Quantum theory and information theory (again)

Monday, 7 April 2014
In a previous post we already talked about the relationship between quantum theory and information theory. In it, we saw how Lluís Masanes and collaborators derived quantum mechanics from a few postulates based on the properties that a unit of information should have. 

Today, I came across with two different articles that explore this relationship. In the first one, Stephanie Wehner and Esther Hanggi from the National University of Singapore’s Center for Quantum Technology, showed us that the uncertainty principle is intimately related to the second law of thermodynamics. (Note that thermodynamics are intrinsically related to information theory.) In particular, they saw how by loosening the uncertainty principle, they got more useful energy/information out of the system than they put into it thus violating the second law of thermodynamics. Since the violation of the second law is incompatible with the physics we know, this means that our ability to calculate the state of a particle with infinite accuracy (the uncertainty principle) is forbidden by the second law. Note that thermodynamics is related to the macroscopic state of a system, whereas quantum mechanics is related to its microstates. 

The second article I found interesting states that macroscopic systems cannot be quantum in nature, that is, we do not observe a superposition of states in the macroscopic world, but one only state. The author, Bolotin, states that the solution of the Schrodinger equation is just unsolvable for macroscopic objects. Bolotin says that the problem of solving Schrodinger equation is NP hard, and he shows, making a few calculations, that the computation time to solve this equation for a macroscopic state will either exceed the time of the universe, or the computation speed should be higher than the Plank time, where no state makes sense.

So the question here is, how does the universe compute its state? How does it go from quantum to macroscopic? 

I think the answer to that question goes again to the field of computational mechanics. In their article, Shalizi and Moore explain how Nature can be described in different levels of detail. They show how macroscopic states can have a higher predictability efficiency than the dynamics of their corresponding microstates. It all falls to information theory again. It their article, they define emergency of one description from the other, that is, a coarse grained version of the microstates, but with higher prediction efficiency than the other. 

It seems to me that the universe describes itself in only one way, it is only the way we look at it that separates between the different levels of description. As Shalizi and Moore put it: “for every question we ask It, Nature has a definite answer; but Nature has no preferred questions.”

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