Ordering A Theory Of Everything
New Scientist, October 15, 2012
Edited by Andy Ross
The laws of thermodynamics are robust. Deep connections between
thermodynamics and information theory let us trace links to quantum theory
Thermodynamics is a theory about heat. The second law
says that unless you do something to stop it, heat will naturally flow from
hotter places to cooler places to even up any temperature differences it
finds. Such processes increase entropy by dissipating heat from places where
it is concentrated, and therefore more ordered, to cooler areas, where it is
not. The universe started in a state of low entropy, but once all heat is
dissipated it dies a heat death.
James Clerk Maxwell said a demon
might try to reduce the entropy of a system. Over a century later, Charles
Bennett used information theory to show that a demon who rearranges things
to lower the entropy of its environment must fill up and then reset its
memory, but dumping information back into the environment increases entropy,
preserving the second law.
Ludwig Boltzmann connected entropy and
probability: S = k log W, where S is entropy, k is Boltzmann's constant, and
log W is the logarithm of a number W of possible states of a system.
Probabilities are fundamentally different in classical and quantum physics.
In classical physics they are subjective quantities that constantly change
as our state of knowledge changes. An omniscient being would not need them.
But in quantum physics they arise from a uncertainty in the world. Quantum
probabilities are objective, and cannot be entirely removed by gaining more
Recently, together with Markus Müller and Oscar
Dahlsten, I have looked at what happens to thermodynamical relations in a
generalized class of probabilistic theories that embrace quantum theory and
much more besides. The relationship between information and entropy
The principles of thermodynamics involve
information theory. Thermodynamics is more fundamental than either quantum
physics or general relativity.
Esther Hänggi and Stephanie Wehner
have shown that a violation of the quantum uncertainty principle would imply
a violation of the second law of thermodynamics.
David Deutsch thinks we should construct
the whole of physics in thermodynamics. The idea is to generalize the logic
of the second law, that in the vicinity of any state of a physical system,
there are other states that cannot physically be reached without an exchange
of heat with the environment.
Can we rewrite physics by enumerating
possible and impossible processes in a given situation? We would observe the
prohibitions in nature, be it on decreasing entropy, getting energy from
nothing, traveling faster than light, or whatever. The correct theory of
physics is the one from which any deviation breaks those taboos.
flow is determined purely in terms of allowed and disallowed processes.
There is no problem of why the universe started in a state of low entropy.
Speculative research suggests that
gravity might be entropy in disguise. In 1995, Ted Jacobson related gravity
and entropy using two disputed ideas:
Jacob Bekenstein considered information falling into a black hole and
concluded that the black hole grew in area in proportion to the entropy that
fell in. Each tiny part of its surface would correspond to one bit of
information. This relationship is now called the holographic principle.
2 Paul Davies and William Unruh argued that
an accelerating body radiates heat. Accelerations far beyond what we can
achieve are required to generate enough radiation to test the idea
Putting these two ideas together with standard
theory, one can construct something like gravity, defined in terms of
entropy. Erik Verlinde has explored this too. Such theories say that when
bodies fall under gravity, the heating maximizes entropy.
AR This is deeply interesting. Entropy and
information are concepts I care about.