Twin paradox with arbitrary acceleration
- Author:
- Frank Schweickert
Twin paradox
Respective age observed from both systems: twin A (inertial system) and twin B (accelerated by force F)
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Which kind of motion makes the relative ageing symmetrical for both observers?
Switch to manual force control for B (click Autopilot button) or velocity control (click twice)
1. Try to meet A with B after 20 years.
2. How does inertia manifest itself?
3. Try a sharp turn far away from A. Can you actually see into the future of A?
Units of classical force F:
F = 1 means an acceleration of 1 ly/y² = 9,5Newton per kg of B's space ship, i.e. similar to gravity on the surface of Earth.
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The calculation of the proper time of B is carried out for every time step using Runge-Kutta 4.
Grey lines: Both observers A and B find the other's current age in global coordinates of inertial systems that are at rest in respect to themselves.
Observer B swaps these inertial systems when accelerating (tilting grey axis of simultaneity)
On the right, the calculated ages of the other twin are plotted against the respective proper time of A and B. The blue line is the age of B calculated by A according to his/her own inertial coordinate frame.
Yellow lines: Additionally, both observers receive radio signals from each other (yellow arrows). These are denoted as secondary age observations for every moment of their proper time (yellow graphs).