Thought Experiment: Where Does the Missing Energy Go?

[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?

 

[russ_watters]

There is no missing energy: energy is frame dependent.

 

[Drakkith]

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.

 

[Andrev]

Thanks for your replies!

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?

 

[Drakkith]

That's correct.

 

[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.

 

[Drakkith]

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

 

[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.

 

[backward]

I quote from the thread
http://preposterousuniverse.com/writings/cosmologyprimer/faq.html#energy
Is energy conserved in an expanding universe?
This is a tricky question, depending on what you mean by "energy." Usually we ascribe energy to the different components of the universe (radiation, matter, dark energy), not including gravity itself. In that case the total energy, given by adding up the energy density in each component, is certainly not conserved. The most dramatic example occurs with dark energy -- the energy density (energy per unit volume) remains approximately constant, while the volume increases as the universe expands, so the total energy increases. But even ordinary radiation exhibits similar behavior; the number of photons remains constant, while each individual photon loses energy as it redshifts, so the total energy in radiation decreases. (A decrease in energy is just as much a violation of energy conservation as an increase would be.) In a sense, the energy in "stuff" is being transferred to the energy of the gravitational field, as manifested in the expansion of the universe. But there is no exact definition of "the energy of the gravitational field," so this explanation is imperfect. Nevertheless, although energy is not really conserved in an expanding universe, there is a very strict rule that is obeyed by the total energy, which reduces to perfect conservation when the expansion rate goes to zero; the expansion changes the rules, but that doesn't mean that anything goes.
I think this is about the best one can do to meet the paradox.

 

[Andrev]

Interesting, thank you.