Malintent
Veteran Member
No it doesn't. Neither observer ever experiences the year infinity; The pilot likely dies fairly young, and the mission controller lives a normal human lifespan - during which time he never sees the spacecraft cross the event horizon. Even his distant decendants never see that happen. Because it never does happen IN THEIR FRAME OF REFERENCE.
There is no paradox here.
Okay maybe it's just troubling. Because, for the people passing through the horizon, the universe outside of the black hole would be infinitely old. They would have exhausted an infinite amount of time external to them. It's just disturbing.
Well that's just the problem with infinities. Archimedes described the paradox of dichotomy, which we can relate to the two frames of reference. It goes like this.
From one point of view, I can walk across my yard in 1 minute. I spend duration T = 0 to T = 1 performing the task of traversing the yard.
From another point of view, before I can possibly walk all the way across the yard, I first have to walk halfway. at T = 1/2 I am halfway across the yard. Before I can walk the rest of the way across the yard, I first have to walk halfway the remaining distance. T = {1/2 + 1/4}.
we can keep dividing the remaining distances in half...
T = {1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64....}
The one performing the task of traversing the distance will take an infinite amount of time to traverse the finite distance.
The observer, however, can still say that it takes 1 minute to traverse the distance.
The solution is simple. T =1. therefore,
{1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64....} = 1
The infinite set sums to a finite number. From one point of view it takes forever to get where you are going, but from the other, it is finite.