# Thought experiment

1. Jul 8, 2014

### Andrev

Hi,

I figured out a thought experiment/problem, here it is:

A friend of mine is living in a galaxy far away. He has a machine which can make individual photons with a definite frequency (lets say blue light) and can emit them toward me. Here I have machine which can detect these photons and can tell their frequency. While they get here their wavelength increase because of the Doppler effect and the cosmological redshift. So I detect red light instead of blue.

If I calculate the energy of the photon (E=hf) when it was emitted and when I detected it, there will be a difference between the results. Where is the missing energy?

2. Jul 8, 2014

### Staff: Mentor

There is no missing energy: energy is frame dependent.

3. Jul 8, 2014

### Drakkith

Staff Emeritus
Consider throwing a dart off the back of a moving train towards an observer on the ground. In the frame of the thrower on the train, they give the dart kinetic energy and it flies away from them. But according to the observer on the ground, the dart loses kinetic energy and falls straight to the ground.

Both frames are correct. In one frame the thrower gives the dart kinetic energy and in the other frame the dart loses it. As Russ said, energy is frame dependent.

4. Jul 8, 2014

### Andrev

Lets say we have an indicator (for example a photocell) which can only indicate photons which have enough energy (hf>W_out). This photocell would work at the galaxy but wouldn't work here, would it?

5. Jul 8, 2014

### Drakkith

Staff Emeritus
That's correct.

6. Jul 8, 2014

### Andrev

Well, the energy of the two photons should be different then, right?

I can not imagine it except if it lost energy during its way.

7. Jul 8, 2014

### Drakkith

Staff Emeritus
Accelerate towards the incoming photon enough and you will measure it as being its original frequency. Where did they energy come from?

8. Jul 8, 2014

### Andrev

That's a good question as well and I think I know what you are pointing at.

However, it's still interesting - for me at least - that at a point the photon has enough energy to react, at another one it doesn't.

I guess we can pick similar examples at your classical physics situation.

9. Mar 13, 2015