Science, Philosophy, and the Big Questions

The revolution in physics during the first three decades of the twentieth century swept away the intuitive and palatable theories of classical physics and brought forth the puzzling and seemingly paradoxical new theories of special and general relativity as well as of quantum mechanics. Modelled on John Norton's Einstein for Everyone, this course will introduce and explain the exciting and important ideas at the core of this revolution to students with little or no background in physics. Focusing on Albert Einstein in particular, it will answer many questions you had about Einstein and his singular achievements but never dared to ask. It is perfect for everyone who understands that Einstein's work in the foundations of physics has forever changed physics and the way we think about our world, but never had a chance to explore just how it did so.

We will approach Einstein's theories with a trifold interest in their science, their philosophy, and their history. Naturally, there will be quite a bit of straight exposition of the physics of special relativity, general relativity, and quantum theory. We will also be tracing the revolution's history and analyze and discuss the philosophical underpinnings and consequences of the new theories. This will lead us to deep philosophical questions about space, time, causality, the constitution of matter, and determinism, as well as to the measurement problem in quantum mechanics which challenges the very way in which physical existence was cast since Aristotle's time.

Course Materials

Course materials such as lecture notes, handouts, etc will be made available as they will be used in class.

John Norton's Einstein for Everyone, linked by module:

Lecture notes:

The following materials are mandatory for this course:

  • John Norton, Einstein for Everyone. This book is available free of charge at this website.
  • You will need to purchase an i>clicker, the student response system used in this class. These 'clickers' are available at the Price Center bookstore and cost $46.75 (new) or $35.10 (used). Make sure to get an i>clicker and not a di?erent system such as H-ITT or PRS. For more information, visit

In lieu of a study guide, I make the clicker questions available to help you reviewing the material:

Homework assignments

Additional Readings and Materials

Note: These additional materials will not be tested in exams. They serve to give you some background or to offer some additional food for thought.

The Stanford Encyclopedia of Philosophy (SEP) is an excellent source for academically serious, yet relatively accessible survey articles on many, many topics in philosophy, including philosophy of spacetime theories and of quantum mechanics. For this course, the following articles are relevant:

Grading Comments

HW 1: generally solved very well, with a class average of 3.62 (out of 4).

Quiz 1: The class average was 3.83 (quizzes are always out of 5).

  • (5) Many didn't get the second part of this question right. The answer can be found here. Notice that this is a 'why'-question.

HW 2: generally solved very well, with a class average of 1.88 (out of 2).

Quiz 2: The class average was 3.67.

  • (1) The left or rear light actually flashes first. Ask me and I'll draw a spacetime diagram on the board in class.
  • (5) Surprisingly many didn't get this one right. But I actually explained the answer to this in the lecture before the quiz! You absolutely have to know how Einstein's simultaneity works!

HW 3: generally well solved very well, with a class average of 3.41 (out of 4, although no one scored 4 points). For the first problem, I would have expected that you don't simply state what is moving with respect to what, but also what electric currents are present.

Quiz 3: The class average was 3.46 (highest score was 4).

  • (2) I told you in my comments after last time that you absolutely have to know how Einstein's simultaneity works, but many didn't...
  • (3) It's exactly the same procedure, but the result will be different, as simultaneity is, after all, relative.
  • (4) It doesn't suffice to just remark that the hypersurface is tilted so that when A reads '4', B's clock only reads '3'; it is that the actual time lapsed between equidistant hyperplanes of simultaneity is shorter on B's clock than on A's. Look it up here.

Quiz 4: The class average was 4.00.

  • (1) It is important not to just state that the discovery of non-Euclidean geometry threatened Kant's theory, but how.
  • (4) Actually, I really wanted you to mark a circumference and radius in the drawing.
  • (5) Notice that there are two parts to the question.

HW 6: The class average was 5.28.

  • (5b) Many didn't really draw worldlines in a space-time sheet of masses aligned at the same altitude but just some group of converging geodesics.
  • (6b) Stating that Minkowski spacetime is flat and therefore must have vanishing stress-energy tensor (presumably by virtue of the Einstein equations) doesn't answer the question. Instead, one needs to first state both that it is flat and is a vacuum solution, and that therefore, the Einstein equations are satisfied.

Quiz 5: The class average was 3.36.

  • (2) Almost everybody chose the bending of light.
  • (3) Spatial geometry: in GR, space-space sheets are curved, which they are not in Newtonian theory; Big bang: in Newtonian theory, the big bang is the expansion of a nugget of matter into a pre-existing spacetime, whereas in GR, it's the explosion of space itself, as it were.

HW 7: The class average was 3.9. Some of you have now reached 25 points and need not submit any more homework. I will, however, still correct it if you do!

  • (3c) Many of you didn't get this one. Perhaps we should go over it in class.
  • (4)-(6) I only gave you a maximum of 2 points for these three exercises.

Quiz 6: The class average was only 2.58, with the highest score being 4.

  • (1) Notice that this question, like a number of others in this quiz, contain several sub-questions!
  • (2) Again, there are two things you're supposed to do. First, say that this is a conformal diagram of a Schwarzschild spacetime.
  • (3) Bohr's theory contradicted classical electrodynamics because it assumed stable (and discrete) orbits on which the move without radiating off energy. (And there's a second sub-question)
  • (4) momentum = h / wavelength (Plus another sub-question)
  • (5) The answer can be found in the chapter on relativistic cosmology ("The cosmological constant (lambda)")

Final exam: The class average was 20.1 (out of 30), however, with a rather large standard deviation.

Have a happy spring break!