Introduction
Einstein's Special Relativity (1905) revolutionized physics by showing space and time are interconnected and relative to observer motion. Based on two postulates, it modifies Newtonian mechanics at high velocities, with consequences including time dilation, length contraction, and E = mc2. It is one of the best-tested theories in physics.
First Postulate - Relativity Principle
The laws of physics are the same in all inertial reference frames. No preferred inertial frame exists. All inertial observers agree on physical laws. Extends Galilean relativity to include electromagnetism and all physical phenomena. Mechanics, electromagnetism, and all fundamental interactions obey this principle.
Second Postulate - Speed of Light
The speed of light in vacuum c is the same in all inertial frames, regardless of source or observer motion. c = 299,792,458 m/s exactly (now definition of meter). Contradicts Galilean velocity addition; requires modification of space and time concepts. Verified to extreme precision in countless experiments.
\nIntroduction
Einstein's Special Relativity (1905) revolutionized physics by showing space and time are interconnected and relative to observer motion. Based on two postulates, it modifies Newtonian mechanics at high velocities, with consequences including time dilation, length contraction, and E = mc2. It is one of the best-tested theories in physics.
First Postulate - Relativity Principle
The laws of physics are the same in all inertial reference frames. No preferred inertial frame exists. All inertial observers agree on physical laws. Extends Galilean relativity to include electromagnetism and all physical phenomena. Mechanics, electromagnetism, and all fundamental interactions obey this principle.
Second Postulate - Speed of Light
The speed of light in vacuum c is the same in all inertial frames, regardless of source or observer motion. c = 299,792,458 m/s exactly (now definition of meter). Contradicts Galilean velocity addition; requires modification of space and time concepts. Verified to extreme precision in countless experiments.
\nConsequences of Postulates
Simultaneity becomes relative. Time intervals and spatial distances depend on observer motion. No object with mass can reach speed c. Cause and effect order preserved for timelike separations. Energy and mass are equivalent. Space and time are unified into spacetime. These are profound changes from Newtonian concepts.
Historical Context
Developed from need to reconcile Maxwell's electromagnetism with mechanics. Michelson-Morley experiment (1887) failed to detect ether. Lorentz and Poincaré developed transformations. Einstein provided physical interpretation in 1905. Verified by countless experiments: particle accelerators, cosmic rays, atomic clocks, GPS.
Scope and Limitations
Special Relativity applies to inertial frames and gravity-free situations. General Relativity (1915) extends to accelerating frames and gravity. Newtonian mechanics is limit of SR at v << c. SR is accurate for all observed phenomena except strong gravity (near black holes, early universe).
\nSolved Example: Light Speed Invariance
A spaceship moves at 0.8c relative to Earth. It fires a laser beam forward. (a) What is light speed measured by Earth? (b) What is light speed measured by spaceship? (c) If spaceship fires projectile at 0.5c relative to ship, what is projectile speed measured by Earth? Solution: (a) By second postulate, Earth measures light speed = c exactly, regardless of spaceship motion. (b) Spaceship also measures light speed = c exactly, regardless of its own motion. (c) Projectile: uses relativistic velocity addition, not simple addition. u = (u' + v)/(1 + u'v/c2) = (0.5c + 0.8c)/(1 + 0.5×0.8) = 1.3c/1.4 = 0.929c. Projectile moves at 0.929c relative to Earth, not 1.3c. Classical addition fails at high speeds. If spaceship could reach c (impossible for massive object), and fired light forward: u = (c + c)/(1 + 1) = 2c/2 = c. Light speed remains c even when 'added' to c, satisfying second postulate.
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