# I Photons under gravity

1. Feb 9, 2017

### calinvass

Why does the energy of a photon increase when falling into a gravitational field ?
If we use the equation E=hf, then the energy of the photon increases, but I understand that we also need to add the potential energy to find the total energy. Et=Ep+hf. The potential energy decreases by the same amount the hf term increases.
Is this correct?

2. Feb 9, 2017

### Umaxo

Since we are in forum on relativistic physics, this is not true. In general, potential energy of gravitational field in general relativity cannot be defined and notion of conservation of energy doesnt work here. What is happening is simply the fact that time and space is "different in different places" so in one place you will measure different energy simply because your measurement tools are different. How different they are is given by spacetime metric.

However, thanks to the equivalence principle, the conservation of energy (and whole of physics) holds for "one point", i.e. in small enaugh region the physics works same as in universe without gravitation. But the "small enaugh" region is important, you cannot extend it too much.

Last edited: Feb 9, 2017
3. Feb 9, 2017

### Orodruin

Staff Emeritus
This is not quite true. If we want to be rigorous about it, the tools should be assumed to be the same. What changes is the relation between the parallel transported 4-momentum and the 4-velocity of the observer. What is generally referred to as "gravitational redshift" presumes stationary observers in a stationary spacetime.

4. Feb 9, 2017

### jartsa

Let's say twins Bob and Jim are electrically charged. Bob descends in a gravity well, Jim stays up. When Bob observes Jim living his life, Bob sees Jim aging quickly, darting around quickly, and producing such EM-waves were a crest follows a through quickly.

Bob might think: There is some chemical energy in Jim, and that energy has some potential energy. When some of Jim's chemical energy is converted to EM-waves, the EM-wave energy has potential energy, so we might say that when energy is converted, the potential energy of the former energy becomes the potential energy of the latter energy.

Where was I going with this ... Let me ask: Does E=hf hold for potential energy?