presto said:
This very correct and even accepted by the standard science.
Good, I'm glad we agree on that. However, the rest of your post is inconsistent with what you have just said is correct. See below.
presto said:
You just try to improvise with the naked facts!
I'm afraid I fail to see why concentrating on the facts is a problem. ;)
presto said:
Your presumption about the dependence of energy on the frame is wrong.
But you just agreed that "energy is observer-dependent" and "there is no absolute notion of energy" were correct. Now you're saying those statements are incorrect. Which is it?
presto said:
Even in the Doppler effect the energy is conserved
Same comment here; if "energy is observer-dependent" is correct, then energy changes in the Doppler effect, obviously, because the whole point is that the receiver is moving relative to the emitter, so his notion of "energy" is different. So you're saying two inconsistent things here.
presto said:
but it is more hard to notice, than in the case of the gravitational redshift,
where the situation is completely fixed - stationary, therefore simpler - the simplest possible.
No, the stationary situation is in fact the
only situation where we can define an invariant notion of "energy" that works globally, instead of just locally. (Note that we can always define an invariant local notion of "energy", namely the stress-energy tensor, which obeys a well-defined local conservation law. The issue we are discussing here is about how to define a single notion of "energy" that applies at different, separated events in spacetime.) This is because, to define an invariant notion of energy that works globally, we need a timelike Killing vector field, and that is only present in a stationary spacetime.
All of this is very basic GR, by the way, and it is not at all controversial. If you want to continue arguing against it, you're going to need to give mainstream references and show your math explicitly. First, as I requested above, you're going to need to take one consistent position and stick to it.
presto said:
The actual temperature of the CMB is perfectly consistent with the energy conservation principle.
Please show explicitly, with math, how this is true.