The context for this page: On the investing in nanotechnology page, I mentioned some things that could be done with nanotechnology and related technologies. The third was the development of a new source of energy: Eventually somebody will invent a transducer that will be a direct link between the subatomic world and our world, so atomic energy can be brought up here to our level in a useful form, not as heat but as coherent energy.
I don't know how to do it. Not yet. But here are some thoughts that may point in the right direction.
The way to understand quantum physics is to stop listening to the older generation of physicists who tell you "This is weird, it's crazy, the world can't be like that, God doesn't play with dice, blah blah blah..." Turn those voices off, take a deep breath, and just accept the fact that atomic reality is what it is. It makes perfect sense if you accept it on its own terms. Yes, Professor Feynman, the world is like that. Yes, Professor Einstein, "spooky action at a distance" does occur. So what? Why does it bother you? What's spooky about it?
Electrons are not objects in three dimensional space, they are something else, a different kind of entity altogether. Not weird, just different. They are what they are. There's no use expecting them to be anything else. Their domain is as real as ours. Neither is any more weird than the other. The next step in physics will be taken by a new generation of scientists (quantum geeks) who have developed their intuition for the quantum domain as well as the classical domain.
Try going over to the other side of the window and looking back, i.e. looking at things from the inside out. What does our world (the macroscopic three dimensional world) look like from an electron's point of view?
Putting it mathematically, what does R3 look like from C2 ?
In other words, what does a space of three "real" dimensions look like from a space of two "complex" dimensions? The latter is actually a four dimensional space, since each complex dimension has two components, but C2 isn't the same as R4.
R3 isn't a subspace of C2. Nevertheless they do coexist and interact with each other. The question is how.
In the 15th century, artists learned to imagine and draw the world in three-dimensional perspective. That was a giant step at the time. Now we need to take the next step, and learn to think in two complex dimensions. We have to develop an easy familiarity with C2. It's like becoming fluent in a language. When you learn German, you don't just memorize the vocabulary, you immerse yourself in it and learn to think in German. That's what we have to do with C2.
We also have to learn to go back and forth easily between C2 and R3. (This will probably require seeing both of them as subspaces of some higher space.) Then the quantum domain will be open to us, and we can tap into its energy.
Don't tell me it can't be done. It's no harder for us than 3D was for Brunelleschi.
Since the 1920's it has been known that protons, electrons, etc. are not really particles at all, they are entitities which sometimes appear to be particles and other times appear to be waves. Physicists say there is a "wave-particle duality." They say that, but they don't really believe it. If you look in any college catalog, in the physics department, you will find courses about "particle physics." They also have courses about waves, but those courses are concerned with sound and electromagnetic waves, not electrons and protons. If you want to learn about protons, you have to sign up for "particle physics." There are books and journals devoted to "elementary particles," but you never see books about "elementary waves." After more than 75 years, we still think of them as particles.
We aren't really going to get anywhere with this subject until we start taking seriously the fact that they are waves. Of course they aren't just waves, but at this point it would be a good idea to overemphasize the wave aspect and think of them as primarily waves which under some circumstances behave like particles.
In nanotechnology (as conceived by Eric Drexler) the idea is to completely ignore the wave aspect and treat atoms as parts for 19th century machines. That's why I describe his machines as horseless carriages.
Suppose you take seriously the idea that in the quantum domain everything is a wave. How do you build a machine out of waves? What would such a thing look like?
Music is an articulated structure composed of waves. It's not obvious what music has to do with energy, but then it never occurred to anybody that mass had anything to do with energy until Einstein made his famous imaginative leap. Real nanotechnology will arrive when we stop thinking about gears and bearings and start thinking about fugues and dances.
Human speech is also an articulated structure composed of waves. There is no reason why language couldn't exist in the quantum domain. The idea that language has something to do with energy is even more of a stretch, but that's one of the things I'm pursuing.
Even if you can design and build machines in the quantum domain, that's only half the problem. The other half is how to build an interface between the quantum domain and the macroscopic domain.
Michael Faraday's great insight was that electricity and magnetism work at right angles to each other. They are orthogonal. That's what enables us to get leverage on them and make motors and generators. The quantum domain and our domain are also "orthogonal" in some nonobvious sense, and that may be the key that lets us create a linkage between them.
In the subatomic world of waves, there are no individual objects. Electrons are exact clones. In programming, when you have a pattern of bits you can make any number of copies of it, and they are exactly the same. Subatomic waves are like that. Electrons are indistinguishable from each other. When objects become unique and distinguishable, you have crossed the boundary and entered the macroscopic world, our world. This observation may be a clue to finding the way into Alice's rabbit hole (and the way back out).
1. Peter F. Strawson, Individuals: An Essay in Descriptive Metaphysics. Strawson was one of John Searle's teachers. Individuals is one of the best philosophy books from the mid-twentieth century. The most interesting thing for our purposes is chapter II, "Sounds," in which he imagines a world of sounds and tries to work out the metaphysics of such a world. I will have an extended review of this book the next time I update this page.
2. R. I. G. Hughes, The Structure and Interpretation of Quantum Mechanics. At the beginning of section 1.7, Hughes says "To echo Eco, every book defines the role of its ideal reader. Even so, some do it less subtly than others. Here are a few problems on the space C2."
In other words, an ideal reader of this book will work these problems. Other readers are wasting their time. There is no use proceeding with the rest of the book (or any other book about quantum mechanics) until you get this section nailed down.
3. Sin-Itiro Tomonaga, The Story of Spin - A book about how quantum physics got to be the way it is, written by one of the pioneers who was there.
4. The Flash Math Creativity site. Check out these animations:
There are lots of ways to do graphics, but Flash seems to be emerging as the program of choice for out of the box mathematics. The fmc site doesn't have much mathematical content yet, but that can be fixed. What needs to be done, of course, is to animate the mathematics of the quantum domain, starting with section 1.7 of the Hughes book. (There is a book called Visual Quantum Mechanics which attempts to do something along these lines, but it's pretty dull.)
The animations on the fmc site indicate what math looks like in the mind's eye, in my mind at least. They point in the direction I want to go. The idea is to get away from the standard classroom scenario in which the wooden math teacher stands there lecturing to a room full of bored students, repeating the same clichés teachers have been repeating for decades if not centuries. As Aristotle said: "Let's make a fresh start!"
What I want to do is create interactive animations and VR environments that will enable us to develop our intuition for the quantum domain, and beyond that, to learn new ways of thinking that will lead us to transhuman consciousness or hyperlucidity (see the Singularity page).
That, after all, is the point of investing in nanotechnology, or any new technology, or anything else. I want to put myself in a position where I can do that.
Note added in the spring of 2006.
This page has been dormant for a couple of years, but I have finally turned my attention to it. I have deleted some of the "references" that were here before.
As I said above, the FMC site does not have much mathematical content yet. I have written a new page about what kind of content should be added: Riemann for Anti-dummies: Introduction and Critique. This is about Leibniz, Gauss, Riemann, V.I. Arnold, and their way of doing mathematics, which is quite different from what most of us are taught. I think the Gaussian way of doing math will be essential for new breakthroughs in atomic physics, or, more precisely, in femtochemistry. I think that is where coherent energy will come from.