HOMESTEADING IN HILBERT SPACE
More than a hundred years passed between Columbus' first, confused sighting of America in 1492 and the vanguard of English colonization, at Jamestown in 1607. A shorter interval separates us today from Planck's first confused sighting of the quantum world, in 1899. The quantum world is a New New World far more alien and difficult of access than Columbus' Old New World. It is also, in a real sense, much bigger. While discovery of the Old New World roughly doubled the land area available to humans, the New New World exponentially expands the dimension of physical reality.* (For example, every single electron's spin doubles it.) Our fundamental equations do not live in the three-dimensional space of classical physics, but in an (effectively) infinite-dimensional space: Hilbert space. It will take us much more than a century to homestead that New New World, even at today's much-accelerated pace.
We've managed to establish some beachheads, but the vast interior remains virgin territory, unexploited. (This time, presumably, there are no aboriginals.) Poking along the coast, we've already stumbled upon transistors, lasers, superconducting magnets, and a host of other gadgets. What's next? I don't know for sure, of course, but there are two everything-changers that seem safe bets:
• New microelectronic information processors, informed by quantum principles—perhaps based on manipulating electron spins, or on supplementing today's silicon with graphene—will enable more cycles of Moore's law, on several fronts: smaller, faster, cooler, cheaper. Supercomputers will approach and then surpass the exaflop frontier, making their capacity comparable to that of human brains. Improved bandwidth will put the Internet on steroids, allowing instant access from anywhere to all the world's information, and blurring or obliterating the experienced distinction between virtual and physical reality.
• Designer materials better able to convert energy from the hot and unwieldy quanta (photons) Sol rains upon us into more convenient forms (chemical bonds) will power a new economy of abundance. Evolution in its patient blindness managed to develop photosynthesis; with mindful insight, we will do better.
As we thus augment our intelligence and our power, a sort of bootstrap may well come into play. We—or our machines, or our hybrid descendants—will acquire the wit and strength to design and construct still better minds and engines, in an ascending spiral.
Our creative mastery over matter, through quantum theory, is still embryonic. The best is yet to come.
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*This is established physics, independent of speculations about extra spatial dimensions (which are essentially classical).
