Theory of Relativity (Video Notes)

Vocabulary flashcards covering Galilean relativity, special relativity postulates and consequences, relativistic mass/energy, spacetime concepts, and general relativity ideas.

Inertial reference frame

A frame of reference that is not accelerating; the laws of mechanics hold the same for all inertial observers.

Galilean relativity (classical relativity)

The principle that the laws of mechanics are the same for all observers in uniform motion relative to one another.

Galilean transformations

Relations that connect coordinates and velocities between inertial frames moving at a constant velocity V: x′ = x − Vt and v′ = v − V.

x′ = x − Vt

Transformation equation relating position in one frame to another moving at speed V.

v′ = v − V

Transformation equation relating velocity in one frame to another moving at speed V.

Absolute time (classical physics)

The concept that time is the same for all observers, regardless of their motion.

Principle of Invariance (Galilean relativity)

Core idea that certain physical laws (e.g., Newton’s laws) remain unchanged under Galilean transformations.

Newton’s second law (F = ma) under Galilean relativity

Newton’s laws retain validity in all inertial frames moving at constant velocity.

Postulate of Relativity (Special Relativity)

The laws of physics are the same for all observers in all inertial frames of reference.

Constancy of the speed of light (c)

The speed of light in vacuum is the same value for all inertial observers, independent of source or observer motion.

Time dilation

Moving clocks are observed to tick slower than stationary clocks.

Length contraction

Moving objects appear shorter in the direction of motion to a stationary observer.

Relativity of simultaneity

Whether two spatially separated events occur at the same time depends on the observer’s frame of reference.

Lorentz transformation

Equations that relate space-time coordinates between inertial frames in special relativity.

Twin paradox

A thought experiment illustrating differential aging for a traveling twin versus a stay-at-home twin.

Relativistic mass

Mass increases with velocity and tends toward infinity as velocity approaches c.

Rest mass (m0)

Mass of an object measured in its own rest frame.

Relativistic momentum

Momentum that includes the increase of mass with speed; p = mv with relativistic mass m.

E = mc^2 (mass–energy equivalence)

Mass and energy are interchangeable; a small amount of mass can be converted into a large amount of energy.

Rest energy (E0 = m0c^2)

The energy of a body at rest, derived from its rest mass.

Total energy (E) in relativity

E^2 = (pc)^2 + (m0c^2)^2; total energy includes rest energy and kinetic energy.

Four-dimensional space-time

A single framework combining the three spatial dimensions and time into a 4D continuum.

Event

A specific point in space-time described by its position and time.

Minkowski space-time

The four-dimensional space-time of special relativity used to describe events and intervals.

Worldline

The path of an object through space-time plotted on a space-time diagram.

Light cone

The boundary in space-time separating events that can be causally connected by light signals from those that cannot.

Minkowski diagram

A graphical representation showing time, space axes, worldlines, and light paths to illustrate relativity concepts.

Spacelike vs Timelike vs Lightlike intervals

Classification of space-time separations: spacelike (outside light cone), timelike (within light cone and causally connected), lightlike (connected by light).

Gravitational lensing

Bending of light by gravity, causing distorted, magnified, or multiple images of distant objects.

General relativity

Einstein’s theory extending relativity to gravity and accelerated frames; gravity is the curvature of space-time caused by mass-energy.

Gravity as curvature of space-time

Mass-energy tells space-time how to curve; curved space-time guides the motion of matter.

Spacetime curvature analogy (rubber sheet)

Analogy where a heavy mass curves a sheet, illustrating how gravity can alter the path of nearby objects.

GPS relativistic corrections

GPS satellite clocks are affected by time dilation due to speed and weaker gravity; corrections are required for accuracy.

Key predictions of general relativity

Gravitational lensing, black holes, and gravitational time dilation observed in systems like GPS.