Galileo and Einstein Home Page

Galileo and Einstein Home Page

Galileo and Einstein

Michael Fowler - University of Virginia Physics

This course explores two revolutions in our perception of the universe. The first, in which Galileo played the leading role, was the realization that what we see in the heavens—the Moon, the planets, the Sun and stars—are physical objects. For example, the Moon has a rocky surface, not unlike some parts of Earth, and is not made of some exotic ethereal substance, as had been generally believed before Galileo. This discovery, together with the mounting evidence that the Earth went round the Sun, led Newton to the realization that the motions of the Moon and planets obeyed the same physical laws as ordinary things (like flying cannonballs) here on Earth. Newton put this all together to give the first unified picture of the Universe.

The second revolution was Einstein’s realization that this was not the whole truth—space and time are not as straightforward as they first appear, but are related to each other in a simple but unexpected way. Among other results, this leads to the surprising consequence that mass and energy are different aspects of the same thing!

A Very Brief Outline

The course will follow the development of ideas approximately in the historical sequence. After looking over the first recorded real mathematics, that of the Babylonians, we'll review some of the Greek contributions to math and science, which were essential to both Galileo and Einstein in their work. We shall prove—and find very useful—Pythagoras’ theorem, and a few other ideas about triangles. We'll also look at Greek ideas about the Solar System, and how they measured the distance to the Moon quite accurately (using the ideas about triangles!). We will examine how these ideas reached western Europe by way of the Arab world.

We'll do some of Galileo’s actual experiments that led to understanding motions of projectiles, and show how Newton connected these results with the motion of the Moon, and then to all the planets. Next, we'll examine the nature of light, for this is what led Einstein to question the traditional concepts of space and time. Finally, we'll develop the theory of Special Relativity, including time dilation, relativistic mass increase, and E = mc2.

The Lectures

The lectures fall into three groups: the first third or so of the course is the development of mathematical and physical (mainly astronomical) ideas before Galileo, the next third is the successful development of our understanding of the solar system, and how its motions follow the same rules as motion on Earth, largely the work of Galileo and Newton. In the last third, we examine Einstein's revolutionary thinking, that Newton's picture was not complete -- space and time are subtly intertwined, and mass can be converted to huge amounts of energy.

Lecture List

PDF of Complete Set of Lecture Notes

Applets: Physics Animations

I'm working with a team of students to get all these into JavaScript, some are still in Java, which is becoming increasingly difficult to run. Those in JavaScript will perform on any device.

List of Applets

Flashlets: Animations Using Flash (not mobile-friendly)

Many of these excellent Flash animations were created over ten years ago by some talented students, Wan Ching Hui and Heather Welch. Unfortunately, Flash does not play on some devices, and may eventually disappear, so we are actively recreating these in JavaScript as Applets.

List of Flashlets

Homework and Exam Problems

Some of this is really active learning: finding height of actual buildings as the Greeks did, by pacing out shadows. There's also simple astronomical observation (non telescopic), and much else.

List of Homework Questions

List of Exam Questions

Galileo's Ideas In His Own Words (well, in translation...)

Galileo's book Dialogue Concerning Two New Sciences was the text for part of our course. For the first time in history, this book gives a clear quantitative account of acceleration, and how the parabolic trajectory of a projectile can be understood as a consequence of constant downward acceleration. . There is also an illuminating discussion of scaling: why bigger animals have out-of-proportion thicker bones, and building plans can't just be scaled up withthe same proportions and materials for a bigger building. Fortunately, the classic translation is out of copyright, so we can provide here some interesting excerpts from the book.

Two New Sciences

Selections with Commentary

Exploring Special Relativity Further

In the last third of Galileo and Einstein, we've given a basic introduction to Special Relativity. My Modern Physics course provides a more in-depth treatment, beginning at the level of the present course (there's overlap) but going on to more quantitative considerations, at the introductory physics major level.

My Other Courses

My Physics 152 Course has far more mathematical detail on planetary orbits, plus much other material on waves, fluids, heat, etc.

I also have complete notes for Graduate Quantum Mechanics, and a series of PowerPoint slides for introductory general physics.

Assorted Teaching Materials

This is a grab bag of lectures, etc., that I've given at various times in the past that do not fit in well with Galileo and Einstein, or Modern Physics, but which are in fact widely used, partly since they've been on the web a long time. Much of this material was originally presented in summer courses for high school physics teachers.

General Planetary Information.