"The string landscape can be visualized schematically as a mountainous terrain in which different valleys represent different forms for the extra dimensions, and altitude represents the cosmological constant's value."
With my Imagining the Tenth Dimension project, I begin by saying that a point indicates a position in a system. In Imagining the Sixth Dimension, I mentioned that thinking about the set of all possible states for our unique universe would be thinking about our universe's phase space. In fact, that's the definition of phase space: a space in which all possible states of a system are represented. I believe there's a way to apply this thinking to every single dimension - in a sense, a dimension when considered as a "set of all possible states for that dimension" becomes a finite but unbounded hypersphere, and that hypersphere becomes a point in the next dimension up. Let's go back and see how that logic holds up.
If I'm on a boat in the middle of the ocean, I can see a horizon that appears to be the same in every direction. From this I can deduce that there is a slight curvature to the surface of the ocean, which is topologically speaking a 2D plane, and understand that I'm really on a 3D sphere. From the 2D topological perspective, I could head in a specific direction forever, giving me the impression that I was on an infinitely flat surface, but with the added curvature of the third dimension we can see how "apparently infinite" can be equated with "finite but unbounded".
With the knowledge that it takes a certain amount of "time" for light to reach our eyes, we realize that what we're seeing around us is not space, but space-time, and that as counter-intuitive as this may seem at first it's actually impossible for us to see 3D space: we can imagine and use the logic of 3D shapes, but we can only see them from our moving position within 4D space-time.
From our position within 4D space-time, we look out to the furthest reaches and see a cosmological horizon which is the same in all directions. From this we can deduce that there is a slight curvature to space-time, and that we're really a point moving on the surface of a 5D hypersphere. There are many other indications that our reality comes from the fifth dimension: back in 1921 Einstein accepted this idea as proposed by Kaluza. Holographic universe theories propose that we are an interference pattern projected from the fifth dimension, or from the "edge of the universe" but I disagree with those who say that this edge is far, far away. Think of it like this: the third dimension is at the "edge" of the second dimension no matter where our imaginary 2D flatlanders are located. In the same way, this "edge" they speak about in holographic universe theories as being at an additional right angle to our space-time reality is not far away, it's right "here" in the next dimension up, no matter where we are within our space-time reality. And Hugh Everett, even through he didn't propose extra dimensions with his Many Worlds Interpretation, did propose that the branching universes derived from quantum mechanics occur within a space which is orthogonal (at right angles) to space-time.
Some quantum physicists are fond of saying that extremely unlikely events such as one of us suddenly disappearing from here and reappearing on the moon are allowable within the quantum wave function, but they are so unlikely that they would take longer than the life of the universe to occur. Likewise, Everett talked about how there are branching tree-like structures which are causally connected, and he even allowed for the possibility that some of those branches might fuse back together further down the causal chain, but he was very clear that causality could never be violated - so the universe where dinosaurs never became extinct or JFK was never murdered or where I died in a car crash last year would exist within the universal wave function as described by the Schrödinger equation, but they are now inaccessible from the universe we are currently observing. Those other universes, in a manner of speaking, are beyond the horizon of our 5D probability space, which leads me to conclude that we are a 5D point moving on the surface of a 6D hypersphere.
This sixth dimensional "phase space", as some have called it, includes all possible versions of our universe, from its beginning to its end. But within that phase space, we never wander off into one of the other universes with different physical laws, because those are in effect "beyond the horizon" of our universe's phase space, and from this we can deduce that the system representing our universe as a timeless whole is a point on a 7D hypersphere.
From here we are beginning to move into discussions of information flow rather than physical realities, but we're not all the way there yet.
In his book Just Six Numbers, Sir Martin Rees tells us that we only need to define six "deep forces" to describe our unique universe. Adjusting any one of those parameters by surprisingly small amounts would cause our universe to fall apart as the laws of physics break down. So if our unique universe is located at a position within the multiverse landscape, or constrained by a D7 brane as some string theorists have suggested, then are we moving, or are we stationary on the surface of this 7D hypersphere? There has been some evidence that the basic physical laws of our universe may have been slightly different at the earliest history of our universe, which would indicate that perhaps we have changed our 7D position slightly according to the logic we're pursuing here. But the idea that there is a certain natural selection occurring at the seventh dimension and beyond also makes sense - if we move too far away from our position, the incredibly delicate balance of forces that allow our universe to exist would collapse, so at nearby positions within this multiverse landscape there might not be universes that cohere into any meaningful structures, but further away another universe completely different from ours could be assembled with its own unique set of intricately connected physical laws and its own unique expression within the sixth dimension and below.
We also talked last entry about how we can imagine a data set of universes within the seventh dimension which would then require the "beyond the horizon" additional degree of freedom of the eighth dimension for us to be able to simultaneously consider other data sets not included within the seventh dimensional one: but to be clear, those data sets could be interchangeable, so this is more of a question of reference frames than it is of some data not being part of the seventh dimension. In that sense, the seventh dimension harkens back to the "garden hose" analogy used by string theorists: it's useful to imagine that the seventh dimension looks like a straight line, but when we move closer we can see the dimension has the potential for additional twists and turns that are inside the "rolled up tube" that is, topologically speaking, the "plane" of the eighth dimension.
(We looked at the following animation of vibrating Calabi-Yau Manifolds before in June 2011, in an entry called "Will the LHC Reveal Extra Dimensions?")
What's beyond the horizon of the 8D construct we've just envisioned? String theorists who talk about there being ten to the power of five hundred possible universes are really describing the different possible shapes the extra dimensions could take. In The Hidden Reality, Brian Greene uses the following image to picture the terrain of possible extra-dimensional shapes: he calls this terrain the Landscape Multiverse (as opposed to the Brane Multiverse, the Quilted Multiverse and so on), and describes how quantum tunnelings through this mountainous string landscape realize every possible form for the extra dimensions in one or another bubble universe. To tie this idea to my approach to visualizing the extra dimensions, the topological "plane" of this landscape is the eighth dimension, and the additional degree of freedom allowing this tunneling to occur would be in the ninth dimension.
Back in July 2008 we talked in this blog about Michael Shermer, who's the well-known publisher of Skeptic Magazine. Michael's goal has been to poke holes in the questionable claims of fringe science, the paranormal, and a wide range of other areas that he has targeted with his razor-sharp debunking skills. This is why I found it quite marvelous when I picked up an issue of Scientific American back then, and found that Mr. Shermer's regular column that month was entitled "Sacred Science: can emergence break the spell of reductionism and put spirituality back into nature?".
Mr. Shermer's article is about a fellow who comes from my neighboring province of Alberta, Canada: Stuart Kauffman, founding director of the Institute for Biocomplexity and Informatics at the University of Calgary, who has written a book called "Reinventing the Sacred". To quote from Michael Shermer's article about the book:
Kauffman reverses the reductionist's causal arrow with a comprehensive theory of emergence and self-organization that he says 'breaks no laws of physics' and yet cannot be explained by them. God 'is our chosen name for the ceaseless creativity in the natural universe, biosphere and human cultures,' Kauffman declares.By the time we are thinking about the ninth dimension as selection patterns that represent a generalized preference for one kind of universe over another, I believe we're in the same intellectual neighborhood as the "God 2.0" concept. And I think Michael Shermer, famed atheist and skeptic, got it right when he concluded his article saying that Stuart Kauffman's "God 2.0 is a deity worthy of worship".
Why do I say this? Because by now we're talking about labels: "a rose by any other name would smell as sweet". Whether you want to call these selection patterns that caused our universe to be selected from out of this sea of potential information patterns "God", or some other less emotionally-charged name, doesn't change the ninth dimensional reality that we're describing here. As I say in the last verse of my song The Unseen Eye:
Now the universe of all universesIf you are one of those persons who recoil at the use of words like "God" and "soul", I apologize. This project is not an attempt to enforce a spiritual viewpoint onto the nature of reality, but it also tries to show that there are a great many possible connections between these different schools of thought. If you prefer physics over philosophy, so be it, that is one point of view. But likewise, if you prefer spirituality over science, I'm hoping that this project has given you some new food for thought for where the meeting ground between the two might reside.
If the truth be known
Is an awful bore, viewed as a whole
But just a tiny shard viewed from any angle
It reveals such beauty, reveals a soul
So does it make a difference
How we got to what we see
If it’s really just coincidence
It’s still a wondrous thing
There are 26 songs I attached to this project (I chose that number as a bit of an inside joke for fans of the history of string theory), and the very last one is called "Thankful". Having a sense of wonder and gratitude for the immense processes which selected the universe we are in right here and right now is, to my way of thinking, a completely appropriate response.
Are you enjoying the journey?
Next: Wrapping It Up in the Tenth Dimension
Imagining the Eighth Dimension
Imagining the Seventh Dimension
Imagining the Sixth Dimension
Imagining the Fifth Dimension
Imagining the Fourth Dimension
Imagining the Third Dimension
Imagining the Second Dimension