# Why Are Newton’s Laws of Motion Important?

Isaac Newton first published his three laws of motion in 1687, and physics students have been learning about them in class ever since. I’m sure more than a few of them have wondered: “Why are they teaching me this stuff?” This is an important question that is, unfortunately, not usually addressed in physics classes. I can think of four main reasons:

• They work!
• They represent mankind’s first great success at describing diverse aspects of nature with simple mathematical formulas.
• They form the most intuitively appealing physical theory.
• They lay the groundwork for later physics developments.

Now I’ll explain what I mean.

Note: if you come across unfamiliar notation or ideas in this post, it may be in your interest to take a look at my glossary.

First, I should probably at least say what Newton’s Laws of Motion are. Like many ideas of great importance, there are several ways to express them. Nowadays, they are usually stated in the following form (or something very similar):

1. If there is no net force on an object, it will have no acceleration.
2. If there is a net force ${\bf F}$ acting on an object with momentum ${\bf p}$, then ${\bf F} = \dot{\bf p}$.
3. If object 1 exerts a force on object 2, then object 2 exerts a force on object 1 with the same magnitude but opposite direction.

For the purposes of explaining their importance, however, the consequences of these laws are as relevant as the laws themselves. In this sense, we can think of them as making the following assertions:

1. The other two laws are valid in only in inertial reference frames. These special frames really do exist, and they are easy to identify.
2. There is an equation (${\bf F} = m {\bf a}$) that can determine the position and velocity of an object at any time in the past or future.
3. The momentum of a system is conserved if no forces act on it.

(I explain how to arrive at these conclusions in this post. For another important consequence of the Third Law, see this post.)

Now, let’s get to the juicy stuff.

# Newton’s Laws Work

I have something I need to get off my chest: Newton’s laws of motion are not correct. They are based on a flawed interpretation of nature that has been superseded by special relativity, quantum mechanics, and field theory. Newton’s laws fail miserably inside molecules and in distant outer space; in fact, they fail to even explain some important features of classical electromagnetism. However, there’s a catch: all these other theories reduce to Newton’s laws in the realm of everyday life. For a wide variety of situations, Newton’s laws work just fine. This is why physicists didn’t discover any problems with them for over two hundred years! Newton’s laws can predict the motion and interactions of objects well enough to:

This list could go on forever, but I think you get the point. Nearly everything you experience in daily life that involves motion can be explained by Newton’s laws in very accurate ways, and nearly everything you use in daily life was designed with Newton’s laws in mind.

# Newton’s Laws Are A Triumph For Humanity

Newton’s laws were not the first mathematical description of the universe. People have actually been using math to predict the movement of the planets since Claudius Ptolemaeus developed his model in the second century AD. This system was eventually replaced with the Copernican system and even later by Kepler’s laws.

However, these systems all had numerous and/or arbitrary sets of rules. They worked, but made very little sense. Newton’s laws of motion (along with his law of universal gravitation, which gave the appropriate form of the force to use in the Second Law) were able to explain planetary motion with fewer concepts; furthermore, those same three laws applied to things on Earth as well.

The importance of this cannot be overstated!

Newton showed that the same laws govern celestial motion and terrestrial motion. For all of history until that point, people had believed that the heavens were so sacred that they constituted a totally different realm. Newton proved otherwise!

Newton showed that the human brain was capable of understanding deep properties of the natural world!

This accomplishment was totally unprecedented and it greatly influenced scientific and religious communities.

Alexander Pope may have described it best:

Nature and nature’s laws lay hid in night;
God said “Let Newton be” and all was light.

# Newton’s Laws Are The Most Intuitive Physical Theory

Other than Newton’s laws, physicists have quite a few ways to describe the universe. These include:

• Lagrangian mechanics
• Hamiltonian mechanics
• Quantum mechanics
• Field theories
• Special relativity
• General relativity
• String theory

Most of these are more accurate and “correct” than Newton’s laws, but their accuracy comes at a price: they are far removed from the everyday experiences of most people. Lagrangian and Hamiltonian mechanics describe the world by “minimizing action,” quantum mechanics describes the world in terms of probabilities, and field theories (not surprisingly) describe the world using fields. Special relativity removes the special status given to time, and general relativity explains gravity using “spacetime curvature.” String theory is too complicated and weird to even begin to describe here. If all of this sounds abstract and confusing to you, you’re right!

Newton’s laws, however, describe the world using forces. Everyone has pushed or pulled something at least once in their life. Even if the math gets too complicated, most people can intuitively understand concepts like force and mass. Newton’s laws consequently make for a great introduction to physics since they are conceptually easier to swallow.

# Newton’s Laws Laid The Groundwork For Later Theories

I remarked earlier that Newton’s laws are not correct. However, it turns out that two consequences of his laws are correct. All modern physical theories are specified in inertial reference frames and must conserve momentum. Physicists believe that momentum conservation is one of the most fundamental properties of nature. Familiarity with these concepts therefore paves the way to understand more complicated and accurate physics theories.