A direct link to the above video is at http://www.youtube.com/watch?v=OdnhKE95AqM
"...cosmology is simpler in one important respect: once the starting point is specified, the outcome is in broad terms predictable. All large patches of the universe that start off the same way end up statistically similar. In contrast, if the Earth's history were re-run, it could end up with a quite different biosphere."
Let's pull out a piece of paper and ponder this question further.
First of all, put a dot near one edge of the paper, and label it "the big bang". Likewise, place a dot near some other edge of the paper, and label it "the end of the universe". Finally, draw a line that passes through those two points, and place a point somewhere near the middle of that line, which we'll label "you".
Okay, if that middle point represents "you" right now, then let's place another point nearby but not on the line we've just drawn. Do you see how this point could represent some other version of "you", such as the one where a childhood accident completely changed your life, or even just the version of "you" that got bored with this blog entry and stopped reading ten seconds ago? There would be a new line which extends from the big bang and passes through this alternate version of you, and each of those could be thought of as a one-dimensional line: but the only way the line for version "one" and the line for version "two" could be considered simultaneously is if we were to consider the 2D "plane" of the paper we were drawing on. In fact, we could place another point earlier on one of the lines and say that it represents your moment of conception, and then imagine a "ray" of possible lines representing all of the versions of "you" that could possibly have existed from your moment of conception onwards, and they could all be contained within this 2D plane.
Now let's think of a different point, but in this case let's imagine that it's floating a few inches above the paper. Perhaps this new point represents the version of the universe where dinosaurs never became extinct, which would mean that "you" as we know you wouldn't even exist on that line! We can imagine a one-dimensional line that passes through the big bang point on the paper and this new point. We can imagine a different 2D plane that passes through our first or second line and this new "dinosaurs" line. But here's something important about what we've been visualizing: the only way we can consider all three lines at the same time is by using the third dimension.
I hope it's obvious by now that the point-line-postulate tells us the logic we've just used to think about the 1st, 2nd, and 3rd dimension is directly translatable to the 4th, 5th, and 6th. Which means that with a piece of paper and a bit of imagination, we've already visualized the first six dimensions of our reality!
But wait, some critics might be thinking. Wasn't it arbitrary for me to place the "dinosaurs" line outside the plane of my paper? Couldn't I just have easily placed a point at the center of the paper, called it the big bang, then imagined that all around the outside edge of the paper were points representing all the different universes that could have resulted from the initial conditions that created our unique universe with its locked-in fine structure constant? And you may be surprised to hear that I'm willing to agree with that statement. From the initial conditions of our universe, we can get to any of the possible universes which the Many Worlds Interpretation tells us really exist, just as real as the one we're currently observing. From anywhere else beyond the big bang though, we're already seeing a paring away of possibilities - when one version of the universe is observed, the other universes are not, and causality shows us that this renders some of those other universes permanently inaccessible from that point forward on our entropy-driven "line of time".
How would you or I get to the universe where it's this point in time which we call the twenty-first century, but dinosaurs never became extinct? Everett's theory tells us that a version of the universe must exist where dinosaurs are living and dying right "now", and those dinosaurs are observing all the different versions of the universe where they still exist. So why can't you or I get there from here? In other words, if everything is probabilistic outcomes, why does it appear that there is zero possibility that the "next possible now" for us might include this "dinosaurs" world line?
The answer is: there is a missing degree of freedom. If you and I were within the sixth dimension rather than the fifth, then we would be able to leap across these different world lines, and get to those other versions of the universe which are not causally connected to the one we're in right "now". As we said last time, this is because "you and I are ants, not flies". Every instant that we observe is one planck frame beyond the instant before, which gives us the impression that the fifth dimension is compactified, or curled up on itself. If the fourth dimension is like the straight line of a garden hose stretched out on the ground, the fifth dimension is like an ant walking inside that hose, while a fly inside that hose would be able to flit from one location to another without having to worry about fifth dimensional causality.
What we're talking about with the sixth dimension, then, is the phase space of the set of parallel universes resulting from our universe's unique initial conditions. A phase space, to quote wikipedia, 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."
Hugh Everett III's Theory of the Universal Wave Function is a way of thinking about the phase space of our universe as defined by quantum mechanics and the Schrödinger Equation. The prevailing opinion about this wave function back when Everett published his theory in 1957 was known as the Copenhagen Interpretation, which said that an observer collapses this wave function of all possibilities into just one version, purely through the act of observation. Everett proclaimed this idea to be ridiculous: how could a single observer collapse the wave function of an entire universe? That was the accepted interpretation amongst most quantum physicists of the time, though, and resistance to abandoning that opinion was one of the reasons why it took so many decades for Everett's theory to become more accepted. But within the last ten years or so, more and more people have moved to the idea that his interpretation really is the more elegant one: the phase space of all possible outcomes continues to exist, and you or I are not collapsing the wave function, we are merely observing it in one state out of the many potential versions we could have observed.
Let's sum all this up: Everett's Many Worlds Interpretation says there is a wave function which encompasses every possible state for our universe, and I'm saying that's the sixth dimension. But because we're in the fifth dimension, choosing from a set of causally related outcomes that are available to us one planck frame after another, there are versions of the universe which have nothing to do with us - like the version where I died in a car crash yesterday, or the version where dinosaurs never became extinct. Likewise, the version where I decided to rob a bank yesterday must exist, but with my free will I chose not to observe that universe. All of those "other" universes have nothing to do with the universe I'm observing, even though I can acknowledge their existence within the sixth dimension.
What's Outside Our Phase Space?
Thinking back to that piece of paper we started from there are a few other ideas we can glean from this. First of all, that first and second point we drew, representing the beginning and end of the universe, can be joined with a line. But more properly, what we're talking about then is a "line segment". A true "line" would pass through those two points and extend past the edge of our paper and out towards infinity in either direction. This gives us a way to think about about how both "before" and "after" our universe is the same thing: a return to an underlying state which is outside the system representing all possible versions of our unique universe. Theoretical physicist Sean Carroll makes a similar claim in his recent book "From Eternity to Here".
But wait, there's that word again: "system". In my original animation, I described the "point" we start from as being something that indicates a position within a system. As we just saw, a "phase space" includes all possible versions of a system, with each possible state of the system corresponding to one unique point within the phase space. So we can extend our analogy here to think of our paper as being on an endless landscape covered with other papers, none of them touching, many of them widely separated from each other, each of them representing other universes or "systems" with other initial conditions and basic physical laws: the multiverse landscape. And within some of those other systems would be creatures sufficiently advanced to be able to look around and wonder how they ended up in a universe where the laws of physics appear to have been uniquely fine-tuned in a way to allow their universe to exist.
This idea is known as the Anthropic Principle. As I say in my song "The Anthropic Viewpoint":
If there’s other worlds then we’ve just missed ‘emCoincidentally, as we talk about the sixth dimension, it's interesting to note that cosmologist Martin Rees has told us only six basic physical constants need to be defined to create our unique universe: check out his book Just Six Numbers: The Deep Forces that Shape the Universe for more about these concepts. It's also interesting to note that string theory predicts there could be ten to the power of five hundred other universes out there in the multiverse landscape, each with its own unique physical laws.
No way to know what’s outside our system
We’re like goldfish livin in a bowl
What’s beyond it we can never know
All we can do is theorize
Cause we can never… get outside, outside
In the anthropic viewpoint
The reason we’re here is because we’re here
And if it were impossible
Then we wouldn’t be
So we can't get to those other universes, those other systems, from the sixth-dimensional phase space representing our universe. Why not? Because we haven't achieved that degree of freedom yet within our approach to visualizing the dimensions. Which of course, will lead us to our next entry: Imagining the Seventh Dimension.
Enjoy the journey,
Imagining the Fifth Dimension
Imagining the Fourth Dimension
Imagining the Third Dimension
Imagining the Second Dimension