Space and the size of infinity

Question

If you could build a spaceship and keep travelling in one direction, what would finally happen? One answer is that you would never ever reach the end. But this sounds purely platonic space and comes into conflict with the big bang theory (or the very first big bang, if you claim there have been many big bangs). That is, space was created in the big bang and is expanding and there is no space outside that realm.

So what happens if the spaceship doesn't continue travelling forever? This brings us to the second possible answer: the spaceship would eventually stop travelling farther, change its direction and may return.

To me, both of these answers are equally scary and unconvincing and contradicting. What would be the ultimate fate of the spaceship considering the big bang as the origin of space?

UPDATE:

The attempt here is to also make a distinction between the space produced by the big bang and the dimensions outside the universe or whatever existed before the big bang, and come up with an answer as less contradictory as possible.

Let us, only for the sake of discussion, imagine a virtual spaceship that can overtake the accelerating expansion of the universe and let it travel in a particular direction. When it reaches the edges of the universe, if that is not very inconvenient, it would surpass the universe itself, in case it doesn't go in circle.

Even though this particular thought experiment wouldn't be fundamentally different than the expansion of the universe itself, it may help understand a bit about beyond the universe. Now if the spaceship continues travelling alone outwards, would it be extending the space itself in that particular direction?

Answer 1

Fundamentally, the misconception here is that something that is expanding must be finite.

This is simply not true.

When we say the universe is expanding, we mean the distance between two stationary observers, sitting still as best they can, grows over time. But it is entirely possible for an infinite thing to have this property. Imagine the real number line, extending to $+\infty$ and $-\infty$. Now make every interval twice as long. There, you just expanded a 1D model of the universe.

If the universe is infinite, you can keep traveling in one direction and never come to an end. This has nothing to do with the Big Bang. In fact, if you contract the universe, running time backward, you will see that an infinite universe was always infinite, even back to times infinitesimally close to the Big Bang itself. It's just that points that are now billions of light years apart were in fact just nanometers apart back then.

Now it is possible that the universe has a finite volume, just like the surface of a sphere has a finite area. If you keep going in one direction, you'll eventually get back to where you started. Observationally, though, the universe is "flat" as best we can tell. If it does curve back on itself, it only does so after many, many billions of light years.

Answer 2

If you are sincerely asking about the fate of spaceship departing the solar system, then you are asking a question about the standard model of cosmology.

Instead of worrying about relativistic effects we'll concern ourselves with a photon that leaves our galaxy in a direction so that it hits nothing, and just keeps traveling. Faster than any spacecraft that physics will allow, we travel at the speed of light in any arbitrary direction.

As the photon leaves the galaxy it enters the region of space dominated by our local galactic cluster, the other large galaxy in cluster, Andromeda is about an order of magnitude farther away from us than the width of our own galaxy, which is 100,000 ly wide. So say a few million years of light-time travel to be outside of the gravitation influence of our galactic cluster.

Now we have to worry about the Hubble flow, the constant expansion of space. The distance behind us, between us and the milky way will start to grow larger the farther away and longer we go. The whole while, the distance between us and the some distant objects isn't shortening as the speed of light, the space in front of us is stretching. The farther away something is the faster it recedes, and if it is far enough away, it recedes faster than the speed of light.

There are parts of 'the Universe' that we could never hope to see, in every direction. And likewise, photons from our galaxy will never reach them. As you go to infinity, more space is being created than you can hope to get through.

I use quotes with 'the Universe' because cosmologists generally use than term to describe our observable chunk of what started in the big bang. Our Universe is flat, and underwent cosmic inflation early on, but other parts of what was produced by the big bang could have extreme curvatures and/or not even yet experienced inflation depending on the initial conditions of that particular volume.

Answer 3

To start with, space was not created, space had always been there (yes even before the big bang). What was yet to be created was the incredible and ever expanding universe(Big bang ?). Space is infinite on it`s vastness and time because literally, space is the absence of stuff (sorry, couldnt think of a better word).

Back to the answer:

As you have heard many times space is infinite, although what we consider the universe isn’t. When the universe expands (planets, suns, moons), it expands on the space there is available. Because of the infinity of space, space expands on itself. To understand it, imagine yourself looking at a grid paper. In the paper there is a little circle that is constantly expanding. When you reach the limit of the grid you have, you can zoom out to scale the grid in to place in an even bigger grid. It may sound weird, but infinity is always full and it can always expand indefinitely.

Coming back to your question, if you had an extremely fast “unstoppable” space ship, when you reach the limit of the universe the infinity of space will still be there, and you would continue till the end of eternity.