His bike looked different, but I was not sure how. I unlocked my harness, cracked the bike seals, and forced myself outside onto the dock. As usual my legs were Jell-O. I wobbled my way along to Muldoon’s bike. I knocked urgently on the outside.
“Muldoon! Are you all right?” I was croaking, dry-throated. I didn’t seem to have enough moisture left in my body for one spit.
I hammered again. For a few seconds there was no response at all. Then the cropped head slowly lifted, and I was staring down into a puffy pair of eyes. Muldoon didn’t seem to recognize me. Finally he nodded, and reached to unlock his harness. When the bike opened, I helped him out. He was too far gone to stand.
“I’m all right, Trace,” he said. “I’m all right.” He sounded terrible, anything but all right.
I took another look at his bike. Now I knew why it looked different. “Muldoon, you’ve lost your shielding. We have to get you to a doctor.”
He shook his head. “You don’t need to. I didn’t get an overdose. I didn’t lose that shielding. I shed it on purpose.”
“But the radiation levels—”
“Are down. You saw the forecasts for yourself, the storm was supposed to peak during the Stage and then run way down. I spent most of last night fixing the bike so I could get rid of shielding when the solar flux died away enough. That happened six hours ago.”
I suddenly realized how he had managed that tremendous deceleration at the end of the race. Without an extra hundred kilos of shielding dragging him along, it was easy. I could have done the same thing.
And then I felt sick. Any one of us could have done what Muldoon had done—if we’d just been smart enough. The rules let you jettison anything you didn’t want, empty juice bottles, or radiation shielding. The only requirement is that you don’t interfere with any other rider. Muldoon had thrown a lot of stuff away, but by choosing a trajectory where no one else was riding, he had made sure he could not be disqualified for interference.
“You did it again,” I said. “How far ahead of me were you when you docked?”
He shrugged. “Two seconds, three seconds. I’m not sure. I may not have done it, Trace. I needed three seconds. You may still have won it.”
But I was looking at his face. There was a look of deep, secret joy there that not even old stoneface Muldoon could hide. He had won. And I had lost. Again.
I knew. He knew. And he knew I knew.
“It’s my last time, Trace,” he said quietly. “This one means more than you can imagine to me. I’ll not win any more. Maimonides is quite right, the Tour’s a young man’s game. But you’ve got lots of time, years and years.”
I had been wrong about the moisture in my body. There was plenty, enough for it to trickle down my cheeks. “Damn it, I don’t want it in years and years, Ernie. I want it now.”
“I know you do. And that’s why I’m sure you’ll get it then.” He sighed. “It took me eight tries before I won, Trace. Eight tries! I thought I’d never do it. You’re still only on your third Tour.” Ernie Muldoon reached out his arm and draped it around my shoulders. “Come on now, lad. Win or lose, the Tour’s over for this year. Give a poor old man a hand, and lets the two of us go and talk to them damned media types together.”
I was going to say no, because I couldn’t possibly face the cameras with tears in my eyes. But then I looked at his face, and knew I was wrong. I could face them crying. Ernie Muldoon was still my model. Anything he could do, I could do.
afterword: the grand tour
It would be a mistake to look for deep significance here. This is a lighthearted sports story. The fact that it happens to be a bicycle story set in space is almost irrelevant.
Why biking? Well, I grew up in Hull, a town in the north of England that happens to sit in the middle of a very flat area called the plain of Holderness. The biggest “hills” to be found in Hull were the river bridges and the railway bridges. It was a very benign environment for a push-bike. Even eighty-year-olds rode, creaking their way along flat streets that during the rush hour carried cyclists seven abreast. Automobiles were regarded as interlopers, resented and almost ignored.
Naturally, the big events of my youth were the casual weekend rides to the coast, and the competitive time trials. In the latter; riders were released at one minute intervals early on Sunday morning. We raced a 25-mile fixed course on the open road, trying to beat one hour; or, for the most successful, fifty-seven minutes or even fifty-five. It was forbidden to “slipstream” by riding close behind a truck. It was also extremely dangerous, but that wasn’t enough to discourage people, so observers were planted along the route to look for cheaters.
The reader will probably see Tour de Système in this story, and think Tour de France. But the memory for me is of brisk mornings in East Yorkshire, looping out on roads that carried me to the first gentle slopes of the Yorkshire Wolds. And then painfully back, convinced during the final five miles home that my legs were turning to iron and my heart was about to freeze in my chest.
.
——————————————————————————————————
article: classical nightmares…and quantum paradoxes
“…the quantum mechanics paradoxes, which can truly be said to be the nightmares of the classical mind…”
—Ilya Prigogine
1.THE MIGHTY ATOM
The theory of special relativity tells us that we cannot accelerate an object to move faster than the speed of light. Worse than that, it tells us that as we try to accelerate a body to speeds closer and closer to light speed, we must apply more and more energy because the mass of the accelerating object increases. The same theory tells us that we can’t send messages faster than light, either.
These results are unpopular in science fiction, where ways are needed to get from star to star quickly, cheaply, and easily, or at the very least to communicate over interstellar distances. This has led writers to seek a variety of loopholes. They include such things as:
warp drives—largely undefined, though there is usually a suggestion that the drives can warp space-time in such a way that points physically far apart in real space become closely separated in the warped space;
wormholes—there are singularities in space-time, formed by black holes; wormholes are connections between these black holes and white holes, and the intrepid traveler who enters a black hole will emerge from a white hole;
hyperdrives—which suppose that there are other space-times, loosely connected to ours, in which either the speed of light is far bigger than in our own universe, or the distances between points are far less. You move to one of these other spacetimes to do your traveling.
The advantage of these devices is obvious: they permit interesting stories. The disadvantage of all of them is that they have no relationship to today’s accepted physical theories (for instance, no one has ever fully defined a white hole, or seen any evidence that such a thing can exist). This does not mean that the devices cannot exist—only that they are very, very unlikely. Today’s theories will be supplanted by tomorrows, but surely not in any simple-minded way arranged for the convenience of science fiction writers. Warp drives and their relatives are varieties of wishful thinking.
A much better way to look for faster-than-light travel techniques is to seek the places where today’s theories are incomplete or, better still, inconsistent. For if two independent theories tell us two different and incompatible things, something must be wrong, and that is fertile ground for discovery.
Where incompatible theories meet, there may be loopholes. We want a particular loophole that allows an object to move from one place to another faster than the speed of light, or permits a piece of information to be transferred faster than light. There is one obvious place to look: at the meeting place of quantum theory and relativity. In the first part of this century, the quantum theory wa
s developed in parallel with, but almost independent of, the theories of special and general relativity. Despite sixty years of effort, the two have never been put consistently together in what John Archibald Wheeler, the physicist who among other things gave us the modern name “black hole” to the end-point collapse of massive stars, has termed “the fiery marriage of general relativity with quantum theory.”
Moreover, when we explore the bases of quantum theory we are fishing in very strange waters. The techniques allow us to compute the right answers, i.e., they seem to describe the way the universe behaves, but they often run counter to the way we feel things should behave. That’s our problem, of course, and not Nature’s. As the late and much-lamented Richard Feynman, one of the sparkling intellects of the century, put it, the problem “is only a conflict between reality and your feeling of what reality ‘ought to be.’ ”
Part of the difficulty is that, until recently, quantum theory seemed to be confined to describing what happened in the world of the very small—atoms, and electrons, and sub-nuclear particles far too little for us to have any hope of seeing them. There was thus no direct physical experience to guide us as to their behavior, and a simple extrapolation of intuition derived from large objects was likely to prove false.
In the next sections we will look at quantum theory and ask how the world would appear if atoms were big, say as big as a basketball. Before we roar with laughter at such a silly idea, we ought to look back forty-some years. When the first atomic bomb was dropped on Hiroshima on August 6, 1945, the average citizen knew not a thing about atoms. Even the name, “atomic bomb,” was evidence of public confusion. Every bomb since the invention of gunpowder was an atomic bomb, since it involved the chemical bonds between the outer electrons of atoms. The new bomb should have been called a “nuclear bomb”—but the media could get away with the term “atomic bomb” because few people seemed to know about atoms.
When a poll was made in 1945, asking the general public among other things how big they thought atoms were, “about the size of a tennis ball” was one popular answer. And have you ever heard the word “atom” before, Mr. & Mrs. Average Citizen? Well, it was the tide of a popular book, The Mighty Atom, by Marie Corelli (a book which had nothing to do with atoms in the scientific sense).
And how about the word “nucleus” applied to atoms? Sorry, that’s new to us.
The bomb was such a sensation that a number of truly amazing rumors made the rounds: e.g., that the bomb itself was far too small to be seen with the naked eye; that Albert Einstein—the one scientist the public had heard of—had personally piloted the plane that dropped the bomb. And my own favorite, the rumor, repeated over British radio, that the container for the first atomic bomb was designed by Bing Crosby. People seemed ready to believe anything.
(Before we laugh, ask if we are smarter now. A country that pays farmers to grow a crop that kills three hundred and fifty thousand of us every year, or cheerfully accepts astrology in the White House, can’t afford to do much mocking of anyone. I’d be interested to hear the answers if you held a poll today and asked people how big an atom is.)
My point is this: Most people knew nothing about atoms, and once they found out just how small atoms were, their amazement took a new direction. How is it possible, they said, for anyone to count, measure, and know the properties of objects that we can’t even see?
That is a very basic and reasonable question, and in some ways the general public was smarter than the scientists. There is no reason to expect that objects too small to see or touch should behave in any way like the large objects of everyday experience. In fact, they don’t. And therein lies quantum theory.
Before we can get to the quantum paradoxes and faster-than-light communications, we will have to say something about the theory itself: where it came from, what it means, why it’s needed.
2.THE BEGINNINGS OF QUANTUM THEORY
Quantum theory has been around, in much its present form, for over sixty years. The basic rules for quantum theory calculations were discovered by Werner Heisenberg and Erwin Schrödinger in 1925. Soon afterwards, in 1926, Paul Dirac, Carl Eckart, and Schrödinger himself showed that the Heisenberg and Schrödinger formulations can be viewed as two different approaches within one general framework.
It quickly became clear that the same theory allowed the internal structure of atoms and molecules to be calculated in detail, and by 1930, quantum theory, or quantum mechanics as it was called, became the method for performing calculations in the small world of molecules, atoms, and nuclear particles.
There have been great improvements since that time in computational techniques, and in our understanding of such things as nuclear models, nuclear scattering processes, and sub-nuclear structure. However, the basic ideas have not changed much since the late 1920’s; and the same mysteries that plagued and puzzled the workers of that time are worries now.
It is, in fact, fair to say that although we have recipes that allow us to compute almost anything we want to, underneath those recipes lurk deep paradoxes and open questions, and they have been there since the beginning. To quote Feynman again, “I think it is fair to say that no one understands quantum mechanics.” We are like people who know very well how to drive a car, but have never looked under the hood and have no idea how the engine works.
If you ask how I have the nerve to write about a subject that I am saying no one fully understands, let me admit the validity of the criticism and point out that such considerations never yet stopped a politician or a preacher. I’m not going to let it stop me.
Harder to answer is the need for yet another discussion of quantum theory and its paradoxes, when so many high-quality detailed discussions already exist in the literature. I argue that my objective is a rather brief article, not a book, and in the final section I point out some of the excellent texts that treat in detail what here I will only mention.
While in confessional mode, I also have to say that I can’t possibly describe quantum theory fully in a few thousand words. There’s too much to it, and it’s a truly difficult subject. If everything I say seems to be perfectly clear, chances are that either I’m missing the point, or you are.
The need for quantum theory emerged gradually, from about 1890 to 1920. Some rather specific questions as to how radiation should behave in an enclosure had arisen, questions that classical physics couldn’t answer. Max Planck in 1900 showed how a rather ad hoc assumption that the radiation was emitted and absorbed in discrete chunks, or quanta (singular, quantum), solved the problem. He introduced a fundamental constant associated with the process, Planck’s constant. This constant, denoted by h, is a tiny quantity, and its small size compared with the energies, times, and masses of the events of everyday life is the basic reason why we are not aware of quantum effects all the time.
Most people thought that the Planck result was a gimmick, something that happened to give the right answer but did not represent anything either physical or of fundamental importance.
That changed in 1905, when Einstein used the idea of the quantum to explain another baffling result, the photoelectric effect. (The year 1905 was unbelievable for Einstein. He produced the explanation of the photoelectric effect, the theory of special relativity, and a paper explaining Brownian motion [see the article, “Counting Up”]. The only comparable year in scientific history was 1666, when Isaac Newton developed the calculus, the laws of motion, and the theory of universal gravitation.)
The photoelectric effect arises in connection with light hitting metal. In 1899, the Hungarian physicist Phillip Lenard had shown that when a beam of light is shone on a metallic surface, electrons begin to pop out of the metal provided that the wavelength of the light is short enough. Note that the result depends on the wavelength of the light, and not its brightness. If the wavelength is short enough, the number of emitted electrons is decided by the brightness, but if the wavelength is too long, no elec
trons will appear no matter how bright the light may be.
Einstein suggested that the result made sense if light were composed of particles (now called photons) each with a certain energy decided by the wavelength of the light. These photons, hitting atoms in the metal, would drive electrons out if the energy provided by the impact was enough to overcome the binding of the electron within the atom. Einstein published an equation relating the energy of light to its wavelength, and again Planck’s constant, h, appeared.
Quanta looked a little more real, but Einstein was only twenty-six years old and still an unknown, so the world did not hang on his every word as they did in his later years. There were certain exceptions, people who recognized Einstein for what he was from the beginning. Max Born, whom we will meet again in the 1920s, wrote: “Reiche and Loria told me about Einstein’s paper, and suggested that I should study it. This I did, and was immediately deeply impressed. We were all aware that a genius of the first order had emerged.” Born here is typically modest. He certainly knew that a genius of the first order had arisen; but he was himself a genius. It takes one to know one.
It might seem that there was nothing particularly surprising in Einstein’s suggestion that light was composed of particles. After all, Newton, over two hundred years earlier, had believed exactly the same thing, and it was known as the corpuscular theory of light. However, early in the nineteenth century, long after Newton’s death, a crucial experiment had been performed that seemed to show beyond doubt that light had to be a form of wave motion. All the evidence since that time had pointed to the same conclusion.
The key experiment was a deceptively simple one performed in 1801 by an English physicist and physician, Thomas Young. (Young was also one of the men who deciphered Egyptian hieroglyphics, thus allowing ancient Egyptian writings to be understood; he can hardly be given the label of narrow scientist.)
Dancing With Myself Page 16