A direct link to this video is at http://www.youtube.com/watch?v=LDajcGcKiAM
One can think of ordinary, real, time as a horizontal line. On the left, one has the past, and on the right, the future. But there's another kind of time in the vertical direction. This is called imaginary time, because it is not the kind of time we normally experience. But in a sense, it is just as real, as what we call real time.
From a lecture by Stephen Hawking
For us, time is a direction in the fourth spatial dimension. That's one of the ideas that is central to the way of visualizing reality that I have advanced in my book and its well-known animation.
In the third dimension, we might visualize the first three dimensions this way:
1st dimension: left/right
2nd dimension: backward/forward
3rd dimension: up/down
There's many other sets of words we could use, but the basic idea will always be the same: within the third dimension, if we think of it as having three dimensions of length, width, and depth, then each of those dimensions has a positive and negative direction. I can stand at a city intersection and visualize north/south, east/west, elevation/submergence: three dimensions, six directions. In an airplane or a spaceship, I can think of pitch, yaw, and roll, and apply positive/negative values to each of those: three rotations, six directions. Look at a wii controller while somebody plays the boxing game: up/down, left/right, forward/backward, all elements combined describe a full range of all possible motions.
By combining those ideas together we arrive at a way to describe any orientation within the third dimension. Is left/right the first dimension, or should it be forward/backward, or up/down? Whatever you prefer. The important thing is not what words we use, but that all three dimensions are at right angles to each other, and once those three dimensions are combined, we arrive at six directions that can encompass all aspects of three-dimensional space.
Do a google search on the words "six directions" and you will see how deeply embedded that concept is into various spiritual/metaphysical systems. Do a google search on "six dimensions" and you will find an interesting mix of musings about business/social connections (the six degrees of separation concept), geometry/physics, and other discussions about the nature of reality from the viewpoint of ancient spiritual systems.
In the way of visualizing reality that we're playing with here, "time" is a direction within the fourth dimension, but all of the above ideas apply again: if "forward" is described as a direction in the first dimension, it is just as much a direction in the third dimension. Here's where I'm going with this: we can use this jumping off point of what we know from the first three dimensions to see how time is a direction in the fourth, fifth, and sixth dimension, and what dimension we choose to place it within has more to do with our point of view than it does with the "direction" we're examining.
Let's Go Back
If the 1st dimension is described as forward/back, then we could build our analogy by calling the fourth dimension time/anti-time. Look up "time reversal symmetry" for more about this concept: even though the phrase "anti-time" is more commonly known from science fiction, you will find the idea of time being a process that makes just as much sense in the reverse direction is an accepted scientific viewpoint.
Now, if we think of the second dimension as left/right, what would the fifth dimension be? No matter what dimension we're talking about, we should be able to make a new dimension by moving at right angles to the current one. Naturally, this gets harder and harder to visualize as the number of dimensions grow, but Stephen Hawking's idea quoted above ties into another basic idea I have promoted here: if fourth-dimensional spacetime is like a flat plane until it is bent by gravity, what is it being bent into? I would say, the fifth dimension. If there are parallel universes being created by choice and circumstance (as per the David Deutsch team's proof I have quoted in this blog so often), then the bush-like structure of those branches would be, in a sense, at right angles to the fourth dimension of time, so those branches must be in the fifth dimension. Everything about our observed reality, then, is being knit together, one planck length at a time, at the fifth dimension into what we think of as a fourth-dimensional line of time.
What More Can There Be?
Kaluza-Klein theory, and the underlying granular nature of spacetime, and the idea that the higher dimensions are, from our vantage point in the fourth dimension, curled up at the planck length... all of these ideas tie together into this way of understanding the fifth dimension. Now let's go one step further - what's at right angles to the fifth dimension?
If we can accept that our fourth-dimensional line of time is analogous to the first dimension as the direction "forward", and the fifth dimension's probabilistic branches coming towards us (and extending out behind us!) are like the "left/right" of the second dimension, what would be the corresponding "up/down"? Let's think back to us standing on the street corner. The north/south, east/west plane of the first two dimensions gave us a way to locate ourselves at a particular intersection, but we needed the third dimension to describe the up/down of "I'm on the third floor" or "I'm in the basement". So, to imagine the sixth dimension, we have to try to imagine what we have described in the fifth dimension, and what it is impossible for us to get to get to without adding an additional dimension, which would again be at "right angles" to the ones below.
You Can't Get There From Here
This is one of the central ideas of this way of visualizing the dimensions. By taking our astonishingly large universe encompassed by the third dimension, then treating that as a line of time being created by quanta that are one planck length after another to imagine time as a direction in the fourth dimension, we are already holding a mind-boggling amount of information in our minds. By imagining that the fifth dimension is a "ray", or a bush-like branching structure of parallel universes at both the quantum and the macro level, we have exceeded what most people are able to hold in their minds simultaneously. The human brain is not built for holding so many differently-scaled concepts in our head at once - we prefer hierarchies of information, groupings, layers of meaning. So, while we know that the fourth dimension is not really as simple as a first-dimensional line, and the fifth dimension is not really as simple as a second-dimensional plane, by taking these higher concepts and simplifying them, this way of visualizing allows us to continue building ideas on top of each other, one layer of meaning stacked upon the next.
Here's the question, then. If our four-dimensional universe of spacetime is being created from a set of choices within the fifth dimension, what choices are not available to us? Now you're starting to think about the sixth dimension.
Enjoy the journey,
Here are some other entries relating to these ideas:
What Was Done Today
See No Future
Big Bang to Entropy
You Can't Get There From Here