Learn Einstein's Special Theory of Relativity with interactive simulations. Understand time dilation, length contraction, spacetime diagrams, and the equivalence of mass and energy with step-by-step visualizations and real-world examples.
Special Relativity is a theory proposed by Albert Einstein in 1905 that describes the physics of objects moving at constant speeds, particularly those approaching the speed of light. It revolutionized our understanding of space and time by showing that they are interwoven into a single continuum known as spacetime.
The theory is based on two fundamental postulates: 1) The laws of physics are the same in all inertial frames of reference, and 2) The speed of light in a vacuum is constant for all observers, regardless of their motion or the motion of the light source.
The foundational postulates of Einstein's Special Theory of Relativity
The laws of physics are invariant (identical) in all inertial systems (non-accelerating frames of reference).
If S and S' are inertial frames, then physical laws have the same form in both.
The speed of light in a vacuum is the same for all observers, regardless of the motion of the light source or observer.
c = 299,792,458 m/s ≈ 3.00 × 10⁸ m/s
Special Relativity predicts several counterintuitive effects that become significant at speeds approaching the speed of light:
Time passes slower for objects in motion relative to an observer at rest.
Δt' = Δt / √(1 - v²/c²)
Objects appear shorter in the direction of motion when moving at high speeds.
L = L₀ × √(1 - v²/c²)
The relativistic mass of an object increases with velocity.
m = m₀ / √(1 - v²/c²)
Mass and energy are interchangeable as described by E=mc².
E = mc²
Events simultaneous in one frame may not be simultaneous in another.
Velocities don't simply add at relativistic speeds.
u = (v + u') / (1 + vu'/c²)
How Special Relativity affects modern technology and our daily lives
GPS systems must account for time dilation effects to maintain accuracy. Without relativistic corrections, GPS would be off by several kilometers per day.
High-energy particle accelerators like the Large Hadron Collider rely on relativistic calculations to accelerate particles to near-light speeds.
Old CRT televisions and computer monitors required relativistic corrections for electrons traveling at significant fractions of light speed.
The E=mc² equation explains how nuclear reactions convert mass to energy, powering nuclear reactors and weapons.
PET scans utilize positron-electron annihilation, a process governed by mass-energy equivalence principles.
Stars shine through nuclear fusion, converting mass to energy according to E=mc², sustaining life on Earth.
Perform calculations for various relativistic phenomena
Calculate how time slows down at high velocities
Dilated Time: 0 seconds
Time Factor (γ): 1
Formula: Δt' = Δt / √(1 - v²/c²)
Calculate how objects contract at high velocities
Contracted Length: 0 meters
Length Factor (γ): 1
Formula: L = L₀ × √(1 - v²/c²)
Calculate how mass increases at high velocities
Relativistic Mass: 0 kg
Mass Factor (γ): 1
Formula: m = m₀ / √(1 - v²/c²)
Calculate energy equivalent of mass (E=mc²)
Energy Equivalent: 0 Joules
Formula: E = mc²
Convert between different units used in relativity
Explore relativistic phenomena through hands-on visualizations
Visualize how time slows down for objects moving at high speeds
Step 1: At rest, both clocks tick at the same rate.
Observe how objects contract in the direction of motion at high speeds
Step 1: Object at rest has its proper length.
Interactive three-dimensional visualization of spacetime and relativistic effects
3D Spacetime Visualization
Interactive 3D model showing spacetime curvature and worldlines
3D representation of how massive objects curve spacetime
Animated visualization of object trajectories through spacetime
Adjust parameters like velocity, mass, and time dilation factor