Special Relativity: Why speed of light is constant ? Length and Time Dilation

In our everyday life, things move pretty slowly compared to the speed of light. For example, the top speed of the world’s fastest train, the Shanghai Maglev, is 460 km/h, which is about 0.128 km/s. The NASA/USAF X-15, the fastest jet ever, reached a speed of 4,520 mph, or approximately 1.26 km/s. But these speeds are tiny compared to the speed of light, which races along at a massive 299,792.458 km/s.

To put this in perspective, the speed of light is about 2.34 million times faster than the Shanghai Maglev and it’s around 238,000 times faster than the X-15 jet.

This is why we’re used to thinking of the world as stable and predictable. However, in the late 1800s, scientists made a groundbreaking discovery about light that changed everything.

The Michelson-Morley Experiment: A Surprising Result

Figure 0: The figure illustrates the hypothetical "aether wind" caused by Earth's orbital motion. According to the aether theory, this would affect light's speed, making it faster when traveling with the wind and slower when moving against it.

Scientists once believed that light, like sound, must travel through some kind of medium, which they called the aether. This mysterious aether was thought to be an invisible substance filling all of space, acting as a carrier for light waves. To test this idea, Albert Michelson and Edward Morley set up an ingenious experiment in 1887 to see if they could detect the effects of Earth's motion through the aether.

Here’s how they approached it: if the aether really existed, then Earth, moving through space at about 107,000 km/h (or around 30 km/s) in its orbit around the Sun, would be plowing through it, as seen in Figure 0 and 1. As Earth moved through this aether “wind,” they reasoned that light traveling in the direction of Earth’s motion would be affected—just like a boat’s speed in a river changes based on the river current. For example, a boat moving downstream with the current moves faster than one going upstream against it. If light behaved similarly, it would travel slightly faster when moving with the "aether wind" and slower when moving against it.

Figure 1. Image of Michelson Morley Interferometer. The light beam is split in two perpendicular beams. The path of the beams should get affected by the presence of ether which can be measured by the detector.
Source : faculty.etsu.edu

To test this, Michelson and Morley designed a setup using a special device called an interferometer as shown in Figure 1. This device split a single light beam into two perpendicular beams, one moving in the same direction as Earth's motion and the other moving perpendicular to it. After traveling different paths, the beams would be brought back together and interfere with each other. If the speed of light was affected by the aether, even by a tiny amount, this interference would show up as a change in the light patterns. 

But to their surprise, no matter how they oriented their equipment or what direction the beams traveled, the speed of light stayed the same. There was no detectable difference between the light moving "with" or "against" Earth's motion through the supposed aether.

This unexpected result shocked the scientific community. It was as if the aether didn’t exist at all, or if it did, it had no effect on light’s speed. This experiment ultimately led to the radical conclusion that the speed of light is a universal constant, independent of any “aether” or the motion of the observer. This realization was a crucial stepping stone toward Einstein’s theory of special relativity, which showed that space and time adjust in ways that keep the speed of light constant for all observers.

Einstein’s Big Idea

Albert Einstein took this discovery further. If the speed of light is always constant, then something else has to change to make that possible. Einstein realized that for the speed of light to stay the same, measurements of time and space must change. This led to two surprising effects: time dilation and length contraction.

What is Time Dilation?

Time Dilation: Slower Time for Moving Objects

Imagine time as a clock ticking away seconds, but this clock doesn’t tick the same way for everyone. In Einstein’s theory of relativity, time dilation means that time actually passes more slowly for objects in motion relative to a stationary observer.

How It Works

Figure2. This figure shows the difference in path of the light in the rest frame of reference (on left) and the moving frame of reference (right). The object in motion travels a longer path as compared to the object at rest. However, as the speed of light is a constant, the time taken by the moving object is shorter as compared to the object in rest.
Source: https://commons.wikimedia.org/wiki/User:Sacamol

To understand time dilation, let’s revisit our example of your friend on a high-speed train in figure2.  Both you and your friend carry clocks that tick by counting the time it takes for a pulse of light to bounce between two mirrors. This “light clock” gives a consistent measure of time in both your and your friend’s frames.

However, from your perspective, the light in your friend’s clock travels a longer, diagonal path, since it’s moving along with the train. But according to Einstein’s discovery, the speed of light stays constant, so the light pulse can’t travel faster in your friend’s clock to keep up with the train. Instead, it takes more time for the light to bounce between mirrors, meaning your friend’s clock ticks slower than yours.

So, from your perspective, as the observer on the platform, your friend’s time appears to slow down. This isn’t just an illusion but a real effect: time truly passes more slowly for objects moving at high speeds relative to you. Below is the real -life example for the time dilation

Real-Life Example: Cosmic Rays and Muons

We see time dilation in action with cosmic rays. When cosmic rays hit Earth’s atmosphere, they produce particles called muons, which decay very quickly—usually within about 2.2 microseconds. Muons travel at nearly the speed of light, so if they experienced “normal” time, they wouldn’t survive long enough to reach the ground. However, because they’re moving so fast, time for them slows down relative to an observer on Earth. As a result, they live long enough to be detected at sea level.

In summary, time dilation tells us that moving clocks run slower, which is why muons can travel far further than we’d expect based on their short lifespans.

What is Length Contraction?

Length Contraction: Shrinking Distances for Fast-Moving Objects

Length contraction is the counterpart to time dilation and affects distances rather than time. When an object moves at a high speed, its length appears to shorten in the direction of its motion relative to a stationary observer

How It Works

Let’s return to your friend on the train. From your friend’s point of view, they’re stationary, and it’s you who are moving backwards. According to Einstein’s theory, you both see each other’s clocks ticking more slowly, but that’s not all: your friend also sees the length of the train and everything around it shrinking in the direction of motion.

This effect is real. Just like with time dilation, length contraction is needed to keep the speed of light constant. Since you both agree on the speed of light, any distance measured along the direction of motion has to adjust. So, your friend on the train experiences a “shortened” view of the distances they travel compared to what you see.

Real-Life Example: The Muon’s Journey (Revisited)

For the muon, length contraction provides an alternative explanation for why it can reach Earth’s surface. From the muon’s perspective, it has a much shorter distance to travel because the atmosphere itself appears compressed in the direction of its motion. This shortening effect, combined with time dilation, ensures that the muon can complete its journey to the surface before it decays.
Why Time Dilation and Length Contraction Happen

Both time dilation and length contraction arise from the Lorentz transformations- the mathematical equations used to switch between the perspectives of observers moving at different velocities. These transformations adjust time and space measurements so that the speed of light remains the same for everyone, regardless of their motion.

In a sense, time dilation and length contraction are the universe’s way of keeping the speed of light constant across different frames of reference. So even if two people are moving relative to each other, they both measure light as moving at the same speed, but they end up with different measurements for time intervals and distances.

One strange outcome of this is that two observers moving relative to each other won’t agree on the timing or simultaneity of events. Even the amount of time that passes can seem different! While it sounds confusing, these effects are now a fundamental part of physics, showing us that reality itself bends to keep the speed of light constant.

Living Longer with Einstein's Special Relativity 

Special Relativity even offers a fascinating way to “live longer,” though not in the usual sense of extending biological lifespan. As the time slows down for anyone moving close to the speed of light, an astronaut traveling at 90% the speed of light might experience only 5 years passing on their ship, while 10 or more years would pass on Earth. To the astronaut, life feels normal, but when they return, they’ll have aged less than those who stayed behind. This effect, famously illustrated by the “Twin Paradox,” shows how high-speed space travel could, in theory, allow humans to outlive their peers on Earth. In fact, astronauts on the ISS already experience this in tiny amounts as they come back just a fraction of a second “younger” than if they had remained on Earth.

In short, the Michelson-Morley experiment set us on a path to understanding the true nature of space and time. Thanks to Einstein, we now know that our universe isn’t as straightforward as it seems - space and time are flexible, changing based on speed and perspective. And it all started with the speed of light.