A framework in physics describing how measurements of space, time, motion, and gravity depend on the observer and the geometry of spacetime

Special Relativity (SR)

General Relativity (GR)

Space and time are not absolute; they form a unified spacetime

Gravity is not a force in the Newtonian sense (in GR) but a manifestation of spacetime curvature

A 4-dimensional continuum: 3 spatial dimensions + 1 time dimension

Events are specified by coordinates (t, x, y, z)

Quantity that remains the same for all inertial observers

In flat spacetime (SR): s^2 = -c^2Δt^2 + Δx^2 + Δy^2 + Δz^2

Light cone structure separates events into

Causality preserved because no information travels faster than light

Worldline: the path of an object through spacetime

Proper time: time measured by a clock moving along a worldline

Applies to inertial frames (non-accelerating observers)

Ignores gravity (or treats it as negligible)

Principle of relativity

Constancy of the speed of light

Replace Galilean transformations at high speeds

Mix space and time coordinates between observers moving relative to each other

Lead to invariance of spacetime interval

Relativity of simultaneity

Time dilation

Length contraction

Velocity addition

Mass-energy equivalence

Treats SR as geometry in 4D spacetime

Metric signature encodes how time differs from space

Extends relativity to include acceleration and gravity

Describes gravity as geometry rather than a Newtonian force

Local equivalence of gravitational and inertial effects

Gravitational mass equals inertial mass (experimentally supported)

Matter and energy tell spacetime how to curve

Curved spacetime tells matter how to move (free-fall follows geodesics)

Conceptual form: curvature ↔ stress-energy

Stress-energy tensor

Solutions correspond to different gravitational scenarios

Free-falling objects move along the “straightest possible” paths in curved spacetime

Explains orbital motion without invoking a gravitational force

Gravitational time dilation

Gravitational redshift

Deflection of light (gravitational lensing)

Perihelion precession

Frame dragging

Gravitational waves

SR: flat spacetime (no curvature)

GR: curved spacetime (curvature produced by mass-energy)

SR: inertial frames only

GR: all frames, including accelerating ones, using general covariance

SR: not fundamentally included

GR: gravity emerges from geometry

GR reduces to SR locally in small regions of spacetime with negligible curvature

GR reduces to Newtonian gravity in weak-field, low-speed conditions

Mass-energy changes spacetime geometry

Objects follow geodesics; perceived as gravitational attraction

Metric tensor

Curvature measures

Event horizons

Formation

Key features

Observational signatures

Expanding universe

Big Bang framework

Dark energy and cosmological constant

Dark matter (within GR framework)

Particle accelerators

Electromagnetism consistency

GPS necessity (SR component)

1919 solar eclipse

Pound–Rebka experiment

Shapiro time delay

Gravity Probe B / LAGEOS

LIGO/Virgo/KAGRA

Precision timing and navigation

Not all quantities are frame-dependent; invariants exist (e.g., spacetime interval, speed of light in vacuum)

It limits information and massive objects from exceeding c, but allows high speeds and expanding spacetime

In GR, gravity is real as spacetime curvature and measurable via tidal effects

They attract like any mass; effects depend on distance and mass distribution

Physics is governed by spacetime structure; motion and gravity are manifestations of that structure

Space and time mix; c is invariant; measurements depend on relative motion

Mass-energy curves spacetime; curvature governs motion; gravity is geometry