You are now in the 2nd one

When we sleep we wake up to another dimension hardly like this one and at that peculiar place we assume we are awake. We remember vague moments of our current actions and call them dreams. When we sleep there we wake up here only remembering the things that are common for both dimensions, but still cannot making sense of them. We assume this one is the real one and other one is dream in each separate plane.

This might look like a wild theory but think about it. Think about what an odd thing sleeping really is. To spend a portion of your day without consciousness or a definite memory. Since we are used to it it feels normal but! ( No need to focus on the little story above, just state your opinions about sleeping )

There's usually a delay between absorption and emission, so in a sense, the photon is "destroyed".  Of course, with all that identical particle non sense, it's hard to say exactly what it means for something to be destroyed and remade.

Since there is a delay, just as you say, the interval between the events is timelike, and that is Lorentzinvariant. Thus the photon really is destroyed and new one created, the whole "identical particles" stuff doesn't really apply.

Oh, and the Hamiltonian is the generator of time-translations. If you look at the Poincare-group (ie. rotations and translations in spacetime), the Hamiltonian and the momentum-operators naturally emerges as the generators of spacetime translations.