NYJC_EJC Special Relativity Notes

9814 H3 Physics Special Relativity Lecture Notes 1 H3 Topic 3: Special Relativity Content • Michelson-Morley experiment • Inertial frames and universal light speed • Lorentz transformations • Length contraction and time dilation • Velocity addition • Energy–momentum relation Learning Outcomes Candidates should be able to: (a) discuss qualitatively the results of the Michelson–Morley interferometer experiment and its implications on the ether theory (knowledge of the details of the experiment is not required) (b) state the postulates of the special theory of relativity, that in all inertial frames, the laws of physics are the same and the speed of light in free space is the same regardless of the motion of the light source or observer (c) appreciate the failure of Galilean transformation equations when applied to a moving source of light (d) discuss the concept of simultaneity (e) show an understanding of the terms proper time and proper length (f) apply the Lorentz transformation equations to solve one-dimensional problems (g) derive the time dilation formula and length contraction formula, making use of the Lorentz factor (h) apply the time dilation formula and the length contraction formula in related situations (e.g. the lifetime of fast-moving muons) or to solve problems (i) use the one -dimensional relativistic velocity addition formula to calculate velocities in different inertial frames or to solve problems (j) use the relativistic energy –momentum relation E 2 = (pc)2 + (mc2)2 to solve problems, and show that it reduces, in the appropriate limits, to: 1. E = pc (for massless particles); or 2. E = mc2 + 1 2 mv2 (for particles moving at low speeds v << c).

9814 H3 Physics Special Relativity Lecture Notes 2 1 Speed of Light and the Michelson-Morley’s Experiment 1.1 Speed of Light 1.1.1 The Measurement of the Speed of Light The speed of light (exactly 299 ,792,458 m s −1, usually denoted c) is an important fundamental constant in physics that is known to great precision today. In fact, one of the base units, the metre, is defined based on the speed of light. Up until late 1600s, however, the speed of light was believed to be infinite. Galileo Galilei (1564 – 1642) was one of the first to question that. On a clear night in the year 1638 (or thereabout), in the Italian countryside, Galileo conducted the first experiment to measure the speed of light with the help of an assistant. Each c arrying a lantern supplied with shutters, Galileo and his assistant placed themselves as far apart as they could stand yet still able to see each other (about 1.5 km from each other). Galileo’s instruction to his assistant was to flash his lantern as soon as he saw Galileo’s lantern flash. Knowing their physical separation, Galileo had hoped that the time delay between his lantern flash and his observation of the lantern flash of his assistant would allow him to calculate the speed