Imagining the Seventh Dimension

A direct link to the above video is at http://www.youtube.com/watch?v=2FWRndF01xI

"...much as the many different forms for DNA provide for the abundant variety of life on earth, so the many different forms for the extra dimensions may provide for the abundant variety of universes populating a string-based multiverse".

- Brian Greene, in his book The Hidden Reality

A point represents a position within a system, and as we add dimensions, the system becomes more complex. In the Imagining the Tenth Dimension animation, we're asked to think of our universe with its locked in fine structure constant as a "point" at a position within the system of the seventh dimension, which means some other seven-dimensional "point" would be a way to get to some other universe with different basic physical laws than our own. Just how crazy is this idea?

Some string theorists have said there are ten to the power of five hundred other universes out there, in something we can call the "string theory landscape". Other cosmologists have suggested that the number of other possible universes out there approaches infinity, and because of that we are just in a tiny sliver of something called the multiverse. Either way, what we're trying to visualize here is a position within that landscape, and within that position we would find a way to get to Everett's universal wave function representing all possible outcomes for our particular universe.

Here's a graphic which was part of a great article published in November 2007's Scientific American: written by Cliff Burgess and Fernando Quevedo, the article is called "The Great Cosmic Roller-Coaster Ride".

(this graphic © 2007 by Scientific American)

You can click on this graphic from the article to see a higher-resolution version, but while you're here I'll quote the text:

According to string theory, our observable universe is a small part of a larger space having more dimensions than the three we directly see. The other dimensions may be microscopic in size (or otherwise difficult to penetrate) and crumpled up in a funky shape known as a Calabi-Yau space. The observable universe may be on a membrane, or simply a "brane," sitting at the tip of a spike (what physicists call a "throat") or composing part of a membrane wrapped around teacuplike handles.

When I published my book in 2006 did I know that string theory proposes that our universe is constrained at the third dimension and the seventh dimension by "branes" in those dimensions? I did not. Still, there seems to be another very interesting parallel here between my proposal that our universe is "locked in" at the seventh dimension, and the string theory idea that our universe is constrained by a seven-dimensional brane. My goal, since the day I launched this project back in 2006, has been to continue to document interesting connections between leading edge science and my approach to visualizing the dimensions, and I believe we're looking at a particularly useful one here.

The word "multiverse" has a number of different meanings for different people, so there are some possibilities for confusion. As you'll see in the wikipedia article on this topic, physicist Max Tegmark has proposed that there are four different levels of Multiverse (some of the following is paraphrased and some is quoted from the wikipedia article):

Level I: Beyond our cosmological horizon

Remember the cosmological horizon? It gives us a way of seeing that each of us is at the center of our own version of the observable universe, and that if we were on a planet billions of light years from here, we would still see ourselves to be at the very center of a different but essentially similar cosmological horizon. Those two would overlap much like a space-time Venn Diagram. But what if an observer were so far away that their cosmological horizon didn't overlap with ours at all? In a Level I multiverse, space-time is perfectly flat. On that flat "sheet" of space-time there are an infinite number of self-contained universes, all with the same physical laws and constants. Almost all will differ from our own universe. However, because there are infinitely many, there will eventually be similar, and even identical, configurations.

Even though this version of this multiverse has many supporters, particularly since it doesn't require the existence of any extra dimensions, this one feels extremely unlikely to me. 

Max Tegmark estimates that within a Level I multiverse, an identical volume to ours should be about 10¹⁰¹¹⁵ meters away from us (a number larger than a googolplex). 

If that's the case, then how far away is the one where I got up five minutes earlier this morning? And how far away from that one is the one where I got up four minutes and fifty-nine seconds earlier? It's easy to see why some people who are taught this version of the multiverse dismiss it as being ridiculously extravagant.

With my project, I've proposed that the cosmological horizon is the space-time equivalent of the 3D horizon we see around us when we're in the middle of the ocean - it's the same in every direction because of an underlying curvature. Topologically speaking, if we think of our 4D space-time as a flat plane, or the surface of the ocean as a flat plane, where is the curvature? In either case, I would say it's in the next dimension up. So our observable 4D universe is really on the surface of a 5D hypersphere! Which means that if Tegmark's calculation is correct we have a measurement of the circumference of that hypersphere. Just as we could travel east on the surface of the earth and eventually end up back where we started, this would indicate that if we traveled 10¹⁰¹¹⁵ meters, we would traverse the 5D hypersphere and end up at the same place we are right now. It also means that if I had adjusted my angle ever so slightly, I could have ended up in the universe that is really very nearby ours in the fifth dimension, where I got up five minutes earlier this morning.

Level II: Universes with different physical constants

In this version, the multiverse as a whole is stretching and will continue doing so forever, but some regions of space stop stretching and form distinct bubbles, like gas pockets in a loaf of rising bread. Such bubbles are embryonic level I multiverses.

With my project, I have referred to this as the multiverse landscape, and placed it in the seventh dimension and above (depending on the context of the discussion), but within Tegmark's classification system his Level II universe does not require the existence of extra dimensions, and is on an infinitely flat expanse of spacetime.

Level III: Many-worlds interpretation of quantum mechanics

Hugh Everett III's Theory of the Universal Wave Function, commonly known as the Many Worlds Interpretation, tell us that observation causes one universe out of many to be selected, but the others continue on, just as real as the one we're in. Tegmark argues that a level III multiverse does not contain more possibilities than a level I or II multiverse.

In effect, all the different "worlds" created by "splits" in a level III multiverse with the same physical constants can be found in some Hubble volume in a level I multiverse. Tegmark writes that "The only difference between Level I and Level III is where your doppelgängers reside. In Level I they live elsewhere in good old three-dimensional space. In Level III they live on another quantum branch in infinite-dimensional Hilbert space." Similarly, all level II bubble universes with different physical constants can in effect be found as "worlds" created by "splits" at the moment of spontaneous symmetry breaking in a level III multiverse. Related to the many-worlds idea are Richard Feynman's multiple histories interpretation and H. Dieter Zeh's many-minds interpretation.

At last we get to extra dimensions, even if they're infinite within Tegmark's classification system. With my project, I have suggested that these "other" universes resulting from different physical constants are at different positions within the multiverse landscape of the seventh and eighth dimension, and that having arrived at any particular location within that landscape there is a potential for there to be a wave function of possible states (in other words, a set of parallel universes for the resulting universe) within the first through sixth dimension.

Level IV: Ultimate Ensemble

The Ultimate Ensemble hypothesis of Tegmark himself. This level considers equally real all universes that can be described by different mathematical structures. This does not include different low-energy physical laws not of our observable universe. Tegmark writes that "abstract mathematics is so general that any Theory Of Everything (TOE) that is definable in purely formal terms (independent of vague human terminology) is also a mathematical structure. For instance, a TOE involving a set of different types of entities (denoted by words, say) and relations between them (denoted by additional words) is nothing but what mathematicians call a set-theoretical model, and one can generally find a formal system that it is a model of." He argues this "implies that any conceivable parallel universe theory can be described at Level IV" and "subsumes all other ensembles, therefore brings closure to the hierarchy of multiverses, and there cannot be say a Level V."

"Ultimate Ensemble" certainly works as a description of the tenth dimension within my approach to visualizing the dimensions, and I've been saying that to avoid confusion it's better not to call this over-arching concept a multiverse, but rather The Omniverse. This helps to keep it separate in our minds from the parallel universe versions of our own universe (Tegmark's Level I, which I have also referred to as our universe's "phase space"), and the multiverse landscape of possible universes (Tegmark's Level II and/or III). On top of that I have added the ninth dimension, which encompasses the dimensions below but moves beyond any physical expressions and into patterns of information only, and by then we are arriving at what Tegmark calls Level IV. The omniverse, then, becomes either the ninth dimension in its entirety, or the tenth dimension in its unobserved state: a single "point" representing the ultimate ensemble of all possible patterns and shapes, ready to be created through symmetry breaking to spill us back into the realities of the dimensions below.

So. What is unique about the seventh dimension? Our universe never wanders off into the other different initial conditions universes as we observe the quantum wave function of possible outcomes for our universe because it is constrained by its position (or a D7 brane as we saw in the string theory graphic above) within the seventh dimension. Moving to another "position" within the seventh dimension and above precipitates a completely different universe with different basic physical laws, and for that universe its expressions in the lower dimensions will be just as real as our own, and just as locked in by their position within the seventh dimension and above as our own universe is. In that sense, what we are talking about here is easily connected to what physicist Lisa Randall talks about in her book "Warped Passages": there are are other regions of the multiverse (and ultimately the "omniverse") where other universes with different basic physical laws from our own exist, and it's because they stem from a different "position" within the underlying structures of reality that we can't get to them, and they can't get to us.

As I have cautioned people from the outset of this project, my "new way of thinking about time and space" is not the explanation for string theory, it's just an innovative way to visualize ten spatial dimensions, something that most people would have said was impossible to do. I have always remarked, though, that I find it interesting to see how many different spiritual and metaphysical systems have also placed a heavy significance on the number seven: so much so that one of the 26 songs I've attached to this project is called "Seven Levels". Just for fun, we'll look at a video for that song at the end of this entry.

But before we do that, let me close with this thought: if Information Equals Reality, then absolutely everything about our reality can be thought of as patterns and shapes within the information that is the fabric of quantum indeterminacy, or Tegmark's Ultimate Ensemble. Subatomic particles, fractals, life, consciousness, and our observed universe are all structures that result from these underlying patterns that reside in that place where the distinction between past present, and future is meaningless. Our own observed reality is being created at the fifth dimension, so anything beyond that becomes part of a "you can't get there from here" list, unless we can some day navigate within those extra dimensions beyond the fifth. And as we get closer to ten, we are now starting to move away from the reality side of the equation and more towards the information side. We'll continue this exploration next time with Imagining the Eighth Dimension.

Enjoy the journey!

Rob Bryanton



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

Next: Imagining the Eighth Dimension

Previous:
Imagining the Sixth Dimension
Imagining the Fifth Dimension
Imagining the Fourth Dimension
Imagining the Third Dimension
Imagining the Second Dimension