extraphysical "makers").
Figure 5 shows two time slices in the now well-known Bénard
experiment which consists of a viscous liquid held in a circular
dish between a uniform heat source below and the cooler temperature
of the air above. The difference in temperatures constitutes
a potential (or thermodynamic force F) the magnitude of which
is determined by the extent of the difference. When F is below
a critical threshold the system is in the disordered or linear
"Boltzmann regime", and a flow of heat is produced
from source to sink (entropy is produced) as a result of the
disordered collisions of the molecules (conduction) and the macroscopic
state appears smooth and homogeneous (left). As soon as F is
increased beyond a critical threshold, however, the symmetry
of the disordered regime is broken and order spontaneously emerges
as hundreds of millions of molecules begin moving collectively
together (right).
According to Boltzmann's
hypothesis of the second law such states are infinitely improbable,
but here, on the contrary, order emerges with a probability of
one, that is every time F is increased above the critical
threshold. What is the critical threshold? It is simply the minimum
value of F that will support the ordered state. Just as
the empirical record suggests that life on Earth, the global
ordering of the planet, occurred as soon as minimum magnitudes
of critical thresholds were crossed (e.g., an Earth cool enough
so its oceans would not evaporate in the origin of life, or the
levels of order that |
apparently arose as soon as minimal levels
of atmospheric oxygen were reached), so too here spontaneous
ordering occurs as soon as it gets the chance. But what is the
physical basis for such opportunistic ordering?
Return to the Balance Equation of
the Second Law
Returning to the balance equation of the
second law provides the first clue. The intrinsic space-time
dimensions for any system or process are defined by the persistence
of its component relations. Since in the disordered regime there
are no component relations persisting over greater distances
or longer times than the distances and times between collisions
(mean free path distances and relaxation times) it is easy to
see that the production of order from disorder thus increases
the space-time dimensions of a system. In the Bénard case,
for example, the intrinsic space-time dimensions of the disordered
regime are on the order of 10-8 centimeters and 10-15 seconds
respectively. In stark contrast, the new space-time level defined
by the coordinated motion of the components in the ordered regime
is measured in whole centimeters and seconds, an increase of
many orders of magnitude. Bertalanffy and Schröedinger emphasized
that as long as an autocatakinetic system produces entropy fast
enough to compensate for its development and maintenance away
from equilibrium (its own internal entropy reduction) it is permitted
to exist. With the understanding of the relation between intrinsic
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