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 velocities approaching the speed of light. It is fundamental to Einstein's theory of 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: The factor approaches infinity as velocity approaches the speed of light, explaining why massive objects cannot reach light speed.

3. Importance in Special Relativity

Details: The Lorentz factor appears in all relativistic 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). Default speed of light is set to 299,792,458 m/s but can be adjusted for educational purposes.

5. Frequently Asked Questions (FAQ)

Q1: What happens at v = c?
A: The denominator becomes zero, making γ undefined (infinite), which is why massive objects cannot reach light speed.

Q2: What's a typical Lorentz factor for spacecraft?
A: Even the fastest spacecraft (≈60,000 km/h) have γ≈1.000000005 - relativistic effects are negligible at everyday speeds.

Q3: How does γ relate to relativistic energy?
A: Total energy E = γmc², where m is rest mass. The (γ-1)mc² term represents kinetic energy.

Q4: Can γ be less than 1?
A: No, γ ≥ 1 always. At v=0, γ=1 (Newtonian case). As v→c, γ→∞.

Q5: What's the Lorentz factor for 0.9c?
A: At 90% light speed (v=0.9c), γ≈2.294 - time runs 2.294 times slower for the moving object.