One of Galileo Galilei’s many contributions to science was his understanding of relative motion – that the physics within a system do not depend on the speed at which the system moves relative to external systems, provided the original system is not accelerating. This idea would go on to form the foundations for Einstein’s Relativity Principle which required that the physics of the system does not depend on the inertial frame chosen to study it. Though subtly different, modern physics often conflates these ideas leading to conflicting resolutions to Galileo’s initial problem. Sebastián Murgueitio Ramírez argues that by distinguishing between an "internal" and "external" version of the principle, we can right this, clarify its original meaning and appreciate just how far ahead of his time Galileo truly was.

When going about our daily routine, it is too easy to forget that we are moving around the Sun at thousands of kilometers per hour. It certainly does not seem as if we were moving that fast when we walk around the neighborhood or when we look at the night sky. In fact, that things do not seem as if we are moving that fast (or moving at all) was for more than a thousand years cited as a reason in favor of a geocentric universe, with the Earth motionless at its centre. But given that we are moving fast around the Sun, why, then, do we not notice such motion?

Almost 400 years ago, in Dialogue Concerning the Two Chief World Systems, Galileo provides an answer to that question. In “Day Two” of that book, Galileo presents the following now very famous passage with the aim of illustrating that the motion of the Earth, just as the uniform motion of a ship, is not detectable from “within”:

Shut yourself up with some friend in the main cabin below decks on some large ship, and have with you there some flies, butterflies, and other small flying animals. Have a large bowl of water with some fish in it; hang up a bottle that empties drop by drop into a wide vessel beneath it. With the ship standing still, observe carefully how the little animals fly with equal speed to all sides of the cabin. The fish swim indifferently in all directions; the drops fall into the vessel beneath; […] When you have observed all these things carefully […], have the ship proceed with any speed you like, so long as the motion is uniform and not fluctuating this way and that. You will discover not the least change in all the effects named, nor could you tell from any of them whether the ship was moving or standing still. In throwing something to your companion, you will need no more force to get it to him whether he is in the direction of the bow or the stern, with yourself situated opposite. […] the butterflies and flies will continue their flights indifferently toward every side, nor will it ever happen that they are concentrated toward the stern, as if tired out from keeping up with the course of the ship, from which they will have been separated during long intervals by keeping themselves in the air. […] the cause of all these correspondences of effects is the fact that the ship's motion is common to all the things contained in it, and to the air also (Galilei, 1967, p. 186).