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 Originally Posted by wufwugy
where most of my confusion arises is how the ant on the balloon can travel in a constant direction and reach a spot he was before while a man in a magic-fast spaceship (presumably) cannot.
Don't be so positive about that spaceship. Space contraction and time dilation could give him a serious advantage.
As you move closer and closer to the speed of light, distances in your direction of travel are contracted. The universe becomes pancaked in your direction of travel. Also, clocks outside your ship tick more slowly. So the rate of the universe's expansion would be slowed as well.
Now to create a ship that can hold a constant acceleration indefinitely and see if it can accelerate enough to overcome the universe's accelerating expansion.
Originally Posted by wufwugy
unless the balloon is constantly inflating. then the ant never reaches the same point twice.
that makes sense, but i guess im confused on how that doesn't make the balloon surface infinite.
How can that be confusing? It's just a balloon that is inflating. Still finite at any finite future time.
(We must assume this balloon is made of some material with infinite stretchiness and infinitesimal thickness.)
Originally Posted by wufwugy
i mean, if there is always a new point in spacetime, that means there are infinite points in spacetime, which means spacetime is infinite right?
There are always more numbers between 0 and 1 than can ever be listed, therefore the distance between 0 and 1 is infinite, right?
No.
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