Physics and Computation

2009

September 7-11th 2009

Ponta-Delgada, Azores, Portugal

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## Talk from Pablo Arrighi.

### Title:

The quest towards universal physical phenomena.

### Abstract:

In theoretical physics one often draws a distinction between a mechanics and the actual physical phenomena which are expressed in that mechanics. Usually a mechanics would take the form of a mathematical theory together with a set of postulates, which serve as a framework in order to describe all of the allowed physical phenomena in the given mechanics.

In theoretical computer science one often draws a distinction between a model of computation and the computational phenomena which are expressed in that model of computation. Usually a model of computation would take the form of a mathematical theory together with a set of axioms, which serve as a framework in order to describe all of the allowed computational phenomena in the given model of computation.

Les us dig further into this analogy between mechanics and models of computation on the one hand, and between physical phenomena and computational phenomena on the other hand, by means of an example. As computer scientists our canonical example of a mechanics / model of computation is the definition of a Turing Machine. Then the physical / computational phenomena would be the instances of the definition. A remarkable and well-known fact is that in this mechanics / model of computation there a universal physical / computational phenomenon; i.e. there a physical / computational phenomenon which is capable of simulating all others.

We begin to investigate the question whether other mechanics, which are more relevant to physics, admit such a universal physical phenomena. 1/ We explain why it is important to port the computer science concept of universality into theoretical physics. 2/ We discuss how the notion of simulation has to be modified in order to be relevant in physics. 3/ We provide some concrete examples of universal physical phenomena for some simplified but non-trivial version of quantum mechanics.