To understand problems in biology, chemistry, engineering, and materials science from first principles, one can start, as Paul Dirac advocated, with quantum mechanics.1 Scientific advances made since the early 20th century attest to that view. But solving practical problems from a quantum mechanical perspective using the Schrödinger equation, for example, is a highly nontrivial matter because of its various complexities. To overcome the mathematical difficulties, researchers have proceeded along three lines of inquiry: looking for simplified models, finding approximate solutions using numerical algorithms, and developing multiscale models.
Each of those approaches has advantages and disadvantages. Simplified models—a constant theme in physics—capture the essence of a problem or describe some phenomenon to a satisfactory accuracy. Ideally, simplified models should have the following properties: They should express fundamental principles, such as conservation laws; obey physical constraints, such as symmetries and frame indifference; be as universally applicable as possible; be physically meaningful...