Does Mass and Energy Affect the Path of Light Differently in General Relativity?

[talksabcd]

We know that Mass wraps space-time according to Einstein's General theory of relativity. This implies that light would travel in a curved path around mass and all the colors travel in the same path or direction.

But according to Stephen hawking, not only mass but also energy wraps
space-time. If this is the case then photon (E=hv) should also wrap space-time. As different colors has different energy then each color should wrap space-time with different magnitude.

Then shouldn't different colors travel in different direction under the influence of mass considering each color has its own energy/mass ? (Analogous to splitting of colors under refraction)

 

[cesiumfrog]

No. (Analogous to the equal acceleration of different objects when dropped.)

 

[talksabcd]

Thanks for your simple answer. I know my question is the result of too much thinking and I know that different masses would fall with same acceleration under influence of gravity but I totally forgot this in the case of a photon. Thanks again.

 

[MeJennifer]

No. (Analogous to the equal acceleration of different objects when dropped.)

The mass or the energy of a particle does contribute to the path taken in space-time. Two particles with a different mass or energy will follow a different path in space-time.

 

[talksabcd]

Could you please give brief explanation on how masses with different energy follow different paths or can you direct me to any internet link which explains this ?

Thanks,
talksabcd

 

[MeJennifer]

Could you please give brief explanation on how masses with different energy follow different paths or can you direct me to any internet link which explains this ?

Each object that has either energy or mass will contribute to the curvature of space-time as described by the Schwarzschild or Kerr metric.

 

[pmb_phy]

Could you please give brief explanation on how masses with different energy follow different paths or can you direct me to any internet link which explains this ?

Thanks,
talksabcd

Different particle mass-energy means a different velocity. Consider the simple example of two free particles traveling in flat spacetime in an inertial frame. Each particle will trave out a straight line in spacetime but the slopes will be different due to the different velocities.

Best regards

Pete

 

[talksabcd]

Different particle mass-energy means a different velocity. Consider the simple example of two free particles traveling in flat spacetime in an inertial frame. Each particle will trave out a straight line in spacetime but the slopes will be different due to the different velocities.

Best regards

Pete

Do you mean that different colors of the light(different energies) travel at different speeds considering velocity of light is constant in free space for all the colors ?

 

[cesiumfrog]

Each object that has either energy or mass will contribute to the curvature of space-time as described by the Schwarzschild or Kerr metric.

Technically there is some truth in this. Each object does contribute to the curvature of space-time (although the listed metrics only describe the space-time around a single isolated point mass, rather than the contribution of successive objects). But..

Two particles with a different mass or energy will follow a different path in space-time.

You contradict the equivalence principle to argue that different masses fall differently.

There was a https://www.physicsforums.com/showthread.php?t=151716" discussing how technically, in some sense, a heavy brick falls to Earth faster than a lighter coin. The truth is that the Earth curves space-time in a manner that will affect the motion of any object equally (regardless of mass-energy), although the heavier object will pull the Earth up more (leading them to meet sooner than if the object had less mass-energy). You can easily understand why such a difference/separation does not exist, even technically, if both objects are dropped at the same time from the same place, which is indeed the relevant case here (asking whether photons with different mass-energies will be *separated*).

Its also worth noting that even planets do follow geodesics, for all relevant purposes. Technically there are some issues regarding extended bodies, angular momentum, etc, but these issues are practically negligible. Even if such technicalities were applicable to photons, the result would only be more negligible (since a photon's gravity has so much less impact, compared to a planet's, against such a massive object like the sun).

Different particle mass-energy means a different velocity. Consider the simple example of two free particles traveling in flat spacetime in an inertial frame. Each particle will trave out a straight line in spacetime but the slopes will be different due to the different velocities.

This is obviously just mistaken; different mass-energy (unlike, say, "same rest mass + different kinetic energy") doesn't always mean different velocity. In this case the photons have different mass-energies but the same velocities ("c"), and so there would be no such "different slopes".

Having said all that.. there are some situations where you might expect gravity to sort photons, particularly where the photons have a wavelength on the same length scale as the region of strong space-time curvature. This is an issue of interference between different paths rather than a debate over any specific local path. Such long wavelengths likely aren't practically measurable in EM, but this could be relevant to lensing of gravitational waves.

 

[MeJennifer]

You contradict the equivalence principle to argue that different masses fall differently.

Different mass do fall differently!
The equivalence principle only applies to test particles!

There is no single particle I know of that does not create its own gravitational field. And thus it must contribute to the combined field.

The truth is that the Earth curves space-time in a manner that will affect the motion of any object equally (regardless of mass-energy).

That is true.
But it is also true that each particle in that field creates its own gravitational field.
So they have to be combined, and combining them is far from trivial.
But basically that is what we are supposed to do, adding all the little Schwarzschild and Kerr shaped fields together.

Its also worth noting that even planets do follow geodesics, for all relevant purposes.

Sure they do, unless they rotate.

Technically there are some issues regarding extended bodies, angular momentum, etc, but these issues are practically negligible.

But that does not mean they don't exist!

Even if such technicalities were applicable to photons, the result would only be more negligible (since a photon's gravity has so much less impact, compared to a planet's, against such a massive object like the sun).

A photon has energy so it creates its own gravitational field and of course it is very small, but that does not mean it is not there.

For instance, in principle it is impossible to setup an experiment that would confirm any exact solution of Einstein's field equations.

I say, in principle, since obviously we could easily ignore the gravitational fields of the particles involved in the measurement by considering them test particles without a gravitational field.
But, in principle, it is impossible!

 

[cesiumfrog]

MeJennifer, just to clarify, are you actually asserting that a beam of white light passing by a massive object *will* be separated into a rainbow (like by a prism)?

 

[MeJennifer]

MeJennifer, just to clarify, are you actually asserting that a beam of white light passing by a massive object *will* be separated into a rainbow (like by a prism)?

"Gravity's rainbow" as it is called by some papers.

The dispersion seems to be a lot more complicated than a simple rainbow though.

 

[cesiumfrog]

Heh. OK. So if I've understood the literature (eg. PRD v.51 p.2584, 1995) then:

1) There should be such a thing as gravitational birefringence - whereby (according to QED) the pointlike photon temporarily dissassociates into a pair of virtual particles, the virtual particles acquire a spatial separation (dependent on the photon polarisation), so the differing "tidal forces" (across that separation) induce a polarisation-dependent deviation in the photon's trajectory.

2) There may be such a thing as a colour dependence in photon trajectory - for example if (according to some variants of string theory) the photon is somehow composed of "strings" having spatial extent dependent on the photon's energy... but that is speculative at this time.

3) Neither of these effects are expected to be detectable under any realistically attainable cirumstances.

A photon has energy so it creates its own gravitational field and of course it is very small, but that does not mean it is not there.

The effects seem to result not from the gravitational field of the photon itself, but only from the external gravitational field.

That is, if by some (quantum/nonclassical) mechanism we can attribute a nonzero spatial size to the photon, then the parts in different locations may naturally tend to fall along different paths (as would test particles at different locations, since the gravitational curvature is location-dependent), and so the total (averaged?) motion will depend on the the photon's spatial extent (which in turn, it is theorised, may depend on the frequency of the photon).

 

[russ_watters]

MeJennifer, just to clarify, are you actually asserting that a beam of white light passing by a massive object *will* be separated into a rainbow (like by a prism)?

Technically speaking, every satellite we send in orbit around the Earth will affect the Earth differently, but we don't bother calculating it because the difference is far too small to notice.

[edit:clarification] Just to clarify, I'm not saying that the effect exists, but just that even if it did it would probably not be detectable.

 

[hellfire]

"Gravity's rainbow" as it is called by some papers.

The dispersion seems to be a lot more complicated than a simple rainbow though.

I don't think you are right, because you are considering low energy and high energy photons separately.

Consider a very massive body like the sun and a very distant light source at infinity. If this source emits a single low energy photon, space-time near the sun would look different than if it emits a single high energy one. Both photons would move through null geodesics, but that geodesics would be in different space-times. This would lead to different deflection. This is the phenomenon you have pointed out.

However, a distant star usually emits a beam of photons streaming with a constant total density per time and area. For observational purposes such a beam does not start nor end and all photons in all energy ranges can be found there in a homogeneous energetic mix (e.g. for each energy with a specific rate).

So there is one single static space-time to be considered and in such a space-time the determination of null geodesics is unique. All photons would move through the same paths.

May be I have missed something, anyway, it would be nice if you could provide some references to that papers about "gravity rainbow".