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Symmetry principles in physics are a very powerful guiding principle. Sometimes they are so powerful that they can determine a theory completely. This talk will be a tour from the Standard Model of particle physics to string theory compactifications using mostly symmetry arguments.

Taking our intuitive understanding of the quantum world gained by studying a particle in a one-dimensional box, we generalize to understand a quantum harmonic oscillator.
Learning Outcomes:
• Introduction to the classical physics of a ball rolling back and forth in a bowl, a simple example of a very important type of bounded motion called a “harmonic oscillator.”
• The quantization of allowed energies of a harmonic oscillator: even spacing between energy levels, and zero point energy.
• Being able to sketch the allowed wavefunctions and particle probability patterns of a quantum harmonic oscillator, including a new phenomenon called “tunnelling.”

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.”

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.

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.

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.

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.