“Time is relative” is a saying that we hear every so often. Whether it be a phrase overly used by that geeky friend of ours or a punchline in a Sci-fi movie as a dramatic scene unfolds, but still, what does it really mean? Why is time relative, and if it is, how does it affect our day-to-day life? And if we take a step back, what is time?

What is time – a scientific definition

Time is something that we are all familiar with. Yet, when we are asked to explain what it is, it can suddenly feel rather tricky and difficult to put it into words. Some might say time is a description of the Sun’s position in the sky or a just number that is displayed on the clock. Or, as the saying goes, time is what keeps everything from happening at once, so we can do tasks one after the other with coffee/tea breaks in between. As much as it’s easy to give time a trivial definition, these descriptions just don’t seem to grasp the complex meaning of which time represents.

I have measured out my life with coffee spoons.

A line from T.S. Eliot’s poem “The Love Song of J. Alfred Prufrock”. It illustrates how routines and rituals can make time feel measured and experienced uniquely by each individual.

In physics, time represents the continuous progression of events and serves as reference points we assign to moments so that we can derive other physical quantities of a real object, such as its velocity and position. With this notion of time, we have been able to discover new laws of physics, achieve extraordinary technological advancement and strengthen our understanding of the universe.

The relativistic nature of time

The relativistic nature of time is first formulated in the theory of special relativity by Albert Einstein more than a century ago. While the mathematics Einstein used in his derivation is not at all simple, it is undoubtedly a genius and beautiful set of rules underlying how the universe works. Below, without using complex equations, I would like to share a perspective that has helped me better understand why time is relative.

Space time

To take a glimpse into the relativistic nature of time, we must first introduce a concept called “spacetime”. In simplest terms, a spacetime or a space-time continuum denotes a model that combines a three-dimensional space with an additional dimension for time. You can try to make sense of it with an example of a moving spaceship in space: in addition to the three conventional directions of motion (x y z) where the spaceship can move (i.e., up-down, left-right, and forward-backwards), there is an extra fourth axis that the spaceship also travels upon – “time”. Therefore, when describing an object’s state in spacetime, one needs to specify not just the spatial coordinates x-y-z (i.e., object’s position) but also its temporal coordinates t (i.e., at a specific time).

In other words, under the framework of a four-dimensional coordinate, the motion of an object through spacetime can be expressed by its four-velocity, which combines its motion through x-y-z space and its progression through time. Now, the catch here is that by unifying space and time into a single four-dimensional continuum, an elegant consequence emerges: the magnitude of this four-velocity is always constant and equal to the speed of light.

We can understand this outcome by first considering a simpler two-dimensional example. On a xy-plane, a constant magnitude of a two-velocity corresponds to an object travelling for a fixed distance from its initial position. Since the distance can be expressed as

this means that a fixed distance is conserved as long as x and y have the right values to satisfy the condition. For example, if the fixed distance = 5 in units of distance, then both the (x = 3,  y = 4) and (x = 4, y = 3) pairs are possible solutions.

Similarly in four-dimension, a constant magnitude of four-velocity required all objects to move through the space-time continuum at the same speed. In fact, this constant quantity is known as the spacetime interval and is mathematically defined as

where Δs² is the spacetime interval, c is the speed of light, Δt is the time interval denoting the temporal separation of events, and ΔxΔyΔz is the spatial component denoting spatial separations of the events along the x-y-z axis in the chosen reference frame. You can read more about the formulation of the expression here, but the main point I want to get across is that, just like how we can keep distance fixed in a 2D plane by varying x and y, in a 4D spacetime continuum, the variation between space (x-y-x) and time (t) is what keeps the spacetime interval Δs² constant.

In other words, because all object moves through spacetime at a constant speed, if an object moves more in space, it moves less in time. Conversely, if it moves less in space, it moves more in time. Consequently, this trade-off between space and time is precisely the reason why the passage of time varies, hence the famous saying that goes – the faster you move, the slower your time passes. That’s Relativity!

Having said that, we will almost never feel the relativistic nature of time because of how minuscule this effect is. In fact, for any noticeable slowdown in time to even take place, one will have to travel at a speed somewhat comparable to the speed of light, a speed that is still very out of reach even with today’s technology. You can play around with different speeds and see how much time slows down with this calculator. Therefore, even if it’s true that time does pass slower if you go faster, you will probably never travel fast enough to use it as an excuse and say to your boss that you’re late for work because his/her watch is too fast.

A different kind of relativity in time

A few days ago, I came across a YouTube video by Simply Aviation in which the channel documented a passenger fight experience from Taipei to Osaka on the airline carrier Starlux. The video provided a comprehensive onboard review, covering various aspects such as in-flight entertainment, meals, cabin’s interior design, and even the authentic branding of the onboard items. It concluded with an overall positive review on nearly every aspect of the flight, and a particular line that was said by the narrator caught my attention and left me in thought.

“For us humans, time isn’t just measured, it’s felt. And if you spent 3 hours enjoying yourself versus 3 hours in discomfort. Those 3 hours will feel vastly different in length.”

I think in many ways, this line captures an interesting philosophical sentiment – “to live is to feel”. The existential fact that we are alive gives us a purpose to experience and feel about what life has to offer. Whether it’s the touch of the tangible – like the breeze on our skin or the embrace of a loved one – or the intangible, such as happiness, fear, or curiosity, life invites us to engage with the world around us.

In the context of the relativistic nature of time. I find it somewhat incredible that while our monkey-evolved brains were never designed with a purpose to perceive the world through the lens of the theory of relativity, and to ever notice its consequences such as the relativistic passage of time. Yet each one of us is still capable of making time relative in our own way simply because we can feel.