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.