According to Einstein's theory of relativity, if you were able to travel at the speed of light, time would not pass for you. However, it is important to note that it is impossible for an object with mass, such as a spaceship with humans onboard, to reach or exceed the speed of light. As an object with mass approaches the speed of light, its relativistic mass increases, requiring an infinite amount of energy to reach that speed.
Nonetheless, we can consider a scenario where you travel close to the speed of light, but not at it. In this case, time dilation effects would still occur. As you approach the speed of light, time would slow down for you relative to an observer on Earth.
Let's imagine that you embark on a journey in a spaceship traveling at a high fraction of the speed of light, and you go on a round trip. When you return to Earth, you would have experienced less time compared to your friends who remained on Earth. This effect is known as "time dilation."
To estimate the time difference, we can use the equation for time dilation:
Δt' = Δt / √(1 - (v^2/c^2))
Where: Δt' is the time experienced by the traveler (you) on the spaceship. Δt is the time experienced by your friends on Earth. v is the velocity of the spaceship. c is the speed of light.
Let's assume that you travel at 0.99 times the speed of light (v = 0.99c) and spend one year (Δt = 1 year) on your journey. Plugging these values into the equation, we get:
Δt' = 1 / √(1 - (0.99^2))
Δt' ≈ 7.09 months
So, from your perspective, approximately 7.09 months would have passed during your journey.
On the other hand, your friends on Earth would have experienced the full year that you were away. Therefore, when you return, your friends would be approximately 4.93 months older than you (12 months - 7.09 months).
This example demonstrates the time dilation effect that occurs as you approach the speed of light. However, it is essential to remember that reaching or exceeding the speed of light is not currently possible for objects with mass based on our current understanding of physics.