Kiefer C. Quantum gravity

322 INTERPRETATION
the existence of life, and a particular efficient process in this respect is photosynthesis.
The huge entropy capacity of the environment comes in this case from
the high temperature gradient between the hot Sun and the cold empty space:
few high-energy photons (with small entropy) arrive on Earth, while many lowenergy
photons (with high entropy) leave it. Therefore, also the thermodynamic
arrow of time points towards cosmology: how can gravitationally condensed objects
like the Sun come from in the first place?
Another important arrow of time is the quantum-mechanical arrow. The
Schrödinger equation is time-reversal invariant, but the measurement process,
either through
• a dynamical collapse of the wave function, or
• an Everett branching
distinguishes a direction; cf. Section 10.1. We have seen that growing entanglement
with other degrees of freedom leads to decoherence. The local entropy
thereby increases. Again, decoherence only works if a special initial condition—a
condition of weak entanglement—holds. But where can this come from?
The last of the main arrows is the gravitational arrow of time. Although
the Einstein field equations are time-reversal invariant, gravitational systems in
Nature distinguish a certain direction: the universe as a whole expands, while
local systems such as stars form by contraction, for example, from gas clouds. It
is by this gravitational contraction that the high temperature gradients between
stars such as the Sun and the empty space arise. Because of the negative heat
capacity for gravitational systems, homogeneous states possess a low entropy,
whereas inhomogeneous states possess a high entropy—just the opposite than
for non-gravitational systems.
An extreme case of gravitational collapse is the formation of black holes.
We have seen in Section 7.1 that black holes possess an intrinsic entropy, the
‘Bekenstein–Hawking entropy’ (7.17). This entropy is much bigger than the entropy
of the object from which the black hole has formed. If all matter in the
observable universe were in a single gigantic black hole, its entropy would be
S BH ≈ 10 123 k B (Penrose 1981). Black holes thus seem to be the most efficient
objects for swallowing information. A ‘generic’ universe would thus basically
consist of black holes. Since this is not the case, our universe must have been
started with a very special initial condition. Can this be analysed further? Close
to the big bang, the classical theory of general relativity breaks down. A possible
answer can thus only come from quantum gravity.
In the following, we shall adopt the point of view that the origin of irreversibility
can be traced to the structure of the Wheeler–DeWitt equation. As
can be seen, for example, from the minisuperspace case in (8.15), the potential
term is highly asymmetric with respect to the scale factor a ≡ exp(α): in particular,
the potential term vanishes near the ‘big bang’ α →−∞.Thispropertyis
robust against the inclusion of (small) perturbations, that is, degrees of freedom
describing density fluctuations or gravitational waves (cf. Section 8.2). Denoting