Special Relativity
Time dilation, length contraction, simultaneity, mass-energy equivalence, and the twin paradox — all from the two postulates.
Relativity
Special relativity, E = mc², general relativity, spacetime curvature, black holes, and gravitational waves — Einstein's revolution in physics.
Special Relativity
Einstein's special relativity (1905) rests on two postulates: the laws of physics are the same in all inertial (non-accelerating) frames, and the speed of light c is constant in all inertial frames regardless of the motion of the source or observer. These two principles, seemingly simple, overturn Newtonian absolute space and time.
The consequences are profound. Time dilation: moving clocks run slow by a factor γ = 1/√(1 − v²/c²). Length contraction: moving objects are shorter along the direction of motion. Simultaneity is relative: two events simultaneous in one frame are not simultaneous in another. And famously, E = mc²: mass is equivalent to energy.
Lorentz Transformations
The Lorentz transformations relate position and time coordinates between two inertial frames in relative motion at velocity v. They replace the Galilean transformations of Newtonian mechanics and reduce to them when v ≪ c. Four-vectors (combining space and time) remain invariant under Lorentz transformations, forming the foundation of relativistic kinematics.
General Relativity
General relativity (1915) extends special relativity to accelerating frames. Its central insight — the equivalence principle — states that a uniformly accelerating reference frame is locally indistinguishable from a gravitational field. Einstein showed that gravity is not a force but the curvature of four-dimensional spacetime caused by mass and energy.
The Einstein field equations G_μν = 8πG/c⁴ T_μν relate the geometry of spacetime (left side) to the distribution of matter and energy (right side). Solutions describe diverse phenomena: the precession of Mercury's orbit, the bending of starlight, the expansion of the universe, and the existence of black holes.
Black Holes and Gravitational Waves
The Schwarzschild solution describes a non-rotating black hole with an event horizon at r_s = 2GM/c². Nothing — not even light — can escape from inside the event horizon. The Kerr solution extends this to rotating black holes. Gravitational waves, predicted by general relativity and first directly detected by LIGO in 2015, are ripples in spacetime caused by accelerating masses.
Learning Pathways
Spacetime Geometry
Four-vectors, Minkowski spacetime, the spacetime interval, causality, and an introduction to the equivalence principle.
General Relativity
Tensor calculus, the Einstein field equations, exact solutions (Schwarzschild, Kerr), geodesics, and gravitational waves.
Key Articles
Special Relativity
A complete guide to time dilation, length contraction, and E = mc².
Read →General Relativity
Einstein's field equations, spacetime curvature, and the geometry of gravity.
Read →The Twin Paradox
Why the travelling twin ages less — and why it is not symmetric.
Read →Time Dilation Near Black Holes
Gravitational time dilation and why clocks slow near massive objects.
Read →Lorentz Transformations
The mathematics of special relativity — deriving the transformation equations.
Read →Physics of Black Holes
Event horizons, singularities, Hawking radiation, and observational evidence.
Read →Frequently Asked Questions
What is the difference between special and general relativity?
Special relativity covers inertial frames and constant-velocity physics. General relativity extends to accelerating frames and explains gravity as spacetime curvature.
What does E = mc² mean?
Mass and energy are equivalent. A small mass m contains enormous energy E = mc² — the basis of nuclear reactions and particle-antiparticle annihilation.
Why does time slow down near a black hole?
Gravitational time dilation: clocks in stronger gravitational fields run slower. Near the event horizon, an outside observer sees clocks approach a stop.
Have relativistic effects been measured?
Yes. GPS satellites require both special and general relativistic corrections — without them, position errors would accumulate at ~10 km/day.