PHYSICS 109N: GALILEO AND EINSTEIN

Course Description

1. Astronomy in really early times: looking at the sky and making predictions.

In contrast to the usually chaotic situation here on earth, the sun, moon, stars and planets move in orderly ways that become predictable after a lot of observation. We discuss how these motions were first understood and interpreted by the Greeks and others, who even figured out over two thousand years ago that the earth was round, how big it was, and how far away the moon was.

2. Breakthrough: Galileo and the telescope.

The greatest advance in astronomical knowledge ever took place in 1610 when Galileo turned his own version of the newly invented telescope to the skies. He kept a diary of his discoveries, a short book called Sidereus Nuncius (the Starry Messenger). We shall read through this book together to see how he came upon a new picture of the universe, and discuss the physical and theological significance of Galileo's discoveries concerning the Moon, Jupiter and its moons, and the phases of Venus. We shall also experiment with lenses to see just how Galileo constructed his telescope.

3. Readings in Two New Sciences.

Another of Galileo's books, one in which he analyzes more down to earth phenomena, and describes some ingenious experiments he performed in an attempt to understand kinds of motion in a quantitative way. We'll do his experiment in class, and see how it led him to a better understanding of motion and in particular acceleration than the Greeks ever managed, even though they discussed the concept of motion for centuries. Galileo was really the first modern experimental physicist. His beautiful arguments about falling bodies, based on his experiments and set out in his book Two New Sciences, were what made it possible for Newton and Einstein to achieve what they did, and thus form the basis of much of modern science. The reason the ancients never analyzed falling motion correctly is that it's all over too fast, we shall use a video camera and freeze frame to get a better look, and confirm Galileo's conclusions which were based on much cleverer arguments.

4. Galileo's and Newton's analysis of projectiles.

We go through Galileo's analysis of projectile motion in Two New Sciences, commenting on its military motivation and practical significance. We then show how Newton extended this work to account for the motion of the Moon, connecting for the first time the motion of ordinary projectiles and heavenly bodies, and therefore strengthening Galileo's earlier argument (based on his telescopic observations) that the heavens and the earth might be composed of the same material, a claim of great theological significance at the time.

5. Newton's Laws of Motion and Universal Gravitation.

The essence of the First Law was already in Galileo's work, as well as some hints towards the Second Law. The crucial new concept is that of a force, and how it relates to motion. We discuss how these new ideas led to the picture of a "clockwork universe".

6. The Nature of Light.

Galileo's attempt to measure its speed. Newton's idea of particles of light. Discussion and demonstration of its wavelike nature, and waves in general. The analogy with sound waves, clearly described by Galileo (and to some extent by the Greeks) as pressure waves in air. The presumption that light must be a pressure wave (or perhaps a shear wave) in some all-pervading material, the ether.

7. Measurements of the speed of light, and attempts to detect the ether.

Observations of the moons of Jupiter, and the aberration of starlight. Earthbound measurements by Fizeau and Foucault, the Michelson-Morley experiment and its paradoxical conclusion.

8. Einstein's Special Relativity: space and time.

There is no ether permeating the universe, with respect to which velocities might be measured. The laws of physics are the same in all inertial frames, in particular, the speed of light is the same in all frames. We shall show that this implies a moving clock runs slow by a definite amount, as has been well-verified by experiment.

9. Einstein's Special Relativity: mass and energy.

When the changes in space and time are put together with the conservation of momentum, it follows that mass increases with speed, and that the speed of light is a natural speed limit for all objects. The momentum carried by a light wave can be used to give a simple demonstration of the equivalence of mass and energy E = mc2.

10. Einstein's General Relativity.

A qualitative discussion of the equivalence of gravitational fields and accelerated frames, experimental verification by observing Mercury; black holes and gravitational waves.

Books: Sidereus Nuncius, Galileo Galilei, translated by Albert van Helden, Chicago.

Two New Sciences, Galileo Galilei, translated by Crew and de Salvio, Dover.

Questions? Call Michael Fowler at 924-6579, or e-mail mfowler@virginia.edu