Newton’s First Law May Have Been Mistranslated for Centuries

When Isaac Newton set down his now-renowned laws of motion on parchment in 1687, he could scarcely have imagined they would still be debated more than three centuries on.

Written in Latin, Newton’s work set out three universal rules for the way objects move throughout our Universe. These principles have since been translated, copied, examined and argued over extensively.

Newton’s first law and a disputed translation

Yet one philosopher specialising in language and mathematics argues that the exact phrasing of Newton’s first law of motion may have been understood incorrectly for generations.

Virginia Tech philosopher Daniel Hoek set out to “set the record straight” after identifying what he calls a “clumsy mistranslation” in the first English rendering, published in 1729, of Newton’s Latin Principia.

That translation has led innumerable academics and teachers to understand Newton’s first law of inertia as saying that an object keeps moving in a straight line, or stays at rest, unless an external force acts upon it.

This account seems sensible until one recognises that outside forces are always operating - something Newton would almost certainly have accounted for when choosing his words.

On returning to the historical record, Hoek found that the familiar interpretation rested on an error that went largely unnoticed until 1999. Two scholars then highlighted the neglected translation of a Latin term: quatenus, meaning “insofar”, rather than unless.

For Hoek, the distinction is crucial. Instead of stating that a body retains its momentum when no forces are exerted upon it, he argues that Newton was saying every alteration in momentum - each jolt, fall, turn and burst forward - results from external forces.

“By putting that one forgotten word [insofar] back in place, [those scholars] restored one of the fundamental principles of physics to its original splendor,” Hoek explained in a blog post outlining his work, which was published in a 2022 academic paper.

Why the revised reading matters

Despite its significance, the correction has not become widely adopted. Even today, centuries of repetition may make it difficult for the revised interpretation to take hold.

“Some find my reading too wild and unconventional to take seriously,” Hoek remarks. “Others think that it is so obviously correct that it is barely worth arguing for.”

To many people, the difference may appear merely semantic. Hoek acknowledges that the reinterpretation has not changed, and will not change, physics. Still, a close reading of Newton’s own words helps reveal the thinking of the pioneering mathematician.

“A great deal of ink has been spilt on the question what the law of inertia is really for,” explains Hoek, who was perplexed as a student by Newton’s intended meaning.

Under the standard translation - in which bodies travel straight ahead until a force makes them do otherwise - an obvious question arises. Why would Newton formulate a law about objects untouched by outside forces, when no such objects exist in our Universe and gravity and friction are always present?

“The whole point of the first law is to infer the existence of the force,” George Smith, a philosopher at Tufts University and specialist in Newton’s writings, told journalist Stephanie Pappas for Scientific American.

Newton’s first law in the real world

Newton himself provided three practical illustrations of his first law of motion. Hoek considers the most revealing to be a spinning top, which slows along an ever-tightening spiral because of friction with the air.

“By giving this example,” Hoek writes, “Newton explicitly shows us how the First Law, as he understands it, applies to accelerating bodies which are subject to forces – that is, it applies to bodies in the real world.”

According to Hoek, this interpretation underlines one of Newton’s central ideas, one that was profoundly revolutionary in its day: planets, stars and other celestial bodies obey the very same physical laws as objects on Earth.

“Every change in speed and every tilt in direction,” Hoek mused - from swarms of atoms to swirling galaxies - “is governed by Newton's First Law.”

It offers a renewed sense of connection to even the most distant parts of space.

The paper appeared in Philosophy of Science.

An earlier version of this article was published in September 2023.