Relativity Calculator

Explore Einstein's theories of special and general relativity

s
Time in rest frame
c
Fraction of light speed
Time Dilation Factor (γ)
2.294
Lorentz factor
Dilated Time (t)
2.294
s
Proper Time (t₀)
1.000
s
Velocity (v)
0.900
c
Time Dilation
2.29x
m
Length in rest frame
c
Fraction of light speed
Contracted Length (L)
0.436
m
Proper Length (L₀)
1.000
m
Lorentz Factor (γ)
2.294
γ = 1/√(1 - v²/c²)
Velocity (v)
0.900
c
Understanding Length Contraction

Length contraction is the phenomenon where the length of an object moving at relativistic speeds appears shorter to a stationary observer. This effect is only noticeable at speeds approaching the speed of light.

  • Proper Length: Length measured in the object's rest frame
  • Contracted Length: L = L₀ / γ
  • Contraction occurs only in the direction of motion
  • At everyday speeds, contraction is negligible
  • At 90% light speed, lengths contract to about 44%
Hz
Frequency in rest frame
c
Fraction of light speed
Relative to observer
Observed Frequency (f)
866.0
Hz
Source Frequency (f₀)
500.0
Hz
Wavelength Shift
-42.3%
Blue/red shift
Velocity (v)
0.500
c
Relativistic Doppler Formulas
Approaching: f = f₀ × √[(1 + β)/(1 - β)]
Receding: f = f₀ × √[(1 - β)/(1 + β)]
β = v/c
Where:
f = Observed frequency
f₀ = Source frequency
v = Relative velocity
c = Speed of light
kg
Rest mass of object
c
Fraction of light speed
Rest Energy (E₀)
8.99e+16
J
Relativistic Energy (E)
2.06e+17
J
Kinetic Energy (K)
1.16e+17
J
Lorentz Factor (γ)
2.294
γ = 1/√(1 - v²/c²)
Mass-Energy Equivalence
Object Mass Rest Energy Equivalent
Electron 9.1e-31 kg 8.2e-14 J 0.511 MeV
Proton 1.67e-27 kg 1.5e-10 J 938 MeV
Uranium atom 3.95e-25 kg 3.55e-8 J 221 GeV
1 gram 0.001 kg 9e+13 J 21 kilotons TNT
Human (70kg) 70 kg 6.3e+18 J 1.5 gigatons TNT
Einstein's Relativity Principles

Einstein's theory of relativity revolutionized physics with two fundamental principles:

  • Special Relativity (1905):
    • The laws of physics are the same in all inertial frames
    • The speed of light in vacuum is constant for all observers
  • General Relativity (1915):
    • Gravity is the curvature of spacetime by mass and energy
    • Accelerated frames are equivalent to gravitational fields
  • Key consequences: time dilation, length contraction, mass-energy equivalence
  • Verified by experiments: GPS systems, gravitational lensing, particle accelerators

Einstein's Theory of Relativity

Albert Einstein's theory of relativity revolutionized our understanding of space, time, and gravity. It consists of two parts: special relativity (1905) and general relativity (1915).

Concept Special Relativity General Relativity
Scope Uniform motion in inertial frames Accelerated motion and gravity
Key Principle Speed of light is constant Gravity as curvature of spacetime
Key Effects Time dilation, length contraction Gravitational time dilation, light bending
Mathematical Framework Minkowski spacetime Riemannian geometry
Applications Particle physics, GPS corrections Cosmology, black holes, gravitational waves

Real-World Applications of Relativity

  • GPS Systems: Must account for both special and general relativistic effects to maintain accuracy
  • Particle Accelerators: Relativistic effects are crucial for understanding particle behavior at near-light speeds
  • Astronomy: Explains phenomena like gravitational lensing and black holes
  • Cosmology: Forms the basis for understanding the expansion of the universe
  • Electronics: Relativity explains why gold doesn't corrode and mercury is liquid at room temperature

Note: Relativistic effects become significant at speeds above 10% of light speed (30,000 km/s). At everyday speeds, Newtonian physics provides excellent approximations.

Key Relativity Formulas
Lorentz Factor: γ = 1/√(1 - v²/c²)
Time Dilation: Δt = γΔt₀
Length Contraction: L = L₀/γ
Relativistic Energy: E = γmc²
Relativistic Momentum: p = γmv

Frequently Asked Questions

Time dilation is the phenomenon where time passes at different rates for observers in different inertial frames. According to special relativity, a moving clock runs slower than a stationary clock. The effect is given by Δt = γΔt₀, where γ is the Lorentz factor. This has been experimentally verified using atomic clocks on airplanes and satellites.

According to special relativity, as an object approaches the speed of light, its relativistic mass increases, requiring more energy to accelerate it further. To reach the speed of light would require infinite energy. Additionally, causality would be violated if information could travel faster than light, as it would allow effects to precede causes in some reference frames.

The twin paradox is a thought experiment in special relativity. One twin travels at high speed to a distant star and back, while the other stays on Earth. Due to time dilation, the traveling twin ages less than the Earth-bound twin. The paradox arises because each twin sees the other's clock running slow during the journey. The resolution is that the traveling twin changes direction (accelerates), breaking the symmetry.

GPS satellites orbit at about 20,000 km altitude and move at 14,000 km/h. Both special relativity (time dilation due to speed) and general relativity (time dilation due to weaker gravity) affect their atomic clocks. Without relativistic corrections, GPS would accumulate errors of about 10 km per day. Engineers account for both effects to maintain accuracy.

E=mc² is the mass-energy equivalence formula from special relativity. It states that energy (E) and mass (m) are interchangeable, with c (speed of light) as the conversion factor. This explains energy production in nuclear reactions: a small amount of mass converts to enormous energy (c² = 9e+16 m²/s²). It underlies nuclear power, atomic bombs, and particle physics.