Intuitively understanding time dilation caused by special relativity can be a bit challenging, but I'll do my best to explain it in a simplified manner.
In special relativity, time dilation occurs because the speed of light is constant for all observers, regardless of their relative motion. This means that the passage of time is not absolute but depends on the observer's relative velocity.
To understand this concept, let's consider a thought experiment involving two observers: Alice and Bob. Imagine Alice is on a spaceship traveling at a significant fraction of the speed of light, while Bob is stationary on Earth.
From Alice's perspective, she sees herself as being at rest, and Bob moving away from her at the same speed in the opposite direction. Likewise, from Bob's perspective, he sees himself as being at rest, and Alice moving away from him.
Now, let's say Alice has a clock on her spaceship, and Bob has an identical clock on Earth. According to Alice, her clock is ticking normally. However, from Bob's perspective, he observes that Alice's clock appears to be ticking slower than his own clock on Earth.
This difference in the rate of ticking is the result of time dilation. The key idea behind it is that as an object (or observer) moves faster through space, its "internal clock" slows down relative to an observer at rest.
So, from Alice's perspective, time seems to be passing normally for her, but from Bob's perspective, time is passing slower for Alice due to her high velocity. The faster Alice travels, the more pronounced the time dilation effect becomes.
This phenomenon has been experimentally verified in various ways, such as with high-speed particle accelerators and atomic clocks placed on fast-moving objects like airplanes. These experiments have consistently shown that time dilation occurs as predicted by the theory of special relativity.
In summary, time dilation in special relativity arises because the speed of light is constant, and as an object's velocity approaches the speed of light, time appears to slow down for that object relative to a stationary observer.