Aren't There Really 11 Dimensions?

(In some ways you could consider this a sequel to the original animation that started it all, which you can view here.)


A direct link to the above video is at http://www.youtube.com/watch?v=UfhOBevrN2U

In science, a physical picture is often more important than the mathematics used to describe it.
- Michio Kaku, in his book Physics of the Impossible

One of the most often-asked questions related to this project is "Aren't There Really 11 Dimensions?". This question relates to the basic idea of what we're talking about here, which is a way of visualizing spatial dimensions. We've talked before about the point-line-plane postulate, which you can look up in wikipedia: it uses a very similar logic to what my way of visualizing dimensions uses, and this postulate states that it can be used to imagine any number of spatial dimensions. Here's how the point-line-plane postulate works:

We start with a point. We can place a point within any specific spatial dimension, and then place another point in that same dimension. The line that passes through those two points can be thought of as having any number of divisions along its length, but ultimately the line extends to infinity in either direction. To define an additional dimension, all we have to do is find a point that isn't on any of the lines we could possibly have just created within the constraints of our current dimension. That additional point can then be used to define a plane that extends to infinity in all four directions within that plane, and this is how we imagine an additional spatial dimension. And finally, to define yet another dimension up from that one, all we have to do is find a point which is not within any of the planes we could possibly have just created.

Right angles to right angles
Using this logic, we can continue to build one spatial dimension upon another. How does this work? It's because each additional spatial dimension is at "right angles" to the one before, and the tricky part for we 3D creatures is trying to find ways to allow our brains to conceive of what "right angles" means as we try to imagine each additional spatial dimension beyond the three with which we're so familiar. The point/line/branch/fold imagery that my project uses is another very similar way of helping us to visualize additional spatial dimensions, using a logical consistency which works no matter what spatial dimension you choose to start from.

When string theory talked about spatial dimensions, for a while there it was nine spatial dimensions plus one of time. When physicist Edward Witten introduced a way to unite five different versions of string theory into what became known as M-Theory, he was describing ten spatial dimensions plus one of time. Because of that shorthand way of saying it, some people jump to the conclusion that this means physicists are saying "time" is the eleventh dimension, but it's not that simple.

"Time" overlaid upon "Space"
What science has traditionally visualized is three dimensions of space, and an additional quality called "time" which is overlaid on space to create the familiar concept of "space-time". In that way of thinking, "time" is not really a full dimension, which is why it sometimes gets counted separately. So with M-Theory's 11 dimensions, it's like we're imagining an eleven-story building, but the fourth floor is somehow not as real as the other floors: no wonder some people are unwilling to accept the existence of additional spatial dimensions when this building looks like it could collapse at any moment!

String theory relies upon extremely complicated math to arrive at its portrayal of reality. My animation is a visualization tool, which provides a comparatively easy window into imagining the extra spatial dimensions, and also has many interesting connections to other ideas from physics and cosmology - for instance, the idea that the fifth dimension is curled up at the planck length because we're experiencing it one planck frame at a time, and the idea that our 3D universe is "constrained" by a seven-dimensional brane can be seen in my "new way of thinking about time and space".

Imagining the Tenth Dimension is a Visualization Tool
What I've created, then, is an intuitive, rather than a mathematical way of visualizing the spatial dimensions. As physicist Michio Kaku says in the opening quote to this entry, sometimes finding a way to visualize a problem is more important than the math used to solve a problem: but saying that in no way diminishes our respect for the difficulty of the rigorous mathematical concepts physicists dealing in cosmology and extra dimensions must use to properly study these ideas.

So here we are with our eleven-story building, somehow managing to stay up even though its fourth floor is not as solid as the others. What's wrong with this picture? If the first three dimensions are spatial, and the fifth dimension and above are spatial (or "space-like" as some physicists prefer to say), and each additional spatial dimension is defined by the one before, then I would say that we have to find a way to agree that the fourth dimension is a full spatial dimension just like the others or the leap from the third spatial dimension to the fifth spatial dimension simply doesn't make sense. We need to show how there is a continuum, from the first dimension to the second, from the second to the third, and so on all the way up to the top of our building.

Many Worlds Leads to Many Dimensions
Here's another continuum that I believe ties in to this way of visualizing. In 2007, a team of scientists at Oxford, under the direction of physicist David Deutsch published a proof demonstrating that there is a direct continuum from the probabilistic outcomes of the quantum world to the macro world of parallel universes resulting from chance and choice (Everett's Many Worlds Interpretation).

If every decision I make, every decision someone else makes, and every random outcome where no one made a choice but something just happened are all creating different versions of our universe, this seems like a mind-boggling amount of universes for us to be asked to imagine. And yet, the Many Worlds Interpretation is gaining ground amongst serious scientists because it answers so many other questions about how our universe works. So, while Everett's MWI still has its detractors, as cosmologist Max Tegmark of the Massachusetts Institute of Technology has been quoted to say,

The critique of many worlds is shifting from 'it makes no sense and I hate it' to simply 'I hate it'.

Here's the intuitive leap my project takes on all this: if there are multiple branching timeline versions of our universe being created by chance, choice, and the actions of others, and yet we somehow can't get to those other universes once a certain outcome has been observed, we are talking about the point-line-plane postulate again: we define a line in a spatial dimension, and we find a point that is not on that line, and that's how we visualize the next dimension up. In other words, with my project I'm contending that the versions of our universe that we can't get to are being defined within additional dimensions, and this aligns with the most basic definition of spatial dimensions.

What's Not On Our Line?
As we discussed recently in Elvis and the Electrons, one of the commonly used examples of a universe we're not in, or a point that is not on our line, is that Everett's MWI says there must be a version of our universe where it's 2009 and Elvis is still alive. In other words, I am insisting that these branching choices, as per the definition of spatial dimensions, come from the next dimension up above our spacetime, a constantly evolving "probability space" which is the fifth spatial dimension. The fact that Kaluza convinced Einstein that the equations for gravity and light for our universe are resolved in the fifth dimension also ties in nicely with this idea.

But in order to get to that conclusion, we still have to fix our ghostly fourth floor. This project does so by insisting that "time" as we experience it is just one of the two possible directions in the fourth spatial dimension. Most scientists are willing to agree with the concept of time reversal symmetry, which says that time's opposite direction is just as valid as the "arrow of time" that we are experiencing within our universe. As per the point-line-plane postulate, my way of visualizing the dimensions uses time reversal symmetry for its reasoning - if we define a point in the fourth dimension, let's call it "now", then we can define a second point any arbitrary amount of time before or after "now" which creates a line that extends to infinity in either direction. Those two directions are "time" and "anti-time", and those two directions combined create a full spatial dimension.

Talking about "time" without acknowledging "anti-time" is like talking about "up" without acknowledging "down". Here's another analogy: if I were to tell you that our 3D physical world is made from length, width, depth, and "forward", you would ask why I was counting "forward" separately. Isn't "forward" already one of the possible directions within our 3D space of length,width, and depth? Of course it is. We reach the same conclusion with the fourth spatial dimension: "time" as we experience is just one of the two possible directions that make sense within that dimension, but it does not belong in a list of length, width and depth: this is why I suggest that the fourth spatial dimension be referred to as "duration".

Which means, then, that by the time we have counted ten spatial dimensions, we have already considered "time" as being one of the possible directions within those spatial dimensions so there's no need to count it separately. To be clear, though, this conclusion is unique to this project, so anyone taking a university class on M-Theory will continue to be told to count time separately.

Like wormholes, or anti-matter, some people jump to the conclusion that because they learned about "time as the fourth spatial dimension" from science fiction (the H.G. Wells novel "The Time Machine" for instance) that means the idea is incorrect, just a figment of overactive imaginations. In fact, the controversy over whether time is part of a full spatial dimension is at the core of many people's criticism of this project. Time, some critics say, is a temporal dimension and thus any additional dimensions based upon my description of the fourth dimension must also be temporal, and not the spatial dimensions that physicists dealing with extra dimensions are thinking about.

Because the idea that "time" is a direction, not a dimension, is so central to my project, I have spent a great deal of time discussing it. Here, to close, are some of the other blog entries where I have explored this idea that time is just one of the two possible directions in the fourth spatial dimension.

Hypercubes and Plato's Cave

Time is a Direction

Time in Either Direction

Scrambled Eggs

Dr. Mel's 4D Glasses

The Big Bang and the Big Pie


Enjoy the journey,

Rob Bryanton

Next: Google and the Group Mind