---
title: "Light Signals and Moving Clocks Interactive Lab | Sandbox Physics"
description: "Why does seeing a clock tick differ from dating it or reading the clock itself? Light needs time to reach you, so you see every tick late."
canonical_url: "https://sandboxphysics.com/labs/light-signal-clocks/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/light-signal-clocks/"
last_modified: "2026-10-29"
---

Special relativity · Measuring time

# Light Signals and Moving Clocks

**Why does seeing a clock tick differ from dating it or reading the clock itself?** Light needs time to reach you, so you see every tick late. Echoes let you subtract that travel time and assign a coordinate time, which depends on how the clocks were synchronized. The moving clock's own reading is a third quantity: it counts time along its own path, and a round trip leaves it behind.

Drag a clock's path through spacetime and compare four times for one tick: when its light arrives, its coordinate time, its radar time from echoes and the clock's own reading.

> Interactive simulation: open this page in a web browser to change the parameters and run the model.

Model assumptions

One space dimension, with light speed set to one light-year per year. Observer A rests at the origin and uses Einstein-synchronized clocks. Clock B moves at a constant speed on each of two legs, so its turn is instantaneous. Flashes and echoes travel on straight light lines. The model has no gravity, no forces during the turn and no optics of real images; the drawing frame only relabels the same events.

Blue uses A's synchronized coordinates; gold is what A sees when the light arrives.

More numbers and the saved record

A's clock when B's record ends $10\,\mathrm{yr}$

B's clock when its record ends $8\,\mathrm{yr}$

Ticks received per year of A, near this tick $0.5$

Time-dilation factor of this leg $1.25$

The JSON record lists every tick of B with its event coordinates, A's send and receive times and the radar time recomputed from that pair.

[Course: relativity as measurement, in eight chapters](https://sandboxphysics.com/stories/relativity-measurement/)

Physics tutorial

## One tick, four times

**Background** A distant clock flashes once a year. Observer A writes down when each flash arrives, sends light pulses that the clock echoes, and later compares notes with the clock itself.

**Why it matters** Physics needs times that do not depend on where the observer happens to stand. Light travel time, synchronization and the clock's own path each change a different number.

Start with the essentials

- **Focus question**: Why does seeing a clock tick differ from dating it or reading the clock itself?
- **One-sentence intuition**: Arrival time is a fact about A's clock, coordinate time is a convention built from echoes, and proper time is a fact about the moving clock's path.

### Core mathematical model

#### Radar coordinates from one echo

$$
t=\tfrac12\,(t_1+t_2),\qquad x=\tfrac12\,c\,(t_2-t_1)
$$

A sends light at its time $t_1$, the light meets the event, and the echo returns at $t_2$. For an observer at rest this reproduces Einstein's synchronization.

#### The spacetime interval

$$
\Delta s^2=c^2\Delta t^2-\Delta x^2
$$

Every inertial frame gives the same value. It is zero along a light ray and positive along the path of a clock.

#### Proper time on straight legs

$$
\tau=\sum_i \Delta t_i\sqrt{1-v_i^2/c^2}
$$

Each leg contributes the square root of its interval divided by c. Out and back at six tenths of light speed for ten years of A's time gives eight years on B.

#### How fast the ticks arrive

$$
\frac{\Delta t_{\text{received}}}{\Delta\tau}=\sqrt{\frac{1+v_r/c}{1-v_r/c}}
$$

Here $v_r$ is the velocity away from A. Receding ticks arrive spread out and approaching ticks bunched together; this is the Doppler effect, not a change in the clock's rate.

### Common difficulties

#### Seeing is not dating

**Typical misconception** The time at which I see a distant event is the time at which it happened.

**Better mental model** The flash needs time to arrive. Coordinate time subtracts that delay using an agreed synchronization, here radar echoes.

#### Bunched ticks are not a fast clock

**Typical misconception** An approaching clock really runs fast because its ticks arrive more often.

**Better mental model** After the light delay is removed, a moving clock runs slow in A's frame whether it approaches or recedes. The bunching comes from the shrinking light path.

#### What the model leaves out

**Typical misconception** The diagram shows how the clock would look through a telescope.

**Better mental model** One space dimension, with light speed set to one light-year per year. Observer A rests at the origin and uses Einstein-synchronized clocks. Clock B moves at a constant speed on each of two legs, so its turn is instantaneous. Flashes and echoes travel on straight light lines. The model has no gravity, no forces during the turn and no optics of real images; the drawing frame only relabels the same events.

### Run the experiment

1. 01

   #### Compare the four readouts

   Start with A round trip leaves fewer ticks and inspect the fourth tick, at the turning point.

   **What to observe:** A dates the turn at five years by coordinates and by radar, sees it at eight years, and B's own clock reads four.

2. 02

   #### Separate delay from dilation

   Choose A distant resting clock only looks late.

   **What to observe:** Every tick is seen five years late, yet coordinate time and the clock's reading agree. Delay alone does not slow a clock.

3. 03

   #### Change the frame, not the events

   Move the frame speed slider or choose Same events, moving frame.

   **What to observe:** The coordinate time of the tick changes, while the arrival time on A and the reading on B stay fixed.

Physical conclusion

Before comparing two times, ask which operation produced each one: receiving light, assigning coordinates, or reading a clock along its path.

## Related experiments and articles

Relativity as measurement · Reading path

### Relativity as measurement: clocks, light signals and four-momentum

Articles on this path that use this experiment, followed by the other experiments they suggest.

1. [Article **Events, light signals and the delay in seeing**](https://sandboxphysics.com/stories/relativity-measurement/events-and-light-signals/)
2. [Article **Setting distant clocks with a light echo**](https://sandboxphysics.com/stories/relativity-measurement/synchronizing-clocks/)
3. [Article **Why moving observers disagree about “at the same time”**](https://sandboxphysics.com/stories/relativity-measurement/relativity-of-simultaneity/)
4. [Article **Proper time is what a moving clock records**](https://sandboxphysics.com/stories/relativity-measurement/proper-time/)
5. [Lab **Twin Clocks and Radar Time** Count the signals each twin receives](https://sandboxphysics.com/labs/twin-radar-time/)

Motion & dynamics · Starter path

## From a falling ball to an orbit

Start by measuring gravity and splitting motion into components. Then add contact forces and collisions, and follow the same laws all the way to an orbit.

[Start here → **Free Fall & Measuring Gravity** Capture a few drops and fit the camera positions to estimate gravitational acceleration. Then add air damping and watch the fit drift from the truth. Observe · 14 min](https://sandboxphysics.com/labs/free-fall/)

1. [1 Free Fall & Measuring Gravity](https://sandboxphysics.com/labs/free-fall/)
2. [2 Projectile Flight Designer](https://sandboxphysics.com/labs/projectile-flight/)
3. [3 Inclined Plane & Friction](https://sandboxphysics.com/labs/inclined-plane/)
4. [4 One-Dimensional Collision Bench](https://sandboxphysics.com/labs/collision-bench/)
5. [5 Mass–Spring Oscillator](https://sandboxphysics.com/labs/mass-spring/)
6. [6 How Orbits Take Shape](https://sandboxphysics.com/labs/orbit/)

[View the full path →](https://sandboxphysics.com/topics/mechanics/#starter-path)