Knocking on Heaven's Door - Lisa Randall [15]
One familiar example of an effective theory might be thermodynamics, which tells us how refrigerators or engines work and was developed long before atomic or quantum theory. The thermodynamic state of a system is well characterized by its pressure, temperature, and volume. Though we know that fundamentally the system consists of a gas of atoms and molecules—with much more detailed structure than the preceding three quantities can possibly describe—for many purposes we can concentrate on these three quantities to characterize the system’s readily observable behavior.
Temperature, pressure, and volume are real quantities that can be measured. The theory behind their relationships is fully developed and can be used to make successful predictions. The effective theory of a gas makes no mention of the underlying molecular structure. (See Figure 4.) The behavior of those underlying elements determines temperature and pressure, but scientists happily used these quantities to do calculations even before atoms or molecules were discovered.
[ FIGURE 4 ] Pressure and temperature can be understood at a more fundamental level in terms of the physical properties of individual molecules.
Once the fundamental theory is understood, we can relate temperature and pressure to properties of the underlying atoms and also understand when the thermodynamic description should break down. But we can still use thermodynamics for a wide variety of predictions. In fact, many phenomena are only understood from a thermodynamic point of view, since without huge computing power and memory, well beyond what exists, we can’t track the paths of all the individual atoms. The effective theory is the only way at this point to understand some important physical phenomena that are pertinent to solid and liquid condensed matter.
This example teaches us another critical aspect of effective theories. We sometimes treat “fundamental” as a relative term. From the perspective of thermodynamics, the atomic and molecular description is fundamental. But from a particle physics description that details the quarks and electrons inside the atoms, the atom is composite—made up of smaller elements. Its use from a particle physics perspective is as an effective theory.
This description of the clean developmental progression in science from the well understood to regimes at the frontier of knowledge applies best to fields such as physics and cosmology, where we have a clear understanding of the functional units and their relationships. Effective theories won’t necessarily work for newer fields such as systems biology, where the relationships between activities at the molecular and more macroscopic levels, as well as the relevant feedback mechanisms, are yet to be fully understood.
Nonetheless, the effective theory idea applies in a broad range of scientific contexts. The mathematical equations that govern the evolution of species won’t change in response to new physics results, as I discussed with the mathematical biologist Martin Nowak in response to a question he had asked. He and his colleagues can characterize the parameters independently of any more fundamental description. They might ultimately relate to more basic quantities—physical or otherwise—but that doesn’t change the equations that mathematical biologists use to evolve the behavior of populations over time.
For particle physicists, effective theories are essential. We isolate simple systems at different scales and relate them to each other. In fact, the very invisibility of underlying