# Galileo and Einstein

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

These Applets will perform on any device, but some need a little more polish for easy phone use.

List of Applets

### 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...)

In Two New Sciences, Galileo presents his novel ideas as theater: a lively exchange between three characters, Sagredo representing the young Galileo, trying to figure things out, Salviati the current Galileo, he’s thought through a lot, and come to some conclusions, Simplicio represents the establishment Aristotelian view of science.

The first “new science” is set as a discussion arising from observing a Venetian shipyard, and noting that in building bigger ships, the necessary supports are scaled up in size more than the ship being built: the old-fashioned view was that if you scale up everything by the same amount, it will work fine, it’s just geometry. But that can’t be right: we know, for example, that bigger animals have out-of-proportion thicker bones. A trenchant analysis is presented in the first four pages of the book.

The second “new science” is that of motion. Galileo begins by demolishing the incredibly naïve Aristotelian description of falling bodies (manifestly not based on observation, except possibly of feathers), that speed of fall is proportional to weight, and falling bodies fall at a steady rate after brief initial acceleration. He appeals to experiment, but also gives simple logical arguments to make his point. (This is pages 61-69 of the book: it’s worth clicking on this link to catch the acid flavor of his remarks to Simplicio, and appreciate why the establishment wasn’t happy—Aristotle was a central figure in their philosophy.)

He goes on to give the first clear quantitative definition of acceleration (and of uniform nonaccelerated motion), the basis of Newton’s Laws and therefore our modern understanding of the universe. These ideas had eluded the Greeks, despite their mathematical excellence. (Selections from pages 153-169).

Finally, he puts these ideas together to analyze the motion of projectiles, of considerable interest to his noble sponsors. He proved that if air resistance is unimportant, the missile will follow a parabolic trajectory, and he calculated the dependence of range on angle of projection. (Selections from pages 244-254).

Long ago, we made a complete web version of Two New Sciences, that version is available here.

### 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 Modern Physics course goes on from the present course in exploring special relativity.

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 Graduate Classical Mechanics.

Here are complete notes for the first semester of Graduate E&M , based on Jackson.

Here are two series of PowerPoint slides for teaching introductory physics:

and second, Electricity and Magnetism, and Waves.

These come up as .pdf's. After loading, simply replace .pdf with .pptx to access the PowerPoint files.

### 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 quite 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.