Kiefer C. Quantum gravity

320 INTERPRETATION
Although most of the fundamental laws of nature do not distinguish between
past and future, there are many classes of phenomena which exhibit an arrow of
time. This means that their time-reversed version is, under ordinary conditions,
never observed. The most important ones are the following:
• Radiation arrow (advanced versus retarded radiation);
• Second Law of Thermodynamics (increase of entropy);
• Quantum theory (measurement process and emergence of classical properties);
• Gravitational phenomena (expansion of the universe and emergence of
structure by gravitational condensation).
The expansion of the universe is distinguished because it does not refer to a
class of phenomena; it is a single process. It has, therefore, been suggested that
it is the common root for all other arrows of time—the ‘master arrow’. We shall
see in the course of our discussion that this seems indeed to be the case. But
first we shall consider in more detail the various arrows of time.
The radiation arrow is distinguished by the fact that fields interacting with
local sources are usually described by retarded solutions, which in general lead to
a damping of the source. Advanced solutions are excluded. They would describe
the reversed process, during which the field propagates coherently towards its
source, leading to its excitation instead of damping. This holds, in fact, for all
wave phenomena. In electrodynamics, a solution of Maxwell’s equations can be
described by
A µ = source term plus boundary term
= A µ ret + A µ in
= A µ adv + Aµ out ,
where A µ is the vector potential. The important question is then why the observed
phenomena obey A µ ≈ A µ ret or, in other words, why
A µ in ≈ 0 (10.42)
holds instead of A µ out ≈ 0. Equation (10.42) is called a ‘Sommerfeld radiation
condition’. One believes that the radiation arrow can be traced back to thermodynamics:
due to the absorption properties of the material which constitutes
the walls of the laboratory in which electrodynamic experiments are being performed,
ingoing fields will be absorbed within a very short time and (10.42) will
be fulfilled. For the thermal properties of absorbers, the Second Law of Thermodynamics
(see below) is responsible.
The condition (10.42) also seems to hold for the universe as a whole (‘darkness
of the night sky’). The so-called Olbers’ paradox can be solved by noting that
the universe is, in fact, not static, but has a finite age and is much too young
to have enough stars for a bright night sky. This is, of course, not yet sufficient