I’m entering the second half of Brian Greene’s The Elegant Universe, and last night read a beautiful, resonant section about Calabi-Yau dimensions. (That page is in French, though Google translate seems to be handling it OK; the image above is taken from that page’s reproduction of the image in the book.)
“If you sweep your hand in a large arc,” Green writes, “you are moving not only through the three extended dimensions, but also through these curled-up dimensions. Of course, because the curled-up dimensions are so small, as you move your hand you circumnavigate them an enormous number of times, repeatedly returning to your starting point.”
Is it just me, or does this relate back to the way that a positron might take an infinite number of paths through the universe, and how everything is actually a probability rather than a certainty? The implication is that there are an infinite number of states/positions/whatever they’re called that a subatomic particle could take through the twists and turns of the tightly-curled Calabi-Yau dimensions (Greene has a great series of diagrams/figures/images that show these features), but the only one that actually is “correct,” i.e. results in the physical manifestation we experience, is the one in which every single subatomic particle lines up exactly as it has.
This also brings to mind some of what Greene said earlier in the book about how it’s amazing that every subatomic weight/force is just exactly what it needs to be to balance everything else.
What I’m enjoying about this book and its propositions (as opposed to what I’m not enjoying – the sometimes dreadful analogies and the too-light touch of its editor concerning specific word choices) is that it really makes me think about existence as a homogeneous stew, rather than as disconnected and distinct particles.