PHYSICS LAB / EXPERIMENT 01
Time is not
universal.
Two clocks leave the same moment. One takes a different journey. When they meet again, they disagree. Change velocity and gravity, then watch Einstein's spacetime turn a paradox into something you can measure.
THE QUESTION
How much time
will you live?
Every clock measures time along its own worldline through spacetime. Speed changes the proper time accumulated by a traveler, and gravity changes the rate of clocks at different locations. This laboratory lets you inspect both effects, with visible diagrams and calculated values tied to the same model.
Watch the spacecraft travel outward and return, then compare both clocks at their reunion. Switch to gravity to investigate GPS satellites or clocks hovering near a hypothetical black hole. The visual sizes and animation speeds are illustrative; the numbers come from the equations shown below.
Compare a departure and a reunion.
Start with synchronized clocks, send one on a high-speed journey, and bring it home to reveal the difference in accumulated proper time.
See why GPS needs Einstein.
Separate the effects of gravity and motion to inspect the net microsecond correction that keeps satellites accurate.
Place clocks near a black hole.
Move a hovering clock closer to the horizon and watch its proper time advance more slowly than a distant clock.
LIVE EXPERIMENT / TWO PATHS, TWO CLOCKS
Change the journey.
Change the time.
Need a starting point? Read the workbench guide ↗
Visual animation is deliberately accelerated and spatial scales are not literal. Gravity mode identifies Clock A and Clock B explicitly. Actual relative rates are shown by default; a labeled control can magnify tiny Earth-clock differences. Numeric readouts always retain physical units. The clock comparisons use stated physical models. All controls work with keyboard input.
THE GEOMETRY
The two paths through spacetime
Vertical time and horizontal distance are compared in the same reference frame.
READ THE RESULT
What your clocks are saying
Choose a setting and compare.
The moving traveler's clock accumulates less proper time for a reunion experiment.
All numeric time differences are derived from the selected model and physical parameters, not estimated from the animation.
Inspect the calculation ↓EXPERIMENT 02 / TAKE THE PILOT'S SEAT
Inside the Starship.
Push toward light speed. Stars crowd toward the forward view while their light changes color and brightness. Drag to look forward, sideways, or back toward Earth. Receive numbered messages from home, then compare the received timestamps with the time accumulated on each clock.
Your seat is waiting.
A 3D journey into Earth's future.
Loads on request · no sound · look around with touch, mouse or keysThe 3D flight deck loads when you enter. Your existing workbench above remains available.
MISSION CHALLENGE / MAKE A PREDICTION
100 years on Earth.
10 years aboard.
Choose your cruise speed and one-way distance. Predict how much you will age, then launch, turn for home, and compare both clocks at reunion.
Crew: 10 yearsMatch within 0.5 Earth years and 0.1 crew years. You can also fly any mission simply to explore.
Optional challenge: choose settings, lock a prediction before launch, and test it on the flight.
Both tracks use the same scale in years. They show time accumulated on each clock, separate from the old Earth timestamps arriving in messages.
A whole round trip plays in about a minute. Before launch, the viewport previews the selected cruise optics. Changing speed pauses and recalculates the whole constant-speed journey at the same path position. Launch, cruise, turn and stopping are idealized as instantaneous; this is a special-relativity experiment, with no fuel, acceleration or gravity model. Sky colors and brightness are compressed for display. The Earth beacon is enlarged to remain findable.
THE EARTH-MESSAGE EXPERIMENT
Home keeps calling.
How fast do you hear it?
Earth sends regular numbered messages. Launch and control the mission right here, then watch the light cross the gap. The flight deck above shares this journey; you can follow the messages without opening 3D.
Launch the default 90%-light-speed journey below. Once open, choose a different mission here, pause, replay, or watch the return. No trip back to the flight deck is needed.
Loads the message experiment only. The 3D flight deck is optional.
Launch here to watch Earth messages arrive.
Message 00 marks the shared departure.
CLOCKS & ARRIVING EARTH LIGHT
The postcard shows the latest numbered message’s sent date. Arriving-light time continues between postcards.
Departure confirmed. We'll keep sending the time from home.
Illustrated teaching messages, decoded by a fictional receiver. Earth’s timestamp is calculated; the artwork is not a live view of a future Earth.
At departure, the clocks begin together.
Message #00 is the shared departure event. Later messages appear here when their light reaches you.
EVERY NUMBERED MESSAGE / TWO TABLES
Follow each message
all the way to the ship.
Messages travel at 100% of light speed.
Message speed: 100% c1 light-year per year · approximately 186,282 miles/s (299,792 km/s). Light’s speed in vacuum is c for Earth and the ship; its arrival rate and color can change.
No numbered messages received yet.
Table 1 / When each message was sent and received
All clocks start at the shared launch. These columns say when an event happened after launch; they are not the message’s travel duration. No calendar year is assumed. Select a received message number to replay its arrival.
| Message / status | Sent after launchElapsed on Earth | Reached ship after launchElapsed in Earth’s frame | Traveler aged at arrivalTime aboard since launch | Ship directionAt reception | Ship speedEarth frame | Message speedEarth & ship frames |
|---|
No numbered messages have arrived yet. Message #00 is the shared departure. Keep flying, choose Watch the return, or select All scheduled messages to inspect predictions.
Table 2 / Travel duration and the wait between messages
Travel duration is the time from Earth sending a message to the ship receiving it, calculated in Earth’s frame. Wait between messages is the time the crew waits from one receipt to the next, measured on its own clock. Both use readable years, months or smaller units. At a fixed return speed, the gap between receipts stays steady while individual message travel durations decrease. This column records the interval between receptions.
| Message | Time spent travelingFrom send to receipt / Earth’s frame | Wait since previous messageMeasured on the crew clock | Ship directionAt receipt | Status |
|---|
Travel durations and receipt gaps appear here as messages arrive. Select All scheduled messages for predictions. The first wait starts at launch (#00).
The arrival counter in Table 1 keeps increasing because the mission continues. In Table 2, the travel duration of successive inbound messages decreases as the ship gets closer to Earth. The first wait is measured from launch; “Spans turnaround” marks a gap including both legs. A displayed month is one twelfth of a modeled 365.25-day year, rather than a calendar date. Calculations keep full precision. The full planned outward-and-return route determines each arrival. Received rows stay fixed as playback advances. Changing cruise speed or distance recalculates the model and both tables. “In transit” and “Not sent” rows are predictions. At the idealized reunion the ship stops; a message sent exactly then has zero travel time. Message #00 marks departure and is not a traveling packet.
Receiving messages faster and accumulating more time are different things. On the return leg, Earth’s old messages arrive in quick succession. Your clock aboard still ticks normally for you. At reunion, compare the elapsed years directly.
Inside the data: sky, light signals and the journey
Earth and the turnaround marker share an inertial frame. Cruise speed is βc, the one-way distance is D, and c = 1 light-year per year. The round trip takes T = 2D/β Earth years and T/γ crew years, with γ = 1/√(1 − β²). The ship's position is x = βt outbound and x = β(T − t) inbound. Earth’s received timestamp is e = t − x, the retarded emission time. Signals move at c, not at the ship’s speed. The displayed Earth-frame elapsed time is a calculated coordinate reading, not an instantaneous visual feed or a claim of universal simultaneity.
Earth's signal is redshifted during recession and blueshifted during approach. Its frequency ratio is γ(1 − β) outbound and γ(1 + β) inbound; dividing the Earth transmission interval by that ratio gives the interval received on the crew clock. Numbered postcards use the same arrival calculation as the signal map. At the idealized instantaneous turn, the received timestamp remains continuous while its rate changes. No time or messages jump into the past.
For a source direction n in Earth's frame, pointing toward the source with +X along the outward route, aberration gives n′ₓ = (nₓ + β)/(1 + βnₓ) and n′⊥ = n⊥/[γ(1 + βnₓ)]. The Doppler factor is γ(1 + βnₓ). Spectral-band boundaries are approximate. The 550 nm beacon can shift into infrared, ultraviolet or soft X-ray wavelengths over the available speeds. The sky contains illustrative distant stars, not a measured catalog. It shows aberration with optional approximate shifted blackbody colors and compressed brightness; it is not a spectrally complete ray tracer. The cabin stays in the ship's local frame and turns at the turnaround. Its rotating navigation hologram is an instrument animation driven by mission progress. A rest-sky comparison changes only the optical display; parallax still follows the ship position. Before departure, cruise optics are previewed while clocks remain at zero. The viewport wavelength readout is for a 550 nm test source at the center of the current ship-frame view: its frequency factor is 1/[γ(1 − β cos θ′)], with θ′ measured from the forward direction. It does not claim every star emits the same wavelength. Changes to cruise speed pause and recalculate the constant-speed mission at the same path position, rather than simulate a realistic acceleration. A fictional nearby star field provides parallax: each source direction is recomputed from the source position and current ship position, then aberrated. Nearby positions are expressed as fractions of the chosen one-way distance, so the field rescales with the mission. Its crowded appearance is chosen for legibility and is not the measured stellar density around Earth. The distant field remains effectively at infinity. Inverse-distance brightness is compressed. Resolved-object distortions, dust, engine physics and realistic radiation hazards are outside this model.
The flight deck uses a compact procedural 3D interior. Native resolution is the default; battery saver is optional. Rendering stops offscreen or when the browser is hidden, and Unload 3D releases its graphics resources. On devices without WebGL, the same interior is shown with a Canvas perspective renderer. No camera is placed in a photon rest frame.
Max Planck / the travelling twins ↗ · Einstein Online / Doppler signals ↗ · MIT Game Lab / visualizing relativistic effects ↗ · NASA / electromagnetic bands ↗
THE THOUGHT EXPERIMENT / WATCH THE LIGHT
One pulse.
Two descriptions.
A light clock consists of two mirrors and a pulse bouncing between them. Inside the spacecraft, the pulse travels vertically. In an external frame where the ship moves sideways, the same pulse follows a diagonal path between moving mirror positions.
Both observers measure the same speed of light, so the time between the moving clock's ticks is longer in the external frame. The nearby visualization is a schematic of the two frames, not a measurement of actual mirror positions.
The pulse path is schematic. Physics: Δt = γ Δτ for an inertial light clock in relative motion.
FOLLOW THE EVIDENCE
Three ways Einstein
changed the clock.
Relativity isn't confined to imagination. It has been tested by precise clocks flown around the world, incorporated into satellite navigation, and used to understand how gravity affects observations near compact objects.
Clocks that flew around Earth
The 1971 Hafele–Keating experiment carried atomic clocks around the world. Eastbound and westbound flights returned with tiny differences matching the combined effects of motion and gravity.
Read the experiment ↗GPS needs relativity
At ordinary GPS orbit height, gravity makes satellite clocks run faster while orbital motion makes them run slower. The net correction is roughly 38 microseconds per day.
Explore the clock tests ↗Does a photon age?
Light travels along a null path with zero proper-time interval. A photon has no valid inertial rest frame, so it is misleading to describe the journey as something a photon personally experiences.
Understand spacetime ↗INSIDE THE DATA / MODEL BOUNDARIES
Check what you're seeing.
Motion: how the returning-traveler comparison is calculated
In the Earth-and-destination inertial frame, the traveler covers a chosen one-way distance D at a constant speed v = βc and returns at the same magnitude of speed. Earth-coordinate time is 2D/v; traveler proper time is (2D/v)√(1 − β²). The default simulator uses light-years and years, so c = 1 light-year per year. The turnaround is treated as instantaneous, which idealizes away acceleration. The final comparison occurs at the same reunion event.
Earth: why gravity and orbiting speed affect the clock
The Earth modes use leading-order weak-field rate corrections. The gravitational contribution over time t is approximately (GM/c²)(1/R − 1/r)t. For a satellite on a modeled circular orbit, the orbital-motion contribution is approximately −v²t/(2c²), with v² = GM/r. The model treats the reference surface clock as nonrotating, and neglects Earth's multipole gravity, atmospheric drag, and system-level timing adjustments. The exact GPS system applies more detailed correction procedures.
Black hole: what the idealized static clocks mean
For two clocks hovering at constant radii outside a nonrotating Schwarzschild black hole, the proper-time rate at radius r is proportional to √(1 − rₛ/r), where rₛ = 2GM/c² is the horizon radius. The lab compares a clock at a user-selected radius with another at 20 horizon radii. Hovering requires acceleration and becomes impossible at the horizon itself. The picture is an artistic illustration inspired by a black-hole shadow, an accretion disk, and gravitational lensing. A shadow is not the event horizon. The separate A/B location guide marks the physical horizon at 1 horizon radius and the hovering-clock radii; its distances are compressed for readability. It is not a photograph or a full ray-traced simulation. The Earth surface rendering uses a transformed NASA Blue Marble texture; satellite and spacecraft designs are fictional teaching illustrations. Actual relative clock rates are the default. Optional Earth-clock magnification multiplies only the tiny fractional rate difference by 100,000,000; it is explicitly labeled and never changes the numerical time readouts. Both illustrated clocks restart together when the settings change. The overall hand animation is accelerated equally; the orbital animation and clock hands are independent teaching diagrams, not synchronized real-time telemetry.
What the visualizations can and cannot show
Spacecraft sizes, optical halos, orbit geometries, color, distances, and playback speed are deliberately illustrative to make the physical relationships legible. Clock numbers are calculated and labeled in years, days, hours, microseconds, or milliseconds as appropriate. The light-clock graphic compares two coordinate descriptions of the same idealized clock. No photon rest frame is used. Small timing effects are made visually salient rather than represented as literal visible clock-hand differences.
Sources, classroom prompts, and further investigation
Try increasing the ship's velocity from 50% to 99.99% of light speed while holding distance fixed. Predict the reunion difference before pressing Compare. Then select GPS and explain why gravity and motion contribute opposite signs. Finally, select near a black hole and explain what it means to be a hovering, rather than freely falling, clock.
Educational use: original interactive teaching model by The Last Transmission, © 2026 DarkScienceDocs.com. Values describe simplified scenarios, not a mission plan or direct astrophysical measurement.