Intuitive explanation of “slowing of time” due to motion

One of the consequences of Einstein’s special theory of relativity (speed of light is constant in all reference frames) is that your clock ticks slower when you move. If you move at the speed of light, time stops!
This is a counter intuitive concept. In my earlier post, I had discussed an intuitive way to understand this. Let’s denote the speed of light by c.

c = distance/time = a measure of space/a measure of time

Einstein’s special theory of relativity says that c should be constant in all reference frames. It means that space (numerator) and time (denominator) adjust, which leads to change in time due to motion.
I find another exposition of time dilation by Brian Greene pictorially appealing.

Let’s suppose that you move along the North with speed v, and let’s say that you cover a distance of D, in unit time. The red line in the picture below denotes this.
Now, you change your direction of motion, while traveling at the same speed. The new direction of motion is depicted by the green line.

Note that in the same unit time, you now cover less distance along vertical direction (d < D), even though you travel at the same speed. It’s because, some of your motion along the North is converted to your motion along the East.

Similar analogy can be used to depict the time dilation.

When you are at rest, your coordinates along space dimension don’t change but since the time is moving forward, your coordinates along the time dimension change. Motion of a stationary body (in space) along time dimension is depicted by the red line.
Now, the body starts moving along space dimension too. The new motion will be along the green line.

Note that the moving body covers less along time dimension (t < T), because some of its motion along time dimension is now converted to motion along space dimension.

It means that measurement of time is slower in moving bodies. Time dilates with motion.
I found this as a good intuitive explanation. Hope you liked it.

This principle is used in GPS to determine the precise coordinates, as explained in the earlier post.