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Is light of different colors affected differently by gravity?

I have a question about gravitational lensing. As a photon goes through a region of curved space, it will find its geodesic and go on its merry way. Does the shape of the geodesic depend on the wavelength of the photon? Or: is space-time dispersive like a prism? I was going to get a spectrograph and a CCD camera to try and answer this question observationally, but thought I might check with the theorists first.

The shape of the geodesic does not depend on the photon's wavelength (i.e. on the light's color). It only depends on the mass distribution of the object that is causing space to be curved. When other objects (photons, particles, etc.) move through this curved space, the particular path that they follow will depend on their velocity, but since all photons have the same velocity they will all follow the same paths and there should be no dispersive effect.

There is, however, an effect called the "gravitational redshift", in which photons moving away from a massive object lose some energy, causing their wavelength to increase, i.e. making them more red. This is an effect of energy conservation - when you throw a ball into the air, for example, it gains potential energy and loses kinetic energy (i.e. its speed decreases). A photon does the same thing, but its speed can't decrease because it is constrained to always move at the speed of light, so the only way it can lose energy is to change its wavelength.

May 2002, Dave Rothstein (more by Dave Rothstein) (Like this Answer)

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