Special theory of relativity - Time Dilation

Yash Soni
Yash Soni / April 7, 2020
5 min read

This is a topic that I have tried reading multiple times from random articles, youtube videos, or discussion with friends. Although I felt like I understood it at that moment, when I stumbled upon this topic a few months later - I was blank.

Today, while reading the book, The Beginning and the end of everything by Paul Parsons, I finally think I understood this correctly. And there is no better way to pen down the learnings.

Special theory of Relativity, was developer by Albert Einstein in 1905. It is known as special relativity because it applies only to special cases; frames of reference in constant, unchanging motion. He later published his General theory of Relativity in 1915 which applied it generally to frames that are accelerating with regards to each other and also taking gravity into consideration.

The seeds for building the Special theory of relativity were sown by Einstein in a thought experiment which he did at the age of 16. According to this thought experiment, he wondered what would happen if one could travel at the speed of light and looked at another light wave moving parallel to him. According to classical physics, the light wave the rider was looking at would have a relative speed of zero. But, this contradicted Maxwell's equations (published in 1861) that showed light always has the same speed: 300,000 km/s. Believing in Maxwell’s theory that speed of light can never change, he set about deriving new ways to calculate relative motion.

In simple terms, it doesn’t matter how fast you travel - the relative speed between you and a light beam will not waiver from 300,000 km/s. When we account for speed and mass into the picture, the laws of “classical mechanics” we studied in high-school, applies to only a specific quadrant.


Time Dilation

Imagine a beam of light moving inside a space rocket. An astronaut inside the rocket and an external stationary observer have clocks to measure the time it takes this beam to travel from point A to point B.

Stage 1: Rocket is stationary Both agree on how long it takes for the light beam to cross the width of the rocket.

Stage 2: Rocket fires up its engines and jets off at close to light-speed For the astronaut inside, nothing has changed and he measures the time taken for the light to reach from A to B. But, for the external observer, they see the light beam travels a greater distance because in addition to cross the width of rocket it also moves forward with the rocket’s motion. Since the light-beam must be moving at the same speed in both frames of reference (Maxwell’s theory), the only way it can cover a greater distance traveling at the same speed is by taking longer to make the journey (speed = distance/time).

If the observer compares the ticking of their clock to that of the Astronaut’s clock, they will find that the moving clock in the rocket is actually ticking slower - less time is passing in astronaut’s frame of reference. This concept is called time dilation.

Head over to this video for better reasoning of this calculation.

As the speed reaches closer to that of light, the time dilation also increases

  • at 86% light-speed, the clock moves at roughly half the speed of the stationary
  • at 99.9% light-speed the factor is reduced by ~20!

Consider this, if a set of astronauts leave earth and travel at 86% of the speed of light for 20 years (measured by their friends back home), when they return back, they would have only aged by 10 years! If the same experiment is done at 99.9% light-speed and they travel for 10 years (measured by them inside the rocket), upon return they will return 220 years in the future! Remember the movie Interstellar?

Time is not a rigid detached parameter. It does not flow at an absolute rate. It is relative. It flows at a different rate for different observers. The faster you move relative to the speed of light, the time will pass slower for you.

The concept of Time dilation is everywhere and has been proven a number of times. We don’t experience it in everyday life because the velocity component is very less compared to the speed of light and hence the Δt component in the above equation is negligible.

The GPS satellites make use of the exact concept of time dilation to ensure we get an exact reading of locations. Check out this MIT lecture where this is explained in detail.

References and further reading