Leibniz and the Miracle Creed Behind Modern Physics

The Power of Leibniz's Principle of Optimality

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.

 

The great German polymath Gottfried Wilhelm Leibniz famously insisted that ours is the best of all possible worlds. The claim that our world couldn’t possibly be better has never been very plausible. It was hard to believe when Leibniz made it in the seventeenth century on the heels of the horrific Thirty Years War. It didn’t seem any more likely when Voltaire heaped ridicule upon it following the Lisbon Earthquake of 1755. And, of course, it will probably not find many adherents today as we trudge along under the weight of a global pandemic, political uncertainty, and an environment on the verge of collapse. Leibniz’s tho

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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