Time dilation

Time dilation is a cool idea in physics. It shows how time can seem to move at different speeds, depending on where you are and how fast you move.

Imagine two clocks next to each other. If one clock moves very fast or is in a place with different gravity, the clocks might not show the same time when put together again. This difference is called time dilation.

This idea comes from the theory of relativity. It has been tested many times and always works as the theory says. Time dilation is important for things like satellite navigation systems. For example, systems such as GPS and Galileo need to think about time dilation to give us correct location information.

Invisibility

Time dilation is about how clocks can show different times depending on how they are moving. When we look at clocks from far away, the light from those clocks takes time to reach us. This can make it hard to see the real differences.

For example, imagine two people watching a train moving very fast—about 86% of the speed of light. They might see their clocks show a difference of 2 seconds, but someone on the train would only see 1 second pass. This shows how motion can change how we measure time.

History

Main article: History of special relativity

Time dilation was predicted by scientists around the year 1900. One of them, Joseph Larmor, noticed that moving electrons take less time to finish parts of their paths. Later, Albert Einstein showed in 1905 that this effect is linked to the nature of time. Hermann Minkowski then added the idea of proper time in 1907, which helped explain what time dilation means.

Time dilation caused by a relative velocity

See also: Special relativity § Time dilation

Special relativity tells us that a moving clock seems to tick slower than a clock that is not moving. The faster something moves, the bigger this effect becomes. When something moves close to the speed of light, time seems to almost stop.

In theory, if someone could travel very fast, they might age slower than someone staying on Earth. For example, a year for a traveler could match ten years on Earth. But with today’s technology, these effects are very small. After six months on the International Space Station, an astronaut ages just a little less — about 5 milliseconds — than someone on Earth.

Simple inference

From the local frame of reference of the blue clock, the red clock, being in motion, is measured as ticking slower.

Time dilation happens because light always moves at the same speed for everyone. This means that when we think about how time passes for moving clocks, they tick slower from our point of view.

Reciprocity

If two people watch each other’s clocks while moving, each will see the other’s clock as ticking slower. This might seem confusing, but it works like how each person can see the other appear smaller from far away — there’s no real contradiction.

Experimental testing

Main article: Experimental testing of time dilation

Moving particles

When scientists study tiny particles called muons moving at high speeds, they live longer than when they are at rest. This matches what time dilation predicts. Similar effects are seen in particle accelerators where particles move very fast.

Doppler effect

Main article: Ives–Stilwell experiment

Transversal time dilation. The blue dots represent a pulse of light. Each pair of dots with light "bouncing" between them is a clock. In the frame of each group of clocks, the other group is measured to tick more slowly, because the moving clock's light pulse has to travel a larger distance than the stationary clock's light pulse. That is so, even though the clocks are identical and their relative motion is perfectly reciprocal.

Experiments with light show that when a light source moves, the color of the light changes in a way that matches time dilation. These tests confirm Einstein’s ideas about how time and movement are linked.

Proper time and Minkowski diagram

In special relativity, the time shown by a clock moving between two points is called “proper time.” This time is always the shortest compared to time measured by clocks that are moving.

Derivation and formulation

The math that describes time dilation comes from the rules of special relativity. It shows that moving clocks run slower, and the effect becomes bigger as the speed gets closer to the speed of light.

Hyperbolic motion

Main article: Hyperbolic motion (relativity)

When something speeds up constantly, like a spaceship, its time passes differently compared to someone not moving. Scientists can calculate exactly how time changes using special relativity.

Clock hypothesis

The clock hypothesis says that how much a clock is affected by time dilation only depends on how fast it is moving, not how much it is speeding up or slowing down. This idea is a key part of special relativity and has been tested many times.

Time dilation caused by gravity or acceleration

Main article: Gravitational time dilation

Time dilation explains why two working clocks will report different times after different accelerations. For example, time goes slower at the ISS, lagging approximately 0.01 seconds for every 12 Earth months passed. For GPS satellites to work, they must adjust for similar bending of spacetime to coordinate properly with systems on Earth.

When you are near a big object like Earth, time moves a little slower for you than for someone farther away. This happens because of gravity.

This effect matters for astronauts on the International Space Station. Even though moving fast makes their time slower, being farther from Earth's gravity makes it faster again, but not as much. If you climb a mountain, time would pass a tiny bit faster at the top than at the bottom.

Scientists have tested this. In 1959, they measured how light changes when it moves up and down in Earth's gravity. In 2010, they used very precise clocks to see this effect with just a height difference of one meter.

Combined effect of velocity and gravitational time dilation

When we keep very exact time, track satellites, and study fast-spinning stars, we must think about how mass and movement change time. This is needed for things like the International Atomic Time and the Barycentric Coordinate Time.

Daily time dilation (gain or loss if negative) in microseconds as a function of (circular) orbit radius r = rs/re, where rs is satellite orbit radius and re is the equatorial Earth radius, calculated using the Schwarzschild metric. At r ≈ 1.497[Note 1] there is no time dilation. Here the effects of motion and reduced gravity cancel. ISS astronauts fly below, whereas GPS and geostationary satellites fly above.

We can calculate these time changes very well for the Solar System and Earth using a special math trick called the Schwarzschild solution.

In 1971, scientists flew special clocks on airplanes around Earth. They compared these clocks to one that stayed on the ground. The clocks in the air were expected to act a little differently because they were higher up and moving, and they did just as scientists thought.
The Global Positioning System helps us test this every day. The clocks on satellites are changed to match clocks on Earth because of both movement and gravity.

In popular culture

Popular misconception

Time dilation can be confusing and often leads to misunderstandings. Some people think it only affects special kinds of clocks, like those that use light, and not other types such as mechanical clocks or atomic clocks.

To help explain this, a thought experiment called Einstein’s Cat was suggested by a scientist named Val G. Rousseau. It imagines a fictional device called the Sync-or-Die clock, which compares a light clock with a mechanical stopwatch. The problem seems to appear when time dilation is thought to affect only the light clock and not the mechanical one. But the answer comes when we see that both types of clocks are affected the same way by time dilation. This shows that time dilation is a basic part of special relativity and works for all types of clocks, no matter how they keep time.

In fiction

Velocity and gravitational time dilation have appeared in many science fiction stories. Movies like Interstellar and Planet of the Apes explore these ideas. In Interstellar, a planet near a rotating black hole makes one hour there equal to seven years on Earth because of time dilation. Physicist Kip Thorne helped create the movie and explained the science in the book The Science of Interstellar.

The Queen song '39, written by musician and astrophysicist Brian May, tells the story of space travelers searching for a new home because Earth is damaged. When they return, they find that everything and everyone they knew are long gone.

Time dilation was also featured in Doctor Who episodes "World Enough and Time" and "The Doctor Falls". These episodes happen on a spaceship near a black hole. Because of the black hole’s strong pull and the ship’s size, time passes faster at one end of the ship than the other. When The Doctor’s companion, Bill, is taken to the other end, she waits years for him to rescue her, but only minutes pass for him. This time difference also lets the Cybermen develop more quickly.

The novel Tau Zero by Poul Anderson is an early example of this concept in science fiction books. In the story, a spacecraft reaches speeds so high that the crew spends five years on board, but many years pass on Earth before they reach their destination. The book explains velocity time dilation using the tau factor. Other books like Rocannon's World, Hyperion, and The Forever War also use relativistic time dilation.