The arrow of time is driven by an increase in entropy, which ultimately originates in the low entropy near the Big Bang, which is a period in the universe’s history when gravity is fundamentally important. We therefore need to know how entropy works in the presence of gravity, but we’re held back by our incomplete understanding of quantum gravity. The one clue we have is Hawking’s formula for the entropy of a black hole, so we would like to follow that clue to see where it leads.
