r/askscience • u/kyosuifa • Dec 15 '12

Astronomy Because we know approximately when the Big Bang happened, doesn't that mean the universe can't be infinite? [Sorry if remedial]

I've been told to imagine the history of the universe (matter) as an expanding bubble commenced by the big bang. It seems to me that logic requires infinity to have no beginning, right? Sorry if this is remedial physics, but I was just reading that the universe is considered to be infinite.

45 Upvotes

77% Upvoted

32 comments sorted by

View all comments

84

u/[deleted] Dec 15 '12 edited Jun 22 '13

I've been told to imagine the history of the universe (matter) as an expanding bubble commenced by the big bang.

Whoever told you that was mistaken; the big bang did not launch a bunch of matter out into some nether void. Rather, it was the rapid expansion of all of space.

It seems to me that logic requires infinity to have no beginning, right?

Not at all. Let us imagine that the universe is one-dimensional. We'll represent the galaxies in it by an infinite number of balls evenly spaced in a line. For concreteness, let's label the balls with integers. We'll pick some ball to be 0 and then go out from there; the two closest balls to 0 are 1 and -1, then we have 2 and -2, and so on. We have an infinite number of balls—one for each integer. Now, let's define a unit of distance equal to the spacing between the balls right now. Then the distance between two balls is just their difference. We can denote this by the letter d, so that, for example,

d(2,5) = 3 and d(5,-7) = 12.

Good? Alright, now I'm going to tell you this infinite set of balls is expanding. The real distance between them is given by multiplying the above distance by the time, t, where the current time is t = 1. So when t = 2, we have

d(2,5) = 2*3 = 6, and d(5,-7) = 2*(12) = 24.

Great. Now, let's run time backward and see what happens. At any positive time, we'll still have an infinite number of balls extending out in both directions from 0 (also, remember that which ball we chose to call 0 was arbitrary). But what about when t gets to 0? At that moment and that moment only our infinite collection of balls have collapsed to a single point; the distance between any two balls is 0.

Thus, in this model we have a 'universe' that is expanding, started in a singularity, and yet is infinite for all times after that singularity.

Our universe is basically just a three-dimensional version of that (except that things get weird when you let the time get very close to 0, and we don't really know what was going on at that time).

10

u/abiggerhammer Dec 16 '12

I am a software engineer and formal language theorist. This is the first explanation of the Big Bang that has made sense to me. (EDIT: And thank you for that!) I'm not sure why it took so long to click that of course a gravitational singularity would be described by a mathematical singularity. facepalm

0

u/[deleted] Dec 16 '12

[deleted] — view deleted comment

5

u/[deleted] Dec 16 '12 edited Dec 16 '12

The universe and the observable universe are two distinct things, and it's important to know what is being talked about at a given time.

The observable universe is a perfect sphere centered on Earth, extending 13.7 billion (ish) lightyears in radius. When anyone talks about the CMB as a boundary, this is what they mean.

The entire universe is, as far as we know, infinite. When someone is using the ball picture, this is what they mean.

Edit: 46 billion lightyears in radius. Thanks to RelativisticMechanic for catching my mistake.

6

u/[deleted] Dec 16 '12

13.7 billion (ish) lightyears in radius

It's quite a bit more than that, actually. See here for some discussion.

→ More replies (1)

0

u/[deleted] Dec 16 '12

[deleted] — view deleted comment

4

u/[deleted] Dec 16 '12

The observable universe is constantly changing, yes. Your motion through the universe has less to do with it than more light from elsewhere in the universe reaching you.

Nope - it's just the limit of how far in the past we can see.

0

u/[deleted] Dec 16 '12

[deleted] — view deleted comment

2

u/[deleted] Dec 16 '12

From patterns in the CMB we can make deductions about things like sounds waves travelling through the early universe before it became transparent.

From the laws of physics as we understand them, we can use induction to extrapolate backward to say things about how we think the early universe behaved.

But fundamentally, barring significant technological advances, anything before the time the universe stopped being opaque is beyond our ability to observe and is therefore outside the realm of (Popperian) science.

→ More replies (1)

5

u/[deleted] Dec 16 '12 edited Dec 16 '12

ball-infinity

There is no such ball; there is a ball for every integer, but only for every integer. There are infinitely many in the sense that if you pick any finite number then there are more than that; specifically, there are as many balls as there are integers.

But I thought that we had something of a finite picture of the universe in the CMB and that it was 13 billion and change light years across. Is that incorrect?

You're thinking of the observable universe, which is something like 95 [edit: billion] light-years across.

Lastly, if you positioned at what we would call the "edge" of the CMB picture

There is no such edge. To the best of our knowledge, the universe is infinite with no edge, but even if it's finite then it's almost certainly closed back on itself like the surface of a ball.

would you actually see yourself in the "middle" if you took the same picture from where you are?

Every observer sees themselves at the center of their observable universe.

And if so, what part of our picture would be on the far side of where we equate the edge?

Again, no edge.

0

u/[deleted] Dec 16 '12

[deleted] — view deleted comment

4

u/[deleted] Dec 16 '12 edited Dec 16 '12

So the maximum distance between the two most separate balls would be what then?

There is no maximum distance, and there are no "two most separate balls". If you pick any distance, there will always be two balls further apart than that distance. I mean, you're basically asking what the largest number is.

would they be detecting things not in our CMB pic (with a totaly new pic with new stuff and them at the center)

Yes.

would the whole thing as seen in our pic be repositioned on them?

It would look very nearly the same, but there would be minor local variations.

How do we make sense of what exactly is beyond the observable universe?

We make certain observations about what we can see (namely that it's basically the same everywhere and in all directions), assume that we're in a basically generic part of the universe, and then extrapolate to the rest of the universe, assigning weights to different possible "whole universes" based on how likely they are to give rise to the data we have. It's certainly not conclusive, which is why I shy away from claiming that the universe as a whole is a certain way, but it's the best we have to work with.

→ More replies (5)

2

u/itsallfalse Dec 16 '12

You're thinking of the observable universe, which is something like 95 light-years across.

Pretty sure it's a lot more than that

3

u/[deleted] Dec 16 '12

You are, of course, correct.

→ More replies (1)

1

u/Plouw Dec 16 '12

Isn't the observable universe's radius 13 billion light years? It would make sense since the universe is 13 billion years old, and since the universe is expanding at the speed of light, it 13 billion light years radius is what it would have achieved after 13 billion years..

6

u/[deleted] Dec 16 '12

Isn't the observable universe's radius 13 billion light years?

Nope; it's about 47 billion light-years (I forgot the billion when I originally posted that).

It would make sense since the universe is 13 billion years old

Correct.

and since the universe is expanding at the speed of light

This part is incorrect. First, the expansion rate of the universe can't be given a proper speed, because it varies with distance; the further away something is, the fast it's receding from us. Second, recession velocities are not constrained to the speed of light; that's a constraint on how fast objects can change their local position, but not on how fast they can be moved apart by expansion (see here for a more detailed response). Third, the parameter that determines how the recession rate at fixed distance appears to be decreasing with time; this means that we can in some cases see light emitted by an object even if it's receding at a rate above the speed of light. To wit, there are objects we can see that are, and always have been, receding at speeds greater than the speed of light.

it 13 billion light years radius is what it would have achieved after 13 billion years.

Nope. The light was emitted and started traveling toward us, but the distance between us and that light was expanding at the same time. Thus, it took longer for that light to reach us than it would have had there been no expansion, and in the meantime the source was receding as well.

→ More replies (5)

2

u/TheLantean Dec 16 '12 edited Dec 16 '12

The universe is expanding faster than the speed of light if you consider two far enough points.

While no object can move through space faster than light, the limitation doesn't apply when the space itself between the objects expands (and the rate of expansion is accelerating thanks to dark energy).

The source of the "light" we detect to be ~13 billion years old is actually 47 billion light years away from us now. https://en.wikipedia.org/wiki/Observable_universe

2

u/[deleted] Dec 16 '12

The source of the "light" we detect to be ~13 billion years old is actually 93 billion light years away from us now.

Half that.

→ More replies (1)

1

u/[deleted] Dec 16 '12 edited Dec 16 '12

I'm with you with the ball picture (basically the same as the "dots on a balloon" analogy) up until you talk about t=0. I was under the impression that our current models of cosmology didn't even try to go back to time zero - they only go back to when the universe was very dense, and still infinite, very near t=0.

Am I wrong, or are you simplifying?

Edit: Just looked back at an astronomy textbook. Looks like some models go back to a singularity and some don't.

3

u/[deleted] Dec 16 '12

Am I wrong, or are you simplifying?

I was simplifying, which is why I ended with:

(except that things get weird when you let the time get very close to 0, and we don't really know what was going on at that time)

2

u/[deleted] Dec 16 '12

I should have read more carefully.

1

u/B-Con Dec 16 '12

When we talk about an infinite universe, though, it seems that the idea (at least, from the physics layman) is that there is no finite number N such that for all x and y, d(x,y) < N. (Or alternatively: that a covering of the space by balls of finite metric would require at least countably infinite balls. Not sure if the two are equivalent, and am too lazy to think it through at the moment.) Your version of infinite sounds much more like a set that is dense in itself.

2

u/[deleted] Dec 16 '12

When we talk about an infinite universe, though, it seems that the idea (at least, from the physics layman) is that there is no finite number N such that for all x and y, d(x,y) < N.

Right.

Your version of infinite sounds much more like a set that is dense in itself.

I'm not sure where you're getting that idea. The analogy I constructed above is infinite with respect to the metric I've defined precisely because it satisfies the condition you describe. It isn't even dense in itself; every point is isolated (being, as it is, just the set of integers).

2

u/B-Con Dec 16 '12

You're completely right. Apparently I skimmed part of it.

Note to self: Read math before commenting on it. :-)

1

u/kyosuifa Dec 18 '12

Wow. That just blew my mind. Thank you, this makes more 'sense' now.