Math II (Несколько текстов для зачёта), страница 23

eBusiness Essentials

And now for something completely different--a clever bit from those wacky British comedians, the boys of BT, or British Telecom. While BT richly deserves to be laughed at for claiming to own hyperlinking, and even filing a lawsuit against an ISP to try to enforce its claim, the company is not all patent lawyers, and some useful work does come out of the company (I mean besides the invention of hyperlinking). As evidence of this, I mention eBusiness Essentials.. Technology and Network Requirements for the Electronic Marketplace, by Mark Norris, Steve West, and Kevin Gaughan (John Wiley & Sons Ltd. BT Series, Chichester, 2000; ISBN 0 471 85203 1).

The book is written for "planners, engineers, managers, and developers" and it seems to hit the right technical level for that mix of readers most of the time. The range of material that is covers is pretty broad: the different models of the electronic marketplace, many different kinds of catalogs and how to implement them, payment systems, trust and security, B2B and the need to move beyond traditional EDI in the supply chain, integration of diverse elements of an e-business, and an overview of underlying technologies and standards.

The overviews are helpful to one who is new to some or all of the subjects. I had just finished reading the book when my partner Nancy called and said she was filling out a form and needed to know what our EDI strategy was. Before reading the book, I could have told her that EDI stood for Electronic Data Interchange and that was about it. After-reading the book, I could chat knowledgeably about different EDI strategies, and tell her that we don't have one, and why we don't want one.

The book isn't a cookbook on setting up an e-business; the cookbook approach necessarily constrains your options, and that's not what this book is about. I was impressed with the variety of approaches presented and pleased to see some very low-tech implementations presented as serious options. For a retail business that already has systems in place for most of the operations of an e-commerce site, it may make sense to piggyback the e-commerce site onto the existing system initially with little or no effort to take advantage of the efficiencies of e-commerce, even to the point of keying in credit-card numbers into a card processor manually. Converting a working manual system into an electronic one may be easier than building the electronic one from scratch.

The two case studies worked through in the book are from the other end of the spectrum--monster e-commerce implementations from Federal Express and Cisco. It would be daunting to delineate the e-commerce strategy of either company, and the book scarcely tries; the case studies chapter is pretty skimpy and unenlightening.

Overall, though, the book is accurate, broad in its coverage, and willing to take a stand when appropriate. I think it's worth a look by anyone starting an e-business.

Of course, the most important piece of advice for anyone starting an e-business is never, ever refer to it as a dot-com. But you already knew that.

100 YEARS OF QUANTUM MYSTERIES

Source: Scientific American, Feb2001, Vol. 284 Issue 2, p68, 8p

Author(s): Tegmark, Max; Wheeler, John Archibald

As quantum theory celebrates its 100th birthday, spectacular successes are mixed with persistant puzzles

In a few years, all the great physical constants will have been approximately estimated, and...the only occupation which will then be left to the men of science will be to carry these measurements to another place of decimals." As we enter the 21st century amid much brouhaha about past achievements, this sentiment may sound familiar. Yet the quote is from James Clerk Maxwell and dates from his 1871 University of Cambridge inaugural lecture expressing the mood prevalent at the time (albeit a mood he disagreed with). Three decades later, on December 14, 1900, Max Planck announced his formula for the blackbody spectrum, the first shot of the quantum revolution.

This article reviews the first 100 years of quantum mechanics, with particular focus on its mysterious side, culminating in the ongoing debate about its consequences for issues ranging from quantum computation to consciousness, parallel universes and the very nature of physical reality. We virtually ignore the astonishing range of scientific and practical applications that quantum mechanics undergirds: today an estimated 30 percent of the U.S. gross national product is based on inventions made possible by quantum mechanics, from semiconductors in computer chips to lasers in compact-disc players, magnetic resonance imaging in hospitals, and much more.

In 1871 scientists had good reason for their optimism. Classical mechanics and electrodynamics had powered the industrial revolution, and it appeared as though their basic equations could describe essentially all physical systems. But a few annoying details tarnished this picture. For example, the calculated spectrum of light emitted by a glowing hot object did not come out right. In fact, the classical prediction was called the ultraviolet catastrophe, according to which intense ultraviolet radiation and x-rays should blind you when you look at the heating element on a stove.

The Hydrogen Disaster

In his 1900 paper Planck succeeded in deriving the correct spectrum. His derivation, however, involved an assumption so bizarre that he distanced himself from it for many years afterward: that energy was emitted only in certain finite chunks, or "quanta." Yet this strange assumption proved extremely successful. In 1905 Albert Einstein took the idea one step further. By assuming that radiation could transport energy only in such lumps, or "photons," he explained the photoelectric effect, which is related to the processes used in present-day solar cells and the image sensors used in digital cameras.

Physics faced another great embarrassment in 1911. Ernest Rutherford had convincingly argued that atoms consist of electrons orbiting a positively charged nucleus, much like a miniature solar system. Electromagnetic theory, though, predicted that orbiting electrons would continuously radiate away their energy and spiral into the nucleus in about a trillionth of a second. Of course, hydrogen atoms were known to be eminently stable. Indeed, this discrepancy was the worst quantitative failure in the history of physics--underpredicting the lifetime of hydrogen by some 40 orders of magnitude.

In 1913 Niels Bohr, who had come to the University of Manchester in England to work with Rutherford, provided an explanation that again used quanta. He postulated that the electrons' angular momentum came only in specific amounts, which would confine them to a discrete set of orbits. Thc electrons could radiate energy only by jumping from one such orbit to a lower one and sending off an individual photon. Because an electron in the innermost orbit had no orbits with less energy to jump to, it formed a stable atom. Bohr's theory also explained many of hydrogen's spectral lines--the specific frequencies of light emitted by excited atoms. It worked for the helium atom as well, but only if the atom was deprived of one of its two electrons. Back in Copenhagen, Bohr got a letter from Rutherford telling him he had to publish his results. Bohr wrote back that nobody would believe him unless he explained the spectra of all the elements. Rutherford replied: Bohr, you explain hydrogen and you explain helium, and everyone will believe all the rest.

Despite the early successes of the quantum idea, physicists still did not know what to make of its strange and seemingly ad hoc rules. There appeared to be no guiding principle. In 1923 Louis de Broglie proposed an answer in his doctoral thesis: electrons and other particles act like standing waves. Such waves, like vibrations of a guitar string, can occur only with certain discrete (quantized) frequencies. The idea was so unusual that the examining committee went outside its circle for advice. Einstein, when queried, gave a favorable opinion, and the thesis was accepted.

In November 1925 Erwin Schr6dinger gave a seminar on de Broglie's work in Zurich. When he was finished, Peter Debye asked, You speak about waves, but where is the wave equation? Schr6dinger went on to produce his equation, the master key for so much of modern physics. An equivalent formulation using matrices was provided by Max Born, Pascual Jordan and Werner Heisenberg around the same time. With this powerful mathematical underpinning, quantum theory made explosive progress. Within a few years, physicists had explained a host of measurements, including spectra of more complicated atoms and properties of chemical reactions.

But what did it all mean? What was this quantity, the "wave function," that Schr6dinger's equation described? This central puzzle of quantum mechanics remains a potent and controversial issue to this day.

Born had the insight that the wave function should be interpreted in terms of probabilities. When experimenters measure the location of an electron, the probability of finding it in each region depends on the magnitude of its wave function there. This interpretation suggested that a fundamental randomness was built into the laws of nature. Einstein was deeply unhappy with this conclusion and expressed his preference for a deterministic universe with the oft-quoted remark, "I can't believe that God plays dice."

Curious Cats and Quantum Cards

Schrbdinger was also uneasy. Wave functions could describe combinations of different states, so-called superpositions. For example, an electron could be in a superposition of several different locations. Schr6dinger pointed out that if microscopic objects such as atoms could be in strange superpositions, so could macroscopic objects, because they are made of atoms. As a baroque example, he described the now well-known thought experiment in which a nasty contraption kills a cat if a radioactive atom decays. Because the radioactive atom enters a superposition of decayed and not decayed, it produces a cat that is both dead and alive in superposition.

The illustration on the opposite page shows a simpler variant of this thought experiment. You take a card with a perfectly sharp edge and balance it on its edge on a table. According to classical physics, it will in principle stay balanced forever. According to the Schr6dinger equation, the card will fall down in a few seconds even if you do the best possible job of balancing it, and it will fall down in both directions--to the left and the right--in superposition.

If you could perform this idealized thought experiment with an actual card, you would undoubtedly find that classical physics is wrong and that the card falls down. But you would always see it fall down to the left or to the right, seemingly at random, never to the left and to the right simultaneously, as the Schr6dinger equation might have you believe. This seeming contradiction goes to the very heart of one of the original and enduring mysteries of quantum mechanics.

The Copenhagen interpretation of quantum mechanics, which grew from discussions between Bohr and Heisenberg in the late 1920s, addresses the mystery by asserting that observations, or measurements, are special. So long as the balanced card is unobserved, its wave function evolves by obeying the Schr6dinger equation--a continuous and smooth evolution that is called "unitary" in mathematics and has several very attractive properties. Unitary evolution produces the superposition in which the card has fallen down both to the left and to the right. The act of observing the card, however, triggers an abrupt change in its wave function, commonly called a collapse: the observer sees the card in one definite classical state (face up or face down), and from then onward only that part of the wave function survives. Nature supposedly selects one state at random, with the probabilities determined by the wave function.

The Copenhagen interpretation provided a strikingly successful recipe for doing calculations that accurately described the outcomes of experiments, but the suspicion lingered that some equation ought to describe when and how this collapse occurred. Many physicists took this lack of an equation to mean that something was intrinsically wrong with quantum mechanics and that it would soon be replaced by a more fundamental theory that would provide such an equation. So rather than dwell on ontological implications of the equations, most physicists forged ahead to work out their many exciting applications and to tackle pressing unsolved problems of nuclear physics.

That pragmatic approach proved stunningly successful. Quantum mechanics was instrumental in predicting antimatter, understanding radioactivity (leading to nuclear power), accounting for the behavior of materials such as semiconductors, explaining superconductivity, and describing interactions such as those between light and matter (leading to the invention of the laser) and of radio waves and nuclei (leading to magnetic resonance imaging). Many successes of quantum mechanics involve its extension, quantum field theory, which forms the foundations of elementary particle physics all the way to the present-day experimental frontiers of neutrino oscillations and the search for the Higgs particle and supersymmetry.