But Newton could not explain why his laws of motion were correct, and why they had no other form. The discovery will come from another legendary but not so well-known genius.

related : Astronaut transforms into billiards to demonstrate Newton’s third law (video)

Lagrange and Newton
We’re used to thinking about motion in terms of force and acceleration – partly because it’s a very intuitive way of looking at the world (e.g. I push something and it moves), and partly because of how Newton formulated his laws (and therefore how we teach them in school).

But examining force and mass isn’t the only way to describe the world around us. Think of a ball being thrown into the air. That ball has many properties that we might find useful – like its position, velocity, acceleration, and mass. Some of these properties may be very useful for predicting the future motion of the ball, while some are less useful.

Newton found that the combination of mass, acceleration and force was indeed very powerful, which allowed him to formulate his famous force = mass * acceleration Equations are the fundamental laws of the universe.

About 150 years after Newton developed his laws of motion, another mathematician, physicist, and all-around genius, Joseph Louis Lagrange, developed his own formula. He discovered that by observing the kinetic and potential energies of objects, he could also derive his own laws of motion.

Specifically, Lagrange’s discovery of the difference between the kinetic and potential energies of objects reveals something very profound about the universe.

static action
If I throw a ball at you, you might have a good chance of catching it. You can do this because in your lifetime you’ve seen a lot of balls thrown at you, and your brain has deciphered that thrown objects follow a fairly common set of trajectories. Newton’s insight lay in his ability to find general laws of motion that could predict the trajectory of a thrown ball.

But why should Newton’s laws be true? Why should a thrown ball follow a familiar path?Why doesn’t the ball jump back first, or shoot towards Mars Are they on their way to you? Why does the same path appear every time? In other words, why do objects behave the way they do and not the other way around? The universe could have chosen any behavior for a thrown ball or any other moving object. What makes Newton’s laws work?

Newton didn’t have an answer, but Lagrange did.

The key is the difference between the kinetic and potential energy of a moving object.For example, if you watch a ball in flight, then at every moment time , you can calculate the difference. At the end of the movement, you can add up all these differences and get a number.For various historical reasons, this number is called action objects in motion.

You can imagine the different possible paths the ball might take when it is thrown at you. These different possible paths will have different actions associated with them. It turns out that the familiar path—the one accurately predicted by Newton’s laws—is the one with the least amount of action.

Create laws of motion
Lagrange discovered what we today call the principle of least action. All the laws of physics, including Newton’s laws, derive from this single unifying principle.

To formulate the laws of motion, you need to follow a simple method. First, you write down the kinetic and potential energies of the object of interest. Then, you make the difference between them. (We now call this quantity a “Lagrangian quantity” in his honor.) You then apply a fancy mathematical technique called variational calculus to find the expression that minimizes the effect. Suddenly there was a whole new law of physics.

All modern physics is written in this language because it is a powerful and clever (and general) way of dealing with dynamics. general relativity , Electromagnetism even quantum field theory and the Standard Model start with the Langrangian operator, and physicists around the world apply Lagrangian rules to derive the laws of motion.

These laws of motion include those that govern the motion of planets on Earth. solar system and cosmic expansion itself. Whether you’re using general relativity or a primitive Newtonian version of gravity, Lagrange’s trick will always give you the answer you’re looking for.

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