Why physics still matters
Part 5 of 5: The physics of disorder
In the late 1980’s, the internal disagreements among physicists about the nature of their “mythological” language leapt into the public eye, via a series of debates about allocation of physics funding.1 One group firmly believed that the narrative about mechanistic reduction and laws of nature captures the deepest truth about the physical world, and that the ultimate aim of physics is to elucidate these fundamental laws. The other party insisted on the importance of constructing distinct systems of laws and concepts specific to different classes of phenomena. This side argued that the “distance” between the microscopic level of fundamental particles and the macroscopic level of relevant technological problems (at this time, chiefly the design of semiconductor materials) is too large for these laws to have much explanatory or predictive power on their own.
Princeton professor Philip Anderson was a leading proponent of the second view, forcefully arguing that theoretical research into the properties of crystalline materials is just as fundamental as investigations of the putative fundamental particles.2 The future of physics depends on taking the message of his essay seriously, recognizing just how “different” the “more” can be.
The kind of physics practiced by Anderson and his colleagues drew heavily from the conceptual apparatus of particle physics, replicating similar mathematical structures at a higher level of organization. In particular, both branches of physics rely heavily on symmetries to constrain the set of possible mathematical expressions for relationships among key quantities. The concept of energy also proves extremely powerful in further reducing the allowed form of the equations. No matter how complex the actual relationship among quantities might be, the approximate expression at low energy can usually be represented by a simple polynomial, leaving only a few parameters to be measured in experiments after imposing the symmetries. The crucial difference between particle physics and the physics of crystalline materials is that the former depends on the symmetries of the vacuum, which are continuous, while the latter is based on the symmetries of a crystal lattice, which are discrete. Anderson argued that the existence of these discrete symmetries — which are crucial for understanding how these materials behave — could never have been inferred or predicted from even the most exhaustive knowledge of the particles, and that studying the consequences of these new symmetries is therefore a truly fundamental activity of theoretical physics.
The most dynamic areas of 21st-century physics take Anderson’s thesis even further, venturing into areas where energy is irrelevant and where no obvious symmetries can be found. As isolated particles and perfect crystals are relatively rare in nature, this symmetry-free realm in fact encompasses most of the entities of our everyday experience. And since most of these objects are in contact with an atmosphere or a body of water that acts as a thermal reservoir, conservation of energy is frequently irrelevant as well.
The account of physics presented in these essays gives every reason for confidence in these new projects. If the purpose of physics is to establish stable patterns among measurable quantities through the careful and creative design of nomological machines, there is no reason why this procedure cannot be carried out in every domain of physical reality. And as we saw in the second installment, this is the only kind of science capable of producing the precise predictions required for establishing technological control in each domain. There are many encouraging developments from the past couple of decades that bolster this confidence, especially in the physics of living systems.
First of all, a growing number of physicists have dedicated themselves to devising adequate nomological machines for establishing quantitative laws in these systems. Many of them are building explicitly on a tradition of rigorous quantitative biological experimentation that began in the early 20th century, but was interrupted by the advent of molecular biology. The resurrection of these traditions makes it plausible that we may soon possess a canonical framework of suitable abstractions analogous to other areas of physics.
Second, theorists in the physics of disordered materials have created an important body of theoretical work showing how to constrain the possible space of mathematical relationships in many of these nomological machines, even when symmetry and low energy expansions no longer apply. In particular, one can often invoke a subtle notion of perfect disorder, whereby some set of quantities can be treated as if they were drawn independently from the same probability distribution. A natural set of small parameters arises when the system is composed of a large number of entities (spins, particles, bacteria, immune cells, genes,...) that all interact with one another: if the number of entities is already large, adding another one only causes a small perturbation to the existing system. The constraints supplied by these insights promise to provide a rigorous foundation for many areas of biophysical theory.
Finally, physicists working on living systems are becoming more aware of the legitimate diversity of formal objects in the study of life. Recall that we defined the formal object of a science as the abstract organizing principle required to assemble a systematic body of knowledge from the concrete objects of experience. The physics of living systems studies life through the lens of measurable quantities, abstracting away from everything else. But the same systems can also be studied by biologists who are interested in their specific attributes, capabilities, and relationships. As physicists work alongside biologists more frequently and intensely, they naturally come to see how many realities that are rightly ignored for the purposes of physics (including life itself!) are still real, and worthy of study.