According to Einstein's theory of relativity, time dilation occurs as an object approaches the speed of light. As a result, an observer moving at relativistic speeds (near the speed of light) would experience time differently than an observer at rest.
Let's consider a hypothetical scenario where you embark on a journey in a spaceship traveling at nearly the speed of light to a distant star and then return to Earth. For the sake of simplicity, we'll assume that the round trip takes a certain amount of time, as measured by clocks on the spaceship.
From the perspective of a stationary observer on Earth, the time on the spaceship would appear to be dilated or slowed down due to its high velocity relative to Earth. This effect is known as time dilation.
The time experienced on the spaceship (Δt_ship) is related to the time experienced on Earth (Δt_earth) by the following equation:
Δtearth=Δtship1−v2c2Δt_earth = frac{Δt_ship}{sqrt{1 - frac{v^2}{c^2}}}Δtearth=1−c2v2Δtship
where v is the velocity of the spaceship, and c is the speed of light.
As the spaceship approaches the speed of light (v ≈ c), the denominator of the equation approaches zero, causing time dilation to become more pronounced. In the limit as v approaches c, the time experienced on the spaceship (Δt_ship) approaches infinity. This means that, from the perspective of the stationary observer on Earth, the journey of the spaceship would take an infinite amount of time.
From the perspective of the travelers on the spaceship, however, they would experience time passing normally during their journey. So, if you were the traveler on the spaceship, you would age as you normally would, and your age would not be affected by the relativistic effects during the journey.
When you return to Earth after your journey, you would find that much more time has passed on Earth compared to the time you experienced on the spaceship. The time dilation effect would have resulted in the people on Earth aging more than you did during your journey, making you "time-travel" into the future relative to Earth.
It's important to note that this scenario assumes an idealized situation and is subject to the laws of physics as described by the theory of relativity. In reality, reaching speeds close to the speed of light with any massive object (such as a spaceship with humans) is currently beyond our technological capabilities.