Hubble expansion

When you learn something very early in life, it is easy to think that it is common knowledge. Recently I observed that many people do not know what Hubble Expansion is, and those that do often have serious misconceptions about how it works. I will share with you how I was taught about Hubble Expansion and the Big Bang in high school with a simple but intuitive model.

I stumbled upon a blog post the other day with essentially the same theme as this article. The post did a good job of highlighting how people misunderstand the Big Bang, and a good overview of the history of Universe in Big Bang mechanics. The summary is essentially that:

• the big bang is an explosion OF space and not IN space
• It makes no sense to talk about where the big bang happened
• it makes no sense to talk about what was before the big bang
• it makes little sense to talk about what the universe is expanding into

The article is great, but reading the comments I saw that it could use a little help. I think it lacked a good intuitive model to help persuade people of the way Hubble Expansion functions. Here I present such a model as it was taught to me.

Imagine you are a two dimensional being, like a small circle or a dot. You have length and width, but no depth. The concept of depth has no real meaning to you. As an aside, this is a similar thought experiment to the book Flatland, which is a classic book for young students interested in Geometry.

As a 2D being, you live on what you would call a 'plain'. It's an expansive flat world wherein you can only move in the two directions you know: North-South and East-West. Consider that you have friends in this world, also represented by dots or circles, and they live some finite distance away from you. They are arrayed around you in all directions, and you have some way of determining the distance to your neighbors.

Now stepping back into our 3 dimensional world, we find that the little dots do not, in fact, exist on an large expansive flat plane, but instead, they all live on the surface of a ballon.

You can simulate this at home by inflating a ballon halfway, and drawing dots around its surface with a black marker.
The curvature of the ballon, as we see it in 3D, means nothing to the dots. They may not have a way to comprehend this 'curvature' because the 'curvature' is in a 'direction' that doesn't exist in their world. They know only of North-South and East-West.

Now let's modify this further. Let us in the 3D world begin to inflate the ballon. We let air into the balloon and it begins to slowly expand. The more investigative dots will notice something strange in their world. They may not notice the radius changing on the balloon, because it is in a direction they can't perceive. But they do notice that their neighbors are slowly moving away from them. Not only that, but the neighbors all seem to be moving directly away from them, as if they are motionless at the 'center' and the other dots are radiating outward.

With our real life model, we can simulate this. Take measurements from each dot to all the other dots and record them along with the balloon radius. Now blow the balloon up a bit and remeasure from each dot. Repeat this several times. You will see that every dot will see every other dot moving away from them.


This is how Hubble expansion works, but with another dimension added on.

• Instead of two dimensional dots, we are a 3D Galaxy.
• Instead of living on the 2D surface of a 3D balloon, we live on the 3D surface of a 4D ballon. (technically, this doesn't have to be a 4d sphere, it could be football shaped or donut shaped or pancake shaped. There is ongoing debate to the actual shape)
  
• At the big bang, the radius of the ballon was zero. 14 billion years later, it is bigger, but we don't exactly know by how much.

So knowing this, we can address some of the common questions or skepticisms regarding the big bang:

if the universe is expanding, what is it expanding 'into'? If it is expanding, doesn't that mean there is more space beyond it?

• This is like assuming that the 'real' Universe is like a big empty room (or maybe an infinite empty room), and the part of the Universe we can see is like a small cloud of debris expanding in the center. But with the ballon model, we can see that this is NOT how it is. The universe is completely contained on the baloon, and what it is expanding into may be nothing like the 'space' that exists on the surface. What exists or doesn't exist outside the ballon is unknown, but it certainly isn't space in anyway we define it, so that is why we say it doesn't make sense to ask what we are expanding into.

If the Universe is expanding, what is it like for galaxies closer to the edge?

• Again, think of the ballon model. Which dots are on the 'edge' of the expansion? The answer is all of them simultaneously, because the entire surface is the 'edge'. It is the same for us, but it is harder to picture our 3D world as a 'surface' expanding 'outward'.

If everything started at the Big Bang and exploded out from there, there should be a place in the Universe where the Big Bang happened. That should be the center of the Universe.

• In the ballon model, ask the dots to point to where the expansion started. They can't say 'down' because 'down' has no meaning to them. Back in the 3D world, we 3D people would point to the center of the ballon...but that exists outside the balloons universe. It is the same for us. You cannot point to the place where the Big Bang happened, because it happened everywhere (or nowhere).

Big bang theory is as egotistical as early religious beliefs because it logically means that we must be at the center of the Universe. That's the only way it could look like everyone else is moving away

• With the balloon model, it is easy to see that EVERY point looks like the center, and all points look like they are moving steadily away from every other point.

There was a time BEFORE the Big Bang

• At time= zero, the ballon had zero radius, space did not exist. One thing I have avoided, because it complicates the model, is to talk about time. Suffice it to say that time is inextricably linked to space, so essentially time only exists when space exists. Before there was space, before there was a balloon, there was no time, so the question makes no sense. It's like asking what is north of the North Pole.