Is an Infinite Size Universe Consistent With a Finite Age?
The Universe is 13.8 Billion years old, i.e. age is finite. As for size there are two options: either the Universe is finite and has a size, or it is infinite and extends forever. Both options are thought-provoking, but recent measurements point towards an infinite Universe. If this is true, can infinity have a shape and how does it correlate with a finite age Universe that started with a finite size singularity?
The problem with spatial dimension
It is important to answer the question of whether the Universe is finite or infinite, because any of the answers will be astonishing and have different implications for our understanding and modelling of the Universe.
The spatial infinity of cosmos is one of the most complex and controversial scientific problems. Ancient philosophers and astronomers tried to solve this question through the simplest logical constructions. To do this, it was enough to assume that it was possible to reach the supposed edge of the Universe. But if you extend your hand at this moment, the border is moved back a certain distance. This operation can be repeated countless times, proving the infinity of the Universe.
An infinite universe is difficult to imagine, but it is no less difficult to try to imagine what a limited world would look like. The obvious question in this case would be: what lies beyond the end of the Universe? Is it a great void? To make it even more confusing, it seems that a finite Universe can have an outside even if it doesn’t have an end.
First one have to define what is meant by “finite” or "infinite". It does not make sense to say that the universe has an edge, because you then have to ask what happens if you go up to the edge and take another step. This means that the only alternative to the universe being infinite is that it somehow winds itself like a sphere or cylinder, so that you can go forever without reaching an edge, but eventually you will return to where you started.
Resent results show that space is flat. In addition, space seems to look the same in all directions, with stars and galaxies. All this indicates that space is infinite, because it is very difficult to imagine that a flat space can end somewhere.
But even if the Universe would be finite (which is still an option), it doesn’t mean that there is an edge or outside. It could be that our 3-D Universe is wrapped into something much larger, with a multidimensional design. If so, our Universe could actually have an “outside” without having an edge or boundary. Our Universe could be a bubble in a multiverse design with an infinite number of bubbles in a huge cosmic foam.
The implications of an infinite Universe
Can infinity take shape? Can it be flat? Or curved? Or maybe square? Logic tells us that only the finite or limited can have a shape, which can be flat, curved or square. Infinity is by definition formless, because it is boundless. And because it is boundless, it contains all shapes — flat, curved, square etc. And all forms or limitations contain infinity, which is the deepest or cosmic-mathematical conclusion of all limitations, and which thus also reveals the limitation or form as an illusion.
Scientists suggest that in the event that the cosmos is infinite, somewhere in its expanses there is a twin of our planet, and, possibly, of the entire solar system. This is sometimes referred to as “von Nägelis Paradox”. In every amount of things, given that the amount is big enough, the same thing must sooner or later appear once again. This implies that if we could search far enough, we would find a Sun that is exactly the same as our own. Somewhere there will be a planet like our own and on one of these planets there will be a person that is your identical twin.
Scientists have tried to find evidence that features at one end of the sky are related to features at the other end. So far, no evidence has been found that the edges of the sky can be connected. But if the Universe is infinite, we should eventually discover entire duplicates of the observable universe, with exact and inaccurate copies of Us. What comes next? Possibly an infinite number of duplicates of observable universes. We do not even have to pull the multiverse card to find them. These are repeating universes within our own infinite universe.
Today we know that von Nägel might have been wrong. Everything does not necessarily have to repeat even in an infinite cosmos. A mathematical set of numbers can be infinite without covering every possible number. The set of numbers may contain only odd numbers and, if so, it will not contain a single even number and it doesn’t contain for example irrational numbers.
The mathematician Georg Cantor concluded, over hundred years ago, that there are infinities that are larger than other infinities. Modern chaos theory also suggests that even the smallest random events will give different outcomes. Everything that could have existed and happened does not necessarily fit even in an infinitely large Universe. Most things never happened and will never happen.
How does infinite size correlate with a finite age?
It has been said that shortly after Big Bang, the entire Universe was the size of a grapefruit or a singularity, i.e. something that is finite in both size and age. The source of confusion between these two concepts - Big Bang singularity and an infinite universe - is the misconception that the Universe originally began as a finite vastness.
This misconception stems from analogies that were not applicable in the early Universe. For example, the comparison with a grapefruit neglects to mention that the grapefruit would have been infinitely larger at that point. If you could go back in time to the Big Bang, you would see an infinite sea of energy, because all energy was side by side (infinitely dense) and expanding rapidly (and therefore cools).
However, it would not necessarily look like space was expanding, but simply like energy and matter were cooling down. For the infinite universe model to work, the Big Bang itself would have happened over infinite space — i.e. the Universes was always infinite. The Uncertainty Principle suggests that a quantum state can never be exactly in one specific place.
Another misconception is that space cannot be both infinite and expanding - that if it expands, it must have been finite before. It is wrong: something that is infinitely large can always be larger, because by definition there is no upper limit to its size. In mathematics you can always add any number to infinity and infinity comes out again.
In conclusion there is no obvious conflict between an infinite size Universe with a finite age. But the infinite Universe is a mathematical model. We do not know whether this is true or not, the Universe might as well be finite in size. Likewise the Big Bang and Inflation-model are theories. We do not even know that time exist, it might as well be just a human concept to make our world more comprehensible. We do not know the order of nature well enough to draw firm conclusions, we can only speculate.
