Activities/Turtle Art/Tutorials/Galilean Relativity

Most people have some vague idea of Einsteinian Special and General Relativity, with variable clock rates, shortening in the direction of motion, and many other effects previously unthinkable. Not so many have heard of the previous version of Relativity, which was almost equally unthinkable in its time. In his theory of mechanics and of uniform gravity, Galileo noticed the fact that we cannot feel uniform velocity, and we cannot detect it without observing something outside our frame of reference. He used the examples of ships sailing on smooth water, and a rider on a horse. In either case, if you drop a ball, it lands at your feet, even though your feet have moved some distance forward while it fell. If you drop it from the top of the mast of a ship, it lands at the bottom of the mast in the same way. If you throw a ball straight up, it comes down into your hand. You can try this in a car, a bus, a train, or an airplane.

Before Galileo, Aristotelean physics denied these possibilities. The claim was that you could feel motion directly, as you would in a cart on a bumpy road. In particular, the Earth could not be rotating according to this view, nor could it be revolving in an orbit around the sun, because in either case we would be left behind or subjected to immense winds. It turns out that in a cart, you can feel side-to-side or up-and-down forces, but (in constant forward motion) no force forward or back. To the contrary. When the cart starts up, we are thrown backwards, as it seems to us, until we accelerate to match the speed of the cart, and similarly we can feel that we are being thrown forward when the cart stops. No, in fact we just continue moving forward for a moment until a backward force can slow us down. Again, you can observe this on any vehicle with significant acceleration and deceleration, although it often happens that a passenger on a train cannot tell whether it is this train or the train on the next track that has just started moving when the start is gentle enough.

An extremely important instance of Galilean relativity is our view of falling objects. The person dropping an object from the top of a mast on a ship sees the object fall straight down, but an observer on shore sees it moving forward with the ship. What is the curve that that falling object takes? Is it different if you drop it from a moving vantage point such as the ship's mast, or throw it sideways from the nearly motionless top floor of the Leaning Tower of Pisa? We can do the experiment at home without needing ship or tower, and we can also get the Turtle to build us a model. The next time you watch a sport played with a ball (soccer, football, tennis, lacrosse, water polo,…) see if you can trace the curve that it takes.

If we have prepared children with experience with a variety of shapes, specifically including the shapes that a flashlight can create on a flat wall (conic sections) children should recognize these shapes as parabolas.

You or a child can easily do a variety of experiments to confirm Galileo's insight into his observations. Here is one of the best, which I saw done in my childhood. Get a yard or meter stick and two coins. If you do this over carpet, use coins big enough so that you can hear them land even across the room. Put a coin on each end of the ruler, and balance the ruler in the middle. Strike one end of the ruler so that it turns in a horizontal plane, and so that one coin starts to move horizontally. The other end of the ruler should slide out from under the second coin so that it drops straight down. What do you hear? What does that mean? This verifies what you see in the TA model, where dots in the line straight down and dots in the parabola are at the same heights.