The Physical Basis of The Direction of Time (The Frontiers ...

3.5 Cosmic Probabilities and History 83
This probability argument requires that the left inequality (3.64) is valid
not only with respect to physical (local) entropy, but also for an appropriate
ensemble entropy that takes into account all those non-local correlations
which represent the convincing consistency of documents. Their existence in
a historical universe is related to Lewis’ ‘overdetermination of the past’ (see
footnote 1 of Chap. 2). 13 While the improbability of the present solar system,
for example, as having occurred in a chance fluctuation would be ‘moderate’
compared to that for a corresponding whole universe, the former would then
have to contain consistent though unexplainable documents about the latter.
David Hume’s fundamental insight that we can never predict anything
with certainty (not even that the sun will rise again) applies to the past as
well – even if we did not question the general validity of the dynamical laws.
Strictly speaking, we cannot be sure about the existence of any facts that we
seem to remember. The reliability of memories and documents is in principle
as doubtful as that of predictions; only the subjective local present cannot be
questioned. Hence, even Kant’s premise that we are making experience cannot
be taken for granted. Not what has been observed, only our (perhaps deceiving)
‘memory’ that we are aware of now is beyond doubt. Saint Augustine
concluded in a similar way in his Confessiones that the past and the future
‘exist’ only in the present – namely as memory and expectation ‘in the soul’.
This long-standing philosophical debate seems to be deeply affected (though
not overcome) by thermodynamical and statistical considerations.
However, Saint Augustine’s epistemologically rigorous concept of reality
is obviously too restrictive for the construction of a ‘world model’, which
must in principle always remain hypothetical (Poincaré 1902, Vaihinger 1911).
The probabilistic objection raised above, even if formally correct, will thus
hardly be accepted as demonstrating that causality is an illusion, based on an
accident. Einstein’s probabilities (3.56) for the occurrence of non-equilibrium
states α, motivated by the statistical interpretation of entropy, can indeed
be justified only for those macroscopic properties α which have a chance of
occurring repeatedly within relevant times (‘quasi-ergodically’) on a generic
trajectory – that is, for properties which are not robust on relevant timescales
(hence not for stable macroscopic properties).
Physical cosmology can fortunately be derived from the more economical
hypothesis of a universe of finite age. A homogeneous (structureless) low entropy
initial state appears more acceptable in this sense than a complex state
with a similarly low value of entropy. Probabilities for later states can then
be calculated as probabilities for histories (products of successive conditioned
probabilities). For example, the folding of protein chains is usually calculated
along trajectories of monotonically increasing entropy (according to a master
equation). Final configurations not accessible through such histories would
thus be excluded even when possessing relatively large entropy. (Quantum
13 States containing consistent (though possibly deceiving) documents were called
time-capsules by Barbour (1994a) – see Sect. 6.2.2.