Energy vs wavelength for a photon in GR

[Pierre007080]

If a theoretical single photon followed a geodesic toward a large mass in space, I understand that the wavelength would shorten as it approached the mass. How would the energy be conserved within the photon, because the frequency must surely remain the same?

 

[Mentz114]

If a theoretical single photon followed a geodesic toward a large mass in space, I understand that the wavelength would shorten as it approached the mass. How would the energy be conserved within the photon, because the frequency must surely remain the same?

If the wavelength changes, then the frequency will change if the velocity is constant, because v=f\lambda.

Energy is not globally conserved in the general theory of relativity. If a chain of observers along the geodedic studied these photons, they would find the speed is the same c, but the frequency and wavelength are different.

 

[Jonathan Scott]

If a theoretical single photon followed a geodesic toward a large mass in space, I understand that the wavelength would shorten as it approached the mass. How would the energy be conserved within the photon, because the frequency must surely remain the same?

From the point of view of any single observer, the energy would remain constant but the coordinate speed of light would decrease, so the magnitude of the momentum, E/c, would increase as the photon moved towards a lower potential.

From the point of view of separate observers at different potentials, each of them is time-dilated according to their potentials, so they see different energy values.

 

[Pierre007080]

Hi Mentz 114,
Thanks for your response. I think I understand your answer about the chain of observers along the geodedic ... but is it allowed for the observer to be in a nearby spaceship observing (from a distance) the shortening wavelength and even a slowing of the speed of light?

 

[Mentz114]

Hi Mentz 114,
Thanks for your response. I think I understand your answer about the chain of observers along the geodedic ... but is it allowed for the observer to be in a nearby spaceship observing (from a distance) the shortening wavelength and even a slowing of the speed of light?

As Jonathan has said, the coordinate speed of light will change. But I don't see how it is possible to measure the wavelength from a distance.

What is observed will depend on what the spaceship is doing. For instance it might be moving (wrt the mass) or hovering.

 

[Pierre007080]

Thanks Guys,
To conceal my ignorance, I think that I must stick to Jonathan's "single observer" status! How will this momentum (E/c) increase be interpreted? Would there be an increased "amplitude" to compensate for the observed shortened wavelength?