# What is time dilation? (2023)

By Andrew May

published

Einstein realized that time is relative and passes at different rates for different people.

(Video) Time Dilation - Einstein's Theory Of Relativity Explained!

• Time dilation defined
• Time dilation and the speed of light
• Time dilation and gravity
• Time dilation equation
• Time dilation in space

Time dilation refers to the seemingly odd fact that time passes at different rates for different observers, depending on their relative motion or positions in a gravitational field.

Here’s how that works. Time is relative. As counterintuitive as that sounds, it's a consequence of Einstein's theory of relativity. In everyday life, we're used to speed being relative — so, for example, a car traveling at 60 mph (97 km/h) relative to a stationary observer would be seen as moving at 120 mph (193 km/h) by a driver going in the opposite direction at the same speed.

This same phenomenon also impacts time. Depending on an observer’s relative motion or their position within a gravitational field, that observer would experience time passing at a different rate than that of another observer. This effect, known as time dilation, becomes detectable only under certain conditions, although at a low level, we're subject to it all the time. Let's take a closer look at the theory of time dilation and some of its consequences, including GPS errors and the famous twin paradox.

### Time dilation defined

Time dilation is the slowing of time as perceived by one observer compared with another, depending on their relative motion or positions in a gravitational field. It's a consequence of Einsteinian relativity, in which time is not as absolute as it might appear; the rate at which it passes is different for observers in different frames of reference.

Einstein's starting point was the fact that light always has the same measured speed regardless of the observer's own motion, according to the late Michigan State University physics professor Jon Pumplin. This seemingly innocuous assumption inevitably leads to the conclusion that "moving clocks run slowly." This phrase is often used as a concise description of time dilation, but it's somewhat misleading because of the emphasis it places on clocks, which are only relevant insofar as we use them to measure time. But we really ought to think of time dilation as "an unexpected truth about space and time, rather than as a property of the clock," Pumplin argued.

(Video) Time Dilation Explained in 6 Minutes

### Time dilation and the speed of light

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The theory of relativity has two parts — special relativity and general relativity — and time dilation features in both. The principle that the speed of light is the same for all observers plays a key role in special relativity. One of its consequences, according to Boston University physicist Andrew Duffy (opens in new tab), is that two observers moving at a constant speed relative to each other measure different times between the same events. But the effect becomes noticeable only at velocities approaching the speed of light, commonly symbolized by c.

Imagine a spaceship traveling at 95% of the speed of light to a planet 9.5 light-years away. A stationary observer on Earth would measure the journey time as distance divided by speed, or 9.5/0.95 = 10 years. The spaceship crewmembers, on the other hand, experience time dilation and thus perceive the trip as taking only 3.12 years. (The math here is a little more complicated, but we'll get to it later.) In other words, between leaving Earth and reaching their destination, the crewmembers age a little over three years, while 10 years have passed for people back on Earth.

Although really striking situations like this call for enormously high speeds, time dilation occurs on a more modest scale for any kind of relative motion. For example, a regular flier who crosses the Atlantic every week would have experienced about a thousandth of a second less time than a non-traveler after 40 years, according to "How to Build a Time Machine (opens in new tab)" (St. Martin's Griffin, 2013). The book also explains how the kind of speeds needed for more impressive feats of time dilation can occur in the real world, at least in the case of short-lived elementary particles called muons. These are created when cosmic rays hit Earth's upper atmosphere, and they can travel at nearly the speed of light. The muons are so unstable that they shouldn't last long enough to reach Earth's surface, yet many of them do. That's because time dilation can extend their lifetimes by a factor of five.

### Time dilation and gravity

Ten years after he postulated special relativity, Einstein expanded his theory to include gravitational effects in general relativity. But time dilation in this theory depends not on the speed of travel but the strength of the local gravitational field. We already live in a moderate gravitational field on Earth's surface, so it turns out, we're subject to time dilation without realizing it. Furthermore, the strength of the effect varies as we move up and down within Earth's field.

Gravity is slightly weaker on the top floor of a high building than at ground level, so the time dilation effect is also weaker higher up. Time goes faster the farther away you are from Earth's surface. Even though the effect is too small to detect with human senses, the time difference between different altitudes can be measured using extremely accurate clocks, as West Texas A&M University physics professor Christopher Baird describes on his website (opens in new tab).

To see a more dramatic example of gravitational time dilation, we need to find somewhere with much stronger gravity than Earth, such as the neighborhood around a black hole. NASA (opens in new tab) has considered what would happen if a clock were put in orbit 6 miles (10 kilometers) from a black hole having the same mass as the sun. It turns out that when viewed through a telescope from a safe distance, the clock would take around an hour and 10 minutes to show a difference of 1 hour.

### Time dilation equation

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Einstein's original time dilation equation is based on special relativity. As daunting as the equation looks at first glance, it's not that difficult if we have a scientific calculator and work through the formula step by step. First, take the speed v of the moving object and divide it by c, the speed of light, and square the result. This should give you a number somewhere between 0 and 1. Subtract this from 1, and take the square root; then invert the result. You should be left with a number greater than 1, which is the ratio of the time interval as measured by a stationary observer to that of the moving observer.

If that sounds like too much work, you can use an online calculator (opens in new tab) provided by Georgia State University. Just type in the speed, v, as a fraction of c, and the corresponding time ratio will appear automatically. The same website (opens in new tab) also has the analogous formula relating to gravitational time dilation.

### Time dilation in space

(opens in new tab)

Time dilation is of double relevance to spacecraft, due both to their high speeds and the changing gravitational fields they experience. In 2020, a group of students at the University of Leicester (opens in new tab) in the U.K. computed the time dilation effects on NASA's Voyager 1 probe in the 43 years following its launch in 1977. Special relativity predicted that Voyager has aged 2.2 seconds less than we have on Earth. But general relativity partially counterbalances this. We experience stronger gravity than the spacecraft, so in this sense, the probe has aged around 1 second more than we have. Combining the two effects, Voyager still turns out to be younger than Earthlings, but by only about 1.2 seconds.

Calculations like these may seem frivolous, but they can be very important in situations in which precise timing is critical. In the case of the GPS satellites used for navigation, for example, timing errors of just a few nanoseconds (billionths of a second) can lead to a positioning error of hundreds of meters, which is clearly unacceptable if you're trying to pinpoint a specific address. To achieve the desired accuracy, the GPS system has to account for time dilation, which can amount to 38 microseconds (millionths of a second) per day, according to Richard W. Pogge (opens in new tab), a distinguished professor of astronomy at The Ohio State University. As in the Voyager example, both special and general relativity contribute to this figure, with 45 microseconds coming from gravitational time dilation and minus 7 microseconds from the speed-related effect.

One of the most mind-bending consequences of time dilation is the so-called twin paradox. In this thought experiment, one identical twin lives on Earth while their twin takes a round trip to a distant star at velocities approaching the speed of light. When they meet up again, the traveling twin — thanks to time dilation of the special relativistic kind — has aged far less than the one who stayed at home. The apparent "paradox" comes from the mistaken belief that the situation is symmetrical — in other words, that you could also say the traveling twin is stationary relative to the Earthbound twin, meaning that the Earthling would have aged less than the star-voyaging twin. .

But that's not the case, because the situation isn't symmetrical. When special relativity talks about relative motion, it's referring to motion at constant speed in a straight line. That's not the case here. Because the twins are together at the start and end of the journey, the traveler has to accelerate from a standstill to top speed and then, at some point, turn around and head back in the opposite direction, before eventually decelerating to a stop again. These phases of acceleration and deceleration bring in general relativity, because they have similar effects to a gravitational field, according to "Paradox: The Nine Greatest Enigmas in Physics (opens in new tab)"(Crown, 2012). When the math is worked out to account for this acceleration, it turns out that, in something akin to time travel, the spacefaring twin does indeed age more slowly than the Earthbound one.

Originally published on Live Science.

(Video) The Science of Extreme Time Dilation in Interstellar

Andrew May

(Video) Neil deGrasse Tyson Explains Time Dilation

Astrophysicist

Andrew May holds a Ph.D. in astrophysics from Manchester University, U.K. For 30 years, he worked in the academic, government and private sectors, before becoming a science writer where he has written for Fortean Times, How It Works, All About Space, BBC Science Focus, among others. He has also written a selection of books including Cosmic Impact and Astrobiology: The Search for Life Elsewhere in the Universe, published by Icon Books.

## FAQs

### What is time dilation explain? ›

time dilation, in the theory of special relativity, the “slowing down” of a clock as determined by an observer who is in relative motion with respect to that clock.

Is time dilation a real thing? ›

Yes, time goes faster the farther away you are from the earth's surface compared to the time on the surface of the earth. This effect is known as "gravitational time dilation". It is predicted by Einstein's theory of General Relativity and has by verified multiple times by experiments.

What was Einstein's conclusion from time dilation? ›

Time dilation

One of the many implications of Einstein's special relativity work is that time moves relative to the observer. An object in motion experiences time dilation, meaning that when an object is moving very fast it experiences time more slowly than when it is at rest.

What is time dilation Class 11? ›

According to the theory of relativity, time dilation is defined as the difference between the elapsed time of the two events measured by either moving relative to each other located differently from gravitational mass or masses.

What is the example of time dilation? ›

Theoretically, time dilation would make it possible for passengers in a fast-moving vehicle to advance further into the future in a short period of their own time. For sufficiently high speeds, the effect is dramatic. For example, one year of travel might correspond to ten years on Earth.

Why time dilation is false? ›

Time Dilation is real insofar as it tells us the rate at which things happen in one reference frame relative to another. However, it is based on clock time, which is virtual. Real time doesn't, and never will vary. Things can still happen at different rates in different reference frames measured against real time.

How strong can time dilation be? ›

These are created when cosmic rays hit Earth's upper atmosphere, and they can travel at nearly the speed of light. The muons are so unstable that they shouldn't last long enough to reach Earth's surface, yet many of them do. That's because time dilation can extend their lifetimes by a factor of five.

Does speed affect time dilation? ›

Time dilates on moving vessels: the greater the speed, the greater the time dilation. Only when such velocities* approach light speed do such effects become significant. If, and this one of those extreme IF's, a vessel could attain light speed, time aboard the vessel would cease altogether.

Why time stops at speed of light? ›

In the limit that its speed approaches the speed of light in vacuum, its space shortens completely down to zero width and its time slows down to a dead stop. Some people interpret this mathematical limit to mean that light, which obviously moves at the speed of light, experiences no time because time is frozen.

Why do we age slower at the speed of light? ›

According to the theory of relativity, the faster something travels, the slower time moves for it. So, if an astronaut leaves earth and travels close to the speed of light, he will feel like 2 years have passed on his journey, but when he returns to earth, 40 years will have passed (or whatever).

### Why did Einstein say time is an illusion? ›

Re: Why did Einstein say that time is an illusion? Einstein is referring to the apparent flow of time, that all space is 3 dimensional, changing in place over time, as opposed to 4 dimensional spacetime with equal ontological status of all events, not separated into being either past, present, or future.

What are the types of time dilation? ›

Two types of time dilation exist; time dilation onset by a difference in relative velocity, and time dilation brought about by the effect of gravity.

Who gave time dilation? ›

Physicists have verified a key prediction of Albert Einstein's special theory of relativity with unprecedented accuracy. Experiments at a particle accelerator in Germany confirm that time moves slower for a moving clock than for a stationary one.

Who Discovered time dilation? ›

Gravitational time dilation was first described by Albert Einstein in 1907 as a consequence of special relativity in accelerated frames of reference.

What are the benefits of time dilation? ›

Time dilation would make it conceivable for the crew of a fast-moving interstellar spacecraft to travel further into the future while aging much more slowly, because enormous speed significantly slows down the rate of on-board time's passage.

How do you solve time dilation? ›

Formula for Time Dilation
1. T =T0 /√1−(v2/c2)
2. T is the time observed.
3. T0 is the time observed at rest v is the velocity of the object.
4. c is the velocity of light in a vacuum (3 × 108 m/s2)
1 Feb 2022

What affects time dilation? ›

Time dilation is triggered by disparities in both gravity and relative velocity. Together these two factors are at constant play in the case of a spacecraft's crew.

Do you age slower in space? ›

Scientists have recently observed for the first time that, on an epigenetic level, astronauts age more slowly during long-term simulated space travel than they would have if their feet had been planted on Planet Earth.

Does speed affect time? ›

At very high velocity, time is dilated with respect to an observer. The speed of light remains constant but since the distance that the light must travel increases, the time that it takes for it to travel from say a point A to a point B is longer than if it were stationary relative to the observer.

Does gravity slow time? ›

Gravity is not just a force.

This effect measures the amount of time that has elapsed between two events by observers at different distances from a gravitational mass. In other words, time runs slower wherever gravity is strongest, and this is because gravity curves space-time.

### Why is time moving so fast? ›

As we get older, we have fewer new experiences and the world around us becomes more and more familiar. We become desensitised to our experience, which means that we process less information, and time seems to speed up.

Does time exist for light? ›

From the perspective of a photon, there is no such thing as time. It's emitted, and might exist for hundreds of trillions of years, but for the photon, there's zero time elapsed between when it's emitted and when it's absorbed again.

Can gravity bend light? ›

Gravity bends light

Light travels through spacetime, which can be warped and curved—so light should dip and curve in the presence of massive objects. This effect is known as gravitational lensing GLOSSARY gravitational lensingThe bending of light caused by gravity .

Can you travel faster than light without time dilation? ›

A reference frame with zero width and with no progression in time is really a reference frame that does not exist. Therefore, this tells us that nothing can ever go faster than the speed of light, for the simple reason that space and time do not actually exist beyond this point.

Does time stop in a black hole? ›

Near a black hole, the slowing of time is extreme. From the viewpoint of an observer outside the black hole, time stops. For example, an object falling into the hole would appear frozen in time at the edge of the hole.

Is time real or an illusion? ›

According to theoretical physicist Carlo Rovelli, time is an illusion: our naive perception of its flow doesn't correspond to physical reality. Indeed, as Rovelli argues in The Order of Time, much more is illusory, including Isaac Newton's picture of a universally ticking clock.

Is gravity caused by time dilation? ›

Gravity does NOT warp the flow of time. It's the other way around the warping of time causes gravity.

At what age do humans start to slow down? ›

New study says decline begins in our 50s

Researchers with Duke University's School of Medicine suggest that physical decline begins in the decade of the 50s and worsens as we age, especially for those who don't exercise.

Why does time go by so fast as you get older? ›

As we get older the rate of new experiences lessens compared with youth, when almost everything is new. That leads to a sense of the days being longer but time passing much more quickly overall.

Is anything faster than light? ›

So, according to de Rham, the only thing capable of traveling faster than the speed of light is, somewhat paradoxically, light itself, though only when not in the vacuum of space. Of note, regardless of the medium, light will never exceed its maximum speed of 186,282 miles per second.

### Is time the 4th dimension? ›

Physics > Space and Time

According to Einstein , you need to describe where you are not only in three-dimensional space — length, width and height — but also in time. Time is the fourth dimension. So to know where you are, you have to know what time it is.

When did time begin? ›

According to the standard big bang model of cosmology, time began together with the universe in a singularity approximately 14 billion years ago.

Can you travel back in time? ›

Time travel is probably impossible. Even if it were possible, Hawking and others have argued that you could never travel back before the moment your time machine was built.

What is the time dilation formula? ›

How to calculate time dilation? Determine the time interval measured by the stationary observer. Substitute the traveling viewer's velocity for v in the Lorentz factor formula, γ = √(1 - v²/c²) . The result is the time as measured by the moving observer.

Why is time slower the faster you go? ›

The speed of an object through space reflects how much of its motion through time is being diverted. The faster it moves through space, the more its motion is being diverted away from moving through time, so time slows down.

Is time a illusion? ›

According to theoretical physicist Carlo Rovelli, time is an illusion: our naive perception of its flow doesn't correspond to physical reality. Indeed, as Rovelli argues in The Order of Time, much more is illusory, including Isaac Newton's picture of a universally ticking clock.

What happens to time in time dilation? ›

In time dilation, time moves slower for an observer who is in motion relative to another observer. To a stationary observer, a moving clock will tick slower than the one the observer is holding. The concept of the time dilation effect comes from Albert Einstein's Theory of Relativity.

Can time be stopped? ›

The simple answer is, "Yes, it is possible to stop time. All you need to do is travel at light speed." The practice is, admittedly, a bit more difficult. Addressing this issue requires a more thorough exposition on Special Relativity, the first of Einstein's two Relativity Theories.

Can we go back in time? ›

The Short Answer: Although humans can't hop into a time machine and go back in time, we do know that clocks on airplanes and satellites travel at a different speed than those on Earth. We all travel in time!

Do you age if you travel speed light? ›

Re: How would you age at the speed of light

The simple answer is, anything moving through space at c, equal to the speed of light in a vacuum, experiences zero time flow. If you were to travel at the speed of light, you would experience no time.

### What does space smell like? ›

We can't smell space directly, because our noses don't work in a vacuum. But astronauts aboard the ISS have reported that they notice a metallic aroma – like the smell of welding fumes – on the surface of their spacesuits once the airlock has re-pressurised.

How cold is space? ›

Space is very, very cold. The baseline temperature of outer space is 2.7 kelvins (opens in new tab) — minus 454.81 degrees Fahrenheit, or minus 270.45 degrees Celsius — meaning it is barely above absolute zero, the point at which molecular motion stops.

## Videos

1. Relativity: how people get time dilation wrong
(Fermilab)
2. Time Dilation - Why an Accelerated Frame of Reference Slows Down Time
(But Why?)
3. What is Time Dilation? (Thought Experiment)
(For the Love of Physics)
4. What is Time Dilation?
(ZAP Physics)
5. Length Contraction and Time Dilation | Special Relativity Ch. 5
(minutephysics)
6. What is time dilation : evidence behind it - muons and clocks and planes.
(PhysicsHigh)
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