Why Our Current Best Theories of Physics Are not Fundamental

3.1 Quantum Field Theory and the Standard Model

We must distinguish between the framework of QFT, and particular QFTs (i.e., the theories formulated within this framework). To begin with, consider the framework of QFT; there are three inter-related reasons it is not considered fundamental.

The third reason the framework is not considered fundamental is that, although it utilises special relativity, it is not generally relativistic—it does not take into account our best theory of spacetime. Many physicists interpret this as the cause of the ill-definedness of the framework, as well as the singularities that appear within its theories. The modern interpretation of QFT holds that these singularities are artifacts of a non-fundamental framework, and that their appearance in our QFTs is the result of our ignorance of the more-fundamental physics at shorter-length scales beyond— physics that includes a quantum theory of gravity (discussed below). Thus, QFT is treated as an effective framework; i.e., as EFT.

Apart from being products of a non-fundamental framework, there are four reasons why QFTs are considered non-fundamental. (1) Some theories are believed to be non-fundamental because they are not UV-complete. Such theories, like quantum electrodynamics (QED, the quantum field theory of electromagnetism, describing light and the interactions of charged particles) break down at some short-distance scale, and are thus EFTs.^[32] (2) Many QFTs are supposedly non-fundamental because they are not exactly solvable (this is due to the ill-definedness of the framework), and so employ the approximation techniques of perturbation theory.

(3) Some QFTs are considered unnatural in a technical sense, that the large- distance theory sensitively depends on the choice of parameters in the more- fundamental (higher energy-scale) theory. This means that, if the high energy param­eters had been the slightest bit different from their actual values, the large distance physics would depart radically from what we observe. If there is such a sensitive dependence on their values, the parameters appear to have been fine tuned: Standing out—to the physicists’ eye—as “unnatural” and in need of explanation [8-10]. In practice, this idea of naturalness is seen as being satisfied when a theory does not contain dimensionless numbers that are either very large or very small. The standard model of particle physics is unnatural in this sense, due to one parameter: The Higgs particle mass. Physicists typically interpret this as meaning that if the Higgs particle mass had been slightly different at high energies, then our universe would likely not exist as we know it.^[33] The unnaturalness of the Higgs is thus thought to require explanation.

(4) Finally, the standard model of particle physics itself is non-unified. Although the standard model can be written as a single theory, it appears as a disjointed amalgam of separate (particle) fields, which drives many physicists to seek a more unified theory beyond [13]. This means that QFTs such as QCD that do not suffer any of the difficulties (1-3) at short-distances are still regarded as non-fundamental—not just because they are products of a non-fundamental framework, but because they are not part of a unified theory.

3.2 General Relativity

The reasons for not believing GR fundamental are the motivations for seeking quan­tum gravity (QG)—the as-yet-undiscovered theory needed to describe physics in the domains where both QFT and GR are thought to be necessary. These domains include, for instance, the Planck scale, which is the unfathomably small distance of 10^-32 cm. The theory is expected to replace GR, and describe the more-fundamental physics that “underlies” spacetime. Since QG is supposed to be a quantum theory of spacetime (i.e., a theory that takes into account both quantum theory and GR) one of its motivations is the desire for unification, as well as a desire for a single theory, rather than multiple frameworks. Another factor driving the search for QG is thepres- ence of (particular types of) singularities in GR such as black hole singularities, and the “big bang” singularity. These are “places” where the theory is formally (mathe­matically) ill-defined—apparently representing a breakdown of spacetime—and QG is supposed to shed light on these.

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