According to the theory of relativity, as an object with mass approaches the speed of light, its relativistic mass increases, and time dilation occurs. Time dilation means that time appears to pass more slowly for the moving object relative to a stationary observer.
If you were able to travel at the speed of light, time dilation would be extreme. From your perspective, time would effectively stop. However, from the perspective of an external observer, time would still pass normally.
To calculate the time experienced by the external observer, we can use the time dilation formula:
t' = t / √(1 - v^2/c^2)
Where: t' is the time experienced by the external observer. t is the time experienced by the moving object. v is the velocity of the moving object. c is the speed of light in a vacuum.
Plugging in the values: t = 5 seconds v = c (speed of light) c ≈ 299,792,458 meters per second
t' = 5 / √(1 - (c^2/c^2)) t' = 5 / √(1 - 1) t' = 5 / √0 t' = 5 / 0
The equation yields a division by zero, which is undefined. This indicates that it is impossible for an object with mass to reach the speed of light, according to our current understanding of physics.
Therefore, from the perspective of an external observer, no time would have passed for you if you were able to move at the speed of light for any duration. However, it's important to note that this scenario is purely theoretical, as it is not currently possible for an object with mass to reach or exceed the speed of light.