally by the light beam. Otherwise, it seems to violate Newton's law of action and reaction.

Now if two light beams with different frequencies were to take that journey, it seems the answer to the OP's question would be yes.

Well, this get's back to a Newtonian example I gave some years ago: If you 'drop' a Jupiter mass BH from a tower, it will reach the ground faster than a canonball - because the Earth moves so fast to the common center of mass. But this violates the the common understanding that we are discussing test objects of miniscule mass compared to Earth - even if one might be thousands of times the mass of another. This is not considered a violation of 'universal free fall' because it is outside the bounds of applicability of that principle.

In this sense, if you somehow had a light pulse whose total energy were a significant fraction of Earth's in their common center of momentum frame, passing earth, it would behave differently than one with plausible energy. However, a key difference is that in the COM frame you would have measurable motion of the earth.

 

[Nugatory]

But what's behind the statement of "even light can't escape the gravitational pull of a black hole", is it not due to photons having mass therefore are subject to the pull?

It is not.
Light always travels in a straight line (formally called a “lightlike geodesic”) through spacetime. The apparent deflection of light in a gravitational field is actually the light moving in a straight line through curved spacetime, somewhat analogous to how a straight line on the curved surface of the Earth appears curved on a two-dimensional flat map (look at the airplane route between Tokyo and Chicago for an example).

Inside the event horizon of a black hole, the spacetime is so curved that no lightlike geodesic in any direction will pass out through the event horizon; instead they all eventually reach the singularity. The most intuitive way of seeing this may be to Google for “tipped light cone black hole” which will bring up some good diagrams.

 

[PeterDonis]

Since high frequency photons have more relativistic mass, should we expect them to bend more than lower frequency lights when traveling through a gravitational field

No, because, even leaving aside the other valid objections that others have already made, in GR an object's trajectory through spacetime does not depend on its mass. Gravity is not a Newtonian force in GR; it's spacetime geometry. An object's trajectory (assuming no non-gravitational forces act on it, which applies to the scenario you are posing) depends only on its initial 4-velocity and the geometry of spacetime.

 

[PeroK]

I can forewarn you that if your answer includes the word "tensor" I will not understand it. I spent about a week trying to figure out what those are, but I could find no clear examples.