Thursday, 9 July 2009


Classical physics is a science upon which our belief in a deterministic,
time-reversible description of Nature is based. Classical physics does
not include any distinction between the past and the future. The
Universe is ruled by deterministic laws, yet the macroscopic world is
not reversible. This is known as Epicurus' clinamen, the dilemma of
being and becoming, the idea that some element of chance is needed to
account for the deviation of material motion from rigid predetermined
The astonishing success of simple physical principles and mathematical
rules in explaining large parts of Nature is not something obvious from
our everyday experience. On casual inspection, Nature seems extremely
complex and random. There are few natural phenomenon which display
the precise sort of regularity that might hint of an underlying order.
Where trends and rhythms are apparent, they are usually of an
approximate and qualitative form. How are we to reconcile these
seemingly random acts with the supposed underlying lawfulness of the

For example, consider falling objects. Galileo realized that all bodies
accelerate at the same rate regardless of their size or mass. Everyday
experience tells you differently because a feather falls slower than a
cannonball. Galileo's genius lay in spotting that the differences that
occur in the everyday world are in incidental complication (in this case,
air friction) and are irrelevant to the real underlying properties (that is,
gravity). He was able to abstract from the complexity of real-life
situations the simplicity of an idealized law of gravity. Reversible
processes appear to be idealizations of real processes in Nature.
Probability-based interpretations make the macroscopic character of our
observations responsible for the irreversibility that we observe. If we
could follow an individual molecule we would see a time reversible
system in which the each molecule follows the laws of Newtonian
physics. Because we can only describe the number of molecules in each
compartment, we conclude that the system evolves towards equilibrium.
Is irreversibility merely a consequence of the approximate macroscopic
character of our observations? Is it due to our own ignorance of all the
positions and velocities?
Irreversibility leads to both order and disorder. Nonequilibrium leads to
concepts such as self-organization and dissipative structures
(Spatiotemporal structures that appear in far-from-equilibrium
conditions, such as oscillating chemical reactions or regular spatial
structures, like snowflakes). Objects far from equilibrium are highly
organized thanks to temporal, irreversible, nonequilibrium processes
(like a pendulum).

The behavior of complex systems is not truly random, it is just that the
final state is so sensitive to the initial conditions that it is impossible to
predict the future behavior without infinite knowledge of all the motions
and energy (i.e. a butterfly in South America influences storms in the
North Atlantic).

Although this is `just' a mathematical game, there are many examples of
the same shape and complex behavior occurring in Nature.

Individual descriptions are called trajectories, statistical descriptions of
groups are called ensembles. Individual particles are highly
deterministic, trajectories are fixed. Yet ensembles of particles follow
probable patterns and are uncertain. Does this come from ignorance of
all the trajectories or something deeper in the laws of Nature? Any
predictive computation will necessarily contain some input errors
because we cannot measure physical quantities to unlimited precision.
Note that relative probabilities evolve in a deterministic manner. A
statistical theory can remain deterministic. However, macroscopic
irreversibility is the manifestation of the randomness of probabilistic
processes on a microscopic scale. Success of reductionism was based on
the fact that most simple physical systems are linear, the whole is the
sum of the parts. Complexity arrives in nonlinear systems.

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