Not long ago Jim Evins, a senior student from Mountain Vista High School in Highlands Ranch, CO sent me a list of questions for a school paper he was writing about my approach to visualizing the dimensions, and I thought his questions did a good job of underlining some of the misconceptions that can arise. We'll look at his questions over the next couple of entries. Jim's first questions was this:
"How would you conceptualize a line in the 6th and 9th dimensions? From your description in the book all I gathered is that those two dimensions are more or less empty space for the 5th and 8th dimension to fold through."And my response:
My approach to visualizing the dimensions is related to the point-line-plane postulate, which is the accepted methodology for visualizing any number of spatial dimensions. Think of dimension “x” in its entirety as a point, then any point not included within that first point would form a line in dimension “x+1”, and any other point not on that line would be part of a plane in dimension “x+2”. You can now start over: think of the plane you just defined as a new single point in a new dimension “x”, and you can repeat this process indefinitely according to the point-line-plane postulate. Try using this approach to visualize the first, second and third dimension, no problem. Try using it to visualize the entirety of 3D space as a point, then some other point not encompassed by that point would be a way to define a line in the fourth dimension, and a point not on that line would be a way to get to the fifth dimension. Try using this to start from the 4th dimension or the 7th dimension, and you will have thought of a way of defining the 6th dimension or the 9th dimension.
The line/branch/fold logic that my project presents can be used to start at any dimension as well, although for simplicity in most cases I have started with the 1st, 4th, or 7th dimension as the line just to avoid some confusion in the discussion. But no matter what spatial dimension you’re describing, if there is a way of describing every possible state within that dimension, then whatever is not encompassed by that set of all possible states gives you a way of getting to the next dimension “up”, or “outside” of the current dimension. The term phase space is useful for these discussions: as it says in wikipedia, this is a “space in which all possible states of a system are represented, with each possible state of the system corresponding to one unique point in the phase space.”
Again, this logic can work no matter what dimension you start from: if you can define the phase space for a particular dimension as dimension “x”, then conceive of that phase space as a single point, then some other point not within that first system allows you to draw a line in dimension “x+1”. Although this gets harder for us to visualize as the number of dimensions increases, what we’re really talking about is that each additional dimension is orthogonal, or at right angles to the previous one. So let’s use all of this logic to answer your question.
Our 3D universe in its entirety can be thought of as a point. This is space, but not space-time. In order to form a 4D line, if we think of our 3D universe in some other state as some other point, that gives us a line which passes through those points and extends in either direction to the beginning and end of our space-time universe. If there were only one possible timeline (or “world line” as some physicists prefer to call it) then this would be as far as we could go. But from any point within that 4D line, quantum mechanics tells us there are many probabilistic outcomes that could occur, and Hugh Everett III’s Many Worlds Interpretation of Quantum Mechanics defines these other possible causally-related outcomes as being in a sub-space which is “orthogonal to space-time”. Although Everett’s theory did not explicitly invoke extra dimensions, I insist that this means Everett’s Many Worlds lie within the dimension which is orthogonal to 4D space-time: the fifth dimension. But the words “causally-related” are important here: Everett did not believe that his Many Worlds theory allowed for us to jump to other versions of our universe which are not logically connected to our own. As Everett put it, “causality cannot be violated”. My project advances the same idea: at any particular point within the fifth dimension there are a number of possible futures and pasts, but causality cannot be violated: so here in 2012 you and I can no longer get to the version of our universe where the twin towers still stand in New York, and so on. In order to get to that version, we would either have to go back in time to 2001 and choose a different fifth dimensional branch (no time machines around yet as far as I know so we can’t do that) or find a way to use the sixth dimension to jump to some other non-causally-connected version of our universe.
What we’re talking about with the 6th dimension then is the phase space of our unique universe: every possible state, every possible outcome for our particular universe as constrained by its deep structure constants. Each possible state of the system corresponds to one unique point in the sixth-dimensional phase space. And unlike the causally-connected lines of the fifth dimension, you would have the complete freedom to travel on a line that passes through any two points within that 6D phase space, like the version of our universe where it’s 2012 and Michael Jackson is still alive.
Now if we happened to live in a different universe with different basic physical laws, the same would apply: we would have a completely different but equally real 6D phase space representing all possible states for that other universe. You could start from any point within one of those 6D phase spaces, but there would be no way for you to get from that phase space to our phase space because they are not connected to each other. But what if we want to? This is how we can imagine the seventh dimension: perceive one phase space as a point, and the other phase space as a point, and the line that passes through those two points is a line in the seventh dimension.
Let’s say that the first point represents all possible outcomes (all possible pasts, presents, and futures) for our unique universe, and the other point represents a universe where the speed of light is different. There could be a line that passes through those two points, and traveling on that line in one direction would be a journey through different possible universes where the speed of light has a higher and higher value, while traveling in the opposite direction would take us through universes where the speed of light is lower and lower. Does this 7D line encompass the multiverse of all possible universes? No! No matter what parameter we adjust, we would need the “plane” of the eighth dimension to be able to get to other universes not included on that line.
Which takes us to the second part of your question. Isn’t the phase space of the eighth dimension as far as we need to go? Within the 8th dimension, no matter what point we define, there can be a line to some other possible universe with different basic physical laws, and in fact this is the conclusion I have drawn as well: for physical manifestations of reality, the 8th dimension is as far as you need to go. The 9th dimension, then, is where I would place information patterns which can have no physical expression, such as naturally arising tendencies or “preferences” towards one kind of reality over another, or impossible universes which can exist as ideas only. Saying that the ninth dimension is empty space, then, is not really accurate. The ninth dimension is more closely related to what quantum physicists like Anton Zeilinger or Seth Lloyd are talking about when they say “information equals reality”: ultimately, everything about our observed reality or any other is derived from an underlying fabric of potential information states. With my project, then, I would say a “line” in the ninth dimension is a way of connecting one unrelated information pattern to another, which is admittedly a very abstract concept, but such is the nature of these biggest-picture-of-all discussions.
To complete this thought: if we take that sea of all possible information patterns and perceive it all as a single unchanging point, that’s how I would propose we think of the tenth dimension. Any attempt to navigate within the tenth dimension, then, immediately spills us back out in the other possible states that are contained within the geometries and patterns of the other dimensions.
In summary, it’s not correct to say that the 6th and 9th dimensions are empty, because they are full of the possibilities of the dimensions they encompass. A 1D line is full of all the points that lie on that line, but there are many other points that lie outside that line. A 2D plane is full of all the lines that lie within that plane, but there are many other lines that lie outside that plane… and so on. Likewise, the 6D phase space for our unique universe is full of its probabilistic outcomes, but there are still many other universes outside our 6D phase space that have their unique and completely separate set of probabilistic outcomes. The 9th dimension, then, is full of the different information patterns that could result in a universe such as ours or could be only abstract concepts. But there is no “other” 9th dimension, which is why I say it’s impossible to draw a line in the tenth dimension without having that line manifest in some way in the other dimensions… or to have superstrings vibrating in the tenth dimension without creating patterns in the other dimensions.
Thanks for the questions, Jim! Next week we'll look at his question: Why Can't We Stop at the 5th Dimension? But coming up next: Abolishing the Fourth Dimension.
Enjoy the journey,