This is how GLO define emergence on page 18 of their March 2009 paper:(adsbygoogle = window.adsbygoogle || []).push({});

http://arxiv.org/abs/0903.3475

Let us ﬁrst of all clarify what we mean by emergence. We call “emergent” some degrees of freedom which are only deﬁned ina given regime, and therein terms ofmore fundamental degrees of freedom. For example, emergent degrees of freedom can be perturbations around some given vacuum state, like in our GFT results, or collective degrees of freedom. In general, the classical theories for these emergent degrees of freedom only give eﬀective theories upon quantization, in other words theirquantum counterpart would be meaningful only in a limitedregime. A complete quantization procedure can therefore take place only on the fundamental degrees of freedom. A symmetry is called “emergent” if it applies to emergent degrees of freedom only and thus is valid only in the same limited regime in which they can be consistently deﬁned. In general, the emergent symmetry is not related to nor part of the symmetries of the fundamental system. Moreover, if the emergent symmetry is not already among the fundamental symmetries, then it is never exact but it is realized only approximately in the eﬀective theory.

To illustrate what they are saying, we could look at the idea of pressure. The pressure of the gas inside a box. Say there are 1000* helium atoms in the box and the classical system is described by 6000 degees of freedom, for each atom we have 3 position and 3 momentum.

The pressure would be "emergent" in the sense described here. It would only be meaningful in alimited regime---not too cold, not too dense, etc. If you quantized the pressure and got a quantum theory of the pressure it would not be meaningful except in a very limited way. And the pressure could, in principle, be expressedIN TERMS OFthe more basic 6000 degrees of freedom

*here 1000 stands for some much larger number

I think the pressure is an example of what GLO refer to as "collective degrees of freedom".

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# Is the GLO definition of emergence a good one? (Girelli Livine Oriti)

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