The problem of time in quantum gravity

5 problems

• How is quantum evolution defined when no global clock exists?

  Open

  Physical clocks in gravitating systems can stop or run backward, and in chaotic systems no variable may serve as a good clock everywhere. The usual recipe for evolution in time then breaks down.

• Do observer-dependent gravitational algebras persist beyond leading order in G?

  Open

  Recent work shows that including an observer with a clock makes the set of measurable quantities in de Sitter space and near black holes well behaved, with finite entropies. These results hold only to leading order in the strength of gravity.

• Are the different relational descriptions of quantum time equivalent?

  Partially resolved

  One proposal measures time through correlations with a physical clock inside the system; others use special combinations of variables that do not change. These approaches agree in simple models, but whether they agree in general is open.

• Do quantum gravity corrections to Schrodinger evolution violate unitarity?

  Contested

  Ordinary time-dependent quantum mechanics can be recovered from the timeless Wheeler-DeWitt equation by treating gravity as a slow variable. The next corrections in this approximation appear to break conservation of probability, and it is unclear whether this is real or an artifact.

• Construct the physical Hilbert space of the Wheeler-DeWitt equation

  Open

  The Wheeler-DeWitt equation is the quantum version of Einstein's equations for the whole universe. There is no rigorous way to normalize its solutions, so probabilities are not defined.