ISSYP Virtual

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.

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.

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.

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.

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.

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 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 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.

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.