History of variational principles in physics involves integrals over an interval of time and (for fields) extended region of space. Moreover, in the usual formulation of classical action principles, the initial and final states of the system are fixed, e.g., In particular, the fixing of the "final" state appears to give the action principle a teleological character which has been controversial historically. This apparent teleology is eliminated in the quantum mechanical version of the action principle. History of variational principles in physics A variational principle in physics is an alternative method for determining the state or dynamics of a physical system, by identifying it as an
Preparation (physics) Preparation (physics) Generally, measuring instruments are meant to get the (pre-)existent value of a physical quantity of a system with as little change of, or interaction with the system as possible. — If a measuring instrument fixes a physical quantity of a physical system for further use (post-existent), then the measurement process is called preparation. For example, a graduated cylinder filled to a definite mark prepares a certain volume of the liquid for further use. Though preparation measures a physical quantity — at least by fixing it — it often destroys previous states of the physical system. This is usually