What is a fundamental theory? As we go to smaller and smaller distances and higher energies we keep finding new entities: atoms, electrons, nuclei, neutrons, protons, quarks, gluons, ...When will it stop?
If we look at a theory, such as a quantum field theory, at a particular energy and length scale, there may be hints that something is going on, such as the existence of new entities, at higher energies. One way to approach this problem is through the renormalisation group and to look at how coupling constants behave as the energy increases. If they start to blow up (diverge) is that a hint of something? But, this requires starting with a renormalisable theory...
An alternative approach is to start with an effective theory that one assumes [hypothesises] is valid at some limited energy scale. This goes against a previous dogma that one should only study renormalisable theories. Amongst elementary particle theorists, led by Steven Weinberg, there was a significant shift in perspective in the 1970s.
In a paper published in 2016, Effective field theory, past and future, Steven Weinberg reflected on how he changed his mind about renormalisability being a fundamental requirement for quantum field theories and how he came to the view that the Standard Model should be viewed as an effective field theory. Here are some quotes from the article. He first describes how in the 1960s he developed a field theory to describe the interactions of nucleons and pions.
"During this whole period, effective field theories appeared as only a device for more easily reproducing the results of current algebra. It was difficult to take them seriously as dynamical theories, because the derivative couplings that made them useful in the lowest order of perturbation theory also made them nonrenormalizable, thus apparently closing off the possibility of using these theories in higher order.
My thinking about this began to change in 1976. I was invited to give a series of lectures at Erice that summer, and took the opportunity to learn the theory of critical phenomena by giving lectures about it. In preparing these lectures, I was struck by Kenneth Wilson’s device of “integrating out” short-distance degrees of freedom by introducing a variable ultraviolet cutoff, ...
Non-renormalizable theories, I realized, are just as renormalizable as renormalizable theories.
For me in 1979, the answer involved a radical reconsideration of the nature of quantum field theory.
The advent of effective field theories generated changes in point of view and suggested new techniques of calculation that propagated out to numerous areas of physics, some quite far removed from particle physics. Notable here is the use of the power-counting arguments of effective field theory to justify the approximations made in the BCS theory of superconductivity. Instead of counting powers of small momenta, one must count powers of the departures of momenta from the Fermi surface. Also, general features of theories of inflation have been clarified by re-casting these theories as effective field theories of the inflaton and gravitational fields.
Perhaps the most important lesson from chiral dynamics was that we should keep an open mind about renormalizability. The renormalizable Standard Model of elementary particles may itself be just the first term in an effective field theory that contains every possible interaction allowed by Lorentz invariance and the SU (3) × SU (2) × U (1) gauge symmetry, only with the non-renormalizable terms suppressed by negative powers of some very large mass M...
... we should not despair of applying quantum field theory to gravitation just because there is no renormalizable theory of the metric tensor that is invariant under general coordinate transformations. It increasingly seems apparent that the Einstein–Hilbert Lagrangian √gR is just the least suppressed term in the Lagrangian of an effective field theory containing every possible generally covariant function of the metric and its derivatives...
it is usually assumed that in the quantum theory of gravitation, when Λ reaches some very high energy, of the order of 10^15 to 10^18 GeV, the appropriate degrees of freedom are no longer the metric and the Standard Model fields, but something very different, perhaps strings...
But maybe not..."
In 2021 Weinberg gave a talk, with a similar point of view, which inaugurated an international seminar series [online during covid-19].
In response to that talk, Peter Woit has a blog post where he objects to Weinberg's point of view that the Standard Model is "just" an effective theory, only valid at low energies.
Reviews of Modern Physics recently published a review that discussed how Weinberg's perspective is worked out in detail.
The standard model effective field theory at work
Gino Isidori, Felix Wilsch, and Daniel Wyler
The discussion above fits naturally with an emergentist perspective: reality is stratified. Effective theories at one strata may have singularities around boundaries between strata, and new entities emerge, both physically and theoretically, as one moves to the next higher or lower strata.
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