What does World Thrift Day have to do with physics?

Nature is thrifty too, as is clear in the principle of least action.

World Thrift Day is observed on October 31 to promote saving money and developing a sense of financial prudence. We’re taught to save for a rainy day, as we grow up from being the owners of a piggy bank to the possessors of a bank account. It so happens that our vast universe’s scheme of operations also has an economical character. That is, our universe is thrifty as well.

Physicists generally attribute this to the principle of least action. Action in physics is defined by the change in energy of a system over time. The conservation laws in physics follow from the principle of least action. They imply that all energy is conserved, as is the total momentum. Nothing is deleted or destroyed, only conserved. All the phenomena that happen, from the subatomic world to the galaxies, follow the path of least action.

The word ‘least’ here doesn’t mean minimality. Instead, it means that a physical system between any two points in space-time evolves along a path that minimises or maximises the action depending on the outcome of the process.

The basic idea is that nature has a certain purpose to fulfil and thus follows an economical path. This is one of the most profound and far-reaching ideas in physics. You can see it by observing a stream. The moving water adapts to the hard rocks and soft soil that come its way and doesn’t insist on moving in a straight line. Similarly, light bends when moving from one medium to another by changing its velocity (refraction).

From the motion of planets around the sun to a ball thrown in the air, bodies go for the path that minimises the action involving their energy. Such selection happens naturally, without any ‘planning’. Water vapour is perfectly aerodynamic in the air but when it falls as rain, they do so as elongated spheres spreading out as little as possible to avoid increasing their surface tension.

The principle of least action is also useful in metaphysics and philosophy. How does nature know to optimise its performance through minimum effort? Scholars continue to debate the answers to this question. Even in formal terms, physicists are yet to understand this principle empirically – through experiment – and wield it only as a mathematical tool or to derive a suitable equation of motion.

But this is wonderful, too: presuming nature’s thrift has yielded bounties in the study of fluid mechanics, thermodynamics, string theory, classical electrodynamics, quantum field theory, and Morse theory in mathematics.

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