Today's historical referendum in Scotland gives me the opportunity to talk about something I have in mind since I came back from the U.S. earlier this year. It's actually a very trivial concept that originates from the fact that:
When outside Europe, I feel European. When within Europe, I feel Southern European/ Mediterranean. When in Southern Europe, I feel Italian and, finally, when in Italy I definitely feel Sardinian.
There is actually no contradiction in this Matrioska-like sense of belonging and I'm sure most people who happen to live abroad (which is already a rather subjective concept....) share the same feeling.
Anyway, this is interesting because in physics there is a much deeper and far-reaching concept that is (vaguely) related to the one above: that of the
running couplings. In a quantum field theory, the coupling "constants" that define the strength of the couplings among quantum fields are not really constant, but actually
their values depend on the energy scales.
As an example, take the most famous coupling constant, Newton's gravitational constant G that appears in the gravitational force law
F= G*mass1*mass2 / distance^2
which simply means that the intensity of the gravitational force between two masses (mass1 and mass2) is proportional to the masses and inversely proportional to the square of the distance. The proportionality factor is nothing but what we use to call Newton's constant and its value is G~6.673×10^{-11} N·(m/kg)^2. Now, Newtonian gravity is a classical theory and there is no such thing like a running G (although the situation might be different in alternative theories of gravity, such as scalar-tensor theories, but this is another story...). Indeed, G is a constant no matter how close the two masses are or how massive the objects are. In a quantum field theory, G would depend on the energy involved, for example on the typical distance of the interaction.
If you think about that, this is a beautiful and elegant concept: it teaches us there's no such thing like "the ultimate theory", but each theory (if consistently quantized) would be different at different energy scales. For example, a theory like electromagnetism (or QED in its quantum version) becomes more strongly coupled as the energy increases. The QED coupling constant (the fine structure constant α) is about α ≈ 1/137 at low energies, whereas one measures α ≈ 1/127 at the scale of the Z boson, about 90 GeV. A theory like quantum chromodynamics (QCD) behaves exactly in the opposite way and it becomes
more weakly coupled at high energies. This phenomenon is called
asymptotic freedom (because the interaction between particles becomes zero at infinite energy) and its discovery (by Frank Wilczek, David Gross and David Politzer) was worth the Nobel prize in 2004.
What does this have to do with Scotland? (if anything...) The idea that can be borrowed from particle physics is that of a "running citizenship". In other words, each person changes her/his sense of belonging to some country/community accordingly to the "characteristic scale of the problem". It's something that European people are already experiencing given that economy in Europe is mainly governed on European scales, whereas local regulations are governed by state laws. Something similar also happens for federal countries, although the idea of running citizenship that i'm trying to describe has more to do with sense of belonging than with politics (politics often tries to change the sense of belonging and to tailor it accordingly, though).
In physics, the theory that studies the running couplings is called
renormalization group and the running is usually called "
flow". In most theories, the coupling either grows or decreases with energy, but for some special theories it asymptotes a constant value, a "fixed point".
As for the running citizenship, my impression is that we better try to have a fixed point for that, because the other two cases are quite catastrophic. The analog of a theory like QED would be a sense of citizenship that becomes smaller and smaller as smaller scales are approached, eventually terminating in individuals that do not belong any community. This would imply a sort of total isolation for each individual. The other case would be funny: an individual would become more and more aware of the global nature of Mankind and would feel like more and more part of the entire Universe as smaller scales are approached (this sounds like a nice outcome but perhaps a bit too Hippie for these times....). The most natural solution would be approaching a limit, a minimum size of the community (which we can perhaps identify with the family or hopefully with something larger than that) and then having each person feeling as a part of a larger community dependending on the context and the environment.
In which category does the running citizenship flow of the Scottish people fall? We shall discover this quite soon and the outcome has probably very little to do with physics.....
