According to our current understanding of physics, it is not possible to travel faster than the speed of light. The speed of light in a vacuum is approximately 299,792,458 meters per second (or about 186,282 miles per second).
To calculate the time it would take to travel a distance of 47 billion light years, we need to convert the distance into a more suitable unit. One light year is approximately 9.461 trillion kilometers (5.878 trillion miles). Therefore, 47 billion light years is equal to:
47 billion light years * 9.461 trillion kilometers/light year = 4.446 trillion trillion kilometers
Now, let's consider time dilation. Time dilation is a phenomenon predicted by Einstein's theory of relativity, which states that time passes differently for objects moving relative to each other. The faster an object travels, the more time slows down for that object compared to a stationary observer.
To determine the required speed, we can use the time dilation formula:
t' = t * sqrt(1 - (v^2/c^2))
Where: t' = time experienced by the moving object t = time experienced by a stationary observer v = velocity of the moving object c = speed of light
In this case, we want the moving object to experience only 20 years (t') while traveling a distance of 4.446 trillion trillion kilometers. Let's assume the stationary observer experiences a much longer time, say one trillion years (t).
20 years = 1 trillion years * sqrt(1 - (v^2/c^2))
Simplifying the equation:
sqrt(1 - (v^2/c^2)) = 20 years / 1 trillion years sqrt(1 - (v^2/c^2)) = 2 x 10^(-14)
Squaring both sides:
1 - (v^2/c^2) = (2 x 10^(-14))^2 1 - (v^2/c^2) = 4 x 10^(-28)
Rearranging the equation:
v^2/c^2 = 1 - 4 x 10^(-28) v^2 = c^2 - 4 x 10^(-28) * c^2 v^2 = (1 - 4 x 10^(-28)) * c^2 v = sqrt((1 - 4 x 10^(-28)) * c^2)
Calculating the speed:
v = sqrt((1 - 4 x 10^(-28)) * (299,792,458)^2) v ≈ 299,792,458 meters per second
This result is approximately the speed of light, meaning that to travel 47 billion light years to the edge of the universe while experiencing only 20 years of time dilation, you would need to travel at nearly the speed of light. However, it is important to note that our current understanding of physics prohibits objects with mass from reaching or exceeding the speed of light, so this scenario is purely hypothetical.