By Vijay Damodharan - Natural Sciences Student @ Christ College, Cambridge

Time dilation is a concept that often receives a lot of media attention due to its counter-intuitive nature. But what actually is it and is it true?

Time dilation is a consequence that arises when one explores the theory of relativity. The fundamental aspect of this theory boils down to two postulates:

a) “All the laws of physics are the same in every inertial frame of reference”

b) “The speed of light in a vacuum is constant in all inertial frames of reference”

A frame of reference just means perspective or viewpoint. So, two different people will have two different perspectives or frames of reference. By inertial, we mean something that doesn’t accelerate. For example, if someone is standing still or travelling at a constant velocity, they will be in an inertial frame of reference. However, if someone is on a train that is accelerating, they will be in a non-inertial frame of reference.

So as long as someone is in an inertial frame, all the conventional laws of physics hold, such as Newton’s mechanics, or energy conservation. There are no surprises there.

However, the second postulate has consequences that are a lot more far-reaching, and it is the basis of time dilation. To understand why it is so significant, we can use a simple thought experiment. Consider a person standing on a train travelling at a constant velocity ‘v’. If they throw an object forward at speed ‘s’, a person standing outside the train will observe the object to have a speed of ‘v + s’.

In other words, the speed of the object they measure is equal to the speed of the train plus the speed at which the ball was thrown. This is obvious and easy to understand from our everyday experiences. However, the second postulate says that this would not be true if the object was light. The person inside the train and outside will both measure the speed of light to be the same!

This is already something that is hard to accept as it disagrees with what we observe in our everyday life. The reason why it’s true boils down to some complicated maths and theory, so we will accept it as a fact for now and see what the consequences are.

Imagine a different thought experiment, where now a person is standing on a rocket (moving at a constant speed) with a torch, underneath a mirror. If they shine the torch onto the mirror, we can expect that they will see the light travel vertically upwards, bounce off the mirror, and return by travelling vertically downwards.

Now consider this same event as observed by a person standing on a planet outside the rocket. Since the rocket was originally moving horizontally, they will not only see the light move vertically when it is turned on but also horizontally. Therefore, from their perspective, the light travels a different distance from what is observed by the person on the rocket.

But now remember the second postulate – both these observers will observe the same speed of light! The two people observe light travelling different distances but with the same speed. How can this be possible? Well from the basic equation: distance = speed x time, we can see immediately that the two observers must have a different experience of time. So simply by virtue of motion, the person standing on the rocket will experience a different time to the person outside. This is time dilation!

Once we accept the fact that the speed of light in a vacuum is constant in all inertial frames, we are forced to accept that time dilation occurs. We are used to thinking about time as a clock that just ticks in the background at the same rate for everyone, unaffected by the world. However, that is just not true, each person has a personal clock that ticks at a different rate depending on their relative velocity.

One may naturally wonder then why people that are travelling in real life don’t (seem to) experience a different time to people who are standing still. This can easily be understood if one calculates the factor by which the time changes for the two frames of reference mathematically. It turns out that for any speed that is not close to the speed of light, this effect if negligible. If we keep in mind that light is able to travel around the equator about seven times in a second, we can see how fast that is!

So then why is it important if we can’t observe it? Well, we may not be able to personally observe the effect of time dilation, however, it does affect many things around us. GPS clocks, for example, go out of sync over time because the satellites are travelling at a different velocity to us on Earth. So even though this effect is small it can accumulate over time if it is not accounted for, and the clocks around the world will go out of sync with the ‘actual’ time.

Another interesting effect is in muon decay. Muons are a type of fundamental particle that enters the atmosphere through cosmic rays. However, since they only have a lifetime of a few microseconds, they should only be able to travel a few meters before they decay. Keeping in mind that the surface is about ten kilometres away from where they enter the atmosphere, we shouldn’t be able to detect them. However, because they are travelling very fast, their time is dilated so a few microseconds in their perspective is much longer for us, allowing them to travel much further than they’d otherwise be able to. As a result, we can observe them even on the surface.

These effects become significant in pretty much any physical phenomenon when the speeds become high enough, and the equations must be adjusted to include a relativistic correction; this idea is not just science fiction but very real.

Does this mean time travel is possible? Suppose a person leaves Earth on a rocket that can travel at half the speed of light and circles back around after 10 years in their frame of reference. However, from the perspective of people on Earth, 11.5 years would have passed. In other words, the person would have travelled 1.5 years into the future! If such speeds could be reached then, time travelling would become a reality (but that remains a very big if!).

**Further Reading:**

1. What is time dilation? Live Science. Andrew May. 17/11/21

2. (Slightly more mathematical) The invisibility of Time Dilation. Theo Hughes and Magdalena Kersting. 2021 Phys. Educ. 56 025011

3. When time breaks down. Space Time. PBS Digital Studios. 13/01/16

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