The nature of the gapless excitations in a quantum many-body system is an emergent property, including underlying order. A simple "classical" example is that the sound waves in crystals result from the breaking of continuous translational symmetry. More profound examples are the Goldstone modes associated with spontaneously broken symmetry and the edge states associated with topological order in fractional quantum Hall states. Furthermore, the presence and gapless character of these excitations are particularly robust against perturbations and variations in microscopic details. This property is dubbed by Laughlin and Pines, a quantum protectorate.
Ross. H. McKensie, The Dirac cone in graphene is emergent 15/04/2013
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 detailsand 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.
... wonderful (and provocative) PNAS article, The Theory of Everything, Laughlin and Pines introduced the term protectorate to describe the insensitivity of higher level laws (organising principles) to the details of lower level laws. For example, the laws of thermodynamics are the same regardless of whether the microscopic dynamics of the constituent particles is quantum or classical. Universality in the theory of continuous phase transitions is another important example. Near the liquid-vapour critical point the critical exponents are independent of the chemical composition of the system or of the interatomic forces involved.
Notice : This is another tentative answer to adress (better than in my former one) the naturalness problem asked by the present stalemate for traditional perturbatively renormalisable Susy-Yang-Mill-Higgs quantum field theories in the LHC phenomenology. It can be formulated briefly as an "educated" guess blending some condensed matter physics intuition and non-commutative vision :
The fine structure of spacetime at the electroweak scale could act as a non-commutative protectorate or ensure a non-commutative asymptotic safety mechanism, something that protects the low mass of the Higgs from quantum fluctuations up to the Planck scale.
That would explain why SUSY predictions in the conceptual framework of perturbatively renormalisable quantum field theory fail because probing the physics of the Higgs to go beyond the Standard Model probably requires to go over much higher energies just like analysing sound waves with the effective theory of hydrodynamics cannot help to uncover the atomic structure of matter...
Moreover progress in the understanding of how non-commutativity could modify the renormalization group flow for the Higgs couplings is already underway.
Then maybe once the proper non-commutative constraint is correctly implemented in physics model-building, one will witness a new increase in "the price of shares of stock in Quantum Field Theory" to quote Weinberg. After all, the Standard Model emerged in the 70s taking seriously non-Abelian gauge groups envisioned in the 50s thanks to the conceptual understanding of asymptotic freedom in chromodynamics, I remind that this last part is still conjectural today! Then it would be quite natural to go beyond the Standard Model in the 2010s thanks to some new non-commutative algebraic ideas developped in the 90s that explain the quantum spontaneous breaking of electroweak symmetry and could be taken seriously modulo some kind of asymptotic safety scenario...
Of course this kind of hypothetical heuristics and epistemological retro-analysis is definitely not a technical answer and I could understand that such a speculation is not suited for Physics SE (I am ready to remove it if required). Adding an "epistemology" tag would have helped but there were allready 5 of them.
Impact of the Higgs discoveryThe minimal SM Higgs: the simplest possible form of spontaneous electroweak symmetry breaking.What was considered just as a toy model, a temporary addendum to the gauge part of the SM, is now promoted to the real thing!The only known example in physics of a fundamental, weakly coupled, scalar particle with VEV.The absence of accompanying new physics puts the issue of the relevance of our concept of naturalness at the forefront.The naturalness argument for new physics at the EW scale is not a theorem but a conceptual demand.... the picture suggested by the last 20 years of data is simple and clear:Take the Standard Model, extended to include Majorana neutrinos, as the theory valid up to very high energy ...Possibly Nature has a way, hidden to us, to realize a deeper form of naturalness at a more fundamental level
Guido Altarelli, Theoretical concluding talk at Higgs' Hunting Conference, 27/06/2013