A2      Galileo Galilei’s Principle of Relativity

Newton was not the first to state that it is impossible to decide whether an object or a coordinate system in absolute space is moving or at rest. We all know the situation from everyday life: Is it our train or is it the one on the tracks next to us that is moving?

Galileo Galilei described this fact, in his typically colorful language, in his famous “Dialogue Concerning the Two Chief World Systems” and was probably not even the first. The original Italian (!) edition [04] appeared in 1632 and was translated in 1641 into Latin. A German edition, anno 2006, is out of print. English, however, offers several different editions. We follow the translation of Drake:

“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 [Note David Eckstein/Samuel Edelstein: This should rather read 'narrow' instead of 'wide'. Think of a bottle with a narrow neck on its top! ] 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; jumping with your feet together, you pass equal spaces in every direction. When you have observed all these things carefully (though there is no doubt that 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. In jumping, you will pass on the floor the same spaces as before, nor will you make larger jumps toward the stern than toward the prow even though the ship is moving quite rapidly, despite the fact that during the time that you are in the air the floor under you will be going in a direction opposite to your jump. 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 droplets will fall as before into the vessel beneath without dropping toward the stern, although while the drops are in the air the ship runs many spans. The fish in their water will swim toward the front of their bowl with no more effort than toward the back, and will go with equal ease to bait placed anywhere around the edges of the bowl. Finally 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.  ...“  [05-187f]

We can summarize this somewhat more soberly:

If a coordinate system B moves uniformly (with constant velocity) in a straight-line with respect to an inertial frame A, then B is also an inertial frame.  Or: Two inertial frames can move only uniformly along a straight-line to each other. It cannot be recognized whether one of the two is at rest in absolute space.

We formulate this as the principle of relativity of Galileo:
From the point of view of mechanics, all inertial frames are equivalent.

One obtains the general principle of relativity, if one omits the restriction on mechanics:
All inertial frames are equivalent.
The physical laws are the same in every inertial frame, including the values of the constants that arise within them.