Galileo and the Dolphins
Page 14
The Sieve of !
When the multiples sublime,
The numbers that remain are prime.
Prime numbers have since exerted an almost mystic fascination. They appear at random, but many philosophers have refused to believe that this randomness is genuine. Some have held that God arranged them according to a hidden pattern which, if ever discovered, will render man ‘divine’.
This prospect alarmed the Church, which feared that only would be malicious enough to make the appearance of primes so unpredictable. ‘The danger already exists,’ thundered St Augustine, ‘that mathematicians have made a covenant with the Devil to darken the spirit and confine man in the bonds of Hell.’
Many people think that the number one ought to be a prime, it being divisible by itself and one, and thus living up to the mathematical definition of a prime. ‘But that wouldn’t be fair to the other prime numbers,’ a mathematician once told me gravely.
Part Four: EDGES OF THE INFINITE
A Sea of Universes
Astronomers are often asked the question: ‘What happened before the Big Bang?’ Until now this question had a standard, if unsatisfying answer: ‘You ask an improper question. Time began with the Big Bang. Asking what happened before it, is like asking what is north of the North Pole.’
But this answer will not do any more. It appears that there was a ‘before’ - not, admittedly, in this universe, but among a vast collection of other universes known as the ‘multiverse’, of which ours was one of the few to evolve with conditions that favoured life. Many of these parallel universes are likely still to exist, says the cosmologist , of the City University of New York.
He tells the anecdote of a Russian physicist visiting the roulette tables at Las Vegas who wagers all his money on a single number. ‘That’s a ridiculous strategy!’, his American friends tell him. ‘You’ll lose it all.’ ‘Perhaps.’ he replies, ‘but in at least one parallel universe I’ll be rich beyond my wildest imagination.’
The reason for thinking in this way is the realization that Einstein’s general theory of relativity, which describes the expansion of the early universe and its coalescence into galaxies, breaks down in the extreme conditions of the Big Bang and must be replaced by quantum cosmology. Temperatures were then 10 degrees, a trillion trillion times hotter than at the centre of an H-bomb explosion, which would have ripped apart all elementary particles except the simplest, the electron.
Now as ’s uncertainty principle shows us, you cannot ever catch an electron. The more you know of its position, the less you know of its speed, and vice versa.
‘The behaviour of the early universe’, explains Kaku, ‘was identical to that of an electron. It existed in an infinite number of different states simultaneously. Some of these were favourable , being the seeds of the fundamental constants that we know, while others had something terribly wrong with, for example, the protons decaying after a billion years so that stars would never form.’
Many of these parallel universes must still exist, perhaps like the one in ’s novel The Gods Themselves whose inhabitants lacked the hydrogen to form sufficient stars, and so started to steal hydrogen from ours.
And so what of the multiverse that spawned our universe? The simplest analogy, says Kaku, is that of boiling water which continually creates bubbles. From these bubbles universes form.
Can we therefore create a universe in a laboratory? In principle, yes, since the task requires zero energy. Universes are constantly being created in a ‘sea of nothing’. But since the heat of the budding universe will be so many trillions of degrees, the experiment might perhaps damage the laboratory.
Scars of Old Collisions
Chesapeake Bay, the site of one of the most famous early English settlements in America, was shaped by the impact of a giant meteorite from space.
The discovery, by an American geology professor, reminds us that the threat of violent destruction by asteroids is ever present - and that there are hundreds of thousands of other craters on the Earth’s surface, still undiscovered because they are hidden by vegetation, erosion or the seas.
‘The Chesapeake Bay crater is one of the ten biggest meteorite craters on Earth,’ says , of the US Geological Survey at Woods Hole, Massachusetts, who made the discovery. In an article in Geology called ‘Meteorite Mayhem in Ole Virginny’, he explains how he discovered in the bay an unusual underground layer of boulders dating back 35 million years.
Using seismic data from oil companies he found a series of concentric rings of which the largest was more than 80 kilometres across and very similar to a smaller underground meteorite crater found recently in Germany.
The finding of these underground rings coincided with the discovery in the region of a layer of ‘tektites’ - distinctive rocks thrown into the air by a meteorite impact. ‘It clearly shows that there is a large impact crater in the southern part of the bay,’ says Poag.
Now the plot thickens. The dry, unchanging surface of the Moon is covered with such craters. They range from a few metres across to scores of kilometres in width. It follows therefore that the Earth, whose surface area is 16 times larger than the Moon’s, and hence much more likely to attract space debris during the 4.6 billion-year history of the Solar System, must be much more richly covered with them.
But where are they? One at least is clearly visible. Barringer crater in the Arizona desert is nearly two kilometres across and 1,200 metres deep. It marks the place where a rock about 15 metres wide crashed into the ground 20,000 years ago. At the other extreme of violence is the undersea crater recently discovered off the coast of Yucatan, caused by an asteroid as wide as Greater London which struck Earth about 65 million years ago, killing most of the dinosaurs. (See Our Improbable Existence, p. 14.)
It is estimated that there have been at least 2,000 major impacts in the last 600 million years, and many times this number of minor ones. The difficulty facing geologists in the search for them is the huge number of seemingly obvious candidates, many of whose dramatic land formations may only be a coincidence.
Setting aside underground or undersea craters, which are the most difficult to find, there are many places on Earth which, because of the sharpness of their outlines, may be thought to have been gouged out by mighty blows from space.
The Barringer crater is roughly circular, with many sharp angles. Places like this include the Wash, where King lost his stolen treasure in 1216, the Gulf of Taranto in the heel of Italy, the Gulf of Carpentaria in northern Australia, the Gulf of Mexico, and the immense Hudson Bay in Canada.
Civilization may at least once have been wiped out by a hammer blow from space. This was not Atlantis, the Minoan civilization centred on Crete, with its well-documented destruction in about 1500 bc by vast sea-waves after the volcanic eruption on the nearby island of Santorini, but the empire of the Mycenaeans which dominated the eastern Mediterranean and mysteriously vanished about 1100 BC.
, in his Timaeus, tells of Solon, the lawgiver of Athens, who, after a visit to Egyptian scholars, returned to Greece to tell of the terrible fate of what must have been the Mycenaean empire, for it is hard to tell what other empire he could have been referring to. He spoke of destruction caused by ‘the bodies that revolve in heaven round the Earth’ that brought a ‘great conflagration’, natural events liable to occur ‘at long intervals’.
Scientific proof of such assertions may come by accident, says Poag - with his data from the oil industry - or perhaps even from a treasure hunt.
The value of King ’s lost jewels and coin is incalculable. It would be ironic if a search for it, thousands of metres under the Wash, revealed instead tektites or concentric rings that would show that one of England’s most famous landmarks was created by an event of almost unimaginable violence.
Check Your Typing!
Budding professional astronomers may have been alarmed by a recent report that there is often a gentle breeze at the La Palma observatory of ‘five kilometres per second’ - a veloci
ty that would that would surely flatten all the buildings.
Saying ‘per second’ instead of ‘per hour’ was typical of the kind of erroneous statement that regularly gets quoted in the ‘Here and There’ column in The Observatory, surely one of the most entertaining regular features in astronomical literature.*
*A journal published by the Royal Astronomical Society.
Astronomical writers - like those on any other subject -are liable to make appalling errors. The problem is seldom ignorance - such people are usually very well informed -but carelessness. They too often fail to check what they have written, and either bad grammar, misspelling, use of the wrong term or omitting a crucial word like ‘million’ or ‘billion’ renders their words hilarious - like the New York Times 1989 announcement that the Galileo mission to Jupiter would cost a mere 1.4 dollars.
Here are some amusing examples from ‘Here and There’: ‘The European solar panels of the Space Telescope will be replaced by astronauts’ - ESA Bulletin, 1993. ‘Clementine is now in low Earth orbit (140 by 160 nanometres)’ (a nanometre is a millionth of a metre) - Lunar and Planetary Information Bulletin, 1994. And, ‘Scotti will use a chronograph to darken the disc of Jupiter’ - Time magazine, 1994. In a similar vein, Nature, in a splendid misspelling in 1989, told of an astronomer who had ‘exploded many stars by computer’.
I myself was once guilty, on the front page of my newspaper, of writing ‘miles’, when I meant ‘light-years’, an error with a factor of six trillion. But it is reassuring to note that many professional publications have made similar distance errors.
‘The Hubble Space Telescope will enable us to see twelve to fifteen light-years beyond our planet,’ said the Astronomy Book Club in 1989. And the Arizona Summer Wildcat, a University of Arizona newspaper, reported in 1991 that ‘astronomers have found a galaxy six million miles away in Pisces’. (‘Something fishy going on’ was the ‘Here and There’ comment on this revelation.)
Some errors are so weird that one cannot imagine how they were made. ‘[The galaxy] NGC4156 does not seem to be associated with NGC4156,’ said Astronomy and Astrophysics in 1984 and the Monthly Notices of the Royal Astronomical Society wrote in 1982 of an object that was ‘hotter than itself.
Sometimes the error is clearly not the author’s fault, like the remark in the New Scientist in 1990 that the Milky Way has ‘roughly 1012 times the mass of the Sun’. The superscript had been omitted, and the number should have been 10 . This is similar to the constantly repeated error, in the days of hot metal typesetting by compositors, of ‘cemetery dust’ in space.
And for sheer incredibility, nothing can surpass the 1989 advertisement in Sky and Telescope for ‘Exciting Full-Size Posters of Mercury, , Earth and Mars!’ Could they be affecting our climate?
Why We Don’t Turn into Werewolves
There is a popular myth, widely held in many parts of the world, in which people are turned into werewolves - or at least behave with violent irrationality - whenever the Moon’s tidal forces are strong.
Assuming that this is a gravitational effect, a professor of astrophysics has calculated how large your head would have to be for it to take place - an interesting examination of the oddities of gravity.
‘If your brain were, say, 13,000 kilometres in diameter (the size of the Earth), then the Moon’s tidal forces would indeed give you an oblong-shaped cranium and induce untold derangements to your mental faculties,’ says Tyson, of Princeton University, in a series of articles in the American journal Natural History.
‘For normal Homo sapiens, however, the difference in the Moon’s gravity from one side of the head to the other is immeasurably small. The weight of a pillow one is lying on imparts a squeezing force that is more than seven trillion times stronger than the Moon’s tidal force, a view not shared by those who write about werewolves.’
For gravitation, although the only one of the four fundamental forces whose effects extend through the universe, is almost immeasurably the weakest. It is normally 10 times (1 followed by 36 noughts) weaker than the next strongest, the electro-magnetic force. But, paradoxically, it can become immeasurably strong, too, in particular beyond the event horizon of a black hole (the remnant of a collapsed star so massive that nothing, not even light, can escape from it).
The recent discovery of a black hole in a galaxy called M101, 20 million light-years from Earth, that appears to be creating stars rather than devouring them - by hurling out from its orbit streams of hydrogen, the raw material of stars -indicates the future surprises we are likely to encounter from gravity. The most extraordinary of these is the prediction that a corridor circling a black hole could be both straight and curved at the same time. (See A Corridor Both Curved and Straight, p. 229.)
When we stand on the ground, gravity is always slightly stronger - by one ten-thousandth of 1 per cent - at our feet than at our heads. But at the opposite extreme, if we were to fall feet first into a black hole, gravity would become so strong that by accelerating one’s feet so much faster than one’s head, ‘the tidal strength would exceed the strength of the chemical bonds of the flesh, and a human body would be stretched into a long string of falling atoms.’
But weak as ‘normal’ gravity may be, it is sufficiently strong for the Moon to act as a brake on the Earth’s rotation. Days are becoming imperceptibly longer as the oceans, moved by the tides, slow the planet’s rotation by friction. A trillion years from now, the rotation will be so slow that an Earth day will equal a lunar month. Since the Sun, as it swells in its dying convulsions, will not be large enough to consume the Earth and Moon, the two bodies will have achieved a solitary ‘double tidal lock’. Like and its moon Charon, one side of each body will permanently face the other.
Gravity can only be created by producing mass, but its effects can be simulated. In a fast-rotating chamber, like the Wall of Death in a fairground, people are pressed against the outside walls by what is unsatisfactorily called ‘centrifugal force’. But what is really happening is that they are being made to rotate relative to the mass of the whole universe, according to .
This observation also explains why astronauts who travel fast enough could return younger than their own children. The friends they left behind would age normally and the accelerated travellers would age more slowly. Why? The travellers move alone, but when the Earth moves the entire universe moves with it.
There is nothing mystical about this prediction. There is no suggestion that the speeding astronauts will turn into werewolves, whatever the gravitational forces.
Coldest of the Cold
The temperature inside the refrigerator in ’s laboratory at Lancaster University is the lowest ever achieved. It is 12 millionths of a degree above absolute zero.
This is about 300,000 times colder than any natural temperature. The empty spaces between the galaxies are almost three degrees above absolute zero, for they are still cooling from the infinite heat of the Big Bang that created our region of the universe some 15,000 million years ago.
Picket and colleagues in the United States are exploring an unknown region where materials behave in extraordinary ways. ‘High-energy physicists are historians of the universe,’ he explained, ‘because they are exploring the infinitely high temperatures and densities of the Big Bang. But we are futurologists, looking at the universe as it will be billions of years hence, when practically all heat has gone.’
Absolute zero is eternally unattainable, according to ’s Third Law of Thermodynamics of 1906, because atoms would be motionless in the total absence of heat, and they are always in motion.
The scale of natural temperatures goes like this:
Where found
Degrees C
The Big Bang
Infinite
Interior of hottest stars
1,000 million
Core of the Sun
30 million
Hydrogen bomb explosion
50,000
Where found
Degrees C
7,000
Iron melts
1,500
Greenhouse Effect on
400
Hottest place on Earth
58
Average on Earth’s surface
20
Coldest place on Earth
-89
Temperature of universe
-270
Lowest temperature of liquids
-272.00001
Lowest temperaturae of metals
-272.00002
Absolute zero
-273.15
‘We can never be sure what we are going to find at these supercold levels,’ said another physicist, , head of the low temperature physics group at Cornell University, Ithaca, New York. ‘We seem to have stumbled upon an entirely new science.
‘If the behaviour of a substance is to be studied at extremely low temperatures it must be liquid. Only two substances remain liquid near absolute zero: the isotopes helium-3 and helium-4. The first is the more interesting of the two, because it is the lighter and therefore moves around faster. It is thus ideal for studying the fundamental properties of matter.’
and his colleague are studying the behaviour of ‘superfluid’ helium-3, a substance with a total absence of friction. It is expected to play an important role in providing stability and reliability to what may be world’s largest solenoid magnets. Their collegues in the United States, meanwhile, are preparing to examine still more exotic phenomena.
One such mystery being studied by at is ’s Uncertainty Principle of 1927, which states that some information is eternally unattainable. The speed and position of an electron cannot be determined simultaneously with absolute accuracy because the more we know of one, the less we can know of the other.