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Currently, we don't know if we live in an infinite or finite universe. But let's say, for the sake of argument, that we do live in an infinite universe. So that if we would have a space ship with an infinite amount of fuel, we could keep on going forever. Infinity is something the human brain can't really comprehend, because from the start of our lives we experience everything to have a beginning and ending, even life... So to think there is something, or in this case everything, that just keeps on going for ever, is really mind bending.

But if our universe is indeed infinite, would this mean that size of any kind becomes purely fictional if we look at the bigger picture? If we look from our own perspective measuring things is no problem, since we are finite in length, width and depth, we can perfectly measure something from our perspective, and even a-dress a number to it. This number will give us an approximation of how big or small an object is.

What if we take a grain of sand on the beach? We could perfectly measure this compared to the size of the beach we found the grain in. But what if we keep on expanding this beach, the grain of sand would get relatively smaller and smaller. So now we take our universe that is in this case infinite, and we compare the Earth to it. The size of the Earth would we infinitely small, compared to an infinite universe. Because the bigger a space gets, the relatively smaller objects within it get.

Like if there where to be a person with an infinite amount of money, (not taking the economical catastrophe of this in to account), from his perspective everything would be free. Because when he would spent a certain amount of money, it wouldn’t be noticeable on his balance.

Does this mean an infinite universe would cancel out size of any sort? I think it does. If we could look from the universe’s perspective, the word 'size' wouldn't exist in our dictionary.

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    Think of the real number line from high school math. It's infinite in length. But you have no problem saying that the length of the line segment between 2 and 5 is 3, right? Just because the entire space is infinite doesn't mean you can't have a sensible notion of size. – user4894 Feb 17 at 6:03
  • Your question's title mentions time, but it appears nowhere in the body. Did you mean to ask about size only, or wanted to ask about the effect of space being negligible on time ? – armand Feb 17 at 8:20
  • @armand I meant size, my bad. I’ve edited it now! – Daan Rijks Feb 17 at 9:13
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    Human brain can easily comprehend infinity, geometers studied infinite lines since before Euclid. "Infinite universe would cancel out size of any sort" type arguments were shown to be fallacious by Cantor, see How does actual infinity (of numbers or space) work? But even if they were not, what difference the actual size of the universe (which we do not even know) can possibly make in measuring finite sizes by comparing them to each other? Something does not become nothing, or fictional, just because "everything" is bigger. – Conifold Feb 17 at 11:21
  • We think the universe is poised on the boundary between being closed & open. In a closed universe, a journey 'across' the universe would see you arrive back at the same point - parallel spaceships would converge. In an open universe, spacetime is the higher-dimensional equivalent of saddle shaped, so parallel flights diverge. We can relate this to cosmological event horizons, where we could not return to where we started ever, like no trajectory can exit a black hole physicsworld.com/a/is-the-universe-saddle-shaped – CriglCragl Mar 25 at 22:29
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A similar idea is used by Dirac in Principles of Quantum Mechanics. You are right that if sizes are only relative, there is hardly any meaning to size.

But Dirac says there is an absolute notion of size. Namely, there are permanent limits to science's powers of investigation and any accompanying physical disturbances prodced via investigation. Limits "inherent in the nature of things and can never be surpased by improved technique or increased skill in the part of the observer". These limits come about because there is no perfectly gentle measurement. And there is no half a photon. Experiments show you always get a photon of a certain energy or no photon. Never anything in between.

With a non-negligible disturbance, how can we ever ask what a particle was going to do? If we measure it to check, we disturb it. "If a system is small [meaning any limiting disturbance is non-negligible], we cannot observe it without producing a serious disturbance and hence we cannot expect to find any causal connection between the results of our experiments".

This is an absolute notion to size. Sure you can still zoom out infinitely to make any finite system nearly imperceptible. But you did not change a fundamental notion of size, just the size of the universe compared to particles/humans or what-have-you. That scaling will do nothing to change the stability quantum particles, or how impossible it is to investigate them without disturbance. They have an absoluteness about them.

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The size of an object is a readily apparent physical characteristic. Every person here has a very good intuition of what it means to discuss the size of an object, how it can be measured, and how sizes can be meaningfully compared.

None of that has anything to do with the size of the universe. It has not been definitively proven whether the universe is finite or infinite, but it doesn't matter at all here. If the news were released tomorrow that the universe was indeed infinite, it wouldn't change your perception of size at all. Similarly, if it was proven that the universe was finite, your perception of size would remain unaffected. Your everyday perception of size does not care where or if the universe ends.

Whether or not the universe is infinite has no bearing whatsoever on your perception of size. We don't even know whether the universe is infinite or not, so the argument that things would be different in the opposite case doesn't really make any sense - we can't even say we're not experiencing that case right now. Size clearly is not a fictional or meaningless concept in our current world, which may or may not belong to an infinite universe. Size can't become meaningless in an infinite universe, because size is not meaningless, despite the fact that we may already be living in an infinite universe.

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Almost exactly the phenomenon you ask about is proposed by Nobel prize-winning physicist Roger Penrose in his conformal cyclic cosmology.

He suggests that the Universe will ultimately expand to a heat death in which all matter has decayed and all black holes have evaporated. Any phenomenon of scale will then be lost. The Universe will continue to expand in exactly the same way that it did at the Big Bang and new scales of space and time will accompany what thus, quite literally, becomes the next Big Bang of an ever-expanding yet cyclic Universe.

There is a lot of solid maths behind the idea; Penrose is also an award-winning mathematician. Fortunately for most of us, he has written a popular account of it as Cycles of Time, Bodley Head, 2010.

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  • I think that what he describes is rather something like "perfect entropy", where energy is dispersed uniformly across the universe to a point that there is virtually none in any meaningful part of spacetime. That is quite different from "but if we are infinitely small compared to the universe, doesn't that mean that we really do not have size at all?", which involves the idea of absolute space/reference frames which Penrose would never subscribe to. – Philip Klöcking Feb 20 at 20:18
  • @PhilipKlöcking Penrose explicitly discusses the relative scales of the two states before and after transition to a new cycle. The scale-insignificance of the small, old stuff is a part of this discussion, as it is a key aspect of the transition. The entropy state is part of the story too, of course, but is far from the dominant one. – Guy Inchbald Feb 20 at 20:55
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Not "fictional", just relative, which we already knew.

Our own size is not zero just because the universe is infinite. Our size would be infinitely small only relatively to the size of the universe, yet, humans have a certain definite size relatively to the size of all the things in their immediate environment, which is what matters because this is why they are adapted to it. They fit into their environment. Without meaning to be too salacious, size matters.

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