Infinity is related to anything which cannot be counted or measured whereas Eternity is related to state of being timeless. Infinity indicates to the units which are immeasurable. Distance, mass, numbers in a number line, stars in the galaxy, vastness of the multiverse, all are infinite.
Anything which has no limit is called infinite and this state of being infinite is called infinity. Infinity is a concept that applies to things that cannot be counted or measured.
Finite or Infinite Universe?
The term ‘Big Bang’ suggests an explosion. But cosmologists often reject the concept of an explosion. They don’t like the term explosion because it conveys the idea of sound, and it doesn’t make any sense to think of it like that. But apart from that, the word explosion is valid. The simplest description of how the Universe originated is an explosion, in the sense that it began from a very small volume and increased very rapidly. That is usually what one means by explosion.
It is unknown if The Universe is finite or infinite. The expanding Universe theory says that the Universe could expand forever. And that is probably the model of the Universe that one feels closest to now.
But it could also be finite, because it could be that the Universe has a very large volume now, but finite, and that that volume will increase, so only in the infinite future will it actually be infinite.
To give an example, imagine the geometry of the Universe in two dimensions as a plane. It is flat, and a plane is normally infinite. But one can take a sheet of paper (an ‘infinite’ sheet of paper *) and roll it up to make a cylinder, and one can roll the cylinder again and make a torus (like the shape of a doughnut). The surface of the torus is also spatially flat, but it is finite. So, one gets two possibilities for a flat Universe: one infinite, like a plane, and one finite, like a torus, which is also flat.
*) The Universe is ‘Euclidean’, meaning that parallel lines always run parallel, and that the angles of a triangle add up to 180o. Now, the two-dimensional equivalent to that is a plane, an infinite sheet of paper. On the surface of that plane one can draw parallel lines that will never meet. A curved geometry would be a sphere. If one draws parallel lines on a sphere, these lines will meet at a certain point, and if one draws a triangle, its angles add up more than 180o. So the surface of the sphere is not flat. It’s a finite space but it’s not flat, while the surface of a torus is a flat space.
But even if with the CMB data one could prove that the Universe was flat, one still wouldn’t know whether it’s finite or infinite.
If the Universe was finite, that would mean that in a two-dimensional geometry, it would be like a torus. Now, think about a torus. In such a Universe, light travelling on the surface of a torus can take two paths: It can go around the sides but it can also go in a straight line.
This means that if the Universe was like a torus, light can have different ways to get to the same point. It could have a long way and a short way. And that would not be true on a plane. But a torus means that space is more complicated. It would mean that when one measures the CMB, one will see strange patterns on the sky, because the light from far away would not have come in quite a straight line because of the topology of the Universe. So the hope would be, eventually, to look for those strange patterns on the sky.
If the Universe was like a torus, one could see something. If the Universe were finite, it would be 100 times larger than the horizon which is the distance the light has travelled since the Big Bang. That would correspond to the size of the ‘doughnut’ of the torus. On the other hand, if the Universe was truly infinite then one would see no signal at all. What one could really say in that case is that the Universe is larger than a certain size. But if it was finite it could be measurable.
If the Universe was finite, it could be as large as 100 times the horizon. That means that the Universe would be as much as a 100 thousand million parsecs, about 300 thousand million light years, if one could measure the topology.
The Infinite Hotel Paradox
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