1. What is the Lorentz Factor?

The Lorentz factor (γ) is a quantity that describes the amount of time dilation, length contraction, and relativistic mass increase that occurs for an object moving at speeds approaching the speed of light in special relativity.

2. How Does the Calculator Work?

The calculator uses the Lorentz factor equation:

Where:

• \( v \) — Velocity of the object (m/s)
• \( c \) — Speed of light in vacuum (299,792,458 m/s)

Explanation: As velocity approaches the speed of light, the denominator approaches zero, making γ approach infinity. This explains why objects with mass cannot reach the speed of light.

3. Importance of Gamma in Special Relativity

Details: The Lorentz factor appears in many special relativity equations including time dilation (Δt = γΔt₀), length contraction (L = L₀/γ), and relativistic momentum (p = γmv).

4. Using the Calculator

Tips: Enter velocity in m/s (must be less than speed of light). The default speed of light is 299,792,458 m/s but can be modified for different media.

5. Frequently Asked Questions (FAQ)

Q1: What does γ = 1 mean?
A: γ = 1 means the object is at rest (v = 0). There are no relativistic effects at this speed.

Q2: What happens when v approaches c?
A: As v approaches c, γ approaches infinity, leading to infinite time dilation and length contraction.

Q3: What is a typical γ value for fast-moving objects?
A: For the International Space Station (v ≈ 7,700 m/s), γ ≈ 1.0000003. For electrons in particle accelerators (v ≈ 0.999999991c), γ ≈ 7,450.

Q4: Can γ be less than 1?
A: No, γ is always ≥ 1 for real velocities between 0 and c.

Q5: How does γ relate to kinetic energy?
A: Relativistic kinetic energy is KE = (γ - 1)mc², which approaches infinity as v approaches c.