If someone were traveling at speeds close to the speed of light, they would indeed observe the effects of time dilation. From their perspective, time would appear to pass more slowly compared to observers in a stationary reference frame.
Here's a hypothetical scenario to help illustrate the effects:
Let's say there are two individuals, Alice and Bob. Alice remains on Earth, while Bob travels on a spacecraft moving at a velocity close to the speed of light, such as 0.9 times the speed of light (0.9c). They both have synchronized clocks initially.
During Bob's journey, he would notice that his clock appears to be ticking normally. However, when he compares his clock to Alice's upon his return, he would find that his clock has ticked significantly less than Alice's clock. In other words, he would have experienced less time compared to Alice.
From Bob's perspective, time dilation has occurred. The effects of time dilation become more pronounced as his velocity approaches the speed of light. The Lorentz factor γ = 1/√(1 - (0.9c)²/c²) would be approximately 2.29 for a velocity of 0.9c. This means that for every second that passes for Bob, approximately 2.29 seconds would pass for Alice on Earth.
So, if Bob were to embark on a journey and return after what he perceives as a few years, he would find that much more time has passed on Earth. For example, if Bob travels for 5 years (according to his clock), he would find that around 11.45 years have passed on Earth according to Alice's clock.
This example demonstrates how time dilation would be observed by someone traveling close to the speed of light. However, it is important to note that this scenario is purely hypothetical, as current technology does not allow for such high speeds.