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**These are excerpts and elaborations from my book "The Nature of Consciousness"**

The single
biggest change in scientific thinking may have nothing to do with Relativity
and Quantum theories: it may well be the discovery that some processes are not
symmetric in time. Before the discovery of the second law of Thermodynamics,
all laws were symmetric in time, and change could always be bi-directional. Any
formula had an equal sign that meant one can switch the two sides at will. We
could always replay the history of the universe backwards. Entropy changed all
that. Entropy was
"discovered" around 1850 by the German physicist Rudolf Clausius in the process of revising the laws proposed by the French
engineer Sadi Carnot, that would
become the foundation of Thermodynamics. The first law of Thermodynamics is
basically the law of conservation of energy: energy can never be created or
destroyed, it can only be transformed. The second law (originally formulated by
William Thompson “Kelvin” in 1852) states that any transformation has an energetic
cost: this "cost" of transforming energy Clausius called "entropy" (which is numerically obtained by
dividing heat by temperature). Natural processes generate entropy. Entropy
explains why heat flows spontaneously from hot to cold bodies, but the opposite
never occurs: “useful” energy can be lost in entropy, not viceversa. There can never
be an isolated process that results in a transfer of energy from a cold body to
a hotter body: it is just a feature of our universe. In a sense, entropy
measures how useful energy is. Before entropy is created, all energy is useful
(e.g., the explosion in the combustion engine). Afterwards, some energy has
become largely useless (e.g. heat, noise, motion). Work is possible only when there is a difference in energy concentration because energy can only spontaneously move from higher concentration to lower concentration (e.g. from higher temperature to lower temperature). Work de facto reduces that difference. Eventually that difference does not exist anymore and work is no longer possible: the system has reached the state of equilibrium. The total amount of energy in the universe is constant: it has always been what it is and will always be what it is. However, that energy is changing form, from usable to unusable. We can use less and less of the energy of the universe. The first law
talks about the quantity of energy, while the second law talks about the
quality of such energy. Energy is always conserved, but something happens to it
that causes it to “deteriorate”. Entropy measures the amount of energy that has
deteriorated (is not available anymore for further work). Clausius summarized the situation like this: the energy of the universe is
constant, the entropy of the universe is increasing. In the 1870s, the German
physicist Ludwig von Boltzmann tried to deduce entropy
from the motion of gas particles, i.e. from dynamic laws that are reversible in
nature. Basically, Boltzmann tried to prove that entropy (and therefore
irreversibility) is an illusion, that matter at the microscopic level is
fundamentally reversible. Convinced that bodies are made of a large number of
elementary particles, Boltzmann used statistics and probability theory to
summarize their behavior, since it would be impossible to describe each
particle’s motion and their innumerable interactions. He noticed that many
different configurations (microstates) of those particles could lead to the
same external appearance (macrostate) of the system as a whole. Boltzmann ended up with a statistical definition of entropy to characterize
the fact that many different microscopic states of a system result in the same
macroscopic state: the entropy of a macrostate is the logarithm of the number
of microstates that can implement that macrostate. Intuitively, the law of
entropy originates from a statistical trend: a system tends to evolve towards
the macrostates with high entropy, i.e. macrostates that correspond to large
numbers of microstates; basically from rare configurations towards more likely
configurations. Boltzmann’s implicit assumption was that
every microstate is equally probable. The other implicit assumption of the
second law is that the universe started in a state of low entropy. That creates
the fundamental asymmetry that we recognize as the arrow of time: entropy tends
to increase because it is a lot easier to increase than decrease, and that is
because the beginning of the story was at low entropy. For example, we assume a
low-entropy past when we trust our memories of it: our memories (including
photographs, videos, diaries) could have been created in a myriad of ways, but
the low-entropy explanation is that they reflect what really happened. Boltzmann’s definition emphasized that
entropy turns out to be also a measure of “disorder” in a system: an ordered
system has fewer microstates corresponding to a given macrostate. The second law of Thermodynamics is an inequality:
it states that entropy can never decrease. Indirectly, this law states that
transformation processes cannot be run backward, cannot be
"undone". Young people can age, but old people cannot rejuvenate. Buildings do not
improve over the years: they decay. Scrambled eggs cannot be unscrambled and
dissolved sugar cubes cannot be recomposed. The universe must evolve in the
direction of higher and higher entropy.
Some things are irreversible. Newton’s equations are symmetric in
time, which means that theoretically the same process can run backwards. It is
the second law of Thermodynamics which makes it impossible to go back in time,
that introduces an “arrow” of time. The universe as
a whole is proceeding towards its unavoidable fate: the “heat death”, i.e. the
state of maximum entropy, in which no heat flow is possible, which means that
temperature is constant everywhere, which means that there is no energy
available to produce more heat, which means that all energy in the universe is
in the form of heat. (An escape from the heat death would be possible if the
energy in the universe were infinite). Scientists were
(and still are) puzzled by the fact that irreversibility (the law of entropy)
had been deduced from reversibility (basically, Newton's laws). Mechanical phenomena
tend to be reversible in time, whereas thermodynamic phenomena tend to be
irreversible in time. Since a thermodynamic phenomenon is made of many
mechanical phenomena, the paradox is how can an irreversible process arise from
many reversible processes? It is weird that irreversibility should arise from
the behavior of molecules which, if taken individually, obey physical laws that
are reversible. We can keep track of the motion of each single particle in a
gas, and then undo it. But we cannot undo the macroscopic consequence of the
motion of thousands of such particles in a gas. If one filmed
the behavior of each particle of a gas as the gas moves from non-equilibrium to
equilibrium, and then played the film backwards, the film would be perfectly
consistent with the laws of Mechanics. In practice, though, systems never
spontaneously move from equilibrium to non-equilibrium: the film is perfectly
feasible, but in practice it is never made. The only reason
one could find was probabilistic, not mechanical: the probability of
low-entropy macrostates is smaller, by definition, than the probability of
high-entropy macrostates, so the universe tends to proceed towards higher
entropy. Thus the second law seems to express the tendency of systems to
transition from less probable states (states that can be realized by few
microstates) to more probable states (states that can be realized by many
microstates). Basically, there are more ways to be disorderly than to be
orderly. And one can
rephrase the same idea in terms of equilibrium: since equilibrium states are
states that correspond to the maximum number of microstates, it is unlikely
that a system moves to a state of non-equilibrium, and likely that it moves to
a state of equilibrium. Back to the beginning of the chapter "The New Physics" | Back to the index of all chapters |