Same universe.
Different clocks.

Mirror separation is D = 0.5 light-seconds, so the rest-frame round trip is 2D/c = 1 second. The moving frame measures γ seconds between the same emission and return events. The two panels share a spatial scale; the scale adjusts to fit the complete paths. The animation synchronizes corresponding events, not the numerical clock readings, and repeats a single tick. Earth here denotes an ideal inertial frame; gravity and acceleration are omitted. This is coordinate time dilation, not a signal-arrival or Doppler effect.

The platform measures the train endpoints at t = 0 and x = ±L/2. In train coordinates, those events are at x′ = ±L₀/2 and t′ = ∓vL₀/(2c²). Hence Δt′ = t′right − t′left = −vL₀/c². The lower diagram uses a fixed time scale in nanoseconds; the horizontal direction identifies the train endpoints. The train is at rest in its own frame. Length contraction applies only along relative motion. This is a coordinate diagram, not a photograph; light-travel-time and visual-rotation effects are not simulated.

The plot keeps the original coordinates fixed. Amber lines are the moving observer’s grid; the event itself does not move when you change observers. The ct′ axis follows x = βct and the x′ axis follows ct = βx. Both axes are calibrated by the Lorentz transformation, not by ordinary Euclidean distance on the tilted lines. Dashed curves through B have the same interval as B. We use Δs² = (cΔt)² − Δx²: positive is timelike, zero is lightlike unless the events coincide, and negative is spacelike. All boosts remain below c.

For one-way Earth-frame distance D and cruise speed v, Earth measures T = 2D/v and the traveler measures τ = T/γ. The diagram is a route map with elapsed-time bars, not a spacetime diagram. Acceleration, braking, and turnaround are approximated as taking negligible time and distance; fuel, gravity, and engineering limits are omitted. Mission scoring uses the complete trip equations, so playing or pausing the preview cannot alter the result. Changing trip parameters resets the preview.

The mass is nonrotating, uncharged, and spherically symmetric. rₛ = 2GM/c² is the Schwarzschild radius, and R = 20rₛ is the reference station’s areal radius. Both stations hover at fixed radii and require support; they are not orbiting or freely falling. All available radii are outside the horizon. The ratio dτlow/dτref equals νref/νlow = √[(1−rₛ/r)/(1−rₛ/R)]. The reference station is at a finite radius, not infinity.

The radius drawing uses logarithmic spacing to keep both stations visible. Small clock faces compare accumulated times over ten reference hours. The two waveform traces each use that observer’s own local seconds; the emitter is assigned a simple 1 Hz signal. They illustrate locally measured frequency, not a simulated photon trajectory or an embedding of curved spacetime.

Distances between observer, lens, and source are held fixed. θₑ₀ is the Einstein angle for a reference mass M₀; all angular values use that unit. The Einstein angle obeys θₑ² = (4GM/c²)Dls/(Dl Ds), and the two signed image positions are θ± = [β ± √(β² + 4θₑ²)]/2. For nonzero offset, total absolute point-source magnification is μ = (u²+2)/(u√(u²+4)), where u = |β|/θₑ.

Exact alignment of an ideal point source makes the formal magnification diverge; the page labels this limit instead of giving a finite brightness. Real sources have finite size. Image markers and ring thickness are enlarged for visibility; the plotted positions follow the equations. Background stars are decoration. This weak-field, thin-lens example does not simulate a black-hole shadow, strong-field photon orbits, diffraction, or extended-source arcs. The center marks the lens position, not a horizon.