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Class begins with clarification of equations from the previous lecture. Four post-Newtonian gravitational effects are introduced and discussed in detail. The first of these is the so-called Perihelion Precession, which occurs when the major axis of a planet’s elliptical orbit precesses within its orbital plane, in response to changing gravitational forces exerted by other planets. Secondly, deflection of light is described as the curving of light as it passes near a large mass. Gravitational redshift is explained as a frequency effect that occurs as light moves away from a massive body such as a star or black hole. Finally, the existence and effects of gravitational waves are discussed. The lecture closes with a brief history of the 1919 eclipse expedition that made Einstein famous.

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One last key concept in Special Relativity is introduced before discussion turns again to black celestial bodies (black holes in particular) that manifest the relativistic effects students have learned about in the previous lectures. The new concept deals with describing events in a coordinate system of space and time. A mathematical explanation is given for how space and time reverse inside the Schwarzschild radius through sign changes in the metric. Evidence for General Relativity is offered from astronomical objects. The predicted presence and subsequent discovery of Neptune as proof of General Relativity are discussed, and stellar mass black holes are introduced.

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The lecture begins with a comprehensive overview of the historical conditions under which Einstein developed his theories. Of particular impact were the urgent need at the turn of the 19th century to synchronize clocks around the world; Einstein’s position at a patent office; and a series of experiments that he himself carried out. In 1905 Einstein published three papers that are still considered the greatest papers in the field of physics. The lecture then moves to General Relativity and how it encompasses Newton’s laws of gravity. A visual demonstration shows how space-time undergoes curvature when mass is introduced. Class ends with a question-and-answer period on a variety of topics in Special Relativity.

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The lecture begins with the development of post-Newtonian approximations from Newtonian terms. Several problems are worked out in calculating mass, force and energy. A discussion follows about how concepts like mass and velocity are approached differently in Newtonian physics and Relativity. Attention then turns to the discovery that space and time change near the speed of light, and how this realization affected Einstein’s theories. Finally, the possibility of traveling faster than the speed of light is addressed, including how physicists might predict from laboratory conditions how this might occur. Muons, unstable particles that form at the top of the Earth’s atmosphere, are used as an example.

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The discussion of black holes continues with an introduction of the concept of event horizon. A number of problems are worked out to familiarize students with mathematics related to black hole event horizons. In a longer question and answer session, Professor Bailyn discusses the more mystifying aspects of the nature of black holes and the possibility of time travel. Finally, the issues of reconciling Newton’s laws of motion with Special Relativity, and Newton’s law of gravity with General Relativity, are addressed.