12. Introduction to Relativity

Professor Ramamurti Shankar introduces the concept of special relativity, distinguishing it from general relativity. He begins by querying the students' understanding of relativity, highlighting that it's about relative speed in two reference systems. The discussion revolves around the fundamental postulates of special relativity, including the constancy of the speed of light and the principle that the laws of physics are the same in all inertial frames.

The professor delves into the paradox of uniform motion, using the analogy of a high-speed train to illustrate the concept. He poses the question of whether one can discern movement while in a uniformly moving train. The key point is that without external references, it's impossible to determine if one is moving or not, emphasizing the relativity of motion and the inability to perceive uniform velocity in a closed system.

Professor Shankar provides historical context by discussing the pre-Einstein theories of relativity, noting that the concept is not new but has evolved over time. He explains that the principles of special relativity were understood even before Einstein, with the laws of physics remaining constant in inertial frames, as established by Newton's laws of motion.

The lecture shifts to defining the concept of an 'event' in the context of space-time. The professor explains that an event occurs at a specific place and time, and to describe it accurately, one needs coordinates for both space and time. This leads to the introduction of the x and t axes, representing space and time, respectively, and the concept of labeling events within this framework.

The professor discusses the Galilean transformation, which is the classical method of relating the coordinates of events as observed by two different inertial frames of reference. He explains how the time is universal across observers and that the velocity of light is expected to appear different when measured from moving frames according to Galilean principles.

The discussion turns to the Michelson-Morley experiment, which aimed to detect the Earth's motion through the 'ether' by measuring the speed of light. The unexpected result was that the speed of light remained constant regardless of the Earth's motion, challenging the Galilean transformation and leading to a fundamental question about the nature of light and the ether.

Einstein's revolutionary postulates are introduced, asserting that all inertial observers are equivalent and that the speed of light is constant for all observers, regardless of their relative motion. These postulates defy the expectations set by Newtonian physics and open the door to a new understanding of space and time in the context of relativity.

The professor outlines the derivation of the Lorentz transformation, which provides the mathematical framework for understanding how space and time coordinates change between inertial frames. The transformation emerges from considering the behavior of light and the need for a new set of rules that differ from the Galilean transformation, especially at velocities approaching the speed of light.

The implications of the Lorentz transformation are discussed, emphasizing that while the coordinates of events may differ between observers, the underlying laws of physics remain the same. The professor clarifies that the transformation relates the coordinates of the same event as observed from different inertial frames, and that these new rules are essential for understanding relativity at high velocities.