Interactive Two-Observer Spacetime Diagrams

How to use this

If you've never studied spacetime diagrams in Einstein's theory of special relativity, jump to the conceptual introduction now. Assuming you recognize what you're lookig at here, I hope the general idea is fairly straightforward. A few details to note:

• All velocities are specified as a fraction of the speed of light (from -1 to 1), but you can treat the units as "" if you'd like.
• The default scenario shown is intentionally very simple: no axes for an Other Frame are shown (because its v is 0), and the Other Frame diagram is hidden (the checkbox is unchecked). Try loading some of the pre-defined examples! Each loads with a brief explanatory note.
• When you press the "Animate Motion" button under the diagrams, a yellow "time slice" line will show where each diagram illustrates the current instant.
• Events (either "standalone" or part of a trajectory) can be dragged around directly on the diagrams (they snap to half-gridlines unless you hold the shift key), or edited in the detailed data lists. (Data for the currently selected event is also shown immediately below the diagram for easy editing.)
• By default, timelike trajectories mark "heartbeats" (or clock ticks) showing the proper time 𝜏 along the trajectory. A radio button sets which event is the zero point. When animating the motion, those "heartbeat" proper times will flash below each moving object.
• By default, trajectories follow constant velocity paths (straight lines) between events. But if you specify an explicit incoming or outgoing velocity for an event (or require the incoming and outgoing velocities to match, for more realistic motion), some segments will have constant (proper) acceleration instead.
• If the next event of a trajectory is not inside the future light cone of the previous one, a constant velocity path between them will be shown with distinct markings to indicate its physical impossibility. Because no massive object could follow such a path, any such step is treated as lasting one graph unit of proper time (think of it as the time it takes for the TARDIS to rematerialize somewhere else). And if a path somehow goes back in time, the animation shows the object in inverted color (in fact, there's an argument to be made that it would look like antimatter).
• You can label an event or trajectory with any symbol you'd like (I recommend just a single character). If you leave it blank, the label will be a simple circle (Clicking in the empty field (twice?) will pop up a list of suggested emoji.)
• There is partial support for visualizing non-inertial reference frames. No Other Frame diagram is shown (for now), but you can select a trajectory event and click the "➔Trajectory Frame" button, and a plausible set of coordinate grid lines as seen by that observer will be shown: constant time in red-orange, constant position in grey. (If you click empty space to remove your selected point, you can push the button again to go back to an inertial frame. Or just set a velocity.) If the angles of time gridlines change too quickly during acceleration, dashed lines will appear to show quarter steps (or dotted lines for very sharp accelerations, just to illustrate the shape). Shaded regions indicate where these coordinates are not well-defined: globally consistent coordinates aren't generally possible in a non-inertial frame. (This coordinate frame is constructed by finding the trajectory observer's instantaneous velocity and then drawing a time slice through that event at the corresponding angle. For experts, this is basically patching together Rindler coordinates and Minkowski coordinates to match each segment of the observer's motion: constant velocity or constant proper acceleration.)