Emergent physics

I am trying to start up some research on the possibility that the Standard Model is emergent, in the sense that the true fundamental theory is constructed with other degrees of freedom, and the the fields of the SM only emerge at low energy. An analogy is how water waves can be treated as objects that satisfy a well defined wave equation, even though the fundamental physics at short scales are atoms bumping into each other, which is described by very different laws. Can photons similarly be the macroscopic description of a very different fundamental theories, where the idea of a photon is not even the right degrees of freedom?

One extreme of this idea has been espoused by H. B. Nielsen. His hypothesis is that at the most fundamental level, the theory is extremely random and chaotic, but that the only excitations that can propagate to long distances are ones that carry a symmetry like gauge fields. This would explain why we see simple gauge fields at low energy. Although this was suggested many years ago, it still in not very well developed.

One motivation for liking the emergent paradigm is because of our goal of having an ultimately finite fundamental theory. The divergences that appear in our field theories are not problems when working only at low energy. However, for a complete theory we would like to have it be finite. While it is possible that in our present theories the divergences are an artifact of the use of perturbation theory, this has not been able to be shown. Emergent theories can solve the finiteness issue by having fewer degrees of freedom at high energy. For example, spin systems and discrete space time can readily be finite quantum systems, while still leading to wave-like solutions at low energies and long distances.

String theory is one way to have a finite fundamental theory. It would be beautiful if it were right, but it nevertheless could be wrong and we don’t yet have experimental evidence either way. String theory solves the finiteness issue in a lovely but unexpected way. The divergences come from having too many degrees of freedom at high energy (i.e. from fields with large momenta, the phase space for which grows). As we go up in energy, string theory predicts more fields and more dimensions, both of which make the divergences more severe. However at the string scale all these fields come together with a special symmetry and instead of getting worse, all divergences disappear, with a lovely rich theory.

Emergence is a much more prosaic solution. Instead of having more fields at high energy, you have less. The extremely high momentum modes of the fields don’t exist. Done properly, this makes a finite theory. It is finiteness for pedestrians.

However, one should not underestimate the challenges to emergent theories. There are good arguments that even the idea of spacetime has to be emergent if this program is to succeed. However, a gazillion physicist-years have gone into developing the standard unification paradigm, while very little has been done on the emergent idea. So that makes it interesting to explore. In addition, there may be new phenomenological signals that occur which could be distinctive of emergent theories, and I have some ideas along these lines. So it may even experimentally feasible to test these ideas.

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