I’ve just been teaching E=hf to year 12 and Doppler shift to year 13. Thankfully none of the students have made this link but incase they do I want your thoughts on this.
So if light is emitted at one frequency, has a set energy E1. If this light is then stretched through cosmic red shift to a lower frequency it will have a lower energy E2. Where has this energy gone? Likewise if it is blue shifted the light will now be at a higher energy E3. Where has this energy come from?
Could it be that energy has gone into the stretching or compression of space itself? Or is Energy a relative thing (Im talking Galleian relativity not Einstein) and so as the frame of reference has changed so has its energy?
The real problem with questions like this is we are usually dealing with much more sophisticated models like general relativity and quantum mechanics. So energy conservation is a consequence of Noethers’s theorem.
Noether’s theorem says that whenever there is a symmetry in physical laws, we get some conserved quantity. For translations in space we get momentum conservation. For rotations conservation of angular momentum and for translations in time, we gets conservation of energy.
From what I can tell from reading around on various discussion groups involving physicists that know their general relativity is that many say that globally energy is not conserved in general relativity. I will read more and try and summarise my own understanding.
I think the thing I have read that I went on to discus with my class this morning is that the universe if the universe is closed and bounded then the cosmological constant is like a pressure term that drives the expansion. If the universe is expanding then work must be done against gravity. I told my students that this is where the energy goes, into the work done in driving the expansion.
I must admit I only really told them this as we are revising and I used it as a way to talk about distances being moved through force requiring work. If any of them go on to be cosmologist, and remember my dodgy answer then hopefully they will come back and tell me the answer to this question.
It is my limited understanding that energy conservation is really only within a frame according to the equations we are using here. Energy is a relative quantity in the sense of it is differences in energy that tell us about what is happening.
So as in the example here. A bullet moving at 40 m/s will if hitting an object that is at a different speed have its speed changed and the change in KE will cause work to be done, usually in deformation.
In special relativity KE is given by the difference between the total energy E and the rest energy mc^2
The conservation of energy in relativity is replaced with the conservation of energy-momentum.
Actually the quantity
is what is conserved.
I think the other thing to add is that when we talk about quantities having the same value in different frames of reference, we are actually saying they are invariant. This is not the same as conserved. A conserved quantity means it does not change in time (within a frame in the example above).