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By applying our understanding of the quantum harmonic oscillator to the electromagnetic field we learn what a photon is, and are introduced to “quantum field theory” and the amazing “Casimir effect.”
Learning Outcomes:
• Understanding that classical electromagnetic waves bouncing around inside a mirrored box will exist as standing waves with only certain allowed frequencies.
• How each of these standing waves oscillates harmonically, and thus why – at the quantum level – their energies must be discrete, which is interpreted as the presence of a discrete number of photons.
• What the zero point energy of the electromagnetic field represents, and its relationship to a remarkable property of the quantum vacuum called the “Casimir effect.”

Learning to use Minkowskian geometry to understand, very simply, a variety of aspects of Einstein’s spacetime.
Learning Outcomes:
• How a straight line is the longest path between two points in spacetime.
• How a light particle experiences space and time: its journey from one location in the universe to another involves zero spacetime distance, and is thus instantaneous!
• How Einstein’s special relativity has no difficulty handling accelerated observers.

A discussion of how to synchronize clocks that are separated in space, and how this leads to the relativity of simultaneity.
Learning Outcomes:
• Understanding that clock synchronization is a physical process, and exploring various methods of synchronization using spacetime diagrams.
• How to measure distance with a clock: the concept of radar ranging distance.
• A profound realization about the nature of spacetime: Events that are simultaneous for one observer might not be simultaneous for another.

Space obeys the rules of Euclidean geometry. Spacetime obeys the rules of a new kind of geometry called Minkowskian geometry.
Learning Outcomes:
• Triangles in spacetime obey a Pythagoras-like theorem, but with an unusual minus sign.
• The true nature of time as geometrical distance in spacetime.
• How to analyse and resolve the Twins’ Paradox using spacetime diagrams in combination with Minkowskian geometry.

Highlighting the essential difference between the classical and quantum worlds.
Learning Outcomes:
• A recap of what we’ve learned so far.
• Understanding that in the classical world we have either “particle moving to the right” OR “particle moving to the left.”
• Understanding that, in the quantum world, OR can be replaced with AND: “particle moving to the right” AND “particle moving to the left.”

A discussion of the Heisenberg Uncertainty Principle as another way to understand quantum weirdness.
Learning Outcomes:
• Some deeper insights into what a particle probability pattern means.
• The Heisenberg Uncertainty Principle gives a limit to the precision with which we can simultaneously know both the position and the momentum of a particle.
• Deriving the Heisenberg Uncertainty Principle from the de Broglie relation.

A more in depth discussion of what the Heisenberg Uncertainty Principle is trying to tell us about the nature of reality.
Learning Outcomes:
• Understanding the strong interpretation of the HUP: “Particles cannot simultaneously possess a definite position and a definite momentum.”
• Why the classical question: “Given a particle’s initial position and momentum, what is its position and momentum as some later time t?” makes no sense in the quantum world.
• Richard Feynman’s remarkable sum over paths interpretation of quantum mechanics.

Deriving the Doppler shift for light, from which all of special relativity follows.
Learning Outcomes:
• Return to the thought experiment in SR-3. By replacing Newton’s assumption of Universal Time with Einstein’s Relativity Principle we arrive at the Doppler shift for light.
• How the Doppler shift for light provides us with important clues about the nature of time as experienced by moving observers.
• Understanding relativistic time dilation in terms of the geometry of spacetime.

Repeating the experiment from SR-3 using light rather than sound, and understanding what Einstein assumed regarding the speed of light.
Learning Outcomes:
• How to draw a spacetime diagram that represents the sending and receiving of a light signal.
• Understanding that Einstein's Speed of Light Principle: "For an observer at rest, the speed of light is c, independent of the motion of the source" is natural and easy to believe.
• Interchanging the words observer and source we arrive at Principle 2*: "For a source at rest, the speed of light is c, independent of the motion of the observer," which Einstein did not assume, because it is very hard to understand how it could be true.