Part philosophical, part scientific, Leibniz believed that our world - "the best of all possible worlds" - must be governed by what is known as the Principle of Optimality. This seemingly outlandish idea proved surprisingly powerful and led to one of the most profound ideas in theoretical physics. Jeffrey K. McDonough tells the story.
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Brian Flanagan 1 7 December 2022
Thanks to Jeffrey K. McDonough and the iai for this informed, intelligent, and well-written article.
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It is a most beautiful and awe-inspiring fact that all the fundamental laws of classical physics can be understood in terms of one mathematical construct called the _action._ It yields the classical equations of motion, and analysis of its invariances leads to quantities conserved in the course of the classical motion. In addition, as Dirac and Feynman have shown, the action acquires its full importance in quantum physics.
~Ramond
Furthermore, and now this is the point, this is the punch line, the symmetries determine the action. This action, this form of the dynamics, is the only one consistent with these symmetries [...] This, I think, is the first time that this has happened in a dynamical theory: that the symmetries of the theory have completely determined the structure of the dynamics, i.e., have completely determined the quantity that produces the rate of change of the state vector with time.
~Weinberg
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