The Question

The Hubble Ultra Deep Field is a snapshot of (that small section) of the galaxy 13 billion years ago. This means that the light that composed the image travelled 13 billion light years, and hence the source is currently ~13 billion light years away. If we say that the universe is 13.7 billion years old, then the observable universe is roughly 13.7 billion light years in radius.

Therefore when the light was emitted, we can assume the observable universe was 700 million light years in radius. Which means that the source should also have been within 1.4 billion light years of Earth. So unless the source and Earth were expanding away from each other at nearly 9/10ths the speed of light, which is obviously untrue...how come the light for this photo didn't pass us billions of years ago?

The Answer

It is also easy to get confused about distances and time in cosmology, because there are different definitions used in different situations, or by different authors. As Prof. Ned Wright says, "The time and distance used in the Hubble law are not the same as the x and t used in special relativity, and this often leads to confusion." See:
http://www.astro.ucla.edu/~wright/cosmo_02.htm#DH http://www.astro.ucla.edu/~wright/cosmology_faq.html#DN http://www.astro.ucla.edu/~wright/cosmology_faq.html#ct2

Some parts of the universe are outside of our horizon, and since the expansion appears to be speeding up, these will never be observable to us.

Some detailed references are:

- Expanding Confusion: common misconceptions of cosmological horizons and the superluminal expansion of the Universe
http://arxiv.org/abs/astro-ph/0310808

- No Superluminal Expansion of the Universe
http://arxiv.org/abs/gr-qc/930300

Hope this helps,
Tom, Koji, Andy, Tess and Mike for "Ask an Astrophysicist"

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