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However convincing they may sound, such a priori arguments
can lead us astray. Voltaire's reasoning is Newtonian:
nature always conforms to itself. But, curiously, today we find
ourselves in the strange world mocked by Voltaire; we are astonished
to discover the qualitative diversity presented by nature.
It is not surprising that people have vacillated between the
two extremes; between the elimination of irreversibility from
physics, advocated by Einstein, as we have mentioned,2 and,
on the contrary, the emphasis on the importance of irreversibility,
as in Whitehead's concept of process. There can be no doubt
that irreversibility exists on the macroscopic level and has an
important constructive role, as we have shown in Chapters V
and VI . Therefore there must be something in the microscopic
world of which macroscopic irreversibility is the manifestation.
The microscopic theory has to account for two closely
related elements. First of all, we must follow Boltzmann in
attempting to construct a microscopic model for entropy
(Boltzmann's .J{ fu nction) that changes uniformly in time. This
change has to define our arrow of time. The increase of entropy
for isolated systems has to express the aging of the system.
Often we may have an arrow of time without being able to
associate entropy with the type of processes considered. Popper
gives a simple example of a system presenting a unidirectional
process and therefore an arrow of time.
Suppose a film is taken of a large surface of water initially
at rest into which a stone is dropped. The reversed
film will show contracting, circular waves of increasing
amplitude. Moreover, immediately behind the highest
wave crest, a circular region of undisturbed water will
close in towards the centre. This cannot be regarded as a
possible classical process. It would demand a vast number
of distant coherent generators of waves the coordination
of which, to be explicable, would have to be shown,
in the film, as originating from one centre. This, however,
raises precisely the same difficulty again, if we try to reverse
the amended film. 3