Yesterday, I wrote:
Well, the power just went out, so it's time for me to pack up my Mac and head out to a cafe with WiFi where I can work on my novel in front of people and get this posted. The weird thing is, while it's likely going to take an hour at least from the time I finish writing this paragraph until it actually posts on the internet, there is no perceived delay from whoever reads this, because as far as you're concerned, the post didn't exist until it was published, though it already existed for me.
Um. Yeah. I'm sure someone who's actually studied physics is going to knock me around for that, but since my knowledge of the field is limited to what I've picked up on my own, it's a fun thought exercise.
Okay, little post, go sit in an eigenstate for the nice people.
Your analogy is reasonable. The post existed on your laptop while you drove to the coffee shop, in a state such that it was stable but not portable. Once you got to the coffee shop, by connecting to the internet, you promoted it to an energy state where it could slide easily through the intertubes to our screens.
Since quantum mechanics describes ONLY the behavior of the very small, it has problems when extended directly to the macroscopic (which the idea of Shroedinger's cat is an illustration). You extended the notion as well as it could be.
The eigenvalue then is just a scalar logical value indicating if the post is visible to the world. Every eigenvalue has to have a corresponding operator; the operator is a complicated set of tests of whether or not if you point our browser at wilwheaton.typepad.com, you get a certain character string that's in the post.
Why yes, I am procrastinating, why do you ask?
Even though I don't understand the math behind quantum physics, I have a good enough grasp of the theory behind quantum physics to allow me to follow along when the math is discussed. Put another way: I know enough French and Spanish to put together what someone is telling me, but not enough to actually sit down and compose a letter in that language.
I'm sure I've just oversimplified the whole thing, and insulted a lot of actual scientists and mathematicians, so let me apologize for that before I continue, because I think I'm about to make it even worse.
I was easily bored as a kid. I wasn't athletic, strong or coordinated, but I was smart and I loved to read. I still enjoyed playing tag, hide and seek, and riding bikes, but none of that stuff satisfied me the same way that exploring imagined worlds in my mind did. Those imagined worlds were usually delivered in the form of Science Fiction and Fantasy books, within D&D modules, and occasionally created (or spun off from existing imagined worlds) using action figures. (I guess it's no surprise, then, that I make my living and found my place in life using my imagination.)
I always loved exploring strange new worlds in books and magazines (Dear Asimov's, I never thought it would happen to me, but …) and there was even a time in my late teens when I actively sought out all the weird conspiracy, occult, UFO and supernatural stuff I could find (I truly despise that crap today) because even though I knew it was bullshit, it was yet another weird and fantastic imagined world to explore.
omeone (I think it was my brother) suggested that I read A Brief History of Time. I picked it up, read it in just a couple of days, and realized that my life could be divided into before I read it, and after I read it. On my next trip to the bookstore, I went straight to the science section, and looked for something – anything – to continue my education.
My eyes fell on a book with an interesting cover, and a provocative title: Hyperspace: A scientific odyssey through parallel universes, time warps, and the 10th dimension. It was written by a guy called Michio Kaku. I pulled it off the shelf, and after just a few pages, I was hooked.
There's a story in Hyperspace, right at the beginning, that I'm going to paraphrase. It's the story that grabbed my attention, captured my imagination, and fundamentally altered the way I thought about the nature of existence. I already had "before and after" with A Brief History of Time, and when I got to the end of this story, I had "before and after I read about the fish scientists." The story goes something like this:
In San Francisco, there's this botanical garden, and near the entrance there is a pond that's filled with koi fish. Dr. Kaku describes standing there, looking at the fish one day, and wondering what it would be like if the fish had a society as complex and advanced as our own, but the whole thing was confined to the pond, and they had no idea that there was a whole other world just beyond the surface of the water. In the fish world, there were fish scientists, and if a human were to pluck one of them from the pond, show it our world, and return it to the pond, it would go back to the other fish scientists and say, "Guys! You're never going to believe this. I was just doing my thing, and suddenly, this mysterious force pulled me from our world and showed me another, where the creatures don't need gills to breathe, and walk on two legs!"
The other scientists would look at it, and ask it how it got to this new world, but it wouldn't be able to explain it. They'd want the scientist to recreate it, but it wouldn't be able to. The fish scientist would know, however, that the other world was there, and that there was something just as complex as life in the pond on the other side of some mysterious barrier that they couldn't seem to penetrate.
I'm sure I've mangled the story, but that's essentially what I remember from it. I thought, "Well, shit, if there could be a world like that in the pond, maybe we are in something else's pond!" I didn't know if it was possible, I didn't know if it was just science fiction, but I didn't care. It was this incredible possibility, and my world opened up again. I felt like I'd been granted membership in a secret society. I devoured the book, and I began to think about the nature of existence in ways that I'd never even considered before. When I finally read Flatland a few years later, I was blown away that Abbot had written essentially the same story a hundred years earlier, in 1884, and I was thrilled that I could actually understand it.
My elementary school teachers were real good at putting the fear of God into us kids, but they were just horrible at teaching us math. I tried and tried, but I never understood it, and "you have to learn this because you have to learn it" wasn't the type of inspiration that worked for me. Even today, I'm not very good at math, never having found that teacher who could translate it into something I could actually use and appreciate.
Growing up, I was a creative kid, an imaginative kid, and while I loved reading and learning about scientists and mathematicians, I never had a teacher or tutor who could help teenage me understand their work the way I understood their lives. (NB: My tutor while I was on Star Trek, Marion, who took me through most of high school, did everything she could to help me get excited about math, but to borrow from a parable: that ground in my brain had never been cultivated, and it just wasn't fertile enough to bear fruit.)
My lack of mathematical ability held me back in science, and it prevented me from ever studying physics or astronomy at anything exceeding the "for dummies" level. Here's a sad and embarrassing truth: I still can't sit down and develop equations for things, I struggle to calculate simple problems that my kids can do in their heads (they were taught math in a fundamentally different way than I was) and few things make me feel as stupid and frustrated as a simple algebra problem.
But when I sit down to read books like Hyperspace, articles about the LHC, anything my friend Phil Plait writes, or comments like the one I quoted above, I understand what they're talking about. I get excited, and take a look at a world that seems fantastic and imagined, but is actually real and right here.
I seem to have wandered away from the reason I sat down to write this post, so let me try to bring it all back together: I love exploring fantastic worlds that only exist in books and my imagination. But I also I love exploring the real world, which is so amazing, it just seems imagined.
(I once read a story about this for an audiobook. I forget the title, but it was about a kid who wanted to leave Earth with a dimension-hopping guy to explore the universe, and the dimension-hopping guy tells him that he shouldn't leave Earth for parts unknown until he really explores all the wonderful and incredible things that Earth has to offer, because due to the laws of dimension-hopping, it's a one-way trip. I wonder if that's still in print? I'd love to listen to it.)
I still wish I had a better understanding of the science and math that makes understanding and exploring the most fantastic parts of our real world possible, but until I do, I'm happy I have a pocket phrase book and a tourist map to help me get around a little bit.