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+--- Thread: The Spacetime Interval — The Geometry of Time (/showthread.php?tid=436)
The Spacetime Interval — The Geometry of Time - Leejohnston - 01-08-2026
## The Spacetime Interval — The Geometry of Time
### 1. The Equation
Spacetime interval:
s² = c²t² − x² − y² − z²
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### 2. What Each Symbol Means
- s = spacetime interval
- t = time difference
- x, y, z = spatial differences
- c = speed of light
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### 3. What the Equation Is Telling Us
Different observers disagree on space and time separately.
But **the spacetime interval is invariant**.
Everyone agrees on it.
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### 4. Where It Comes From (Intuition)
Space and time are not separate.
They are components of a single geometric structure: spacetime.
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### 5. Why This Matters
This equation:
- replaces absolute time
- unifies motion and causality
- underlies all of relativity
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### 6. Real-World Applications
- Relativity
- Particle physics
- Cosmology
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### 7. Common Misconceptions
- Time is just another dimension → incomplete
- Space and time are independent → false
- Geometry is abstract → false (it governs reality)
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### Try It Yourself
Why can two observers disagree on time but agree on causality?