Worldlines & proper time University Physics IV · Special relativity II
Spacetime Courier
Choose two cruise velocities to satisfy a journey endpoint and the traveller's clock limit.
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Challenge 1 of 3
Two-speed outbound route
Earth assigns 3 years to the first leg and 4 years to the second. Both legs run towards the destination.
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Arrive at 4.9–5.1 ly with 4.65–4.95 yr on the courier's clock.
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3 stars on your first test; 2 within three; 1 after that. A first clear earns 100 XP plus 10 per star. Better star records earn the difference; repeating a record earns no extra XP.
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Add the proper time along a piecewise inertial worldline while enforcing its displacement in the common Earth frame.
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From the course to the controls
The physics behind the game
Add the proper time along a piecewise inertial worldline while enforcing its displacement in the common Earth frame.
x/c = β₁Δt₁ + β₂Δt₂; τ = Σ Δtᵢ√(1 − βᵢ²)
Model assumptions. Flat spacetime, two constant-velocity legs and a fixed Earth inertial frame. Turns are idealised as instantaneous and contribute no finite duration. All speeds remain below c. Earth times and proper times are in years; positions are in light-years, so c = 1 ly/yr.