Talks

Development of a successful mathematical model of spin.
Learning Outcomes:
• A review of the mathematics of vectors.
• Applying the experimental results of QM-14 to construct a mathematical model of an electron spinning in any direction as a certain superposition of the spin up and spin down states.
• Discovering that this mathematical model predicts that an electron does not return to its original state when rotated once (through 360 degrees) – it must be rotated twice (through 720 degrees). A discussion of experimental tests of this remarkable prediction.

Using the de Broglie relation as a foundation for understanding the quirky quantum behaviour of particles.
Learning Outcomes:
• Understanding how a particle in one-dimensional box behaves like a superposition of left- and right-moving de Broglie waves, implying that the particle is moving both left and right simultaneously.
• Understanding the relationship between the intensity of de Broglie waves and the probability of finding the particle at specific locations inside the box.
• The general concept that a bound particle corresponds to a bound wave, resulting in only a discrete set of allowed standing waves, and thus quantization of its energy.

A discussion of the surprising results of the single slit and double slit experiments.
Learning Outcomes:
• How the single slit experiment suggests that chance is at the heart of nature, and that the behaviour of particles might need to be described by something different from Newton’s laws.
• How the double slit experiment suggests that understanding the behaviour of particles will require a radically new way of thinking about how nature works at a fundamental level.
• A video of an actual double slit experiment done with a beam of electrons (in case you don’t believe it).

Making the connection between particle probability patterns and wave intensity patterns, leading to the famous de Broglie relationship.
Learning Outcomes:
• Repeating the single slit experiment with waves instead of particles. Seeing that the particle probability pattern is the same as the wave intensity pattern.
• Same as above, but for the double slit experiment.
• Putting it all together to derive the de Broglie relationship between the momentum of a particle and the wavelength of a corresponding wave.

An introduction to spacetime diagrams – a first step towards understanding Einstein’s special theory of relativity.
Learning Outcomes:
• Newton’s absolute space and time vs. Einstein’s relative space and time.
• Bodies move through both space and time – spacetime diagram “worldlines” show both motions.
• Drawing worldlines for bodies in various states of motion: at rest, moving with various constant velocities, and accelerating.

Continuation of a thought experiment from SR-2 leading up to a derivation of the familiar Doppler shift for sound in air. Learning Outcomes: The real meaning of Newton’s assumption of absolute (or universal) time; Understanding the Doppler shift for sound in terms of a spacetime diagram; How to derive the (non-relativistic) Doppler shift formula for sound as a consequence of assuming Newton’s universal time.

Drawing spacetime diagrams of simple thought experiments involving sound in air as a warm up exercise for light in vacuum.
Learning Outcomes:
• Deepening our understanding of how to draw and interpret spacetime diagrams.
• Measuring space and time in the same units – a first step towards unifying space and time into “spacetime.”
• Why, for an observer at rest with respect to still air, the speed of sound is independent of the motion of the source of sound.

An experimental introduction to electron spin.
Learning Outcomes:
• To develop the classical understanding of a spinning bar magnet, and how we would expect it to be affected on passing through a Stern-Gerlach apparatus.
• How actual experiments with silver atoms (containing an electron that acts like a tiny spinning bar magnet) give results that are completely different from the above classical expectations.
• How a variety of different experiments lead to two main conclusions: (1) the spin of an electron is quantized (“spin up” or “spin down”), and (2) probability plays a fundamental role in the spin direction selected by the Stern-Gerlach apparatus.