Universe a grand tour of modern science Phần 6

T he cheap cigars with which the young Albert Einstein surrounded himself in a smoky haze were truly dreadful. If he gave you one, you ditched it surreptitiously in Bern’s Aare River. So when Einstein went home to his wife and son in the little flat on Kramgasse, after a diligent day as a technical officer (third class) at Switzerland’s patent office, he spent his evenings putting the greybeards of physics right, about the fundamentals of their subject. That was how he sought fame, fortune and a better cigar. In March 1905, a few days after his 26th birthday, he explained the photoelectric effect of particles of light, in a paper that would eventually win him a Nobel Prize. By May he had proved the reality of atoms and molecules in explaining why fine pollen grains dance about in water. He then pointed out previously unrecognized effects of high-speed travel, in his paper on the special theory of relativity, which he finished in June. In September he sent in a postscript saying ‘by the way, E ¼mc2.’ RetrospectivelyLouisdeBroglie in PariscalledEinstein’sresults thatyear, ‘blazing rocketswhich inthedark ofthenight suddenlycastabrief but powerful illumination over an immenseunknownregion.’ Allfour papersappearedin quick succession inAnnalen der Physik, butthephysics communitywasslowto react. The patentoffice promotedEinsteintotechnical officer(second class) andhecontinued therefor anotherfour years, beforebeingappointedanassociate professor at Zurich. Onlythen hadhe thetimeandspaceto think seriouslyaboutspacetime, gravityandthegeneraltheoryofrelativity, which would be hismasterpiece. The much simpler idea of special relativity still comes as a nasty shock to students and non-scientists, long after the annus mirabilis of 1905. Schoolteachers persist in instilling pre-Einsteinian physics first, in the belief that it is simpler and more in keeping with common sense. That is despite repeated calls from experts for relativity to be learnt in junior schools. I Tampering with time In the 21st-century world of rockets, laser beams, atomic clocks, and dreams of flying to the stars, the ideas of special relativity should seem commonsensical. 373 high-speed travel Einstein’s Universe is democratic, in that anyone’s point of view is as good as anyone else’s. Despite the fact that stars, planets, people and atoms rush about in relation to one another, the behaviour of matter is unaffected by the motions. The laws of physics remain the same for everyone. The speed of light, 300,000 kilometres per second, figures in all physical, chemical and biological processes. For example the electric force that stitches the atoms of your body together is transmitted by unseen particles of light. The details were unknown to Einstein in 1905, but he was well aware that James Clerk Maxwell’s electromagnetic theory, already 40 years old, was so intimately linked with light that it predicted its speed. That speed must always be the same for you and for me, or one or other of our bodies would be wonky. Suppose you are piloting a fighter, and I’m a foot soldier. You fire a rocket straight ahead, and its speed is added to your plane’s speed. Say 1000 plus 1000 kilometres per hour, which makes 2000. I’d be pedantic to disagree about that. Now you shoot a laser beam. As far as you are concerned, it races ahead of your fighter at 300,000 kilometres a second, or else your speed of light would be wrong. But as far as I’m concerned, on the ground, the speed of your fighter can have no add-on effect. Whether the beam comes from you or from a stationary laser, it’s still going at 300,000 kilometres a second. Otherwise my speed of light would be wrong. When you know that your laser beam’s speed is added to your fighter’s speed, and I know it’s not, how can we both be right? The answer is simple, though radical. Einstein realized that time runs at a different rate for each of us. When you say the laser beam is rushing ahead at the speed of light, relative to your plane, I know that you must be measuring light speed with a clock that’s running at a slow rate compared with my clock. The difference exactly compensates for the speed of the plane. Einstein made a choice between two conflicting common-sense ideas. One is that matter behaves the same way no matter how it is moving, and the other is that time should progress at the same rate everywhere. There was no contest, as he saw it. His verdict in special relativity was that it was better to tamper with time than with the laws of physics. The mathematics is not difficult. Two bike riders are going down a road, side by side, and one tosses a water bottle to the other. As far as the riders are concerned, the bottle travels only the short distance that separates them. But a watcher standing beside the road will see it go along a slanting track. That’s because the bikes move forward a certain distance between the moments when the bottle leaves the thrower and when it arrives in the catcher’s hand. The watcher thinks the bottle travels farther and faster than the riders think. 374 high-speed travel If the bottle represents light, that’s a more serious matter, because there must be no contradiction between the watcher’s judgement of the speed and the riders’. It turns out that a key factor, in reckoning how slow the riders’ watches must run to compensate, is the length of the slanting path seen by the watcher. And that you get from the theorem generally ascribed to Pythagoras of Samos. In the 1958 movie Merry Andrew, Danny Kaye summed it up in song: Old Einstein said it, when he was getting nowhere. Give him credit, he was heard to declare, Eureka! The square of the hypotenuse of a right triangle Is equal to the sum of the squares of the two adjacent sides. Cognoscenti of mathematical lyrics preferred the casting for the movie proposed in Tom Lehrer’s ‘Lobachevsky’ (1953) to be called The Eternal Triangle. The hypotenuse would be played by a sex kitten—Ingrid Bergman in an early version of the song, Brigitte Bardot later. Whether computed with an American, Swedish or French accent, it’s the Pythagorean hypotenuse you divide by, when correcting the clock rate in a vehicle that’s moving relative to you. The slowing of time in a moving object has other implications. One concerns its mass. If you try to speed it up more, using the thrust of a space traveller’s rocket motor or the electric force in a particle accelerator, the object responds more and more sluggishly, as judged by an onlooker. The rocket or particle responds exactly as usual to the applied force by adding so many metres per second to its speed, every second. But its seconds are longer than the onlooker’s, so the acceleration seems to the onlooker to be reduced. The fast-moving object appears to have acquired more inertia, or mass. When the object is travelling close to the speed of light, its apparent mass grows enormously. It can’t accelerate past the speed of light, as judged by the onlooker. The increase in mass during high-speed travel is therefore like a tacho on a truck—a speed restrictor that keeps the traffic of Einstein’s Universe orderly. I A round trip for atomic clocks Imagine people making a high-speed space voyage, out from the Earth and back again. Although the slow running of clocks stretches time for them, as judged by watchers at home, the travellers have no unusual feelings. Their wristwatches and pulse-rate seem normal. And although the watchers may reckon that the travellers have put on a grievous amount of weight, in the spaceship they feel as spry as ever. 375 high-speed travel But what is the upshot when the travellers return? Will the slow running of their time, as judged from the Earth, leave them younger than if they had stayed at home? Einstein’s own intuition was that the stretching of time should have a lasting effect. ‘One could imagine,’ he wrote, ‘that the organism, after an arbitrarily lengthy flight, could be returned to its original spot in a scarcely altered condition, while corresponding organisms which had remained in their original positions had long since given way to new generations.’ Other theorists, most vociferously the British astrophysicist Herbert Dingle, thought that the idea was nonsensical. This clock paradox, as they called it, violated the democratic principle of relativity, that everyone’s point of view was equally valid. The space travellers could consider that they were at rest, the critics said, while the Earth rushed off into the distance. They would judge the Earth’s clocks to be running slow compared with those on the spaceship. When they returned home there would be an automatic reconciliation and the clocks would be found to agree. Reasoned argument failed to settle the issue to everyone’s satisfaction. This is not as unusual in physics as you might think. For example the discoverer of the electron, J.J. Thomson, resisted for many years the idea that it was really a particle of matter, even though his own maths said it was. There is often a grey area where no one is quite sure whether the mathematical description of a physical process refers to actual entities and events or is just a convenient fiction that gives correct answers. For more than 60 years physicists were divided about the reality and persistence of the time-stretching. Entirely rational arguments were advanced on both sides. They used both special relativity and the more complicated general relativity, which introduced the possibility that acceleration could compromise the democratic principle. Indeed some neutral onlookers suspected that there were too many ways of looking at the problem for any one of them to provide a knockdown argument. The matter was not decided until atomic clocks became accurate enough for an experimental test in aircraft. ‘I don’t trust these professors who get up and scribble in front of blackboards, claiming they understand it all,’ said Richard Keating of the US Naval Observatory. ‘I’ve made too many measurements where they don’t come up with the numbers they say.’ In that abrasive mood it is worth giving a few details of an experiment that many people have not taken seriously enough. On the Internet you’ll find hundreds of scribblers who still challenge Einstein’s monkeying with time, as if the matter had not been settled in 1971. That was when Keating and his colleague Joe Hafele took a set of four caesium-beam atomic clocks twice around the world on passenger aircraft. First they flew from west to east, and then from east to west. When returned to the lab, 376 high-speed travel the clocks were permanently out of step with similar clocks that had stayed there. Einstein’s intuition had been correct. Two complications affected the numbers in the experiment. The eastbound aircraft travelled faster than the ground, as you would expect, but the westbound aircraft went slower. That was because it was going against the direction in which the Earth rotates around its axis. At mid-latitudes the speed of the surface rotation is comparable with the speed of a jet airliner. So the westbound airborne clocks should run faster than those on the ground. The other complication was a quite different Einsteinian effect. In accordance with his general relativity, the airborne clocks should outpace those on the ground. That was because gravity is slightly weaker at high altitude. So the westbound clocks had an added reason to run fast. They gained altogether 273 billionths of a second. If any airline passengers or crew had made the whole westabout circumnavigation, they would have aged by that much in comparison with their relatives on the ground. In the other direction, the slowing of the airborne clocks because of motion was sufficient to override the quickening due to weak gravity. The eastbound clocks ran slow by 59 billionths of a second, so round-trip passengers would be more youthful than their relatives to that extent. The numbers were in good agreement with theoretical predictions. The details show you that the experiment was carefully done, but the crucial point was really far, far simpler. When the clocks came home, there was no catch-up to bring them back into agreement with those left in the lab, as expected by the dissenters. The tampering with time in relativity is a real and lasting effect. As Hafele and Keating reported, ‘These results provide an unambiguous empirical resolution of the famous clock paradox.’ I The Methuselah Effect If you want to voyage into the future, and check up on your descendants a millennium from now, a few millionths of a second gained by eastabout air travel won’t do much for you. Even when star-trekking astronauts eventually achieve ten per cent of the speed of light, their clocks will lag by only 1 day in 200, compared with clocks on the Earth. Methuselah reportedly survived for 969 years. For the terrestrial calendar to match that, while you live out your three score and ten in a spaceship, Mistress Hypotenuse says that you’ll have to move at 99.74 per cent of light speed. Time-stretching of such magnitude was verified in an experiment reported in 1977. The muon is a heavy electron that spontaneously breaks up after about 2 millionths of a second, producing an ordinary electron. In a muon storage ring at CERN in Geneva, Emilio Picasso and his colleagues circulated the particles at 377 ... - tailieumienphi.vn