# 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) Press "Start" to begin. (Faster in Google Chrome, it seems) 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.
Press "Start" to begin.
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).