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maandag, augustus 28, 2006
Welcome to the Tenth Dimension
In string theory, physicists tell us that the subatomic particles that make up our universe are created within ten spatial dimensions (plus an eleventh dimension of "time") by the vibrations of exquisitely small "superstrings". The average person has barely gotten used to the idea of there being four dimensions: how can we possibly imagine the tenth?
Imagining the Ten Dimensions
The flash version of this website (www.tenthdimension.com) provides an interactive set of animations with narration and sound effects which explain the basic concepts from chapter one of the book. The media-rich nature of these animations is not recommended for viewing with a dialup connection because of long load times. Below is a transcript of the narration from those animations. The ideas presented here come from chapter one of a new book called "Imagining the Tenth Dimension: a new way of thinking about time, space, and string theory", written by Rob Bryanton.
0. A point (no dimension)
We start with a point. Like the “point” we know from geometry, it has no size, no dimension. It’s just an imaginary idea that indicates a position in a system.
1. The first dimension – a line
A second point, then, can be used to indicate a different position, but it, too, is of indeterminate size. To create the first dimension, all we need is a line joining any two points. A first dimensional object has length only, no width or depth.
2. The Second Dimension – A Split
If we now take our first dimensional line and draw a second line crossing the first, we’ve entered the second dimension. The object we’re representing now has a length and a width, but no depth. To help us with imagining the higher dimensions, we’re going to represent our second dimensional object as being created using a second line which branches off from the first.
Now, let’s imagine a race of two-dimensional creatures called “Flatlanders”. What would it be like to be a Flatlander living in their two-dimensional world? A two-dimensional creature would have only length and width, as if they were the royalty on an impossibly flat playing card. Picture this: a Flatlander couldn’t possibly have a digestive tract, because the pipe from their mouth to their bottom would divide them into two pieces! And a Flatlander trying to view our three-dimensional world would only be able to perceive shapes in two-dimensional cross-sections. A balloon passing through the Flatlander’s world, for instance, would start as a tiny dot, become a hollow circle which inexplicably grows to a certain size, then shrinks back to a dot before popping out of existence. And we three-dimensional human beings would seem very strange indeed to a Flatlander.
3. The Third Dimension – A Fold
Imagining the third dimension is the easiest for us because every moment of our lives that is what we’re in. A three dimensional object has length, width, and height. But here’s another way to describe the third dimension: if we imagine an ant walking across a newspaper which is lying on a table, we can pretend that the ant is a Flatlander, walking along on a flat two-dimensional newspaper world. If that paper is now folded in the middle, we create a way for our Flatlander Ant to “magically” disappear from one position in his two-dimensional world and be instantly transported to another. We can imagine that we did this by taking a two-dimensional object and folding it through the dimension above, which is our third dimension. Once again, it’ll be more convenient for us as we imagine the higher dimensions if we can think of the third dimension in this way: the third dimension is what you “fold through” to jump from one point to another in the dimension below.
4. The Fourth Dimension – A Line
Okay. The first three dimensions can be described with these words: “length, width, and depth”. What word can we assign to the fourth dimension? One answer would be, “duration”. If we think of ourselves as we were one minute ago, and then imagine ourselves as we are at this moment, the line we could draw from the “one-minute-ago version” to the “right now” version would be a line in the fourth dimension. If you were to see your body in the fourth dimension, you would be like a long undulating snake, with your embryonic self at one end and your deceased self at the other. But because we live from moment to moment in the third dimension, we are like our second dimensional Flatlanders. Just like that Flatlander who could only see two-dimensional cross-sections of objects from the dimension above, we as three-dimensional creatures can only see three-dimensional cross-sections of our fourth-dimensional self.
5. The Fifth Dimension – A Split
One of the most intriguing aspects of there being one dimension stacked on another is that down here in the dimensions below we can be unaware of our motion in the dimensions above. Here’s a simple example: if we make a Möbius strip (take a long strip of paper, add one twist to it and tape the ends together) and draw a line down the length of it, our line will eventually be on both sides of the paper before it meets back with itself. It appears, somewhat amazingly, that the strip has only one side, so it must be a representation of a two-dimensional object. And this means that a two-dimensional Flatlander traveling down the line we just drew would end up back where they started without ever feeling like they had left the second dimension. In reality, they would be looping and twisting in the third dimension, even though to them it felt like they were traveling in a straight line.
The fourth dimension, time, feels like a straight line to us, moving from the past to the future. But that straight line in the fourth dimension is, like the Möbius strip, actually twisting and turning in the dimension above. So, the long undulating snake that is us at any particular moment will feel like it is moving in a straight line in time, the fourth dimension, but there will actually be, in the fifth dimension, a multitude of paths that we could branch to at any given moment. Those branches will be influenced by our own choice, chance, and the actions of others.
Quantum physics tells us that the subatomic particles that make up our world are collapsed from waves of probability simply by the act of observation. In the picture we are drawing for ourselves here, we can now start to see how each of us are collapsing the indeterminate wave of probable futures contained in the fifth dimension into the fourth dimensional line that we are experiencing as “time”.
6. The Sixth Dimension – A Fold
What if you wanted to go back into your own childhood and visit yourself? We can imagine folding the fourth dimension through the fifth, jumping back through time and space to get there. But what if you wanted to get to the world where, for example, you had created a great invention as a child that by now had made you famous and rich? We can imagine our fourth-dimensional selves branching out from our current moment into the fifth dimension, but no matter where you go from here the “great child inventor” timeline is not one of the available options in your current version of time -- “you can’t get there from here” -- no matter how much choice, chance, and the actions of others become involved.
There are only two ways you could get to that world – one would be to travel back in time, somehow trigger the key events that caused you to come up with your invention, then travel forward in the fifth dimension to see one of the possible new worlds that might have resulted. But that would be taking the long way. The shortcut we could take would involve us folding the fifth dimension through the sixth dimension, which allows us to instantly jump from our current position to a different fifth dimensional line.
7. The Seventh Dimension – A Line
In our description of the fourth dimension, we imagined taking the dimension below and conceiving of it as a single point. The fourth dimension is a line which can join the universe as it was one minute ago to the universe as it is right now. Or in the biggest picture possible, we could say that the fourth dimension is a line which joins the big bang to one of the possible endings of our universe.
Now, as we enter the seventh dimension, we are about to imagine a line which treats the entire sixth dimension as if it were a single point. To do that, we have to imagine all of the possible timelines which could have started from our big bang joined to all of the possible endings for our universe (a concept which we often refer to as infinity), and treat them all as a single point. So, for us, a point in the seventh dimension would be infinity – all possible timelines which could have or will have occurred from our big bang.
8. The Eighth Dimension – A Split
When we describe infinity as being a “point” in the seventh dimension, we are only imagining part of the picture. If we’re drawing a seventh dimensional line, we need to be able to imagine what a different “point” in the seventh dimension is going to be, because that’s what our line is going to be joined to. But how can there be anything more than infinity? The answer is, there can be other completely different infinities created through initial conditions which are different from our own big bang. Different initial conditions will create different universes where the basic physical laws such as gravity or the speed of light are not the same as ours, and the resulting branching timelines from that universe’s beginning to all of its possible endings will create an infinity which is completely separate from the one which is associated with our own universe. So the line we draw in the seventh dimension will join one of these infinities to another. And, as boggling as the magnitude of what we are exploring here might be, if we were to branch off from that seventh dimensional line to draw a line to yet another infinity, we would then be entering the eighth dimension.
9. The Ninth Dimension – A Fold
As we’ve explored already, we can jump from one point in any dimension to another simply by folding it through the dimension above. If our ant on the newspaper were a two-dimensional Flatlander, then folding his two-dimensional world through the third dimension would allow him to magically disappear from one location and appear in a different one. As we’re now imagining the ninth dimension, the same rules would apply – if we were to be able to instantaneously jump from one eighth dimensional line to another, it would be because we were able to fold through the ninth dimension.
10. The Tenth Dimension – A Point?
Before we discussed the first dimension, we could say that we first started out with dimension zero, which is the geometrical concept of the “point”. A point indicates a location in a system, and each point is of indeterminate size. The first dimension then, takes two of these “points” and joins them with a line.
When we imagined the fourth dimension, it was as if we were treating the entirety of three-dimensional space in a particular state as a single point, and drawing a fourth-dimensional line to another point representing space as it is in a different state. We often refer to the line we have just drawn as “time”.
Then in the seventh dimension, we treated all of the possible timelines which could be generated from our big bang as if this were a single point, and imagined drawing a line to a point representing all of the possible timelines for a completely different universe.
Now, as we enter the tenth dimension, we have to imagine all of the possible branches for all the possible timelines of all the possible universes and treat that as a single point in the tenth dimension. Whew! So far, so good. But this is where we hit a roadblock: if we’re going to imagine the tenth dimension as continuing the cycle, and being a line, then we’re going to have to imagine a different point that we can draw that line to. But there’s no place left to go! By the time we have imagined all possible timelines for all possible universes as being a single point in the tenth dimension, it appears that our journey is done.
In String theory, physicists tell us that Superstrings vibrating in the tenth dimension are what create the subatomic particles which make up our universe, and all of the other possible universes as well. In other words, all possibilities are contained within the tenth dimension, which would appear to be the concept we have just built for ourselves as we imagined the ten dimensions, built one upon another.
Imagining the Tenth Dimension - A Book by Rob Bryanton
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