ISSYP Virtual

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.

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 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.

Einstein"s Relativity Principle applies to both mechanical and electromagnetic phenomena.
Learning Outcomes:
• Understanding Einstein's Relativity Principle: "Given any two inertial observers in uniform relative motion, both are equally entitled to consider themselves to be 'at rest'."
• Einstein based special relativity on Principles 1 and 2, which are both natural and easy to believe.
• Logically, Principles 1 and 2 imply Principle 2*. It is the role of special relativity to show how Principle 2* makes sense, but it requires a complete revision of our concepts of space and time.

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.

A demonstration of electron superposition using an electron diffraction apparatus, plus an introduction to quantum entanglement.
Learning Outcomes:
• Concrete demonstration related to the surprising 360/720 degree prediction discussed in QM-15.
• Understanding how an electron diffraction apparatus works, and how its surprising experimental results are explained by electron superposition, i.e. the electron behaving as if it can exist in multiple paths simultaneously.
• Understanding how superposition applied to two particles can lead to a remarkable phenomenon called quantum entanglement (or, as Einstein called it, “spooky action at a distance”).

Quantum teleportation as a fascinating application of quantum entanglement.
Learning Outcomes:
• Understanding precisely what “teleportation” could mean in our quantum universe.
• How quantum entanglement is the key to making quantum teleportation possible.
• How a quantum teleportation machine functions.

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.

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).

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.

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.