Twin Paradox

One twin stays at x=0 while the other travels to a fixed destination, optionally rests there, and returns. Distances and all event times use the Earth frame. Enter positive speed magnitudes for both legs; the return velocity points toward home. The destination stay is at rest relative to Earth, not a period of moving coasting.

The live comparison shows the full worldlines and final elapsed times. The timeline starts at departure. Scrub, enter an Earth time, select an event, step or play to read both clocks at the same Earth-frame time. Playback compresses the entire trip into eight seconds; it does not divide unequal legs into equal durations. Hidden tabs pause playback. Reduced-motion users can use the timeline and stepping.

For each leg, t=D/β and Δτ=t√(1−β²). The stationary stay contributes its full duration to both clocks. The traveler’s clock is integrated separately over outbound flight, stay and return; its current position uses those same event times. The diagram uses equal x/ct scales with c=1 light-year per Julian year, so light rays are at 45°. Very slow motion produces nearly overlapping worldlines. Clock readings are proper elapsed times at equal Earth times, not delayed signals received by either twin.

The traveler changes inertial frames at the destination; the home twin remains on one inertial worldline. This breaks the apparent symmetry. Instantaneous velocity changes, flat spacetime and ideal clocks are assumed. There is no finite acceleration, fuel, gravitational or optical-signal model. The old optional five-percent pause is migrated to an explicit stay duration. All calculations stay in your browser.

OpenStax: Time dilation / Twin paradox

The comparison opens live. Changing trip inputs recomputes paused worldlines without rounding entered time; invalid time hides the moving markers and current clocks, while retaining trip references. The time field, timeline and event menu navigate; Reset restores all defaults at departure. Options contains examples and stepping. Only exact trip input text is stored, even partial or invalid values. Time, playback, plots and open menus are not saved. Playback spans the trip in about eight display seconds, with a maximum 50 ms contribution per frame; background lag is not caught up.