Lagrangian Formulation and Mechanical Interpretation

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Abstract
The question is asked whether, as is often claimed, the Lagrangian formulation of a physical theory provides its mechanical interpretation. For purposes of this enquiry, an analysis of physical theories is performed, with special emphasis on classical mechanics, electromagnetism, and quantum mechanics. Three aspects are distinguished and defined: the formulation (statement), the representation (transformation properties), and the interpretation (meaning). Confusion of formalism with meaning is criticized, and is suggested as a source of some misunderstandings of recent reinterpretations of quantum mechanics. Properties and advantages of Lagrangian formulations are listed, and it is recalled that their chief usefulness lies in that they are the most helpful precisely when mechanisms are either ignored or absent. It is concluded that Lagrangian formulations contribute to the demechanization of physics and that the program of reduction to mechanics has not succeeded in physics.

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