Paper people?

So then the question appears: could we be like the beings confined to the 2-dimensional flat universe, unable to perceive that some of the phenomena we encounter are actually arising from events happening in higher dimensions? In effect, are parts of our universe actually 3d "cross-sections" of higher dimensional objects in just the same way our fingers would be perceived as distinct circles in a 2-d world?

A lot of physicists say yes. String theory (or its current incarnation M-theory) maintains that everything in the universe, all matter and energy, is composed of extremely tiny strings (or membranes) of energy. These objects are way smaller than atoms, protons, and quarks and are the building blocks of everything.

How can one string or membrane create all the different types of particles that make up our universe? As it turns out, the strings vibrate the same way cello strings vibrate. If a string vibrates at a certain frequency, it creates a gluon. If it vibrates at a different frequency, it creates some other subatomic building block particle. I really don't know all their names.

Now the interesting part: what determines the frequency at which the strings vibrate? How does the string choose the "note" it plays? Ok, hold onto your brain. In order for M-theory to describe the universe we observe, it requires that the universe be composed of not just the 3 spacial and 1 time dimension we know and love, but rather 11 dimensions: 10 spacial dimensions and 1 time dimension.

If this is the case, it means that there are 7 dimensions existing alongside of us that we just can't perceive just like a 2d being confined to living on a super-thin paper universe could never "look up" and see us.

Take a second. Breathe. Make a face like your brain just swallowed sour milk.

Moving on. So the frequency of the vibrations of the strings is determined in a similar way to how we choose the pitch of a string on a cello. To change the pitch of a cello note, we move our finger which lengthens or shortens the vibrating section of the string. In a similar way, the path the string takes through these 7 invisible dimensions determines the frequency of the string. Different routes and orientations through the 7 dimensions lead to different "pitches" and therefore different particles.

So, some questions I have been grappling with:

1. This theory sounds incredibly unbelievable. Is it true? Answer: not sure. M-theory does apparently accurately describe many phenomena we observe in the real world and it would unify previously conflicting theories of general relativity and quantum mechanics. However, the strings and branes it describes are so small that, until recently we had no way to observe them directly. Apparently the new collider at CERN promises to be powerful enough to detect some particles that M-theory predicts to exist. If those particles (which I believe are called "sparticles") are detected, it would be strong evidence to support M-theory.

2. Why 11 dimensions? Why not 5 or 23 or 47? Basically, 11 is the number that makes the equations work. When they use 11 as the number of dimensions, the equations that pop out accurately describe the particles and interactions we observe in our universe.

3. Why can't we see these other 7 spacial dimensions? My answer: it is impossible for someone at a lower number of dimensions to ever directly perceive a higher number of dimensions. If we were all 2d beings living on an infinitely thin sheet of paper that was floating around on a breeze in my backyard, we would have no idea that we were in fact moving through a 3d world since we could never look up or down.

Physicist answer: It's worse than that. The 3 spacial dimensions we know are special because they have been expanded to a huge size. Which is nice. Gives us room to stretch our legs and for planets to, you know, be big and fly around. The other 7 dimensions are, in contrast, very, very tiny. In fact, each string vibrates in its own personal 7-tiny dimensions (and in our 3 dimensions as well, of course.) This means that there are an almost infinite number of tiny 7d universes attached to every single point of our 3d universe. And the only resident of these tiny 7d universes is a string, just hanging out and vibrating. Oh, these 7d mini-verses are modeled by a mathematical object called a Calabi-Yau manifold. That's the picture at the top of this post. I think it's pretty.

4. Why do the extra 7 dimensions have to be tiny/compactified/folded up? When I was first reading about M-theory, it seemed to me that physicists claimed that they were all folded up and tiny to explain why we don't perceive them. But for the reasons I laid out in the first part of the previous questions, I think the other 7 dimensions would be imperceptible to us even if they were as large as our native 3 dimensions. As it turns out, there's an additional reason they have for why the other 7 dimensions have to be tiny. From what I understand, it has something to do how fast the force of gravity decreases as objects get farther apart. I think the argument goes that if the force of gravity were radiating into more than just 3 dimensions, it would get weaker much faster than we observe. I don't really understand this explanation for the following reason. Maybe the force of gravity is much stronger than we think and a lot of it does dissipate into the other 7, expanded dimensions. All the rules we have for how gravity behaves could just be describing how gravity dissipates/moves in our 3 dimensions. It seems like the arguments claiming that gravity would dissipate more slowly between distant bodies if there were more than 3 expanded dimensions all start from the premise "Given that there exists the same amount of gravity between two bodies as we have in a 3d universe, the predicted force would be weaker than the observed force of gravity." I have a problem with the "Given" in that argument. How do we know that gravity isn't actually much more powerful than it seems to us, but that much of its force is being bled off into higher dimensions? If the gravity "bleed effect" obeyed consistent rules, I don't see why we shouldn't have the consistent rules for how gravity behaves in our 3 dimensions AND have the other 7 dimensions be just as expanded as our own. But I admit, I don't have a very clear understanding of this issue. Hopefully I will find someone who knows the answer (and can explain it in a comprehensible way) soon.

5. Why do I care whether the other 7 dimensions are tiny and folded up or big and expanded? Going back to the 2d sheet-of-paper universe example from the previous post, we had a flat universe that i stuck my fingers through. The residents perceived this as 5 separate circles. They lacked the ability to see that, in a higher dimension, those 5 circles were actually all connected to each other. If any of the other 7 dimensions are expanded, then it is possible that different events/phenomena/energy in our universe could be connected to each other in higher dimensions. This would mean that things that seem separate might actually be manifestations of a single, unified phenomenon occurring in a 4th, 5th, or 6th spacial dimension. To me, this is a fascinating possibility.

If, on the other hand, the other 7 dimensions are compactified, then there is no possibility of connection since there is not a single, unified 7 dimensional universe for things to potentially be connected in, but rather a nigh-infinite number of tiny, individual 7d mini-verses that would all be cut off and independent from each other. In this case, there could be no connections in higher dimensions because even the strings couldn't interact with each other in the higher dimensions. This possibility seems so much less exciting to me.

6. What are the strings made of? If strings make all the forces/energy in the universe, how can strings be made of "energy?" I have no idea what the answer to this question is and I have not seen any discussion of it in any of my admittedly limited reading on the topic.

Dimensionality

The first topic I want to lay out is an understanding of dimensionality. We perceive a four dimensional universe: three spacial dimensions and one dimension of time. For the moment, I want to set time aside because, as dimensions go it is weird and prickly and will, I am sure, get its own post or 50.

The question I'd like to explore here is how a higher dimension phenomenon would appear to an observer perceiving a lower dimension universe. Because it is difficult to envision more than 3 spacial dimensions, I would like to begin by considering the questions "If a three dimensional being interacted with a two dimensional universe, how would the residents of the 2D universe perceive this interaction?"

To begin thinking about this, I imagine a two dimensional universe, something like an infinitely thin sheet of paper. Though the surface of this universe could be any shape, let's imagine it is flat and is actually the size and shape of a piece of notebook paper.

What is life like for the residents of this universe? Well, they can only move forwards/backwards or left/right. There is no such thing as going up or down. The residents of this universe could be any shape, but let's assume they are sentient triangles. Growth in this universe would not be growing taller and in volume like we do, but rather growing in perimeter and area. If anyone has read Flatland by Abbott, you are familiar with this set up.

Objects in this flat universe would be other shapes: squares, pentagons, etc. Unless there was a gap in the perimeter of one of these objects, the residents of the 2D universe would never be able to see the interior of any of these objects. Houses in this 2D universe might look like an architect's blueprint...certainly would lower the cost of new builds. An interesting question might be what blueprints drawn up by the 2D residents would be like...just smaller versions of the actual 2D house?

Ok, so hopefully we have a good idea of what the 2D universe is like. Now the question is, how do the residents of this universe perceive an encounter with a 3D being? Specifically, let's imagine that I take my hand and shove my fingers through the sheet of paper that is their universe. How would they perceive my fingers?

Well, my fingers would appear to be 5 seemingly separate circles that appear in their universe. One of the 2D-ers might be looking at the cross-section of my thumb while another might be looking at the cross-section of my pinky finger. Because they can't "look up" to see the rest of my hand, these 5 mysterious circles would seem utterly unrelated to each other.

Of course, being 3D, I would be able to look down on their notebook paper universe and watch them poking and prodding at these objects. Interactions with these circles could be quite strange indeed. If they poked my thumb, I might twitch my pinky. To them the thumb "circle" and the pinky "circle" might seem be located very far apart (depending on how small the 2D residents are) so to see one circle react to a poke given to a separate circle far away would certainly seem mystifying, perhaps even "spooky action from a distance."

So the question is, how could the 2D beings ever deduce that my finger circles are actually 5 separate manifestations of a larger, higher dimensional structure? Even if I wanted to solve the mystery for the 2D beings, how could I tell them? As a 3D being, the most I could ever show in their 2D universe is a cross-section of myself which would make speaking to them difficult, not to mention that they could only perceive the pieces of the soundwaves that my voice made that happened to lie in their plane. I suppose that if I were really motivated, I could learn their language and try to write them a note. Of course, to execute that, I would have to be able to use a 2D writing utensil to write either a 1 or 2D message. Which, as a 3D being would prove quite difficult.

That lays out the basic metaphor. Let's change it a little. Instead of imagining my 5 fingers intersecting with the 2D universe, let's imagine a hand with a nigh infinite number of tiny fingers piercing the 2D universe. In fact, the entire 2D universe and everything in it is made up of one of these tiny fingers. I am now imagining the 80's novelty "pin impression" item where you could press your face or hand into a bed of hanging pins and see the image arise on the other side. But in this 2D universe, the residents are so much bigger than the pins that the surface of their universe seems smooth to them and they don't see that themselves and every other object is actually made out of these tiny pin fingers.

Of course, eventually if they developed powerful magnification techniques, they might figure it out. Anyway, the pin fingers that happened to fall inside of a 2D being would appear to belong to that particular being, those outside to another object or being. In reality however all of the pin fingers are attached to the same hand and source in 3D.

This is not to say that the 3D pin fingers have any will or volition of their own per se. The only thing we are saying is that the substance of the 2D universe is actually made up of tiny cross-sections of these 3D pin fingers. The pin fingers might be totally inert.

BUT, the fact that the pin fingers are all attached to the same hand in the 3D universe could have bizarre implications for the 2D beings, just like poking my thumb and seeing my pinky twitch would have seemed odd. If all the pin fingers are connected in 3D, then certainly information could be passed from the pin fingers in one being to the pin fingers in another seemingly separate being very quickly, even if the recipient were far away. This would certainly seem inexplicable and weird to the 2D beings.

So this brings me to one of my primary hypotheses: the universe as we perceive it is composed of building blocks that are of a higher dimension than the ones we perceive. We are like the 2D beings that perceive the pin fingers (assuming we detect them) and other objects/forces as separate entities when in fact the substance of the universe as we perceive it is actually a 3D (4 if you include time) cross-section of a potentially linked higher dimensional space. If this is the case, then it raises a lot of questions about how we might be connected, if at all. Perhaps more importantly, it begs the question of what type of super-structure our universe is a "cross-section" of?

Why?

This blog will be about my overlapping interests in several areas and my efforts to organize them into some sort of coherent and plausible theory about what the world actually is. So in general I will be geeking out about physics, math, religion, philosophy, and neuroscience/psychology. My hope is that in writing my ideas down, I can work them together and get feedback from people who are much better subject area experts than myself.