Einstein's Theory of Relativity

Overview

Albert Einstein's theory comes in two parts:

	Special Relativity (1905)	General Relativity (1915)
Deals with	Motion at constant speed, especially close to the speed of light	Gravity and acceleration
Core idea	Space and time are not absolute. They depend on how fast you move	Gravity is not a force. It is the curvature of spacetime caused by mass and energy
Famous results	Time dilation, length contraction, E = mc²	Black holes, gravitational waves, light bending, time running slower near mass

Special Relativity

The Two Postulates

The laws of physics are the same for every observer moving at constant speed.
The speed of light in a vacuum is the same for every observer: c = 299,792,458 m/s, no matter how fast the observer or the light source moves.

Everything else follows from these two rules.

The Lorentz Factor

γ = 1 / √(1 − v²/c²)

At everyday speeds γ is almost exactly 1, so you notice nothing. Close to the speed of light it grows rapidly:

Speed	γ
10 % of c	1.005
50 % of c	1.155
90 % of c	2.294
99 % of c	7.09
99.9 % of c	22.4

Time Dilation

A moving clock runs slow compared to one at rest:

Δt = γ · Δt₀

Example: At 90 % of the speed of light, 1 hour on board corresponds to about 2.3 hours on Earth.

Real-world evidence: muons created in the upper atmosphere should decay before they reach the ground. We still detect them at the surface, because their "clocks" run slow from our point of view.

Length Contraction

Moving objects are shorter in the direction they travel:

L = L₀ / γ

Mass–Energy Equivalence

E = m · c²

Mass is a very concentrated form of energy. This explains why stars shine: the Sun converts about 4 million tonnes of mass into energy every second. It is also what powers nuclear reactors.

The Speed Limit

Anything with mass would need infinite energy to reach c. That is why nothing can travel faster than light.

General Relativity

The Equivalence Principle

You cannot tell the difference between standing still in a gravitational field and accelerating in a rocket. Floating in orbit feels exactly like floating far away from any planet. Einstein took this seriously and concluded that gravity is a property of spacetime itself.

Curved Spacetime

"Spacetime tells matter how to move; matter tells spacetime how to curve." – John Wheeler

A heavy mass bends spacetime the way a bowling ball bends a trampoline. Planets are not "pulled" in the usual sense. They follow the straightest possible path (a geodesic) through curved spacetime.

The full theory is written as the Einstein field equations:

G_μν + Λ·g_μν = (8πG / c⁴) · T_μν

The left side describes the curvature of spacetime. The right side describes the matter and energy in it. Λ is the cosmological constant, see Dark Matter and Dark Energy.

Gravitational Time Dilation

Time runs slower closer to a mass:

Δt₀ = Δt · √(1 − 2GM / (r·c²))

The Evidence

Prediction	Confirmed by
Mercury's orbit slowly rotates by an extra 43 arcseconds per century	Explained by GR in 1915. Newton's theory could not explain it
Light bends around the Sun	Arthur Eddington's solar eclipse expedition, 1919
Gravitational lensing	Galaxies acting as giant lenses, seen in many telescope images
Gravitational redshift	Pound–Rebka experiment, 1959
Gravitational waves	First detected by LIGO in 2015 from two merging black holes (Nobel Prize 2017)
Black holes	Images of M87* (2019) and Sagittarius A* (2022) by the Event Horizon Telescope

Relativity in Everyday Life: GPS

GPS satellites orbit at about 20,200 km altitude at about 3.9 km/s. Two effects change their clocks:

Effect	Change per day
Special relativity (high speed, so the clock runs slower)	about −7 μs
General relativity (weaker gravity, so the clock runs faster)	about +45 μs
Net effect	about +38 μs

Light travels about 11 km in 38 μs. Without correcting for relativity, GPS positions would drift by kilometres every day. That is why the satellite clocks are deliberately tuned slightly slower before launch.