The Principle of Least Action - the most important principle in physics? #shorts #physics

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The Principle of Least Action - the most important principle in physics?

Let’s think about a really simple system - a particle moving through space. This particle has some amount of kinetic energy due to its motion. And it has potential energy if it interacts with stuff around it, whether that be gravitational potential energy or electric potential energy or any other kind.

We’re going to calculate a quantity called the system’s Lagrangian, which is the kinetic energy minus the potential energy. This allows us to define the action via an integral of the Lagrangian over time.

The action, which is a scalar quantity (just a simple number) allows us to figure out what trajectory our particle will take through space and over time. Specifically, the Lagrangian that gives the lowest value of action (technically, stationary action) is the one that corresponds to the particle's trajectory.

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