Slightly Modified Olbers Paradox Question

[SHawking]

I understand the resolution to the typical statement of Olber's paradox, that is, that with a finite horizon distance only light up to a certain distance will have reached Earth. However, let's say that we modify the contents of the universe such that we have an infinite horizon distance. Why, in this case, do we still have a finite brightness?

I think it is that because with red shift the wavelength is being shifted and by the time the light that propagated past a certain distance will have red shifted to wavelengths we no longer detect as light. Is there a better resolution?

Thanks!

 

[Chronos]

Olber's paradox is based on the premise the universe is infinitely old, infinitely large, and contains an infinite number of stars, etc. The resolution is actually quite simple. We know with great confidence the observable universe is not infinitely old. Paradox resolved.

 

[Chalnoth]

I understand the resolution to the typical statement of Olber's paradox, that is, that with a finite horizon distance only light up to a certain distance will have reached Earth. However, let's say that we modify the contents of the universe such that we have an infinite horizon distance. Why, in this case, do we still have a finite brightness?

As long as we have an expanding universe, the redshifting of light will make it so that the temperature luminosity of light from far-away sources is reduced. For Olber's paradox to be a problem, you need far-away light sources to appear the same temperature as nearby ones.