Hanoch Gutfreund is professor emeritus of theoretical physics at the Hebrew University of Jerusalem, where he is also the academic director of the Albert Einstein Archives. Jürgen Renn is a director at the Max Planck Institute for the History of Science in Berlin. His books include The Genesis of General Relativity. A handsome annotated edition of Einstein's celebrated book on relativity After completing the final version of his general theory...

The interferometer from the previous lecture serves as a test case for introducing the formal math of quantum theory. By learning a few symbols and rules, you can describe the states of quantum particles, show how these states change over time, and predict the results of measurements.

You explore the mystery of why atoms are stable. Niels Bohr suggested that quantum theory explains atomic stability by allowing only certain distinct orbits for electrons. Erwin Schrödinger discovered a powerful equation that reproduces the energy levels of Bohr's model.

Study molar and partial molar quantities, which are indispensable for describing what happens when materials are combined. Focus on the case of water mixed with ethanol, which adds up to a surprising volume. These ideas lead to one of the most important variables in thermodynamics: chemical potential.

Trace the growth of physics from philosophy, as questions about the nature of reality got rigorous answers starting in the Scientific Revolution. Then, see how the philosophy of physics was energized by a movement called logical positivism in the early 20th century in response to Einstein’s theory of relativity. Though logical positivism failed, it spurred new philosophical ideas and approaches.

In mechanics (the branch of physics that studies motion), the principle of Galilean relativity holds - meaning that the laws of mechanics are the same for anything in uniform motion. Is the same true for the laws of electromagnetism?

Einstein spent the last decades of his life searching for a unified field theory that would unite general relativity with Maxwell's theory of electromagnetism. But by then, quantum theory had superseded Maxwell's work, rendering the entire exercise futile. See how this quest has nonetheless stimulated ideas for unification in proposals such as string theory.

Turn to the problem of thermal energy flow and volume. This phenomenon causes materials to expand when heated and contract when cooled. Analyze these events at the atomic scale, and study the unusual behavior of water when it freezes - an attribute that is essential to life as we know it.

Take a deeper step into the quantum world, observing how the theory of quantum electrodynamics, or QED, unites quantum mechanics with special relativity. Discover that the handy sketches of subatomic behavior called Feynman diagrams (named after physicist Richard Feynman) are really equations in disguise.

At the beginning of the 20th century, Max Planck and Albert Einstein proposed revolutionary ideas to resolve puzzles about light and matter. You explore Planck's discovery that light energy can only be emitted or absorbed in discrete amounts called quanta, and Einstein's application of this concept to matter.