I write posts with titles such as "The Dirac cone in graphene is emergent" and "Holes are emergent quasi-particles?"
What do I mean?
To me emergent properties and phenomena have the following distinguishing characteristics.
1. They are collective phenomena resulting from the interactions between the constituent particles of the system and occur at different length/energy/time scales.
For example, superconductivity results from interactions between the electrons and ions in a solid and involves energy (temperature) scales much less than the underlying interaction energies.
2. They are qualitatively different from the properties of the constituent particles.
For example, individual gold atoms in a metallic crystal are not "shiny". One cannot speak about superfluidity of individual (or small groups of) atoms.
3. The property is difficult (or almost impossible) to anticipate or predict from a knowledge of the microscopic constituents and the associated laws. In particular, emergent properties and phenomena (especially new phases of matter) are almost always observed experimentally first before they are explained theoretically. They are often discovered by serendipity.
4. The property is weakly dependent on microscopic details and can occur in a chemically and structurally diverse range of systems.
For example, many different metals are "shiny". Adding impurities or changing the mass of the electron has little effect. One can observe superfluidity in liquid helium and in cold atomic gases.
5. Understanding and describing the property involves introducing new concepts and organising principles. For example, symmetry breaking and order parameters.
Some of these ideas are contained in an old post, "Illustrating emergence with an example from geometry," which generated some nice comments.
I thank Fei Zhan for asking me the question.
I welcome comments.
Do you think the characteristics above are reasonable criteria?
How might they be sharpened or modified?