Is the inertial mass of light relative?

[GW Leibniz]

By the equivalence principle, the gravitational mass of light is its inertial mass, which it has because it has momentum. Light can impart some of its the momentum to massive objects, upon which it will lose energy, which is manifested by its frequency (the basic principle behind doppler velocimetry, as I understand it).

a) Does this mean that higher energy light (e.g., gamma waves) are going to be more affected by a nearby massive object than lower energy light (e.g., radio waves)?

If yes, then...

b) As I understand it, light has no absolute frequency -- if an observer is moving toward the oncoming light, she will measure a higher frequency, and likewise if an observer is moving in the opposite direction, she will measure a lower frequency. So, then, does it follow that the degree to which the path of light is bent by a massive object depends on the frame of reference in which that deflection is observed? It seems unlikely to me but I don't know why.

If the answer to a is no, is the answer also no for wave-particles that do have a rest mass, like say an electron? (if gravity would be irrelevant because it would be overwhelmed by some other force for some reason, bracket that off for the purpose of this question)

Also, if the answer to a is no, and if the reason is that the only thing that matters is the speed, and the speed is constant, then why doesn't the light's energy factor into its gravitational mass?

I hope this isn't too incoherent...

 

[Dale]

By the equivalence principle, the gravitational mass of light is its inertial mass

In GR there isn't a such thing as gravitational mass in general. The source of gravity in GR is the stress-energy tensor, which is a rank 2 symmetric tensor (i.e. it has 10 independent compnents). You cannot distill that down into a single scalar number in general.

The reason this is important and makes answering the rest of your question difficult is that light, in particular, has a stress-energy tensor of a form where there does not exist any reference frame where all of the terms but one vanish. So there is no such thing as the gravitational mass of a plane wave of light.

What you can say is that light gravitationally follows null geodesics in all frames and that the gravitational influence of light is determined by the Einstein field equations in all frames.

 

[GW Leibniz]

In GR there isn't a such thing as gravitational mass in general. The source of gravity in GR is the stress-energy tensor, which is a rank 2 symmetric tensor (i.e. it has 10 independent compnents). You cannot distill that down into a single scalar number in general.

The reason this is important and makes answering the rest of your question difficult is that light, in particular, has a stress-energy tensor of a form where there does not exist any reference frame where all of the terms but one vanish. So there is no such thing as the gravitational mass of a plane wave of light.

What you can say is that light gravitationally follows null geodesics in all frames and that the gravitational influence of light is determined by the Einstein field equations in all frames.

Ok, fair enough. But empirically, do we observe that waves of light with different wavelengths or intensity respond differently to the same massive object?

 

[A.T.]

Ok, fair enough. But empirically, do we observe that waves of light with different wavelengths or intensity respond differently to the same massive object?

No. Light is no different than other free falling objects here. Starting at the same position and velocity two objects follow the same path, even if their momentum is different.

 

[Dale]

I agree.