## Concept explanation In **relativity**, time is not a single universal quantity that every observer must measure the same way. If two observers begin at the same **start event** and compare clocks again at the same **end event**, they can still disagree about how much time passed in between if one observer was moving relative to the other. In this simplified picture, the moving observer’s clock accumulates less **elapsed time** as speed increases, which is the effect called **time dilation**. ## What you see You’re looking at two synchronized clocks connected to the same pair of event markers. The left clock represents a stationary observer, while the right clock represents a moving observer. When you start the animation, both clocks begin together at the left marker and stop at the same right-side marker, but the moving clock advances more slowly as its speed gets closer to `c`, the speed of light. The small progress bars at the bottom make the difference in accumulated time easy to compare. ## Try it yourself - **Press `Start`** and watch both clocks begin from the same start event. - **Move the speed slider upward** and notice that the moving observer’s clock hand sweeps around more slowly. - **Compare the numeric readouts** under the clocks to see that the moving observer records less elapsed time by the end. - **Watch the `γ` value** in the control panel as you increase speed; higher `γ` means stronger time dilation. - **Press `Reset`** and run the clocks again at several different speeds to compare how the gap grows. - **Try a low speed, then a high speed** to see that the effect is tiny at first and much more dramatic near `c`. ## Concept explanation A **light clock** measures time by repeating a simple physical process: a pulse of **light** travels from the bottom mirror to the top mirror and then back again. Each full round trip takes the same amount of time if the mirrors stay fixed, so the bouncing pulse acts like the regular swing of a pendulum or the vibration in a quartz watch. When the light returns to the bottom mirror, the clock records one more **tick**. ## What you see You are looking at one vertical light clock with two mirrors and a glowing pulse moving straight up and down between them. The line between the mirrors shows the light’s path, and the counter on the right increases whenever the pulse completes a full cycle by returning to the bottom mirror. Together, the repeated motion and the growing count show how a steady repeating process can serve as a clock. ## Try it yourself - **Click Play** and watch the glowing pulse bounce between the mirrors. - **Watch the tick counter** and notice that it increases only when the pulse comes back to the bottom mirror. - **Pause the animation** to freeze the clock and connect one snapshot of motion to one moment in time. - **Adjust the speed slider** to make the pulse move faster or slower while keeping the same rule for when a tick is counted. - **Press Reset** to return the pulse and counter to the starting state, then observe a fresh sequence of equal ticks. ## Concept explanation A **light clock** measures time by letting a pulse of **light** bounce between two mirrors. If the clock is at rest, the light travels straight up and down. But if the whole clock moves sideways, an outside observer sees the pulse trace a longer diagonal route between the same mirror hits. Because the **speed of light** stays fixed, a longer path must take more time, so each tick of the moving clock lasts longer. This is the visual heart of **time dilation**. ## What you see You can compare two clocks side by side. The blue clock is stationary, so its pulse moves vertically. The teal clock slides sideways while its pulse still bounces between its mirrors, leaving a faint diagonal trail that shows the longer path seen by an outside observer. The control panel reports the vertical path, the diagonal path, and the tick stretch factor so you can connect the geometry to the slower ticking. ## Try it yourself - **Drag the clock speed slider** and watch the teal pulse path tilt more strongly as the clock moves faster. - **Notice the light speed readout stays fixed** even while the diagonal path length grows. - **Compare the blue and teal clocks** to see that the moving clock needs a longer route for the same bounce. - **Adjust the light baseline slider** to change the overall animation pace while keeping the geometric idea the same. - **Press Reset pulse** and follow one half-bounce from the lower mirror to the upper mirror. - **Look at the tick stretch value** and connect it to the longer diagonal path of the moving clock. ## Concept explanation In relativity, **proper time** is the time measured by the single clock that is present at both events. Because that clock travels along the events’ path, it records the **shortest elapsed time** between them. An outside observer can still describe the same two events, but if the clock is moving relative to that observer, the outside frame assigns a larger elapsed time. This is the core idea of **time dilation**: the moving clock’s own reading stays smallest, while other frames can measure a longer duration for the same event pair. ## What you see The left panel shows the clock riding with the events, so both events happen at one place in that clock’s frame and its display is the proper time. The right panel shows an external comparison view, where the same clock is moving and the two events are separated in space. Both panels track the same event pair `E1` and `E2`, but their elapsed-time readouts differ more as speed increases. ## Try it yourself - **Move the speed slider** from low values toward `0.9c` and watch the right-hand elapsed time grow faster than the rider clock. - **Switch the observer view** to compare how the same event pair is presented from different named frames. - **Press Pause** at any moment and compare the two time displays side by side. - **Press Reset** and replay the scenario at a new speed to see how the gap depends on velocity. - **Set the speed near `0c`** and notice that both clocks nearly agree when relative motion is small. - **Increase the speed again** and confirm that the riding clock always keeps the smallest elapsed-time reading. ## Concept explanation **Gravitational time dilation** means that time itself passes at different rates in different strengths of gravity. Near a very massive object, spacetime is more strongly curved, so a clock deeper in that gravitational field runs more slowly than a clock farther away. The effect is tiny for everyday situations on Earth, but it becomes important near very massive planets, stars, and black holes. ## What you see You’re looking at a massive world at the bottom of the scene, with a stronger gravity region shown by denser curved field lines and a brighter teal glow near the surface. Two clocks sit at different heights above it: the lower clock is closer to the mass, while the upper clock can be moved. As you change the upper clock’s height, the clock faces keep ticking, and the comparison card shows how much slower the lower clock runs relative to the upper one. ## Try it yourself - **Drag the upper clock** upward and notice that the difference between the two clocks grows as the height separation increases. - **Drag the upper clock** downward toward the planet and watch the two clocks become more similar when they are closer together. - **Move the Planet mass slider** to make the gravitational field stronger or weaker and see how the time-dilation effect changes. - **Adjust the Effect scale slider** to exaggerate the small real difference so you can see the lower clock lag more clearly. - **Press the Reset heights button** to return to the starting arrangement and compare again from the default view. ## Concept explanation **Time dilation** means that time can pass at different rates for different observers. In **special relativity**, a clock moving at very high **speed** runs slow compared with a clock at rest. In **general relativity**, a clock deeper in a strong **gravitational field** also runs slow compared with a clock farther away. These are different physical situations, but they produce the same basic pattern: the affected clock shows less elapsed time than a reference clock. ## What you see You are comparing two side-by-side scenes. On the left, a spaceship moves faster and its onboard clock accumulates less time than the outside reference. On the right, a clock moves lower toward a planet and, as gravity gets stronger, it also accumulates less time than the higher clock. The matching numeric readouts and bars at the bottom let you compare how both changes reduce elapsed time, even though one effect comes from motion and the other from gravity. ## Try it yourself - **Drag the spaceship speed slider** upward and watch the ship's elapsed-time readout drop below the reference. - **Drag the clock height slider** downward toward the planet and notice the lower clock lose elapsed time. - **Compare the two readouts** to see that high speed and strong gravity both slow time in the same general way. - **Press `Match slowdown`** to set the gravity scenario close to the same slowdown as the spaceship scenario. - **Press `Reset`** to return to the starting comparison and try a new pair of values. - **Look at the bottom bars** after each change to judge which scenario is slowing time more strongly. ## Concept explanation **Time dilation** means clocks can tick at different rates depending on motion and gravity. For navigation satellites, both effects matter: **special relativity** makes a fast-moving satellite clock run a bit slower, while **general relativity** makes a clock higher in Earth’s weaker gravity run faster. In systems like GPS, these are real, measured effects, not just theory. If engineers did not correct for both, the time stamps sent by satellites would drift away from Earth-based clocks, and position calculations would quickly become wrong. ## What you see You are looking at Earth with several orbiting satellites, each carrying a clock. The right-hand comparison card shows the Earth clock, the satellite clock offset, and the resulting navigation error. On the globe, the gold marker is the ground receiver, and the red displaced marker shows where an uncorrected timing mismatch can push the computed position. The offset bar shows whether the satellite clocks are ahead or behind, while the error bar turns that timing difference into a distance error. ## Try it yourself - **Turn off special relativity** and notice how the offset changes sign and size. - **Turn off general relativity** and compare how much error remains when only speed effects are active. - **Leave both effects on** and watch the net drift become the combination of the two contributions. - **Check Apply correction** to force the effective offset to `0` and see the navigation error collapse. - **Uncheck Apply correction** to see how even a few microseconds become hundreds or thousands of metres of position error. - **Use Reset clocks** and watch the drift build up again from the start. - **Toggle Orbit trails** if you want a cleaner view of the links between satellites and the receiver.