Imagining the Third Dimension

A direct link to the above video is at http://www.youtube.com/watch?v=-D4swzK4sKk

Some people dismiss discussions of the second dimension, saying it would be impossible to see something with no depth. What if I told you the third dimension is also impossible for us to see?

In my original Imagining the Tenth Dimension animation, I said that imagining the third dimension should be the easiest for us, since that's what we see around us every day. But there is a problem here: most of us, when we imagine the third dimension, also imagine energy, change, and life itself as being in the third dimension. But how can any of those processes be part of the third dimension when what we're talking about is space without time?

In the remarkable television series Through the Wormhole with Morgan Freeman, physicist Julian Barbour says this: "In my view of the universe, it's just like a huge collection of snapshots which are immensely, richly structured. They're not in any communication with each other, they're worlds unto themselves. ...In some very deep sense, the universe, a quantum universe, is static. Nothing changes." What Dr. Barbour is conveying here is that our 3D universe is like a giant flipbook animation, and even though it feels to us like our observed reality is continuous, each of those "snapshots" he's referring to represents a frame of 3D space without time. Each of those frames is defined by the speed of light and Planck's constant, which is the smallest possible distance that can be observed, and the smallest possible duration that our reality can have before words like "distance" and "duration" lose their meaning. So, the only way for change to occur is to string those "snapshots" together and view them from the fourth dimension, one Planck frame after another.

There's a second problem with the way people tend to think about the third dimension: it's so easy to forget that it takes time for light to travel to our eyes. So even if we look at our own hands, there was already a tiny delay for the time it took for the light rays to bounce off our hands and arrive at our retinas. If we're trying to imagine the third dimension, then, as space without time, we're already imagining something that can't be seen! This is easier to think about when we move out to the vast distances of the nearby stars - if I'm looking in the night sky at a star that's ten light years away, I'm looking at what that star looked like ten years ago. I'm not looking into space, I'm looking into space-time. And right next to that star could be a different one that's twenty light years away. There those two stars are, seemingly side by side, and yet when I'm looking at one I'm looking ten years into the past, and when I'm looking at the other I'm looking twenty years into the past.

Isn't it amazing to think about how all the different distances of galaxies, stars, planets and satellites that we might see through a telescope blend together into a vision not of 3D space, but of 4D space-time? And even though it's on a much smaller scale, the same is true if we look at our hands, then look at some other object that's further away - even though our brains tell us we're looking at a 3D world, the time it takes for light to reach our eyes from any particular object will be defined by how far away that object is from our eye, and what we're seeing at any particular instant is really a blend of those tiny delays, a snapshot of 4D space-time.

The next time someone tells you that the first and second dimension don't exist because something with no depth is impossible, think about how the third dimension has the same problem - in our minds we can visualize objects that are constructed from length, width, and depth, but we can't actually see them with our eyes unless they have duration within 4D space-time. Does that mean the third dimension doesn't exist? Of course not! But those 3D "snapshots" of space without time are much stranger than our intuition might tell us - because within each of those snapshots lies the potential for quantum entanglement which can occur at any distance across the universe. Remember - those connections and superpositions are not just faster-than-light, they're instantaneous: as Julian Barbour says, a "frame" of the quantum universe exists in a place where time doesn't exist. And if that idea seems unimaginably strange to us, perhaps that's because it's so easy for us to forget that you and I are really part of something larger than the third dimension.

Next: Imagining the Fourth Dimension

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