## Relativity before Einstein

### Galilean Relativity

The first modern scientist to think carefully about the relativity of motion was Galileo Galilei. In his Dialogue Concerning the Two Chief World Systems, Galileo describes a series of experiments that could be performed to determine whether the motion of a sailing ship makes any difference to physical processes that occur inside the ship:

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; and, in throwing something to your friend, you need throw it no more strongly in one direction than another, the distances being equal… When you have observed all these things carefully (though doubtless when the ship is standing still everything must happen in this way), 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.Dialogue Concerning the Two Chief World Systems, translated by Stillman Drake, University of California Press, 1953, pp. 186 – 187

As Galileo correctly predicts, the steady motion of a ship (relative to the earth) makes no difference to physical processes that occur inside the ship. Things inside the ship behave in the same ways regardless of whether the ship is moving, so long as the ship’s velocity remains constant. If the ship’s motion is “fluctuating this way and that,” on the other hand, the effects will be noticeably different. The sailor’s experiments will yield varying results; he may also feel a little woozy from motion sickness!

Galileo’s observations about the sailing ship illustrate an important distinction between two types of motion: inertial motion and non-inertial motion. An object moves inertially when the net force on the object is zero. As you may recall from chapter 2, Newton’s first law of motion (which was actually discovered by Galileo) says that an object’s velocity doesn’t change unless a force acts on it. This law holds in all inertial reference frames—that is, in all reference frames that consider at least one inertially-moving object to be at rest.

However, the first law of motion does not hold in frames that regard some non-inertially moving object as being at rest. To see why, imagine two sailors who are throwing something—a dead parrot, say—back and forth in the ship’s cabin. So long as the ship is moving inertially, the parrot will appear (from the sailors’ perspective) to follow the first law of motion: its speed and direction won’t change while it is “flying” from one sailor to the other, except to the extent that the force of gravity pulls it downward. But suppose a large wave suddenly jostles the ship to one side, just as a sailor tosses the deceased pet. From the sailor’s perspective, regarding the ship as being at rest, the parrot will appear to accelerate sideways even though no force is acting on it. Thus, the first law of motion doesn’t hold in a non-inertial reference frame—a frame that regards some non-inertially-moving object (e.g. a ship rocking in the surf) as being at rest.

Newton’s second law of motion, likewise, holds only in inertial frames. Consider the example given previously. In the reference frame of the swaying ship, the dead parrot seems to accelerate sideways even though the only force acting upon it is the downward force of gravity. So, from the sailor’s perspective, the total force on the parrot is not equal to the parrot’s mass times its acceleration. The second law fails to hold in non-inertial frames like that of the swaying ship.

Galileo’s insight, stated in contemporary terminology, is that the laws of motion hold in all inertial frames. Of course, Galileo didn’t spell out this idea in terms of Newton’s laws. (He died the year Newton was born.) Though he discovered the first law, Galileo hadn’t figured out exactly what the other laws of motion were. Nor did he introduce the notion of reference frames. But the crucial idea is essentially his. If you are moving inertially and you regard yourself as being at rest, then from your perspective the laws of motion (whatever they may be) will hold in precisely the same way, regardless of how quickly or slowly you are moving relative to other objects. This simple yet profound theory is known today as Galilean relativity.

Technically, no one has ever been in a perfectly inertial frame. We are constantly accelerating (changing direction) due to the force of gravity, which holds us to the surface of our planet as it rotates and orbits the sun. But our acceleration due to the earth’s motion is small enough that we don’t notice it in the sorts of experiments that Galileo described, so for practical purposes we can often regard ourselves as moving inertially.