Newton cannot see anything wrong with Lagrange’s analysis but he is confident in his own abilities and convinced that gravity is the correct explanation. As he sees it, gravity only exists in Newton’s head. This leaves Newton utterly confused as Lagrange talks about the apple’s energy, but does not name any type of attraction between the apple and the Earth.īut Lagrange does not need a force of attraction to describe the apple’s fall. In the case of an apple falling to the ground, the straight line path that we observe is the one of least action. It’s is known as the principle of least action in physics. Lagrange postulates that among the many possible routes, the apple follows the path of least action. Mathematically, the action is the kinetic energy (energy associated with movement) minus the potential energy (energy associated with position) integrated over the time it takes to complete the motion along path. Read More: Tiny gravitational changes indicate loss of glacial ice Lagrange ascribes each possible path a quantity, which he calls “the action.” For any given path, one can compute its action by looking at the apple’s velocity and energy along that specific path. “But why does it follow a straight line? In the same period of time it could have followed any other imaginable path.” “In the time it takes the apple to fall, it follows a direct path towards the Earth,” notes Lagrange. “The apple falls because from an energy perspective, it follows a stable path,” says Lagrange with confidence. After some time, Lagrange exclaims, “aha!” Newton waits in suspense to see whether Lagrange is clever enough to figure it out. With a sly smile he asks Lagrange to explain why the apple fell to the ground. And Newton, who has just discovered gravity, decides to challenge his friend. The important thing is that Lagrange takes a completely different approach to mechanics than Newton.īoth of them watch the apple fall. Lagrange actually lived 100 years after Newton, but that doesn’t matter for the purposes of our thought experiment. Imagine Newton sitting in the orchard with a friend (rumour has it that he didn’t have many). Read More: Cosmic neutrinos reveal the universe’s violent history (Illustration: Niels Jakob Søe Loft)īut instead of saying that Newton “discovered” gravity, we should instead say that he “invented” it.
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