1. What is the Lorentz Factor?

The Lorentz factor (γ) is a quantity that describes how much time, length, and relativistic mass change for an object moving at a significant fraction of the speed of light. It's fundamental in 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: 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 in Special Relativity

Details: The Lorentz factor appears in:

• Time dilation: \( \Delta t' = \gamma \Delta t \)
• Length contraction: \( L' = L / \gamma \)
• Relativistic momentum: \( p = \gamma mv \)
• Energy-mass equivalence: \( E = \gamma mc^2 \)

4. Using the Calculator

Tips: Enter velocity in m/s and speed of light in m/s (default is 299,792,458 m/s). Velocity must be less than speed of light.

5. Frequently Asked Questions (FAQ)

Q1: What happens when v approaches c?
A: The Lorentz factor γ approaches infinity, which is why infinite energy would be required to accelerate a massive object to the speed of light.

Q2: What are typical γ values for everyday speeds?
A: For everyday speeds (e.g., 100 km/h ≈ 27.8 m/s), γ ≈ 1.0000000000043 - practically indistinguishable from 1.

Q3: What γ would a spacecraft at 0.9c have?
A: At 0.9c (90% light speed), γ ≈ 2.294 - meaning time runs 2.294 times slower for the spacecraft.

Q4: Can γ be less than 1?
A: No, γ is always ≥ 1. At v=0, γ=1 (Newtonian mechanics applies).

Q5: How does this relate to GPS satellites?
A: GPS satellites move fast enough (about 14,000 km/h) that both special relativity (γ factor) and general relativity must be accounted for to maintain accuracy.