Does size become fictional in an infinite universe?

Question

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.

Answer 1

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.

Answer 2

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.

Answer 3

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.

Answer 4

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.

Answer 5

In an infinite universe, the concept of "size" becomes a more complex and nuanced one, and it may be more appropriate to describe objects in terms of their relative scale rather than their absolute size.

In an infinite universe, there is no boundary or edge, and space extends infinitely in all directions. This means that there is no fixed reference point or standard unit of measurement for size. Instead, objects can only be described in terms of their size relative to other objects in the universe.

Additionally, the scale of objects in an infinite universe can vary widely, from subatomic particles to galaxies and beyond. In such a vast and varied universe, it may be more useful to describe objects in terms of their mass, energy, or other physical properties, rather than their size.

It is worth noting that the concept of size itself is a human construct, and is based on our perception and understanding of the world around us. In an infinite universe, our traditional notions of size and scale may need to be reevaluated or redefined in order to accurately describe and understand the universe as a whole.