## Wednesday, August 24, 2011

### Imagining the Fifth Dimension

"The further back one looks, the further ahead one can see"

- a 'fifth dimensional' way of viewing reality commonly attributed to Winston Churchill, for more

We keep returning to this idea - every time we add a spatial dimension, we need to find a way to think about how the new dimension is at right angles to the ones that have come before. Another word for this concept is that each new dimension is orthogonal to the previous ones.  Here's the definition of that word from the Merriam Webster online dictionary:
Orthogonal
a : intersecting or lying at right angles
b : having perpendicular slopes or tangents at the point of intersection
Last entry we looked at how it makes the most sense to say that the fourth dimension is space-time, a dimension which enfolds length, width, depth, and duration, and to accept that the fourth dimension is spatial. Yes, as creatures who get their energy from chemical processes that obey the thermodynamic laws of entropy, we appear to be moving in only one direction within that dimension, a direction which we call "time". But the evidence is strong that the opposite direction, anti-time, is just as valid and just as real, and having two opposing directions is one of the basic attributes added by any additional spatial dimension.

So what's at right angles to space-time?

It's interesting to read this quote from a lecture by Stephen Hawking:
"One can think of ordinary, real, time as a horizontal line. On the left, one has the past, and on the right, the future. But there's another kind of time in the vertical direction. This is called imaginary time, because it is not the kind of time we normally experience. But in a sense, it is just as real, as what we call real time."
And it's interesting to think about this: one of the central ideas to this project's approach to visualizing the extra dimensions is Everett's Many Worlds Interpretation of quantum mechanics, which explains how every possible outcome for our universe is equally real, but as observers we can only see one of those universes at a time. According to Everett's "Theory of the Universal Wave Function", the reason we can't see any of the other universes is because they exist within a subspace which is orthogonal to the one we are are observing at any particular instant.

But even though Hawking has talked about another kind of time which is at right angles to our space-time, and Everett has talked about the other parallel universes being orthogonal (at right angles) to the version of the universe any one of us is observing right "now", neither of them have said that these additional realms are in the fifth dimension. Why is that? Is this a failure of imagination from two of the most brilliant minds of the twentieth century?  Or is this a free will discussion?

Both Hawking and Everett have said they believe free will is an illusion. From Hawking's viewpoint, free will is a convenient fiction, only useful in recognizing how complex the factors are that cause one inevitable outcome or another to occur. Everett's viewpoint was similar - because an observer can only see one outcome, even acknowledging the existence of the other outcomes makes no difference to any one observer - because within the world line that they occupy, stretching from the beginning to the end of the universe, only one outcome could possibly have occurred. And Everett's viewpoint was that for a different version of the same person, within their parallel universe where they observe a different set of outcomes, those would be equally as inevitable! In either case, the other possible outcomes become part of a set of universes which are inaccessible, or decoherent, to the one being observed.

Is it easier to believe that free will is an illusion if there's nothing beyond space-time? And even when great minds like these are talking about versions of our universe which are at right angles to our space-time, is that why they continued to portray these as being part of the fourth dimension? Perhaps that's a philosophical rather than a scientific question. If so, then my philosophy is that the fifth dimension exists, and that's where each of us have the free will to navigate through the branching possibilities that Everett's Many Worlds Interpretation tells us really do exist.

Last entry we talked about how envisioning 3D space in its largest possible state is a way to think of a "quantum frame", and thinking about 4D space-time in its largest possible state encompasses an entire "world line" for our universe, extending from its very beginning through its very end. But you and I are not infinitely large within 3D space or 4D space-time, and what we're trying to visualize here is how those dimensions can have an additional degree of freedom that allows those connections to occur. This is where my project's line-branch-fold concept for imagining dimensions becomes particularly useful: the 5th dimension, by virtue of being at right angles to all of the dimensions that have come before, gives us a way to get to those other connections of the quantum world and Everett's Many Worlds that might seem unimaginable  from the viewpoint of someone who believes there's nothing more than 4D space-time.

I have a lot of respect and admiration for physicist David Deutsch, so you can imagine how excited I was to receive an email from him about this project back in 2007. David wrote to say he enjoyed my animation but thought it made no sense past the fourth dimension, and he added this explanation: "the multiverse is simply not a manifold, or space, whose 'points' are universes, nor are the universes 'stacked' or 'clustered', with a notion of near and far, adjacent etc". My question back to him was this:
"As I understand it, the term "multiverse" has two aspects to it: there is the multiverse represented by the bush-like branching structure of a potentially observed wavefunction for our own universe from instant to instant, and there is the multiverse of other universes with different basic physical laws. As our own universe makes its selections from the quantum wavefunction, it never wanders off into those other different-initial-conditions universes, even though those other universes are just as real as our own. If there is no near/far/adjacent within the probability space of the "next available set of choices" at the quantum and physical levels for our universe, then what constrains those choices to keep us from jumping around in the multiverse with no logical progression, no coherent experience?  This is what I like about the idea of our limited fourth-dimensional "line of time" actually being selected from within a bush-like branching structure of fifth-dimensional paths, that are still constrained by their "position" within the multiverse.  It also gives us a way to see how the past is just as fluid as the future - as per Feynman's sum over paths, there are many ways we could have gotten to this instant in time that we call "now"."

David Deutsch has long been a strong supporter of Everett's Many Worlds Interpretation. What I was trying to get him to discuss with me is how the many universes of Everett's Relative State Formulation (and the ten to the power of 500 other universes with different basic physical laws potentially described by string theory) exist out there within the timelessness that a number of the great minds of the twentieth century have told us we should imagine as "really existing, in the same way that space really exists" (to use a phrase from Brian Greene's The Fabric of the Cosmos).

Dr. Deutsch never responded to that question, I'm sure he's a very busy man and I'm grateful that he took the time to write me at all. My own answer would be that ultimately we're talking about an underlying structure where all those universes exist not sequentially, but simultaneously, within an underlying state that everything we are witness to (and not witness to!) comes from. So the universe where I got up five minutes earlier this morning is not in some other part of an infinitely large 4D plane (even though that is the way some cosmologists describe it): as I say in my song The Unseen Eye, that other universe is "just around the corner in time", accessed via the fifth dimension. And I contend that those other universes with different physical constants from ours (each with their own unique set of all possible states within the lower dimensions) can only be accessed by moving in a higher dimensional multiverse landscape which is well beyond the fifth dimension.

In 2007, a team of scientists at Oxford under the direction of David Deutsch published a new proof equating Everett's MWI with the probabilistic outcomes at the quantum level and the parallel universes resulting from chance and choice, and New Scientist magazine declared this to be one of the top science news story of the year. In 2010, a team of scientists at Oxford participated in a speculative art project created by Jon Ardern and Anab Jain as "Superflux": "The Fifth Dimensional Camera Project". David Deutsch acted as one of the consultants on this project too, but of particular note is the following video featuring Dr. Simon Benjamin, who is from the QIP IRC (Quantum Information Processing Interdisciplinary Research Collaboration), based at Oxford University. If you jump to the 5:43 mark, you will see he shows a diagram very similar to the ones from my project, of branching timelines resulting from chance and choice, and he suggests that these are occurring at the fifth dimension. Jon and Anab did show my tenth dimension animation to these scientists, so this is not just a coincidence. Is my idea of the fifth dimension as our probability space catching on with the mainstream? Inch by inch, it would appear to be so.

Einstein, another of the great minds of the twentieth century, accepted the existence of the fifth dimension. He did take a while to get used to the idea, but in 1921 he eventually gave his approval to Theodor Kaluza's proposal that the field equations for gravity and light are resolved for our space-time when they're calculated at the fifth dimension. The fifth dimension, then, becomes a way to combine Einstein's theory of general relativity with Maxwell's equations describing electromagnetism. A few years later, with Oskar Klein's additional input, the resulting Kaluza-Klein theory would eventually become the starting point for string theory.

But if we're talking about something that is at right angles to space-time, why can't we see it? Well, we've already talked about our mythical 2D flatlanders, who would be unable to perceive "up and down" because it was outside of the length and width of their 2D world. And we've also discussed that although we've been taught that the world around us is 3D, the startling fact is that the time it takes for light to travel to our eye means it's impossible for us to see the third dimension by itself. So asking why we can't see the fifth dimension may be like asking why we can't see the other side of a building as we stand in the middle of a street: it's not that the back of the building isn't there, or that it's impossible to see, it's just that we can't see it from our current reference frame.

But the standard explanation for why we can't see the fifth dimension (and beyond) is because it's compactified, or "curled up at the planck length". Since we've already established that our 4D space-time is not continuous, but is divided into 3D frames, or quanta, I have proposed that it follows that our physical "window" into the fifth dimension is only one planck frame wide, and that various aspects of our awareness can, as we saw in our opening quote from Winston Churchill, connect into the fifth dimension more fully.

Make no mistake about it: with this project I am insisting that we are really not in the third dimension, or even the fourth dimension. Our "now" is a moving point within a fifth dimensional probability space, and I believe the more that people embrace this idea the deeper their understanding of our reality will become.

The analogy often used in string theory is to think of the fifth dimension as being like a garden hose stretched out on the ground. From a distance, the hose looks like a line. But up close, we can see that the walls of the hose are curled up on themselves, so that if an ant were to walk inside that hose, it could go from one end to the other (the "straight line" of the fourth dimension), but be moving in a second dimension as well as the first.

In my Imagining the Tenth Dimension animation, I showed a Möbius strip, and asked people to think about how a flatlander moving on this strip would feel like they were traveling in a straight line, but in reality they would be twisting and turning in the dimension above. This is useful as a way to think about the fifth dimension, but the garden hose analogy adds one further wrinkle - what if a fly were to enter our hose? Unlike the ant, the fly would be able to travel not just in a second dimension but a third: so if our hose were 4D space-time, the ant would be moving in the fifth dimension and the fly would be moving in the sixth!

You and I, it appears, are ants rather than flies. But next entry we'll talk about how that's a good thing, as we move on to Imagining the Sixth Dimension.

Before we finish though, I want to mention one final thing: some critics of this project say I mistakenly try to combine unrelated ideas: that Everett's Many Worlds Interpretation is not related to string theory, that general relativity doesn't require extra dimensions, that anyone willing to consider discussions of the more metaphysical or spiritual ramifications of all this should be immediately dismissed as a lunatic. On the other hand, every day I receive positive feedback from people who see ways in which my approach to visualizing the extra dimensions connects to their own ideas about how reality fits together, and in this blog I have tracked scientific developments that connect to my "new way of thinking about time and space". Needless to say, I was thrilled to read recently that well-known physicists Leonard Susskind and Raphael Bousso have published a proof equating the branching probabilistic outcomes of Everett's Many Worlds with the string theory multiverse. Here's a link to Sean Carroll's blog entry about the new proof, and here is a link to the paper as it was published at arxiv.org. And while we're looking at links, here's a Discovery channel blog entry about a new theory analyzing black holes from the perspective of the same compactified fifth dimension we've been talking about in today's entry.

Enjoy the journey!

Rob Bryanton

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

P.S. - After publishing this entry I forwarded it on to David Deutsch to see if he had softened his position on this concept of the "fifth dimension as a representation of the probability space of Everett's Many Worlds". He did reply, and his answer was short and to the point: " 'Fraid not.". Oh well!

Anonymous said...

The space of possible universes emerging from the current universe is infinite dimensional - so it is not only the fifth (or sixth) dimension - but many many possible outcomes...

Rob Bryanton said...

Here's how I think of it - with a 1D line there are an apparently infinite number of points that could be found on the 2D plane that 1D line is found within. In the same way, there is not just one fifth dimensional point found outside our current "now" of 4D space-time, so there is plenty of room for lots of possible outcomes when you consider the additional degree of freedom supplied by adding just one additional dimension. And that freedom increases exponentially as we add more and more dimensions.

Anonymous said...

Can you please clarify the relationship between your idea of the fourth dimension and the fifth dimension. How is it exactly that we can imagine ourselves as a long undulating world line with a beginning and an end, if according to your idea of the fifth dimension, the end is not determined yet seeing as we have the ability to move freely, albeit unknowingly, through the various possibilities of the fifth dimension? I understand that each fifth dimensional possibility contains its own four dimensional world line, each with a separate beginning and end, however, if we are to bring ourselves into the fourth dimension from the point we are currently at, what determines which world line we see from which fifth dimensional possibility? Is it completely random, in which case can the fourth dimension be thought of as the collapse into a single possibility (possible world) from the fifth dimensional superposition of possibilities (infinite worlds branched from current state) that occurs upon observation? Similar to wave function collapse in quantum mechanics. Or, is it that the world line of us that would be viewed in the fourth dimension is the world line that would take shape from the point immediately before we were to take a viewing in the fourth dimension?

Rob Bryanton said...

The idea of a single world line from a person's conception to "now" feels like it is carved in stone, but in fact that is just as much an illusion as the idea that we each have only one fate, one destiny, as part of a worldline inexorably set in motion by a deterministic chain of events stretching from the beginning to the end of the universe.
The reason I introduce the "long undulating snake" - the spime, if you will, representing a person in the fourth dimension - is because it helps to start us thinking about how we are part of dimensions beyond the 3D spatial set we are embedded within. I've talked about how that 4D world line might seem like a dandelion gone to seed: a long stem leading to now, then a bloom of potential outcomes extending from now, only one of which we end up observing. But in my book and these blogs I've concluded that a more useful image is a tree - the trunk represents now, the branches represent the potential futures, and the roots represent the many paths we could have travelled to get to "now". And I insist that this "now" is in the fifth dimension, which is where all the other branches that logically extend behind and ahead exist simultaneously.
Which brings us to your question - what determines which outcome we experience? Clearly randomness is part of this, and that's just as true at the quantum or subatomic level as it is in our observed physicality. I sum it up as "choice, chance, and the actions of others". Are the words I'm typing right now the result of randomness? Or am I choosing to type one word instead of another? I believe I'm choosing, but there are those who believe that's an illusion, that I was always destined to write these words. Still, clearly if a plane were to drop out of the sky right now and destroy my house that would not be my choice, it would be a result of randomness and the actions of others. So hence the balancing act - I choose what I can choose, and if I don't choose then randomness and the actions of others will choose for me.
Here's a blog entry which has lots of links to other people's articles which explore these ideas further: http://imaginingthetenthdimension.blogspot.ca/2008/06/local-realism-bites-dust.html

aliyahs art said...

Hi Rob,

I am writing a book and I would really appreciate it if you would review my description of the 4th and 5th dimensions. I use an analogy of a room with facing mirrors to describe the 4th and then add mirrors on the other two walls to describe the 5th. Would you say that this is a good metaphor?

Here is an excerpt:

The Weird Fifth Dimension
Just as the third dimension may be incomprehensible to an inhabitant of the second dimension, so the fifth dimension is very difficult for us to understand, because we are trying to comprehend it from a consciousness rooted in a base assumption of space-time; our minds are conditioned to believe in a linear world of comfortable absolutes. According to these core beliefs, something cannot be in two places at once, however, quantum physics — the science of the subatomic — shows us that it can, and does. Our beliefs limit our perception, and define what is possible in our world.

Our minds may be constrained by our conception of linear timelines and absolutes, but a fifth dimensional being may see infinite numbers of potentials growing from each of a multiplicity of instances. Imagine that you are standing in a room with two facing mirrors: you will see an infinity of your reflections in each direction. This is a metaphor for a singular timeline representing the 4th dimension.

Now, add a couple more facing mirrors on the other walls. Each of those reflections on the first timeline represents a potential you that is now mirrored on its own timeline in the opposite direction. Multiple instances of each you are reproduced and reflected in all directions; each potential choice point in turn producing an infinity of its own possibilities. The fifth dimension could be called a “probability space.” Why is this important? Because probability allows change in more than one direction; causality can move backwards as well as forwards, meaning that you can change the past as well as the future (even though past and future are mere concepts).

In 2014, a very interesting film named Interstellar explored the concept of the fifth dimension. In the movie, the future version of humanity that has evolved to higher dimensional awareness comes “back” to save us. The hero, Cooper, is trying to understand where he is when he enters the tesseract (four-dimensional hypercube). He sees his daughter’s bedroom, showing a kaleidoscope of potential instances.

Rob Bryanton said...

Hello, aliyahs art, thanks for your great note and best of luck with your book! I have one suggestion to propose - to further imply the more fluid nature of the fifth dimension versus the linear quality of our bodies moving through 4D space-time as seen in your first and second mirrors reflecting back upon each other, what if the third and fourth mirrors you add were warped like fun house mirrors? Then, as you moved around you would be able to see a constantly changing vista as the differently angled surfaces reflected back upon one another. This reminds me of one of my personal favorite blog entries, "You Have a Shape and a Trajectory": http://imaginingthetenthdimension.blogspot.ca/2009/02/you-have-shape-and-trajectory.html

Thanks for thinking deeply about these ideas!

Rob