Ordering A Theory Of Everything

By Vlatko Vedral
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 and relativity.

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 information.

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 survives.
>>> arxiv.org/abs/1107.6029

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.
>>> arxiv.org/abs/1205.6894

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.

Time 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.

Gravity

Speculative research suggests that gravity might be entropy in disguise. In 1995, Ted Jacobson related gravity and entropy using two disputed ideas:

1 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 experimentally.

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.