#### Publication Date

4-1999

#### Abstract

It is well known that equations of motions and equations which describe the dynamics of physical fields can be deduced from the condition the action S (determined by the corresponding Lagrange function) is optimal. In other words, there is an optimality criterion on the set of all trajectories, and the actual trajectory is optimal with respect to this criterion.

The next reasonable question is: where does this optimality criterion on the set of all trajectories (i.e., the corresponding Lagrange function) come from? It is reasonable to assume that (similarly) on the set of all Lagrange functions, there is an optimality criterion, and the actual Lagrangian is optimal with respect to this criterion.

In this paper, we show that, under reasonable conditions on this optimality criterion, this approach leads to the standard Lagrange functions for General Relativity, Quantum Mechanics, Electrodynamics, etc. Thus, the Lagrange functions (and hence equations) of our world are indeed the best possible.

## Comments

UTEP-CS-99-19.