Special Relativity 1 - Spacetime Diagrams
Speaker(s): Richard Epp
Abstract: 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.



Special Relativity 2 - Spacetime Diagrams for Sound Travelling in Air
Speaker(s): Richard Epp
Abstract: 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.



Special Relativity 3 - The Doppler Shift for Sound
Speaker(s): Richard Epp
Abstract: 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.



Special Relativity 4 - Einstein's Speed of Light Principle ("Principle 2")
Speaker(s): Richard Epp
Abstract: 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.



Special Relativity 5 - Einstein's Relativity Principle ("Principle 1")
Speaker(s): Richard Epp
Abstract: 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.



Special Relativity 6 - Doppler Shift for Light
Speaker(s): Richard Epp
Abstract: 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.



Special Relativity 7 - Minkoskian Geometry
Speaker(s): Richard Epp
Abstract: Space obeys the rules of Euclidean geometry. Spacetime obeys the rules of a new kind of geometry called Minkoskian 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.



Special Relativity 8 - Applications of Minkowskian Geometry
Speaker(s): Richard Epp
Abstract: 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.



Special Relativity 9 - Synchronization of Clocks
Speaker(s): Richard Epp
Abstract: 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.



Special Relativity 10 - Coordinate Axes and Length Contraction
Speaker(s): Richard Epp
Abstract: A discussion of the space and time axes of a moving observer and an introduction to length contraction.
Learning Outcomes:
• Understanding why and by how much a moving observer’s position axis is “tilted in time.”
• Understanding how a moving platform appears to a stationary observer.
• Beginning to understand the cause of length contraction.



Special Relativity 11 - Simultaneity and Length Contraction
Speaker(s): Richard Epp
Abstract: A continuation of the SR-10 discussion on length contraction. Resolving Principle 2*.
Learning Outcomes:
• Relativity of simultaneity revisited – gaining a deeper understanding of what it means.
• A full understanding of the nature of length contraction based on relativity of simultaneity.
• Resolving a key paradox in special relativity: Principle 2*, introduced in SR-4. How it is possible to measure the same speed for the light whether you are running toward or away from a flashlight.



Special Relativity 12 - Einstein's Rotating Disk Thought Experiment
Speaker(s): Richard Epp
Abstract: 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.



Special Relativity 13 - Artificial Gravity Provides Hints about Real Gravity
Speaker(s): Richard Epp
Abstract: 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.



Special Relativity 14 - The Curved Geometry of a Rotating Space
Speaker(s): Richard Epp
Abstract: 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.