Matt Strassler 11/07/11
When I’m chatting with a non-physicist, and the topic turns to the possibility that space might have additional dimensions that we aren’t aware of, the most common question that I get is this one: “How do you folks think about extra dimensions? I can only imagine three and have no idea how you would go beyond that; it doesn’t make any sense to me.”
Well, what we physics folks don’t do (at least, no one I know claims to do this) is visualize extra dimensions. My brain is just as limited as yours, and while that brain effortlessly creates a three-space-dimensional image of a world that I can move around in, I can’t make it bring to mind a picture of a four- or five-dimensional world any more than yours can. My survival didn’t depend on being able to imagine anything like that, so perhaps it isn’t surprising that my brain isn’t wired to do it.
Instead, what I do (and what I am pretty sure most of my colleagues do, based on how we all exchange ideas) is develop intuition based on a combination of analogies, visualization tricks, and calculations. We’ll skip the calculations here, but a lot of the analogies and visualization tricks aren’t that hard to explain.
There are actually two parts to learning to think about extra dimensions.
- The first is easy: learning to represent or describe a world with extra dimensions. You already know how to do this in several different ways, even though you may not realize it — and you can learn some more.
- The second is harder: learning how things work in a world with extra dimensions. How do you thread a needle in four dimensions rather than three, for instance; would planets orbit a sun with six space dimensions; would protons form, and would atoms? Here you need to learn tricks that are unfamiliar, thinking about how different a world with only one or two dimensions would be from the three-dimensional world we know, and working up by analogy.
So I’ll start with helping you learn to represent a world with extra dimensions. To answer that requires we think about how to represent any dimension of any sort. Let’s start at the beginning.
- A zero dimensional world is a point. There’s not much to say about it right now, but we’ll make use of it later.
- But a one-dimensional world is already pretty interesting. Click here to learn more.
- Here’s an article on two-dimensional worlds. A lot more going on here!
- It’s important to avoid confusion about spatial dimensions and the more general concepts of the word “dimension” as used in English and even in mathematics or statistics. A few comments about that are here.
- And then here are some examples of extra dimensions, emphasizing what the “extra” really means conceptually, and how it could be that the world has spatial dimensions of which we are completely unaware.
After these articles, you can start to learn how we might figure out that extra dimensions actually exist, by clicking here.