Universe a grand tour of modern science Phần 6 potx

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 ¼ mc2

.’

Retrospectively Louis de Broglie in Paris called Einstein’s results that year, ‘blazing

rockets which in the dark of the night suddenly cast a brief but powerful

illumination over an immense unknown region.’ All four papers appeared in quick

succession in Annalen der Physik, but the physics community was slow to react. The

patent office promoted Einstein to technical officer (second class) and he continued

there for another four years, before being appointed an associate professor at

Zurich. Only then had he the time and space to think seriously about spacetime,

gravity and the general theory of relativity, which would be his masterpiece.

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.

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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.

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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.

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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,

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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

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99.94 per cent of the speed of light and recorded their demise with electron

detectors. The high-speed travel prolonged the muons’ life nearly 30-fold.

The Methuselah Effect in muons has physical consequences on the Earth.

Cosmic rays coming from the stars create a continuous rain of fast-moving

muons high in the Earth’s atmosphere. They are better able to penetrate the air

than electrons are, but they would expire before they had descended more than

a few hundred metres if their lives were not stretched by their high speeds. In

practice the muons can reach the Earth’s surface, even penetrating into the

rocks. You can give Einstein the credit or the blame for the important part that

muons play in the cosmic radiation that contributes to genetic mutations in

living creatures, and affects the weather at low altitudes.

If you want to exploit special relativity to keep you alive for as long as possible,

the most comfortable way to travel through the Universe will be to accelerate

steadily at 1g—the rate at which objects fall under gravity at the Earth’s surface.

Then you will have no problems with weightlessness, and you can in theory

make amazing journeys during a human lifetime. This is because the persistent

acceleration will take you to within a whisker of the speed of light.

Your body-clock will come almost to a standstill compared with the passage of

time on Earth and on passing stars. Through your window you will see stars

rushing towards you, and not only because of the direct effect of your motion

towards them. The apparent distance that you have to go keeps shrinking, as

another effect of relativity at high speeds.

In a 1g spaceship, you can for example set out at age 20, and travel right out of

our Galaxy to the Andromeda Galaxy, which is 2 million light-years away. By

starting in good time to slow down (still at 1g) you can land on a planet in that

galaxy and celebrate your 50th birthday there. Have a look around before setting

off for home, and you can still be back for your 80th birthday. But who knows

what state you’ll find the Earth to be in, millions of years from now?

If stopping is not an objective, nor returning home, you can traverse the entire

known Universe during a human lifetime, in your 1g spaceship. Never mind that

it is technologically far-fetched. The fact that Uncle Albert’s theory says it’s

permissible by the laws of physics should make the Universe feel a little cosier

for us all.

I ‘A sure bet’

Astronomers have verified Einstein’s intuition that the speed of light is

unaffected by the speed of the source. For example, changes in the wavelength

of light often tell them that one star is revolving around another. Sometimes it is

swinging towards us, and sometimes receding from us on the other side of its

companion. For a pulsating star, the time between pulses varies too.

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Suppose Einstein was wrong, and the speed of light is greater when the star is

approaching, and slower when it is receding. Then the arrival times of pulses

from a pulsating star orbiting a stellar companion will vary in an irregular

manner. That doesn’t happen.

X-rays are a form of light, and in 1977 Kenneth Brecher of the Massachusetts

Institute of Technology applied this reasoning to an X-ray star in a nearby

galaxy, the Small Magellanic Cloud. There, the X-ray source SMC X-1 is orbiting

at 300 kilometres per second around its companion, yet there is no noticeable

funny business in the arrival of the X-rays. So the proposition about the

invariance of the speed of light from a moving source is correct to at least one

part in a billion.

By 2000 Brecher was at Boston University, and using observations of bursts of

gamma rays in the sky to make the proposition even more secure. The greater

the distance of an astronomical source, the more time there would be for light

pulses travelling at different speeds to separate before they reach our telescopes.

The gamma bursters are billions of light-years away.

In all credible theories of what these objects may be, pieces of them are moving

relative to one another other at 30,000 kilometres per second or more. Yet some

observed gamma-ray bursts last for only a thousandth of a second. If there were

the slightest effect of the motions of the sources on the light speed, a burst

could not remain so brief, after billions of years of space travel.

With this reasoning Brecher reduced any possible error in Einstein’s proposition

to less than one part in 100 billion billion. He said, ‘The constancy of the speed

of light is as close to a sure bet as science has ever found.’

E For E ¼ mc2 as the postscript to special relativity, see Energy and mass. For general

relativity, see Gravity. For other tricks with clocks, see Time machines.

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