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Lorentz Factor Formula:
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The Lorentz factor (γ) is a quantity that appears in several equations in special relativity. It describes how much time, length, and relativistic mass change for an object while that object is moving relative to an observer.
The calculator uses the Lorentz factor formula:
Where:
Explanation: The factor approaches infinity as the velocity approaches the speed of light, and equals 1 when the velocity is zero.
Details: The Lorentz factor is fundamental to special relativity, appearing in equations for time dilation, length contraction, and relativistic mass. It's essential for understanding high-velocity physics and correcting GPS satellite timing.
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 the speed of light.
Q1: What happens when velocity equals the speed of light?
A: The denominator becomes zero, making the Lorentz factor undefined (approaches infinity). This reflects that objects with mass cannot reach the speed of light.
Q2: What is a typical value for the Lorentz factor?
A: For everyday speeds, γ is extremely close to 1. At 10% of light speed, γ ≈ 1.005; at 90% of light speed, γ ≈ 2.294.
Q3: How does Lorentz factor relate to time dilation?
A: Time dilation is calculated as Δt = γΔt₀, where Δt₀ is the proper time interval between two events.
Q4: Can the Lorentz factor be less than 1?
A: No, the Lorentz factor is always greater than or equal to 1 for all real velocities.
Q5: What are practical applications of the Lorentz factor?
A: It's used in particle accelerators, astrophysics, satellite navigation systems, and any technology involving high-speed particles or precise timing.