# How infinite is the universe? [duplicate]

When cosmologists are explaining the universe to laypeople they generally skip over a couple of details without addressing the apparent contradictions that these omissions introduce.

e.g. for the longest time the abrupt change from the usual mantra that nothing can move faster than the speed of light to the idea that the observable universe consists of things we can see - thins that are moving slower than the speed of light and on the other side of the boundary exist (in a sense) things that are going faster than the speed of light which are hence, unobservable. Some kind of small footnote about the speed of light limit applying locally rather than globally 20 years ago or so would have been appreciated.

So now I am trying to understand the implications of the usual - to laypeople - descriptions of the Big Bang. Statements are made like: at some time, some number of fractions of a second after the Big Bang, the universe was as big as a pea. I presume this means the observable universe. With the idea that, if we could somehow observe this universe, we could move our point-of-view to the edge of that pea (that would eventually expand out to be our current observable universe), and we would be at the centre of another pea. And this pea too would have a symmetrical view of the matter around it.

This clarification (if "true" as this simplified explanation can be said to be true) is important as, if at any point in this process there was an actual edge, a point-of-view anywhere in the very early expanding universe where there was less 'stuff' in a particular direction, then very very bad things should have or would have happened.

So as I understand it now, the early universe was in no way like an explosion. Explosions being probably defined by stuff moving from an area of high pressure to an area of low pressure. The stuff in the early universe on the other hand simply had no where to go. Every direction was equally as dense. Which - given a newtonian understanding of gravity was helpful - with equal stuff in all directions there would be no net gravitational field. And, without a special direction (or point) to collapse down into, the early stuff couldn't collapse immediately into a black hole despite how dense it was. GR probably explains this differently. At any rate, the space between things literally expanded rather than them rushing away from each other.

So now, if we continue with the metaphor that the observable universe being the size of a pea at some time very close to 0, and you can move a hypothetical observer to the edge of a pea and simply be in the centre of a different pea... how many peas were there?

If I understand it (via this ridiculous metaphore) correctly, if we are in a closed universe, then there would be a finite number of peas you could possibly travel to the edge of, before noticing that you were now observing peas you'd seen before. And a flat or open universe would mean that you could always keep on moving your pov to the edge to get a completely new view.

But how does this work if you keep on dividing time closer to t=0? With a non-closed universe: at the time t when our entire observable universe was squashed into a pea, we could nonetheless move our hypothetical observer around enough to observe, well, as many peas that would fit into our current observable universe. And then we could say that, there must be some time closer to 0 when that entire volume of peas was itself, packed into the size of a pea. And we could then do the thought experiment again.

Where do the bloody peas end?

## marked as duplicate by John Rennie, sammy gerbil, Bill N, Jon Custer, Community♦Jul 10 '18 at 15:47

• This sounds like a problem with the nature of infinity or of continua rather than a problem with physics: how many reals are there between $0$ and $1$? OK, so divide by two and how many are there between $0$ and $1/2$? OK, now pick any $\epsilon > 0$ and how many reals are there between $0$ and $\epsilon$? – tfb Jul 10 '18 at 9:34
• Possibly. But here the 'bits' were all filled with 'hot soup'. – Chris Becke Jul 10 '18 at 9:41
• That's fine: an infinite universe has an infinite amount of stuff in it. – tfb Jul 10 '18 at 9:44
• John's answer at the question he linked is very good, but if it doesn't cover everything you're asking about, please edit your question to highlight specifically those issues, otherwise this question is likely to be closed as a duplicate. Note that we need a theory of quantum gravity to talk about the very earliest epoch of the BB, on the order of the Planck time. At that level, spacetime might be quantized, and time itself might not be well-ordered at that scale. – PM 2Ring Jul 10 '18 at 11:27

Some kind of small footnote about the speed of light limit applying locally rather than globally 20 years ago or so would have been appreciated.

I'm not sure I understand this remark/gripe:).

If you read popular science books they do explain fast how the expansion of space was, if the inflationary model is true. You got the idea, but admittedly there are plenty of badly written books and TV analogies that are not helpful to lots of people.

So now I am trying to understand the implications of the usual - to laypeople - descriptions of the Big Bang. Statements are made like: at some time, some number of fractions of a second after the Big Bang, the universe was as big as a pea. I presume this means the observable universe. With the idea that, if we could somehow observe this universe, we could move our point-of-view to the edge of that pea (that would eventually expand out to be our current observable universe), and we would be at the centre of another pea. And this pea too would have a symmetrical view of the matter around it.

This is where your own attempt at analogy breaks down (as does everybody's else's. )

Any idea relating to an edge or volume, however you try to put it using the concepts behind the words of English language, does not make sense, as anything on the other side is also part of the universe.

Our desire to explain the universe in terms of a 3 D world is understandable, after all what else can we relate it to?

But it will always lead us astray, as putting the universe in terms of anything like the world around us is as fruitless as trying to explain to a dog how his food comes in tincans. This applies to all humans stuck on a 3D planet.

So locally, we (think) we can understand things in one set of terms, but globally (especially when we try to achieve a proper theory of quantum gravity) we will probably need to take really good look at the foundations of mathematics and the price we may need to pay for understanding the universe in mathematical terms is to totally give up trying to understand it in ordinary language terms.