The Advent Calendar of Physics: Action and Reaction

We kicked off our countdown to Newton’s birthday with his second law of motion, so the obvious next step is to go to his third law of motion:


This one was also originally in Latin, because that’s how Ike liked to roll:

Lex III: Actioni contrariam semper et æqualem esse reactionem: sive corporum duorum actiones in se mutuo semper esse æquales et in partes contrarias dirigi.

In English, this comes out as:

Law III: To every action there is always opposed an equal reaction: or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.

That first sentence is one of the most widely known phrases from physics, and probably rings a bell even for people who profess to hate the subject.

So, why is this important? Because while it looks deceptively simple, it actually tells us something very deep about the way the universe works.

Another way to express the core idea of the third law is to say that all interactions between objects go both ways. If I push on something, that thing pushes back on me. The gravitational force of the Sun on the Earth is paired with a gravitational force from the Earth on the Sun.

Newton’s third law tells us that there can’t be anything that acts to move another object while itself remaining unmoved. The effect may be very small– the change in the Sun’s motion due to the Earth is about 1/300,000th the change in the Earth’s motion due to the Sun– but it’s there.

The third law is a big part of the reason why the universe we live in is comprehensible. If unidirectional forces existed, everything would be vastly more confusing. thanks to the third law, though, if we know how one object affects another, we also know how the other affects the one. It tells us that the key to understanding the operation of the universe is to consider interactions between pairs of objects, each affecting the other in the same way.

This law also turns out to be extremely practical– in fact, you use it all the time without even knowing it. If you’re sitting in a chair to read this, you’re being held up by Newton’s third law: the gravitational force of the Earth pulls you down into the chair, exerting some force on it. The reaction force from your “push” on the chair is an equal and opposite push back on you, which keeps you in place, not moving.

If you get up from the chair and go to the kitchen for a snack, you manage to walk because of Newton’s third law: you push down and back on the floor, and the floor pushes up and forward on you, causing you to move. If you blow up a balloon and release it, it flies across the room thanks to Newton’s third law: the balloon pushes the air out, and the air pushes back on the balloon, propelling it forward.

Newton’s third law is also what first let us know that there are planets outside our solar system. The earliest extrasolar planet detection experiments used the Doppler effect to detect the tiny change in the velocity of distant stars due to the gravitational tug of unseen planets orbiting them.

So, as we continue our countdown to Sir Isaac’s birthday, take a moment to appreciate the power and beauty of his third law, which lets us move around our universe, and understand the stuff that’s in it. And come back tomorrow to see the next equation of the season.

3 thoughts on “The Advent Calendar of Physics: Action and Reaction

  1. I always liked opening the Advent calendars on the days before Christmas as a kid. I looked forward to the treats we got. This is just as enjoyable! Thanks for doing it!

  2. The balancing of action-reaction also shows why purported explanations of the Lewis-Tolman right-angle-lever paradox that don’t invoke stress correction (ie, Nickerson/McAdory) are faulty: if you apply torque, then the application process induces a change in the angular momentum of the subsystem doing the applying. Therefore, the lever must itself exhibit compensatory change in its angular momentum, meaning that the “energy current” (equivalent to the stress correction I noted in the previous “Advent” thread) is real and not a fiction of “non-covariant formulation” etc.

    “Fine minds make fine distinctions.”

Comments are closed.