## Thursday, April 19, 2012

classic cosmology question: why is it dark at night? what are minimal assumptions for answering this, and how would you reply with the knowledge of a FLRW-cosmology? are there other (astrophysical) explanations you can think of? could you construct an alternative whacky cosmology (i.e. non-FLRW) that would resolve the paradoxon?

bonus question: what's $(\pi+20)^i$ with $i=\sqrt{-1}$? surprised?

1. Nice question, I would propose an answer like this, but correct me if I am wrong with it.

If Olber's paradox generally states that the universe and the amount of light sources are of infinite size, we can apply the assumption of a finite speed of light and therefore create a horizon in the universe which would naively restrict the amount of possible light sources to a finite number.

In case of an FLRW cosmology we can apply the argument that photons emitted form distant sources are redshifted due to the global expansion. This redshift causes the energy density of photons being diluted by $\rho_\gamma \sim a^{-4}$, such that for example a thermal photon emitted at CMB redhift at T=3000K (orange light) corresponds to T=2.7K today which is far off the visible range.

The definition of a redshift $$1+z=\frac{1}{a}$$ is basically independent of the cosmological model, so we do not need to create an FLRW model to define a redshift, so even non-FLRW models can be considered that cause photons to be redshifted.

$$(\pi+20)^i \approx e^{i\pi}=-1$$

2. Almost -1

http://mathworld.wolfram.com/AlmostInteger.html

1. Dear Cusp,
we'd like to ask you if we could interest you in a guest post here on CQW!

please tell us what you think. :)

3. http://xkcd.com/1047/