Wednesday, August 31, 2011

Imagining the Sixth Dimension


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."

- Cosmologist Martin Rees, from his book Just Six Numbers, the Deep Forces that Shape the Universe


What's the difference between the fifth dimension and the sixth dimension? With this approach to visualizing the dimensions, that question comes up a lot. After all, if the fifth dimension includes every possible state for the universe which can be connected to the "now" any one of us are currently observing, why do we need to talk about anything beyond that?

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.

Phase Space
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 ‘em
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
Coincidentally, 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.

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,

Rob Bryanton

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

9 comments:

Tony1 said...

OK, let me get this right. In the fifth dimension, reality branches off every Plank unit of time from right now. The sixth dimension is all of those branches that have splintered off in the past.

I'm not a scientist!

Rob Bryant should have an article on him in the English Wikipedia. I'd like to create it, but is he willing/able to send a photograph of himself that can be released with a CC-by-SA license (which regrettably would involve the photographer's permission, directly by email)?

Tony

Neven Maric said...

You say that the sixth dimension represents the phase space. I find it easier to visualize that it's all six dimensions that make up the phase space, each being a degree of freedom, each orthogonal to the rest. The first three are length, width, and height.

According to the point-plane postulate, the 4th, 5th, and 6th should also have such a relationship. The 4th dimension is time. We are always moving forward in time. As we know, time must run orthogonal to the dimensions above and below it, meaning that our perception, which is aligned with forward moving time, also runs orthogonal.

You mention that chance occurs in the fifth dimension. We experience quantum wave collapse seemingly randomly; this is because it occurs in the fifth dimension, which runs orthogonal to the fourth. It appears to us as a seemingly random event only because we cannot see the direction of the fifth dimension - we are perfectly aligned with the direction of time and can only experience changes in the fifth dimension indirectly - what we call chance occurrence.

If we liken this representation of the 4th and 5th dimensions to a 2D plane (where we see ourselves going in the direction of time, yet are pushed up and down on the plane by chance), it leaves us with one more possible direction in which orthogonality occurs.

This brings me to my interpretation of the 6th dimension. I do not see the 6th dimension as the phase space in itself - it is another degree of freedom in the phase space that we can liken to a 3D space (for purposes of visualization). This leaves us with another variable to describe the 6th dimension. I call this variable choice. Choice and chance are often lumped into the same category, though I see them each as their own dimensions, two variables, alongside time, that determine our universe's position in the phase space (position meaning the possible universe we are living in, other points being other possible universes).

One can write an equation using the first 3 dimensions that denotes where certain positions in space are for given parameters such as z=x+y. For any x and y, z can be determined. For every x and z, y can be determined. I'd like to project this onto the phase space created by the 4th, 5th, and 6th, dimensions.

Our initial conditions are like that equation that determines the plane of possible positions in three dimensions. Our initial conditions are an equation that creates a plane/object in the phase space which contains a plethora of possibilities for our universe based on the combination of three variables: time, chance, and choice, each running orthogonal to one another. However, we are still limited in our travels through phase space regardless of what we choose for the variables time, chance, and choice, as the equation may only cover a certain part of the phase space; others are only accessible through different equations, or different initial conditions. Regardless of which choices, chances, or times occur, some possibilities may never be accessible. Of course, there may be a universe in which the initial conditions, or equations, span a large part of the space, with many different possible outcomes (like the equation for a really large sphere in 3D space).

It helps me to try to visualize everything geometrically and mathematically. What do you think of my interpretation of the phase space? Is it right to separate chance and choice? I, personally, see them as fundamentally different and independent, running orthogonal to time and one another. We cannot perceive them directly or as deterministic, but that may just be because our perception are aligned with a direction in time, which happens to be orthogonal to the dimensions above. It's like we're being blindsided by chance and choice because we are only looking in one direction. Perhaps these two anomalies are deterministic, and we are just unable to perceive their direction, and end up seeing things as "random".

Rob Bryanton said...

Hi Neven, thanks for your extensive note! For me, chance and choice are the same thing: if you don't make a choice randomness makes a choice for you. And the difficulty with placing choice within the phase space of all possible outcomes (which you're right, is made up of six dimensions) is that no matter how much I try to exercise my free will, I can't choose to be in the universe where it's 2013 and Elvis is still alive, or the Twin Towers still stand in New York. Likewise, no amount of random outcomes can move me to those versions of the universe, there's zero possibility of me now observing those events.
However, if I could somehow be plucked out of my fifth dimensional probability space and moved within the phase space of the universe I could then violate those laws of probability and be able to see those 2013/Elvis/TwinTowers version of the universe: but because my physical body is rooted to these 3D atoms and molecules, I don't see us being able to do such a thing.
Thanks for writing!
Rob

Neven Maric said...

Rob,

Thanks for writing back. From a young age, I've always been very interested in your work; it's a pleasure to hear from you.

I am starting to see where you are coming from regarding choice and chance, how they happen on the same level and are indistinguishable (as you said, if one does not make a choice, chance will). Thanks for clearing that up.

What do you think of our initial conditions as an equation for phase space that restricts our possible universes (where phase space contains all possible universes with such physical constants)? For example, in two dimensions, the equation y=2x will never ever cross the point (1,5) because of the restrictions placed by the equations. What I am saying is that each universe spans not just 5-dimensions but a 6-dimensional phase space that is restricted by an initial equation. There is only a set amount of possibilities based on the initial equation, and this is what restricts us from jumping to the universe where the twin towers still stand, or where Elvis is alive and well in 2013. Assume in our y=2x example that x refers to time and y refers to the state of the universe. Then, past a certain x, y will never be able to achieve a certain state. Obviously, this linear equation is a gross oversimplification. And I understand that my geometrical representation may just be an illusion created by my visual thinking mind - what do you think?

Because I am trying to liken this to 3D space, I am trying to find another variable that affects our position in phase space which we can call the 6th dimension. I understand now what it means to use the 6th dimension to "fold" between two points in the plane created by the 4th and 5th dimension - but what exactly causes deviations in the 6th dimension? I called this choice, but I realize that I might have made this determination prematurely. Just like the folding of a 2D sheet doesn't describe the third dimension as well as calling it "depth" does by giving it independence - how do we give independence to the sixth dimension (instead of describing it in terms of the fourth and fifth) - I tried to do this by introducing choice. What would you say?

Rob Bryanton said...

Hi Neven, the idea that the sixth dimensional phase space representing all possible outcomes for a particular universe can be defined by an "equation" is for me, the same as saying it is defined by its initial conditions, or by its unique set of physical constants that it maintains throughout its existence. Regardless of how you think about it, the 6D phase space for one universe is self-contained, self-consistent, and completely separate from the 6D phase space representing some other universe, and this is why I insist each of these phase spaces can be thought as occupying a unique position within the multiverse landscape, or to use the terminology from my original video, locked in at a "point" within the seventh dimension and above.

I would say that using what we know about the three or four dimensions we're intimately familiar with to try to visualize the extra dimensions is fair game, and that's exactly what the point-line-plane postulate says as well. So while our monkey brains may be ill-equipped to simultaneously imagine six spatial dimensions, I believe it makes perfect sense to use what we know about the 1st, 2nd, and 3rd dimensions to visualize the 4th, 5th, and 6th dimensions, and beyond.
Thanks for writing!
Rob

Anonymous said...

Hey Rob i wanted to know that if at x plank seconds from big bang i have a choice of eating a kitkat bar and an apple and i choose the kitkat bar, then there will be a timeline where i choose the apple. At x+1 plank seconds the kitkat me has 2 more choices whether to eat kitkat as a whole or to break and eat individual pieces. At the same time the apple me would also have 2 choices whether to eat the apple without cutting or to eat the apple after slicing it. The timeline when i slice the apple and the one where i dont would have the same 5th dimensional coordinate as the one where i chose the apple but would have a different 5th dimensional coordinate than the one where i chose to eat the kitkat isnt it? One more question in the beginning of the video you talked about 3 timelines one where the you were making this video, one where you had a childhood incident and one with dinosaurs. I understand that the one making the video and the dinosaur one have different 5th dimesional coordinates but wouldnt the one with the childhood incident and the one where you are making the video also have different 5th dimesional coordinate?

Rob Bryanton said...

Hi Anonymous, thanks for writing! With the timelines example, I asked that we imagine the "dinosaurs" point floating above the page because that is not a part of our current reality. So yes, all the possible versions of "me" or "you" are part of a constantly evolving 5D system of branching outcomes (the page), while the "dinosaurs are still alive this long after the beginning of the universe" timelines would be part of a different 5D system which you and I can't access from here. If we did have some way to leap across from one logically inaccessible 5D system to another, we would be using an additional dimension to do so - the sixth dimension.

Anonymous said...

Hey Rob so to travel between the childhood incident timeline and this timeline i would need to use the 6th dimension?

Rob Bryanton said...

Yes, within the logic of my approach that's what I'm proposing - that the version of the universe where I had a debilitating accident as a child is not accessible from our current fifth dimensional probability space. so you would need to somehow get "outside" of the fifth dimension to move to that version of the universe where it's 2016 and something bad happened to me as a child.

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