ISSYP Virtual

We shift our ideas from Newton’s law of gravity to a new set of equations that describe how gravity is a consequence of the curvature of spacetime.
Learning Outcomes:
• John Michell and his hypothetical object called a dark star.
• How to determine the mass of a planet required for the escape velocity of an object to be the speed of light.
• Einstein’s Equivalence Principle.

Spacetime tells matter how to move, and matter tells spacetime how to curve.
Learning Outcomes:
• Why gravity can be seen as a curvature of spacetime.
• That Einstein’s field equations describe how matter curves spacetime.
• How Sir Arthur Eddington verified Einstein’s theory of general relativity by measuring the change in position of stars during a solar eclipse.

The mathematical predictions made by scientists tell a story of the life and death of stars.
Learning Outcomes:
• How the Hertzsprung-Russel diagram describes the life cycle of stars.
• Depending on its mass, how a star ends its life as a white dwarf star, a neutron star, or a black hole, and where super novas fit in.
• How the mathematical predictions of white dwarf stars, super novas, and neutron stars are slowly verified by the advancement of the astronomical equipment used by astronomers.

An introduction to a few of the major scientists who applied Einstein's ideas to better understand the life cycle of various stars.
Learning Outcomes:
• How Subrahmanyan Chandrasekhar resolved the paradox of the white dwarf star, and how Walter Baade and Fritz Zwicky described the dynamics of neutron stars.
• Yakov Zel'dovich develops the nuclear chain reaction that is the engine that keeps stars burning.
• The roles Robert J. Oppenheimer , John Wheeler, and Roger Penrose played in moving the concept of a black hole from a object of pure theory to a physical object in the universe.

The anatomy of a black hole.
Learning Outcomes:
• What are the mass requirements for a star to become a black hole?
• The anatomy of a Schwarzschild black hole, including the singularity and the event horizon.
• What a traveller would experience if he orbited a black hole, or had the bad luck to fall through the event horizon.

The physical attributes of a black hole and what types of physical evidence astronomers use the locate them.
Learning Outcomes:
• What are the physical requirements for a star to become a black hole, and what properties of that star remain after the black hole is formed?
• The types of black holes, including: the Schwarzschild black hole, the Reissner-Nordström black hole, the Kerr black hole, and the Kerr-Newman black hole.
• What a traveller would experience if he orbited one of these more general black holes, or fell through to the singularity.

The spacetime diagram of a rotating Bob is analyzed, leading us to conclude that his spatial geometry is curved.
Learning Outcomes:
• Understanding the physical effects of the rotation on the rotating observers, metal panels of the cylinder and so forth.
• Understanding the properties of a rotating cylinder using a spacetime diagram.
• Understanding curved spaces: The negatively curved space of a rotating observer and the positively curved space representing the real gravitational field of the Sun.

Analyzing the artificial gravitational field inside a rotating cylinder to discover hints about the nature of real gravitational fields.
Learning Outcomes:
• How to compare relativistic effects of an accelerated observer who is inside the rotating cylinder to observers at rest in the inertial reference frame outside the rotating cylinder.
• Understanding that the relative time dilation effect decreases as the rotating observer moves toward the axis of rotation, and how this suggests that a real gravitational field might warp time.
• Understanding that the circumference of the cylinder as measured by the rotating observers increases, and how this suggests that a real gravitational field might warp space.

Introduction to Einstein's famous rotating disk thought experiment, which he used to help him understand the true nature of gravity.
Learning Outcomes:
• Understanding that an observer placed at the edge of a rotating disk (or inside a rotating cylinder) experiences an artificial gravitational field related to his centripetal acceleration.
• Appreciating the ways in which this artificial gravitational field exactly mimics the real gravitational field we experience near the Earth's surface.
• How Einstein realized Newton's model of gravity must be wrong: it does not correctly predict the observed motions of the planets, and it does not respect the speed limit of the universe.

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.

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.