# Some thoughts on energy and momentum

1. May 9, 2010

### espen180

Scenario 1:
A photon is travelling straight towards a star. As it goes deeper in the star's gravitational well, its frequency grows, coresponding to an increase both in energy and momentum.

Scenario 2:
A photon is travelling towards a star, but not head on. As it passes the star, its path changes direction. This corresponds to a chang in momentum.

In both of these scenarioes, the momentum vector of the photon changes. In order for momentum to be conserved, the star will have to gain momentum in the direction of the photon.

This in turn means that there is a net increase in kinetic energy of the system (counting the photon's E=hf as kinetic). Therefore, the photon must have a potential energy with respect to the star, which shouldn't be extremely hard to calculate.

By the theorem $$\vec{F}=\nabla E_p$$, there is excerted forces between them; gravitational forces. This is equivalent to the photon curving the spacetime around it.

Now back to Scenario 1: Since energy and momentum is conserved, and the photon makes the star accelerate towards itself, does that not imply that the gravitational interaction propagates faster than light?

2. May 9, 2010

### meopemuk

Observations of gravitational effects on photons can be derived from this simple Hamiltonian

$$H = Mc^2 + pc - \frac{2GMp}{cR}$$

where M is the star's mass, p is the photon's momentum, G is the gravitational constant, R is the distance between the photon and the center of the star. Star's kinetic energy term $$p^2/(2M)$$ is negligibly small and ignored.

Eugene.

3. May 9, 2010

### lightarrow

I'm not an expert on GR but I would say that the photon interacts locally with the field around the star, not with the star itself (or its core).

4. May 9, 2010

### Vanadium 50

Staff Emeritus
Replace the gravitational field with an electric field and the photon with an electron. This argument then proves that the speed of light is faster than the speed of light.

5. May 9, 2010

### espen180

Looking back, I realize that I have fallen victim to a bare assertion fallacy by not taking the interation delay into account in the first place.

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook