Reality depends on your velocity - time, space, and simultaneity are observer-dependent!
← Backγ = 1/√(1 - v²/c²)
This one factor controls ALL relativistic effects!
• At v = 0 (rest): γ = 1 (no effects)
• At v = 0.5c: γ = 1.15
• At v = 0.866c: γ = 2 (time slows by half!)
• At v = 0.9c: γ = 2.29
• At v = 0.99c: γ = 7.09
• At v = 0.999c: γ = 22.4
• At v → c: γ → ∞
Events simultaneous in one frame are NOT simultaneous in another!
Δt = γvΔx/c²
The "time gap" between events depends on their spatial separation (Δx) and relative velocity (v).
Example: Lightning strikes 100m apart on a train. For the train conductor (moving), they're simultaneous. For platform observer, one happens first!
Moving objects appear shorter!
L = L₀/γ
A 100m spaceship moving at 0.866c appears only 50m long to a stationary observer!
But: From the spaceship's perspective, THEY are stationary and the universe is contracted!
Moving clocks run slower!
τ = τ₀/γ
Twin travels at 0.866c for 10 years (their time), returns to find Earth twin aged 20 years!
Paradox resolved: The traveling twin accelerates/decelerates (breaks symmetry), so they're the one who ages less.
Only the speed of light (c) is the same for all observers.
Everything else - time intervals, spatial distances, simultaneity - depends on your reference frame!
Spacetime interval is invariant: s² = c²Δt² - Δx²
All observers agree on this quantity, even though they disagree on Δt and Δx separately!
This is why we say "observer-dependent reality"! Different observers literally experience different realities - different passage of time, different lengths, different simultaneity. Yet they're all equally valid!
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