Is the Universe finite or infinite? Is it infinite or does it loop back on itself? This is what would happen if you traveled indefinitely.

Our view of what is observable from our view point within the Universe is fundamentally limited by the speed of light and the time since the hot Big Bang. On larger scales than what we can see, the Universe may be closed, curved, or even loop back on itself. So, what if you went into space and traveled in a straight line indefinitely? Could you ever get back to where you started? It’s an intriguing question, and we know the answer.

The Universe is vast, wondrous, and strange. From our point of view within it, we can see for 46 billion light-years in all directions. We see a Universe full of stars and galaxies everywhere we look, but are they all unique? Is it possible that if you look far enough in one direction and see a galaxy, you’ll also see that same galaxy from a different perspective in the opposite direction? Could the Universe actually repeat itself? And, if you traveled far enough in a straight line, would you eventually return to your starting point, just as if you traveled in any one direction on the Earth’s surface for a long enough period of time? Or would you be stopped by something?

It’s an intriguing question to consider, and one that Bill Powers wants us to look into, asking:

“Space and time are mind-boggling to me. It seems like if you traveled in a straight line, you could travel forever. What would stop you? A wall? [And if so,] what’s on the other side of the wall?”

Although it may appear ludicrous, the answer is both. You could travel indefinitely, but something would stop you. The key is to comprehend the expanding Universe, which is one of the most perplexing concepts of all.

When we gaze out into space, we are not seeing objects as they currently exist. From our perspective, the Big Bang occurred 13.8 billion years ago, but literally everything else we see is younger.

Why is that the case?

The Big Bang happened all at once, and if we were anywhere else in the Universe, the same 13.8 billion years would have passed. However, if we looked at planet Earth from that location, we would have to consider that we are not seeing Earth as it is today. Instead, we’d see Earth as it was when the light we’re seeing now was emitted by it. We’d be able to see Earth’s past.

That light would be 1.3 seconds old if we were on the Moon. That light would be 4.3 years old if we were on a planet orbiting Alpha Centauri. That light would be 2.5 million years old if we were in the Andromeda galaxy.

When we look at a distant object from our own perspective, we are seeing those objects as they were when the light that is now arriving was emitted. Only, when we look beyond our Local Group’s moons, planets, stars, and galaxies, there’s an additional factor at work: the space that the light is traveling through is expanding.

The discovery that the Universe is expanding in the twentieth century was one of the most significant revolutions in our understanding of the cosmos. The farther away a galaxy is — assuming it is not gravitationally bound to ours — the more its light is redshifted, or stretched to longer wavelengths.

In the Universe, three things can commonly cause a redshift:

• when a source and an observer are moving away from one another,
• when emitted light must climb out of a large gravitational potential well
• or when the space between two objects expands as the light travels.

Although the first two effects can be significant over short distances, only the expansion of the Universe matters on the largest cosmic scales.

The fact that the Universe is expanding is significant for a variety of reasons, particularly from a cosmic point of view. It enables us to infer our cosmic history and our emergence from a hotter, denser, more uniform, and faster expanding state. It enables us to infer the various types and ratios of energy that comprise the Universe if we can measure how the expansion rate has changed over time.

And, if we know how the Universe is expanding as well as what’s inside it, we can predict how it will expand in the future and what our ultimate cosmic fate will be.

“Yeah, yeah, fine,” I can hear you grumble. “But what, then, does that have to do with the question of what would happen to you if you traveled in a straight line, forever, through the Universe?”

We’re almost there, but first, consider what your options would be if you traveled in a straight line, forever, through a Universe that wasn’t expanding, but rather was static and unchanging.

Everything would depend on what we know mathematically as the topology of the Universe in the case of a static, unchanging Universe. The realization that space itself is not simply describable by a rigid, absolute, three-dimensional grid made of straight lines was one of the great revolutions brought about by Einstein’s General Relativity. Instead, the presence (or absence) of matter and energy curvatures space itself. There is more (positive) spatial curvature where there is a large, dense collection of matter and/or energy, and less (negative) curvature where there is a below-average or even negative amount.

In General Relativity, the spacetime you inhabit can also have a global structure. Your spacetime can be positively curved, like a (higher-dimensional) sphere; negatively curved, like a (higher-dimensional) saddle; or flat, with no positive or negative curvature on the largest, overall scales.

While it’s easy to see how a positively-curved space can be finite and closed, it’s a little less intuitive to realize that a flat space can also be finite and closed. To understand, imagine a long, straight cylinder that is bent into a donut-like shape until the two ends connect. This shape, known as a torus, is spatially flat as well as finite and closed.

There are only two possibilities if the Universe does not expand.

• Regardless of its curvature, the Universe could be finite and closed. If you travel far enough in one direction for a long enough period of time, you will eventually return to your starting point. Even if space itself is topologically strange, such as a Möbius strip or a Klein bottle, you can simply keep going and eventually return to where you started.
• Alternatively, the Universe could be infinite and open, regardless of its curvature. No matter how far you traveled in any direction, or how long you spent on that journey, you’d always come across “new space” that you hadn’t seen before. There would be nothing to stop you, but there would also be nothing to allow you to return to where you started unless you turned around and reversed your journey.

We’ve looked at the Universe in every way we know how, at the galaxies within it, at the gas and plasma we can map, at the radiation emitted by stars, molecules, and even the Big Bang itself, looking for repeating patterns, hoping to find evidence that the Universe might be finite on scales we can observe.

But such luck does not exist. Indeed, we can confidently state that there are no repeating structures, no locations where we see objects in one direction that match objects in another, and no patterns in even the earliest light that can be identified as identical across two different regions.

In fact, the only time we’ve ever seen multiple images of the same astronomical source has been when there is a large gravitational mass somewhere in space, and light from a background source is bent and distorted into multiple different paths that all successfully arrive at our eyes. While this optical and scientific phenomenon, known as strong gravitational lensing, is phenomenal, it is limited to very narrow, localized angles and regions of the sky.

But now, we come to the simultaneously important and uncomfortable reality of the situation: the Universe isn’t static, but rather is expanding. However, it isn’t only expanding; because it’s filled with matter and energy, it’s also gravitating as it’s expanding. You can imagine, at least in principle, a few possibilities for what this would mean for our far future.

• The gravitating effect could be more powerful than the current expansion, which would mean the Universe would expand for a time, reach a maximum size, and then reverse directions, contracting, and potentially even ending in a “Big Crunch” just as we began with a “Big Bang.”
• The gravitating effect could be less powerful than the current expansion, implying that the Universe will continue to expand permanently, although at a slower rate.
• The effect of gravitation and the initial expansion may perfectly balance each other, implying that the expansion rate will asymptote to zero but will never reverse or recollapse.

For the majority of the twentieth century, cosmologists considered these three major possibilities, and the quest to measure the expansion rate and history of the Universe was meant to distinguish between these options.

If the first option described our reality, you couldn’t travel in a straight line forever because the Universe would only exist for a finite amount of time, so you’d hit a sort of wall: a time wall. You could travel in that straight line back to your starting point before the Universe completely recollapsed, but you might only be able to enjoy it for a short while.

If the second or third option described our reality, you would eventually be able to “catch up” to any galaxy or object out there, even those that are rapidly expanding away from us. Over time, the rate of expansion would slow, and more and more distant galaxies would first appear, only to be overtaken by a space traveler who kept moving in that same straight line for long enough. If the Universe were infinite, we’d be able to catch up to anything; if the Universe was finite, we’d be able to return to our starting point.

However, and this is a big but, none of these scenarios adequately describe how our Universe is expanding. In reality, we live in a Universe dominated by dark energy: a type of energy inherent in the fabric of space that maintains a constant energy density at all times. Even as space expands, the density of dark energy never decreases, so the expansion rate remains positive and finite. This drastically alters our expected fate, and it means that if you put your finger on any galaxy that isn’t gravitationally bound to us, you’ll find that once it expands beyond a certain distance from us, we’ll never be able to catch up to it. Effectively, it will have disappeared from our reach, no matter how long we traveled for and no matter how close to the speed of light we were able to reach.

And, sadly, that is where we find our answer. If you traveled in a straight line, you could travel in time forever, but you would only be able to reach a very tiny proportion of the observable Universe. Everything beyond our current cosmic horizon — beyond the limit of what we can see — is forever out of reach. In fact, anything more than 18 billion light-years away is already unreachable. This means that, of everything we can see, only 6% of the objects in the universe are potentially reachable by us. Every second, the expanding Universe pushes tens of thousands of stars over that critical boundary, causing them to change from “reachable” to “unreachable,” even if we left on a journey for them, today, at the speed of light.

Regardless of the possibilities that account for the Universe’s shape, curvature, and topology, traveling in a straight line, even forever, will never return you to your starting point. The facts combined that:

• the Universe is expanding,
• dark energy is causing the expansion to accelerate,
• it’s already 13.8 billion years after the Big Bang,
• and the Universe does not repeat and is not finite on scales smaller than ~46 billion light-years,

Ensure that we will never be able to circumnavigate the Universe as we can the Earth. On some very grand cosmic scale, the Universe may be truly finite in nature. But even if it is, we will never know. While we can travel through space as far as we want, as fast as we want, for as long as we want, most of what is in the Universe is already out of reach. There is a cosmic horizon that limits how far we can travel through the expanding Universe, and objects that are more than 18 billion light-years away are effectively gone at the moment.