Classical explanation of Olber's paradox is, the dark matter between stars prohibits us to see the light of stars filling whole night sky. Such explanation is relevant for most distant active gallactic nuclei (AGN), observable only in infrared due the dust cover (so called the spherical dust galaxies revealed by Spitzer infrared telescope).
If we consider the finite speed of light, then the fact night sky is black would mean, the Universe can be larger, then the finite speed of light allows. Big Bang theory considers, light emanated by primordial matter was of very high frequency, therefore it can be observed as a CMB by now. If we consider cosmological principle of uniform isotropic universe, then the presence of CMB supports rather idea of infinitely large Universe, from which only the visible portion of light can be perceived. Radiofrequency part of CMB is forming a thermal noise of matter at the zero temperature (ZPE). As we can see, Olber's paradox cannot be used as an evidence of finite Universe and Big Bang theory reliably. AWT is assuming, observable Universe generation appears like rather common AGN from outer perspective, therefore our Universe doesn't differs very much from another quasars (white holes), which are observable inside of our Universe by Copernican principle.
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The aether wave theory is the correct theory of light. Michelson and Morley couldn't find a difference in the speed of light because aether slowly moves into the Earth as it does into all matter instead of the Earth moving through Aether. Light moves into the Earth at 64 ft. per second faster than light moves away from the Earth.
see pantheory.org
By another words, M-M experiment can give null results only locally, in more general scope the omnidirection Universe expansion takes place. It manifest itself by Lense-Thirring effect and Doppler shift of CMB, because limited light speed cannot follow the speed of omnidirectional Universe expansion at large distance.
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