Special Relativity
⚡ Einstein's Revolutionary Theory
In 1905, Albert Einstein published a paper that revolutionized physics: special relativity. Two simple postulates—the laws of physics are the same in all inertial frames, and the speed of light is constant—led to profound consequences: time dilation, length contraction, simultaneity is relative, and energy and mass are equivalent (E = mc²).
🎯 Key Concepts
- • Spacetime and Minkowski diagrams
- • Lorentz transformations
- • Time dilation and length contraction
- • Relativistic energy and momentum
🔬 Applications
- • Particle accelerators and colliders
- • GPS satellite time corrections
- • Nuclear energy and mass-energy equivalence
- • Foundation for general relativity
📐 Fundamental Principles
First Postulate: Principle of Relativity
The laws of physics are the same in all inertial reference frames. There is no absolute rest frame or absolute motion—only relative motion between observers matters.
Second Postulate: Constancy of Light Speed
The speed of light in vacuum (c ≈ 3 × 10⁸ m/s) is the same for all observers, regardless of their motion or the motion of the light source. This leads to the unification of space and time.
📊 Key Equations
Lorentz Factor
Appears in all relativistic transformations. γ → 1 as v → 0 (non-relativistic limit). γ → ∞ as v → c.
Time Dilation
Moving clocks run slower. Δτ is proper time (clock's rest frame), Δt is dilated time (observer's frame).
Length Contraction
Moving objects are contracted in the direction of motion. L₀ is proper length (object's rest frame).
Mass-Energy Equivalence
The most famous equation in physics. Mass and energy are interconvertible. At rest, E = m₀c².
Energy-Momentum Relation
Relates total energy E, momentum p, and rest mass m₀. For photons (m₀ = 0): E = pc.
Spacetime Interval
The invariant spacetime interval. All observers agree on Δs², even though they disagree on Δt and Δx separately.
📚 Course Content
Spacetime Foundations
- • Historical context: Galilean relativity and Maxwell's equations
- • Michelson-Morley experiment and the aether
- • Einstein's postulates and their consequences
- • Minkowski spacetime and light cones
- • Proper time and worldlines
Lorentz Transformations
- • Derivation from Einstein's postulates
- • Time dilation and length contraction
- • Relativity of simultaneity
- • Velocity addition formula
- • Lorentz transformation as rotation in spacetime
Relativistic Mechanics
- • Four-vectors: position, velocity, momentum, acceleration
- • Relativistic momentum: p = γmv
- • Relativistic energy: E = γmc²
- • Mass-energy equivalence and nuclear reactions
- • Conservation laws in relativistic collisions
Electromagnetism in SR
- • Electric and magnetic fields are frame-dependent
- • Electromagnetic field tensor F^μν
- • Covariance of Maxwell's equations
- • Four-current and charge conservation
- • Transformation of E and B fields between frames
🔗 Connections to Other Courses
Prerequisites:
- • Classical Mechanics: Lagrangian formalism
- • Tensor Calculus: Four-vectors and tensors
- • Waves & Optics: Electromagnetic waves
Leads to:
- • General Relativity: Curved spacetime and gravity
- • Quantum Field Theory: Relativistic quantum mechanics
- • Cosmology: Expanding universe
📺 Video Lectures
World-class lectures on special relativity from leading physicists and science communicators.
WSU: Space, Time, and Einstein with Brian Greene
Physicist and acclaimed science communicator Brian Greene delivers an engaging lecture at Wright State University, exploring Einstein's special relativity. He explains how space and time are interwoven into a single spacetime continuum, and how the counterintuitive consequences of relativity emerge from Einstein's two simple postulates.
Topics Covered:
- The constancy of the speed of light and its implications
- Time dilation and the twin paradox
- Length contraction and relativity of simultaneity
- E = mc² and the equivalence of mass and energy
- Spacetime diagrams and Minkowski geometry
MIT 8.20 Special Relativity - Prof. Markus Klute
MIT's undergraduate course on Special Relativity taught by Prof. Markus Klute. These lectures provide a rigorous introduction to Einstein's special theory of relativity with historical context and modern applications.
L1.2: Prof. Klute's Research
Introduction to high-energy physics research at MIT and CERN.
L1.3: History of Special Relativity
The historical development of special relativity from Galileo to Einstein.
L1.4: Space, Time, and Spacetime (Guest)
Guest lecture exploring the conceptual foundations of spacetime.
L1.5: Categories of Physics
Overview of different branches of physics and their interconnections.
L2.1: Events
Introduction to events as fundamental objects in spacetime.
L2.2: Galilean Transformation
Classical Galilean relativity and coordinate transformations.
Leonard Susskind's Theoretical Minimum Series
This course also features 10 lectures from Prof. Leonard Susskind's renowned "Theoretical Minimum" series at Stanford. Susskind's clear explanations make even the most counterintuitive aspects of special relativity accessible and understandable.
Watch Susskind Lectures →Learning Path & Prerequisites
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