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The Lorentz Factor — The Core of Relativity - Leejohnston - 01-08-2026
## The Lorentz Factor — The Core of Relativity
### 1. The Equation
Lorentz factor:
γ = 1 ÷ √(1 − v² / c²)
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### 2. What Each Symbol Means
- γ (gamma) = Lorentz factor
- v = relative velocity
- c = speed of light
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### 3. What the Equation Is Telling Us
The Lorentz factor measures **how extreme relativistic effects are**.
As speed increases:
- time dilation increases
- length contraction increases
- energy increases dramatically
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### 4. Where It Comes From (Intuition)
Relativity preserves the speed of light.
To do this:
- time slows
- lengths shrink
- mass–energy rises
γ quantifies all of it.
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### 5. Worked Example
If:
v = 0.8c
γ = 1 ÷ 0.6 ≈ **1.67**
That means:
- time dilation = 1.67×
- energy = 1.67× rest energy
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### 6. Real-World Applications
- Particle accelerators
- GPS corrections
- High-energy astrophysics
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### 7. Common Misconceptions
- γ only affects time → false
- γ becomes infinite gradually → false (it diverges at c)
- γ allows faster-than-light travel → false
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### Try It Yourself
What happens to γ at 0.9c? 0.99c?