What makes Newton's laws true? Here's a simple way

Why do Newton's laws hold true? Here's the answer.

The laws of physics determine the orbits of the planets.

(Image credit: Mark Garlick/Science Photo Library via Getty Images)

Paul M. Sutter is an astrophysicist at Stony Brook University and the Flatiron Institute, host of Ask the Astronaut and Space Radio, and author of How to Die in Space.

We all learned Newton's laws in high school: objects in motion tend to stay in motion, force equals mass times velocity, and for every action there is an equal and opposite reaction. In these laws of motion, Isaac Newton discovered a theory of universal gravitation that applies equally to an apple falling from a tree and to planets in orbit.

But Newton couldn't explain why his laws of motion were correct? Why didn't they have some other form? That discovery would come from another legend, a lesser-known genius.

Lagrange vs Newton

We're used to thinking about motion in terms of forces and accelerations—partly because it's a very intuitive way to look at the world (e.g., I push on something, and it moves) and partly because of Newton's laws (that's what we were taught in school). But forces and mass aren't the only way we describe the world around us. For now, imagine a ball thrown into the air. The ball has many useful properties—like its position, velocity, acceleration, and mass. Some of these properties are very useful in predicting the ball's trajectory, while others are less useful.

Newton discovered that the combination of mass, acceleration, and force was indeed very powerful, which allowed him to establish the equation "force = mass × acceleration" as a fundamental law of the universe.

About 150 years after Newton came up with his laws of motion, another mathematician, physicist, and all-around genius, Joseph Louis Lagrange, came up with his formula. He discovered that the laws of motion could also be derived by looking at the kinetic and potential energies of an object. Specifically, Lagrange discovered that the difference between the kinetic and potential energies of an object could reveal something deeper about the universe.

Stabilizing dose

If I throw a ball at you, you will most likely catch it. You will catch it because, over your lifetime, you have seen so many balls thrown at you that your brain has decoded a fairly common set of trajectories that thrown objects follow. Newton's insight was that he discovered general laws of motion that predict the trajectories of thrown balls.

But why are Newton's laws true? Why do thrown balls follow familiar paths? Why doesn't the ball bounce back first, or launch itself toward Mars on its way to you? Why does it follow the same path every time? In other words, why do objects always behave this way and not some other way? The universe can choose how a thrown ball, or any object in motion, behaves. Here's the question, what makes Newton's laws true?

Newton didn't tell us the answer, but Lagrange gave us the answer.

The key is the difference between the kinetic energy and the potential energy of a moving object. If you watch a ball in flight, for example, at every instant you can calculate this difference. At the end of the motion, you can add up all those differences and get a single number. For various historical reasons, this number is called the action of an object in motion.

When a ball is thrown at you, you can imagine different paths it could take. These different paths are associated with different actions. It turns out that the path we are familiar with, the path accurately predicted by Newton's laws, is the path with the least action.

Creating the Laws of Motion

Lagrange discovered what we today call the principle of least action.

To form the laws of motion, you follow a simple method. First, you write down the kinetic energy and potential energy of the object. Then, you take the difference between the two. (We now call this quantity the "Lagrangian" in his honor.) Next, you apply a fancy mathematical trick called the calculus of variations to find the expression that minimizes the motion. And a whole new law of physics emerges.

All modern physics is written in this language because it is powerful and elegant (and general) enough to discuss dynamics. General relativity, electromagnetism, and even quantum field theory and the Standard Model all began with Lagrangian theory, and physicists around the world used Lagrangian rules to derive the laws of motion.

These laws of motion include those governing the motion of the planets in our solar system, and the expansion of the universe itself. Whether you're using general relativity or Newton's original theory of gravity, Lagrange's approach will always give you the answers you need.

BY:Paul Sutter

FY: Little Star

If there is any infringement of related content, please contact the author to delete it after the work is published.

Please obtain authorization for reprinting, and pay attention to maintaining integrity and indicating the source