EXPANDING UNIVERSE

OLBERS PARADOX

Olbers’ paradox “The night sky is dark.” This statement is called Olbers’ paradox, after astronomer who discussed the subject back in Why is the darkness of the night sky so paradoxical?

not If stars were stuck on a celestial sphere or dome, darkness would not be paradoxical. There are only a finite number of stars on the celestial sphere.

In an infinite universe with infinite number of stars, a paradox arises. Let’s see how bright we expect the sky to be in such a universe?

Olbers’ Paradox for Trees and Stars: In a large enough forest, every line of sight ends at a tree. In a large enough universe, every sight line ends in a star. The sky should not be dark.

infinity Infinity times any finite number, no matter how tiny, is infinity. Leading to Olbers conclusion that the night sky should be infinitely bright. Something must be wrong with one or more of the assumptions! The number of stars goes up at the same rate that the light from each goes down.

Galaxy spectra show redshifts, where all the spectral features shift to longer wavelengths. The amount of the shift increases with distance: more distant galaxies are moving away faster. This linear relation was discovered by Edwin Hubble back in HUBBLE LAW

All distant galaxies have redshifts. (They are moving away from us.)

Let’s simplify the situation: the universe is like the curved surface of an expanding balloon. Draw 10 galaxies on the balloon. Pick a home galaxy. Inflate balloon to 2 different sizes and measure distances from home to the other 9.

Expansion on large scales

Galaxies are all moving away from each other, so every galaxy sees the same Hubble expansion, i.e. there’s no center. The universal expansion results from the unfolding of all of space since the hot big bang, i.e. there is no edge.

The redshift is not a Doppler shift; it is due to the expansion of space itself. Photons are stretched.

Hubble’s law in mathematical form: v = radial velocity of galaxy d = distance to galaxy H 0 = the “Hubble constant” (it is the same for all galaxies in all directions)

What’s the numerical value of H 0 ? What’s the slope of this line? →

important Why it’s important to know H 0 : If two galaxies are separated by a distance d. They are moving apart from each other with speed v = H 0 d. d

How long has it been since all the galaxies were touching?

Basis of the “big bang” concept: At a time in the past (t ≈ 1/H 0 ), the universe began in a very dense state. Hubbletime 1/H 0, called the “Hubble time”, is the approximate age of the universe in the Big Bang Model.

If the universe has a finite age, then the most distant stars haven’t had time to send us the light message “We’re here!” Expansion explains Olbers paradox: