In search of Feynman’s van


Seven years after Richard Feynman died, I visited Caltech for the first time. One reason for the visit was to give a talk about the transactional interpretation of quantum mechanics, which draws so strongly on Feynman’s own unusual ideas about the nature of electromagnetic radiation, now more than half a century old. It was, to say the least, an unusual feeling to be talking not just from the spot where Feynman himself used to lecture, but about his own work. And when, during the question period at the end of the talk, the discussion moved on to QED, the dream-like quality of the occasion intensified — an audience at Caltech, of all places, was asking me to explain QED to them!
But the main purpose of the visit was to fill in the background to the Feynman legend in preparation for writing a book, visiting the places where he used to work and meeting the people he used to work with. In the spring of 1995, after an unusually wet late winter, the Caltech campus seemed to be the ideal place for a scientist (or anyone else) to work. With temperatures in the 80s and a cloudless sky, the green open spaces of the campus, shaded by trees and decked with colourful flowerbeds, offered a calm environment highly conducive to gentle contemplation about the mysteries of the Universe. I was reminded of a visit to Larne, in South Wales, to the modest building where Dylan Thomas used to work, looking out over the spectacular views and thinking “if I’d lived here, even I might have become a poet”; I may not be much of a physicist, but the atmosphere at Caltech makes you think “if I worked here, even I might have one or two good ideas”. And then you think about the people who have worked there, including Feynman himself, Murray Gell-Mann, whose room was separated from Feynman’s only by Helen Tuck’s office, and Kip Thorne, one of the two or three leading experts on the general theory of relativity, still working at Caltech, but not too busy to take time off to discuss black holes, time travel and Feynman. And then you think, “well, maybe my ideas wouldn’t be that good”.
The point about Caltech, in academic terms, is that not only does it bring out the best work from its scientists, it also (partly for that reason) attracts the best scientists. So what you end up with is the best of the best. There are always top people eager to become part of the Caltech scene; but Feynman himself has never been directly replaced, even though, after his death, a committee was set up to seek a replacement. They failed to find one, because there is nobody like Feynman around today — just as there never was anybody like Feynman, except Feynman himself, around before.
There is no formal memorial to Feynman. No grand building, or statue. Even his grave, shared with Gweneth in Mountain View Cemetery in Altadena, is very simple. His real memorial is his work, his books, and the video tapes on which he can still be seen, lecturing in his inimitable style, making difficult concepts seem simple. But there is one artefact which strikes a curious resonance with anybody who has ever heard of Feynman, and which I had been urged, by a friend who knows next to nothing about science but still regards Feynman as a hero for our time, to track down while I was in Pasadena.
The opportunity came at the end of a long talk with Ralph Leighton, in the lobby of my hotel on Los Robles Boulevard. My host in Pasadena, Michael Shermer of the Skeptics Society, sat in with us for a conversation which ranged not only over Feynman’s life and work, but also over the reaction of the world at large to his death, and the reaction of Feynman’s family and friends to the way he had been presented in various books and articles since then. That conversation brought me as close as I could ever hope to get to the man himself, confirming and strengthening the impressions I already had about what kind of person he was, and shaping the book which you now hold. Richard Feynman was indeed, as well as being a scientific genius, a good man who spread love and affection among his family, friends and acquaintances. In spite of the dark period in his life after the death of Arline, he was a sunny character who made people feel good, a genuinely fun-loving, kind and generous man, as well as being the greatest physicist of his generation. And it is that spirit, rather than the physics, which makes people so curious about the artefact — Feynman’s famous van, replete with diagrams.
Our conversation with Leighton had been so intense that I hesitated to bring up the relatively trivial question I had promised to ask. But as we walked him back to his car in the spring sunshine, I reminded myself that a promise is a promise. “By the way,” I said, “whatever happened to Feynman’s van?”
“It’s still in the family, so to speak,” he replied.
Michael Shermer’s ears visibly pricked up at the news.
“It needs some work. It’s parked out at the back of a repair shop in . . . ” and he gave us the name of another part of the Los Angeles urban sprawl, out to the east of Pasadena.
That, I thought, was the end of it. I had no transport of my own in Pasadena, and although I’d kept my promise to ask after the van, I wouldn’t be able, as I’d hoped, to get a picture of it for my friend. I had a radio talk show engagement ahead of me, and an early flight out the next morning. But Shermer had other ideas. He offered to drive me over to find the van as soon as I’d finished at KPCC-FM, and seemed at least as eager as I was to make the pilgrimage. A couple of hours later, we were cruising around the location that Leighton had pointed us towards, stopping to call him on Shermer’s car phone for directions each time we got lost. Just as the Sun was setting, we found the repair shop, parked, and walked around the back. There it was. Feynman’s van, nose up against the wall, looking slightly battered but still with its decorative paintwork of Feynman diagrams. It had clearly been there for some time, and delicate spring flowers wee growing up around its wheels.
We took our pictures and left, congratulating ourselves on completing the “Feynman tour” successfully. Twelve hours later, I was in San Francisco, and it was only on my return home that I heard from Shermer about the sequel to the story. The next day, he had happily recounted the tale of our search for Feynman’s van to a friend who works at the Jet Propulsion Laboratory, a space research centre in Pasadena. The friend, a sober scientist himself, and hardly an obvious science “groupie”, eagerly asked for directions to the repair shop, and went out there the same day, armed with his own camera. Shermer’s joke about the Feynman tour has now almost become reality, with a succession of visitors to the relic — and out of all the pictures I brought back from my California trip, the ones that continue to rouse the most interest are the ones of a beaten up old van parked at the back of a repair shop somewhere east of Pasadena.
I’m not sure why, even though I share something of this enthusiasm. But it’s nice to know that something which demonstrates so clearly Feynman’s sese of fun and irreverence, as well as referring to his Nobel-prizewinning work, still exists. Leighton suggests that the symbol is particularly appropriate, because the van itself is a symbok of Feynman’s free spirit, a vehicle of exploration and discovery of the everyday world, while the diagrams symbolise his exploration and enjoyment of the world of physics. Together, they represent what Feynman was all about — the joy of discovery, and the pleasure of finding things out. Leighton says he will make sure the van stays in the family of Feynman’s friends, and suggests that it might one day form the centrepiece of a travelling Feynman exhibit. Now, that sounds like the kind of memorial even Feynman might have approved of.
Extract from RICHARD FEYNMAN: A life in science, by John & Mary Gribbin. Published in March 1997 by NAL/Dutton in New York and Viking Penguin in London.


Wallace, Darwin, and the origin of the Origin

There has been some attention recently devoted to the “neglected” Alfred Russel Wallace.  He was, of course, “neglected” to the point of being appointed to the Order of Merit, Britain’s highest honour, and getting credit in every good book about evolution.  But I thought it worth spelling out here just how he prompted (or provoked) Charles Darwin into writing his masterpiece.

Alfred Russel Wallace was born in 1823.  His background was very different from that of Charles Darwin, with no inherited wealth to rely on, and no illustrious scientific ancestors.  He was the eighth out of nine children, the son of an unsuccessful solicitor, and had to leave school at thirteen to earn a living.  After a year working for a joiner, he became an apprentice to his elder brother William, a land surveyor, and spent the years up to the age of twenty helping to survey‹d‹
railways, canals, and the land enclosures that were a hot political issue at the time.  This took him out in the countryside and encouraged him to become a keen naturalist, who made his own observations and read avidly about the natural world.
     In 1843, Wallace lost his job as the country was gripped by an economic recession, and he worked for a time as a schoolmaster, continuing to study natural history, and becoming friendly with a colleague, another eager amateur naturalist, Henry Bates.  Among the books they read and discussed together were Malthus’ “Essay” and the infamous “Vestiges”, which set them thinking about evolution.  They also read Lyell’s “Principles of Geology” and the new edition of Darwin’s “Journal”.
     In 1847, Wallace decided to try his luck as a freelance naturalist in the New
World.  There was a great demand for new specimens of all kinds both by private collectors and museums, and good prices would be paid for rare examples.  Together with Bates, Wallace planned an expedition to the Amazon, first boning up on natural history at the British Museum, and seeking help from Sir William Hooker at Kew.  They set sail in 1848, when Wallace was
25, three years older than Darwin had been when he departed on the“Beagle.”
     More than four years spent exploring and collecting under difficult conditions gave Wallace the same sort of “hands on” knowledge of natural history that Darwin had gained some twenty years earlier; but disaster struck on his return voyage.  The ship in which he was traveling was lost by fire, taking virtually all of his collection with it, and the crew and passengers were only rescued after ten days at sea in open boats.  Wallace returned to England as penniless as when he had left, with no collection to sell, but armed with a much greater understanding of the natural world.  Bates, who had stayed in South America, returned three years later, without any significant damage to his specimens.
     Wallace stayed in England only long enough to regroup and plan another expedition, this time to southeast Asia.  Darwin read some of Wallace’s published work, and was immediately impressed by what the thirty-year-old self-taught naturalist had to say about the extreme variability of species of butterflies in the Amazon valley.  This led to an exchange of letters between Darwin and Wallace that continued intermittently over the next few years, while Wallace was naturalising in and around Borneo.  It also led to Darwin becoming one of Wallace’s
customers, purchasing specimens from him, and sometimes complaining mildly in his private notes about the cost of having them shipped back to Britain.
     He was eager for more specimens because hiss thoughts were concentrating once again on the species question. “From September 1854 onwards,” he wrote in his “Autobiography”, “I devoted all my time to arranging my huge pile of notes, to observing, and experimenting, in relation to the transmutation of species”.
     Darwin’s solution to the problem of why speciation occurs was that “the modified offspring of all dominant and increasing forms tend to become adapted to many and highly developed places in the economy of nature”.
     This was very much an idea of its time, in the first industrialised economy in the world.   Division of labour and specialisation in the industrial world were familiar concepts to Darwin, both in the abstract and as a member, by blood and by marriage, of the Wedgwood clan whose fortunes were founded on the successful application of production-line factory techniques to their business.  Any individual that could exploit a vacant niche in‹d‹ nature would be successful, Darwin realised, like an entrepreneur who identified a gap in the economic market place and moved in to it.
     He was still reluctant to publish, but in April 1856 he at last confided in his mentor, Charles Lyell, when he visited Down House for a few days.  This was no impulsive decision, but part of a careful broadening of the circle of colleagues with whom he could discuss evolution.  In the same month, Darwin also sent invitations to Hooker, Huxley and Vernon Wollaston, a beetle expert from the British Museum, to attend a weekend gathering at Down House to thrash out ideas.  Also invited, but unable to attend, was Hewett Watson, a botanist who had expressed evolutionary views, and who Darwin had already partially confided in.  Lyell was informed of their discussions, and of the extent of Darwin’s theory.
     Astonished, and far from being entirely convinced, Lyell wrote to his wife’s brother-in-law, the botanist Charles Bunbury, “I cannot easily see how they can go so far, and not embrace the whole Lamarckian doctrine”.
    But of one thing he was certain — these ideas were too important to be restricted to discussions among a narrow circle of scientists meeting for the odd weekend at a country house in Kent.  On 1 May, Lyell wrote to Darwin, urging him, in no uncertain terms, to publish.  Like most modern scientists, Lyell was worried about establishing priority, proposing the idea of publishing just a brief paper so that Darwin could prove, if the theory did turn out to be correct, that he had come up with the idea before anyone else had.  That was far from Darwin’s mind, partly because he genuinely was not greatly bothered about establishing his priority to the idea, and partly because he seems to have had a blind spot concerning the possibility of someone else coming up with the idea.  He had sat on it now for nearly twenty years, and it seems never to have occurred to him that in all that time someone else might follow the same path that he had to the same conclusions.  Nevertheless, the outcome of the April 1856 meetings in which he had at least slightly expanded the audience for those ideas was that, prompted by Lyell and encouraged by Hooker, he at last decided that he would publish.  Not brief paper that could hardly do justice to the theory, but a proper book, a weighty scientific volume that might take him two years to complete.  And he also spread his ideas still further afield, writing about them in a letter to Asa Gray, an American botanist with whom he corresponded, which provided just the kind of outline of the entire theory that Lyell had urged him to publish.
     Perhaps because of his isolation in Down House and his reluctance to attend scientific meetings, Darwin seems to have been blind to the possibility that Wallace was on the same trail that he had followed, although he did take the
trouble to send Wallace a coded “hands off” message in a letter in May 1857, hoping to make his own position clear without giving his hand away, as well as commenting that “we have thought much alike and to a certain extent have come to similar conclusions”, he wrote:

This summer will make the 20th year (!) since I opened my first
note-book, on the question how and in what way do species and
varieties differ from each other.  I am now preparing my work
for publication, but I find the subject so very large, that
though I have written many chapters, I do not suppose I shall go
to press for two years.

     If the letter of May 1857 was intended as a “hands off” warning to Wallace, it did not succeed.  Indeed, it had exactly the opposite effect.  Cut off in the East Indies, Wallace was unaware that anyone had noticed his paper, and wrote back to Darwin indicating his intention of pressing on with his ideas.  Responding in December 1857, Darwin stressed both his enthusiasm for Wallace’s work and the
high opinion his colleagues had of it.  “I am extremely glad to hear that you are attending to distribution in accordance with theoretical ideas,” he said.
   All of this rekindled Wallace’s enthusiasm, encouraging him to press on with his theorising.  
   Wallace’s letter to Darwin that arrived on 18 June 1858, containing the manuscript of a paper headed “On the Tendency of Varieties to Depart Indefinitely from the Original Type”, asking Darwin to show it to Lyell and requesting their views on its contents, is often presented in the Darwin story as a bolt from the blue, a fully-fledged theory of evolution coming from an obscure and unfamiliar naturalist.  In fact, Wallace was known to the scientific community in general, and very well known (at least as a correspondent) to Darwin, who had actively encouraged him to develop his theory!  The pedigree for Wallace’s version of the theory was, indeed, at least as good as the pedigree Darwin’s theory would have had if he had published in 1844, when he would have been the same age (35) that Wallace was in 1858.
     But it was too late to think about what might have been in 1844.  After twenty years thinking about evolution, Darwin had been pre-empted.  Wallace might have sent the paper direct to one of the learned journals, with consequences we can only guess at; what actually happened is that Darwin duly sent the paper on to Lyell, with an anguished covering letter.

Your words have come true with a vengeance — that I should be
forestalled .  .  .  I never saw a more striking coincidence; if
Wallace had my MS sketch written out in 1842, he could not have
made a better short abstract!  .  .  .  He does not say he
wishes me to publish [his paper], but I shall, of course, at
once write and offer to send it to any journal.  So all my
originality, whatever it may amount to, will be smashed, though
my book, if it will ever have any value, will not be
deteriorated; as all the labour consists in the application of
the theory.
   Lyell, in consultation with Hooker, came up with a happy compromise.  A meeting of the Linnean Society was due to be held on 1 July.  Brushing aside Darwin’s doubts that it might not be quite the gentlemanly thing to do, they arranged for a joint presentation at that meeting of Wallace’s paper, Darwin’s 1844 outline of his theory, and the letter to Asa Gray from 1857, which helped to establish Darwin’s prior claim.  Darwin himself could not attend the meeting.  It is unlikely that he would have done so anyway, but the death of his baby son on 28 June, followed by his burial and the evacuation of the other children to stay with Emma’s sister Elizabeth on 2 July, made any trips to London out of the question.
     The presentation of the evolution theory at the meeting on 1 July caused only a minor stir.  The cat was out of the bag at last, but nobody seemed unduly bothered.  It was the last meeting before the summer break, six papers in all were presented to the meeting, and there was important Society business to attend to.  Even so, it comes as something of a surprise to a modern reader to find that
almost a year later, on 24 May 1859 (the anniversary of the birth of Linnaeus), the President of the Linnean Society summed up the events of the past twelve months with the comment:

The year which has passed  .  .  .  has not, indeed, been marked
by any of those striking discoveries which at once
revolutionise, so to speak, the department of science on which
they bear.
Journal of the Proceedings of the Linnean Society, Zoologyï,
volume IV, page viii, 1860.

Before the year was out, he must have wished he had never made that
    Even when the “joint paper” by Wallace and Darwin was published in the Proceedings of the Linnean Society, it received only a muted, and largely negative, response.  The reaction of Samuel Houghton, addressing the Geological Society of Dublin in February 1859 is not untypical.  He suggested that the only reason anybody had taken any notice of the joint paper was because of: the weight of authority of the names [Lyell and Hooker] under whose auspices it has been brought forward.  If it means what it says, it is a truism; if it means anything more, it is contrary to fact.

But by the time those words were spoken Darwin’s masterwork was
almost ready for publication.
     Prompted by the fear of being further pre-empted by a book from Wallace (in fact, Wallace gave up any plans to write such a book after the publication of the Origin), in the summer of 1858 Darwin began serious work on what he intended to be an “abstract” of his great book on Natural Selection.  At first, he intended this to be a substantial scientific paper; by the autumn, he had realised that he would need a small book to contain everything he had to say.  In the end, it turned out to be quite a large book, running to more than 150,000 words.
     Even when Darwin began discussing the book with its eventual publisher, John Murray, his working title was still An Abstract of an Essay on the Origin of Species and Varieties through Natural Selection; at Murray’s prompting, by the time it was published in November 1859 the title had been slimmed down to On the Origin of
Species, with the words by Means of Natural Selection in smaller type, followed by a typical Darwin afterthought or the Preservation of Favoured Races in the Struggle for Life.  No matter how Darwin might have wished to explain everything in the title alone, though, it has always been known simply as the Origin.
     Nobody involved expected the book to be a commercial success.  Murray initially planned to print 500 copies, but increased this to 1250 once he saw the finished work.  In the event, the booksellers subscribed for 1500 copies (so although it was not sold out on the day of publication, as folklore claims, every copy was in the shops) and an immediate reprint (actually a second edition, since Darwin was still tinkering with the text) was immediately set in motion.

Inflation for beginners

Another old essay.  Still accurate as far as the history goes, although there have been further developments in the 21st century.


INFLATION has become a cosmological buzzword in the 1990s. No self-respecting theory of the Universe is complete without a reference to inflation — and at the same time there is now a bewildering variety of different versions of inflation to choose from. Clearly, what’s needed is a beginner’s guide to inflation, where newcomers to cosmology can find out just what this exciting development is all about. This is it — new readers start here.

The reason why something like inflation was needed in cosmology was highlighted by discussions of two key problems in the 1970s. The first of these is the horizon problem — the puzzle that the Universe looks the same on opposite sides of the sky (opposite horizons) even though there has not been time since the Big Bang for light (or anything else) to travel across the Universe and back. So how do the opposite horizons “know” how to keep in step with each other? The second puzzle is called the flatness problem This is the puzzle that the spacetime of the Universe is very nearly flat, which means that the Universe sits just on the dividing line between eternal expansion and eventual recollapse.

The flatness problem can be understood in terms of the density of the Universe. The density parameter is a measure of the amount of gravitating material in the Universe, usually denoted by the Greek letter omega (O), and also known as the flatness parameter. It is defined in such a way that if spacetime is exactly flat then O = 1. Before the development of the idea of inflation, one of the great puzzles in cosmology was the fact that the actual density of the Universe today is very close to this critical value — certainly within a factor of 10. This is curious because as the Universe expands away from the Big Bang the expansion will push the density parameter away from the critical value.

If the Universe starts out with the parameter less than one, O gets smaller as the Universe ages, while if it starts out bigger than one O gets bigger as the Universe ages. The fact that O is between 0.1 and 1 today means that in the first second of the Big Bang it was precisely 1 to within 1 part in 1060). This makes the value of the density parameter in the beginning one of the most precisely determined numbers in all of science, and the natural inference is that the value is, and always has been, exactly 1. One important implication of this is that there must be a large amount of dark matter in the Universe. Another is that the Universe was made flat by inflation.

Inflation is a general term for models of the very early Universe which involve a short period of extremely rapid (exponential) expansion, blowing the size of what is now the observable Universe up from a region far smaller than a proton to about the size of a grapefruit (or even bigger) in a small fraction of a second. This process would smooth out spacetime to make the Universe flat, and would also resolve the horizon problem by taking regions of space that were once close enough to have got to know each other well and spreading them far apart, on opposite sides of the visible Universe today.

Inflation became established as the standard model of the very early Universe in the 1980s. It achieved this success not only because it resolves many puzzles about the nature of the Universe, but because it did so using the grand unified theories (GUTs) and understanding of quantum theory developed by particle physicists completely independently of any cosmological studies. These theories of the particle world had been developed with no thought that they might be applied in cosmology (they were in no sense “designed” to tackle all the problems they turned out to solve), and their success in this area suggested to many people that they must be telling us something of fundamental importance about the Universe.

The marriage of particle physics (the study of the very small) and cosmology (the study of the very large) seems to provide an explanation of how the Universe began, and how it got to be the way it is. Inflation is therefore regarded as the most important development in cosmological thinking since the discovery that the Universe is expanding first suggested that it began in a Big Bang.

Taken at face value, the observed expansion of the Universe implies that it was born out of a singularity, a point of infinite density, some 15 billion years ago (cosmologists still disagree about exactly how old the Universe is, but the exact age doesn’t affect the argument). Quantum physics tells us that it is meaningless to talk in quite such extreme terms, and that instead we should consider the expansion as having started from a region no bigger across than the so-called Planck length (10-35m), when the density was not infinite but “only” some 1094 grams per cubic centimetre. These are the absolute limits on size and density allowed by quantum physics.

On that picture, the first puzzle is how anything that dense could ever expand — it would have an enormously strong gravitational field, turning it into a black hole and snuffing it out of existence (back into the singularity) as soon as it was born. But it turns out that inflation can prevent this happening, while quantum physics allows the entire Universe to appear, in this supercompact form, out of nothing at all, as a cosmic free lunch. The idea that the Universe may have appeared out of nothing at all, and contains zero energy overall, was developed by Edward Tryon, of the City University in New York, who suggested in the 1970s, that it might have appeared out of nothing as a so-called vacuum fluctuation, allowed by quantum theory.

Quantum uncertainty allows the temporary creation of bubbles of energy, or pairs of particles (such as electron-positron pairs) out of nothing, provided that they disappear in a short time. The less energy is involved, the longer the bubble can exist. Curiously, the energy in a gravitational field is negative, while the energy locked up in matter is positive. If the Universe is exactly flat , then as Tryon pointed out the two numbers cancel out, and the overall energy of the Universe is precisely zero. In that case, the quantum rules allow it to last forever. If you find this mind-blowing, you are in good company. George Gamow told in his book My World Line (Viking, New York, reprinted 1970) how he was having a conversation with Albert Einstein while walking through Princeton in the 1940s. Gamow casually mentioned that one of his colleagues had pointed out to him that according to Einstein’s equations a star could be created out of nothing at all, because its negative gravitational energy precisely cancels out its positive mass energy. “Einstein stopped in his tracks,” says Gamow, “and, since we were crossing a street, several cars had to stop to avoid running us down”.

Unfortunately, if a quantum bubble (about as big as the Planck length) containing all the mass-energy of the Universe (or even a star) did appear out of nothing at all, its intense gravitational field would (unless something else intervened) snuff it out of existence immediately, crushing it into a singularity. So the free lunch Universe seemed at first like an irrelevant speculation — but, as with the problems involving the extreme flatness of spacetime, and its appearance of extreme homogeneity and isotropy (most clearly indicated by the uniformity of the background radiation), the development of the inflationary scenario showed how to remove this difficulty and allow such a quantum fluctuation to expand exponentially up to macroscopic size before gravity could crush it out of existence.. All of these problems would be resolved if something gave the Universe a violent outward push (in effect, acting like antigravity) when it was still about a Planck length in size. Such a small region of space would be too tiny, initially, to contain irregularities, so it would start off homogeneous and isotropic. There would have been plenty of time for signals travelling at the speed of light to have criss-crossed the ridiculously tiny volume, so there is no horizon problem — both sides of the embryonic universe are “aware” of each other. And spacetime itself gets flattened by the expansion, in much the same way that the wrinkly surface of a prune becomes a smooth, flat surface when the prune is placed in water and swells up. As in the standard Big Bang model, we can still think of the Universe as like the skin of an expanding balloon, but now we have to think of it as an absolutely enormous balloon that was hugely inflated during the first split second of its existence.

The reason why the GUTs created such a sensation when they were applied to cosmology is that they predict the existence of exactly the right kind of mechanisms to do this trick. They are called scalar fields, and they are associated with the splitting apart of the original grand unified force into the fundamental forces we know today, as the Universe began to expand and cool. Gravity itself would have split off at the Planck time, 10-43 of a second, and the strong nuclear force by about 10(exp-35) of a second. Within about 10-32 of a second, the scalar fields would have done their work, doubling the size of the Universe at least once every 10-34 of a second (some versions of inflation suggest even more rapid expansion than this).

This may sound modest, but it would mean that in 1032 of a second there were 100 doublings. This rapid expansion is enough to take a quantum fluctuation 1020 times smaller than a proton and inflate it to a sphere about 10 cm across in about 15 x 1033 seconds. At that point, the scalar field has done its work of kick-starting the Universe, and is settling down, giving up its energy and leaving a hot fireball expanding so rapidly that even though gravity can now begin to do its work of pulling everything back into a Big Crunch it will take hundreds of billions of years to first halt the expansion and then reverse it.

Curiously, this kind of exponential expansion of spacetime is exactly described by one of the first cosmological models developed using the general theory of relativity, by Willem de Sitter in 1917. For more than half a century, this de Sitter model seemed to be only a mathematical curiosity, of no relevance to the real Universe; but it is now one of the cornerstones of inflationary cosmology.

When the general theory of relativity was published in 1916, de Sitter reviewed the theory and developed his own ideas in a series of three papers which he sent to the Royal Astronomical Society in London. The third of these papers included discussion of possible cosmological models — both what turned out to be an expanding universe (the first model of this kind to be developed, although the implications were not fully appreciated in 1917) and an oscillating universe model.

De Sitter’s solution to Einstein’s equations seemed to describe an empty, static Universe (empty spacetime). But in the early 1920s it was realised that if a tiny amount of matter was added to the model (in the form of particles scattered throughout the spacetime), they would recede from each other exponentially fast as the spacetime expanded. This means that the distance between two particles would double repeatedly on the same timescale, so they would be twice as far apart after one tick of some cosmic clock, four times as far apart after two ticks, eight times as far apart after three ticks, sixteen times as far apart after four ticks, and so on. It would be as if each step you took down the road took you twice as far as the previous step.

This seemed to be completely unrealistic; even when the expansion of the Universe was discovered, later in the 1920s, it turned out to be much more sedate. In the expanding Universe as we see it now, the distances between “particles” (clusters of galaxies) increase steadily — they take one step for each click of the cosmic clock, so the distance is increased by a total of two steps after two clicks, three steps after three clicks, and so on. In the 1980s, however, when the theory of inflation suggested that the Universe really did undergo a stage of exponential expansion during the first split-second after its birth, this inflationary exponential expansion turned out to be exactly described by the de Sitter model, the first successful cosmological solution to Einstein’s equations of the general theory of relativity.

One of the peculiarities of inflation is that it seems to take place faster than the speed of light. Even light takes 30 billionths of a second (3 x 10(exp-10) sec) to cross a single centimetre, and yet inflation expands the Universe from a size much smaller than a proton to 10 cm across in only 15 x 10(exp-33) sec. This is possible because it is spacetime itself that is expanding, carrying matter along for the ride; nothing is moving through spacetime faster than light, either during inflation or ever since. Indeed, it is just because the expansion takes place so quickly that matter has no time to move while it is going on and the process “freezes in” the original uniformity of the primordial quantum bubble that became our Universe.

The inflationary scenario has already gone through several stages of development during its short history. The first inflationary model was developed by Alexei Starobinsky, at the L. D. Landau Institute of Theoretical Physics in Moscow, at the end of the 1970s — but it was not then called “inflation”. It was a very complicated model based on a quantum theory of gravity, but it caused a sensation among cosmologists in what was then the Soviet Union, becoming known as the “Starobinsky model” of the Universe. Unfortunately, because of the difficulties Soviet scientists still had in travelling abroad or communicating with colleagues outside the Soviet sphere of influence at that time, the news did not spread outside their country.

In 1981, Alan Guth, then at MIT, published a different version of the inflationary scenario, not knowing anything of Starobinsky’s work. This version was more accessible in both senses of the word — it was easier to understand, and Guth was based in the US, able to discuss his ideas freely with colleagues around the world. And as a bonus, Guth came up with the catchy name “inflation” for the process he was describing. There were obvious flaws with the specific details of Guth’s original model (which he acknowledged at the time). In particular, Guth’s model left the Universe after inflation filled with a mess of bubbles, all expanding in their own way and colliding with one another. We see no evidence for these bubbles in the real Universe, so obviously the simplest model of inflation couldn’t be right. But it was this version of the idea that made every cosmologist aware of the power of inflation.

In October 1981, there was an international meeting in Moscow, where inflation was a major talking point. Stephen Hawking presented a paper claiming that inflation could not be made to work at all, but the Russian cosmologist Andrei Linde presented an improved version, called “new inflation”, which got around the difficulties with Guth’s model. Ironically, Linde was the official translator for Hawking’s talk, and had the embarrassing task of offering the audience the counter-argument to his own work! But after the formal presentations Hawking was persuaded that Linde was right, and inflation might be made to work after all. Within a few months, the new inflationary scenario was also published by Andreas Albrecht and Paul Steinhardt, of the University of Pennsylvania, and by the end of 1982 inflation was well established. Linde has been involved in most of the significant developments with the theory since then. The next step forward came with the realization that there need not be anything special about the Planck- sized region of spacetime that expanded to become our Universe. If that was part of some larger region of spacetime in which all kinds of scalar fields were at work, then only the regions in which those fields produced inflation could lead to the emergence of a large universe like our own. Linde called this “chaotic inflation”, because the scalar fields can have any value at different places in the early super-universe; it is the standard version of inflation today, and can be regarded as an example of the kind of reasoning associated with the anthropic principle (but note that this use of the term “chaos” is like the everyday meaning implying a complicated mess, and has nothing to do with the mathematical subject known as “chaos theory”).

The idea of chaotic inflation led to what is (so far) the ultimate development of the inflationary scenario. The great unanswered question in standard Big Bang cosmology is what came “before” the singularity. It is often said that the question is meaningless, since time itself began at the singularity. But chaotic inflation suggests that our Universe grew out of a quantum fluctuation in some pre-existing region of spacetime, and that exactly equivalent processes can create regions of inflation within our own Universe. In effect, new universes bud off from our Universe, and our Universe may itself have budded off from another universe, in a process which had no beginning and will have no end. A variation on this theme suggests that the “budding” process takes place through black holes, and that every time a black hole collapses into a singularity it “bounces” out into another set of spacetime dimensions, creating a new inflationary universe — this is called the baby universe scenario.

There are similarities between the idea of eternal inflation and a self-reproducing universe and the version of the Steady State hypothesis developed in England by Fred Hoyle and Jayant Narlikar, with their C-field playing the part of the scalar field that drives inflation. As Hoyle wryly pointed out at a meeting of the Royal Astronomical Society in London in December 1994, the relevant equations in inflation theory are exactly the same as in his version of the Steady State idea, but with the letter “C” replaced by the Greek “Ø”. “This,” said Hoyle (tongue firmly in cheek) “makes all the difference in the world”.

Modern proponents of the inflationary scenario arrived at these equations entirely independently of Hoyle’s approach, and are reluctant to accept this analogy, having cut their cosmological teeth on the Big Bang model. Indeed, when Guth was asked, in 1980, how the then new idea of inflation related to the Steady State theory, he is reported as replying “what is the Steady State theory?” But although inflation is generally regarded as a development of Big Bang cosmology, it is better seen as marrying the best features of both the Big Bang and the Steady State scenarios.

This might all seem like a philosophical debate as futile as the argument about how many angels can dance on the head of a pin, except for the fact that observations of the background radiation by COBE showed exactly the pattern of tiny irregularities that the inflationary scenario predicts. One of the first worries about the idea of inflation (long ago in 1981) was that it might be too good to be true. In particular, if the process was so efficient at smoothing out the Universe, how could irregularities as large as galaxies, clusters of galaxies and so on ever have arisen? But when the researchers looked more closely at the equations they realised that quantum fluctuations should still have been producing tiny ripples in the structure of the Universe even when our Universe was only something like 10(exp-25) of a centimetre across — a hundred million times bigger than the Planck length.

The theory said that inflation should have left behind an expanded version of these fluctuations, in the form of irregularities in the distribution of matter and energy in the Universe. These density perturbations would have left an imprint on the background radiation at the time matter and radiation decoupled (about 300,000 years after the Big Bang), producing exactly the kind of nonuniformity in the background radiation that has now been seen, initially by COBE and later by other instruments. After decoupling, the density fluctuations grew to become the large scale structure of the Universe revealed today by the distribution of galaxies. This means that the COBE observations are actually giving us information about what was happening in the Universe when it was less than 10-20 of a second old.

No other theory can explain both why the Universe is so uniform overall, and yet contains exactly the kind of “ripples” represented by the distribution of galaxies through space and by the variations in the background radiation. This does not prove that the inflationary scenario is correct, but it is worth remembering that had COBE found a different pattern of fluctuations (or no fluctuations at all) that would have proved the inflationary scenario wrong. In the best scientific tradition, the theory made a major and unambiguous prediction which did “come true”. Inflation also predicts that the primordial perturbations may have left a trace in the form of gravitational radiation with particular characteristics, and it is hoped that detectors sensitive enough to identify this characteristic radiation may be developed within the next ten or twenty years.

The clean simplicity of this simple picture of inflation has now, however, begun to be obscured by refinements, as inflationary cosmologists add bells and whistles to their models to make them match more closely the Universe we see about us. Some of the bells and whistles, it has to be said, are studied just for fun. Linde himself has taken great delight in pushing inflation to extremes, and offering entertaining new insights into how the Universe might be constructed. For example, could our Universe exist on the inside of a single magnetic monopole produced by cosmic inflation? According to Linde, it is at least possible, and may be likely. And in a delicious touch of irony, Linde, who now works at Stanford University, made this outrageous claim in a lecture at a workshop on the Birth of the Universe held recently in Rome, where the view of Creation is usually rather different. One of the reasons why theorists came up with the idea of inflation in the first place was precisely to get rid of magnetic monopoles — strange particles carrying isolated north or south magnetic fields, predicted by many Grand Unified Theories of physics but never found in nature. Standard models of inflation solve the “monopole problem” by arguing that the seed from which our entire visible Universe grew was a quantum fluctuation so small that it only contained one monopole. That monopole is still out there, somewhere in the Universe, but it is highly unlikely that it will ever pass our way.

But Linde has discovered that, according to theory, the conditions that create inflation persist inside a magnetic monopole even after inflation has halted in the Universe at large. Such a monopole would look like a magnetically charged black hole, connecting our Universe through a wormhole in spacetime to another region of inflating spacetime. Within this region of inflation, quantum processes can produce monopole-antimonopole pairs, which then separate exponentially rapidly as a result of the inflation. Inflation then stops, leaving an expanding Universe rather like our own which may contain one or two monopoles, within each of which there are more regions of inflating spacetime.

The result is a never-ending fractal structure, with inflating universes embedded inside each other and connected through the magnetic monopole wormholes. Our Universe may be inside a monopole which is inside another universe which is inside another monopole, and so on indefinitely. What Linde calls “the continuous creation of exponentially expanding space” means that “monopoles by themselves can solve the monopole problem”. Although it seems bizarre, the idea is, he stresses, “so simple that it certainly deserves further investigation”.

That variation on the theme really is just for fun, and it is hard to see how it could ever be compared with observations of the real Universe. But most of the modifications to inflation now being made are in response to new observations, and in particular to the suggestion that spacetime may not be quite “flat” after all. In the mid-1990s, many studies (including observations made by the refurbished Hubble Space Telescope) began to suggest that there might not be quite enough matter in the Universe to make it perfectly flat — most of the observations suggest that there is only 20 per cent or 30 per cent as much matter around as the simplest versions of inflation require. The shortfall is embarrassing, because one of the most widely publicised predictions of simple inflation was the firm requirement of exactly 100 per cent of this critical density of matter. But there are ways around the difficulty; and here are two of them to be going on with.

The first suggestion is almost heretical, in the light of the way astronomy has developed since the time of Copernicus. Is it possible that we are living near the centre of the Universe? For centuries, the history of astronomy has seen humankind displaced from any special position. First the Earth was seen to revolve around the Sun, then the Sun was seen to be an insignificant member of the Milky Way Galaxy, then the Galaxy was seen to be an ordinary member of the cosmos. But now comes the suggestion that the “ordinary” place to find observers like us may be in the middle of a bubble in a much greater volume of expanding space.

The conventional version of inflation says that our entire visible Universe is just one of many bubbles of inflation, each doing their own thing somewhere out in an eternal sea of chaotic inflation, but that the process of rapid expansion forces spacetime in all the bubbles to be flat. A useful analogy is with the bubbles that form in a bottle of fizzy cola when the top is opened. But that suggestion, along with other cherished cosmological beliefs, has now been challenged by Linde, working with his son Dmitri Linde (of CalTech) and Arthur Mezhlumian (also of Stanford).

Linde and his colleagues point out that the Universe we live in is like a hole in a sea of superdense, exponentially expanding inflationary cosmic material, within which there are other holes. All kinds of bubble universes will exist, and it is possible to work out the statistical nature of their properties. In particular, the two Lindes and Mezhlumian have calculated the probability of finding yourself in a region of this super- Universe with a particular density — for example, the density of “our” Universe.

Because very dense regions blow up exponentially quickly (doubling in size every fraction of a second), it turns out that the volume of all regions of the super-Universe with twice any chosen density is 10 to the power of 10 million times greater than the volume of the super- Universe with the chosen density. For any chosen density, most of the matter at that density is near the middle of an expanding bubble, with a concentration of more dense material round the edge of the bubble. But even though some of the higher density material is round the edges of low density bubbles, there is even more (vastly more!) higher density material in the middle of higher density bubbles, and so on forever. The discovery of this variation on the theme of fractal structure surprised the researchers so much that they confirmed it by four independent methods before venturing to announce it to their colleagues. Because the density distribution is non-uniform on the appropriate distance scales, it means that not only may we be living near the middle of a bubble universe, but that the density of the region of space we can see may be less than the critical density, compensated for by extra density beyond our field of view.

This is convenient, since those observations by the Hubble Space Telescope have suggested that cosmological models which require exactly the critical density of matter may be in trouble. But there is more. Those Hubble observations assume that the parameter which measures the rate at which the Universe is expanding, the Hubble Constant, really is a constant, the same everywhere in the observable Universe. If Linde’s team is right, however, the measured value of the “constant” may be different for galaxies at different distances from us, truly throwing the cat among the cosmological pigeons. We may seem to live in a low-density universe in which both the measured density and the value of the Hubble Constant will depend on which volume of the Universe these properties are measured over!

That would mean abandoning many cherished ideas about the Universe, and may be too much for many cosmologists to swallow. But there is a simpler solution to the density puzzle, one which involves tinkering only with the models of inflation, not with long-held and cherished cosmological beliefs. That may make it more acceptable to most cosmologists — and it’s so simple that it falls into the “why didn’t I think of that?” category of great ideas.

A double dose of inflation may be something to make the Government’s hair turn grey — but it could be just what cosmologists need to rescue their favourite theory of the origin of the Universe. By turning inflation on twice, they have found a way to have all the benefits of the inflationary scenario, while still leaving the Universe in an “open” state, so that it will expand forever.

In those simplest inflation models, remember, the big snag is that after inflation even the observable Universe is left like a mass of bubbles, each expanding in its own way. We see no sign of this structure, which has led to all the refinements of the basic model. Now, however, Martin Bucher and Neil Turok, of Princeton University, working with Alfred Goldhaber, of the State University of New York, have turned this difficulty to advantage.

They suggest that after the Universe had been homogenised by the original bout of inflation, a second burst of inflation could have occurred within one of the bubbles. As inflation begins (essentially at a point), the density is effectively “reset” to zero, and rises towards the critical density as inflation proceeds and energy from the inflation process is turned into mass. But because the Universe has already been homogenised, there is no need to require this bout of inflation to last until the density reaches the critical value. It can stop a little sooner, leaving an open bubble (what we see as our entire visible Universe) to carry on expanding at a more sedate rate. They actually use what looked like the fatal flaw in Guth’s model as the basis for their scenario. According to Bucher and his colleagues, an end product looking very much like the Universe we live in can arise naturally in this way, with no “fine tuning” of the inflationary parameters. All they have done is to use the very simplest possible version of inflation, going back to Alan Guth’s work, but to apply it twice. And you don’t have to stop there. Once any portion of expanding spacetime has been smoothed out by inflation, new inflationary bubbles arising inside that volume of spacetime will all be pre-smoothed and can end up with any amount of matter from zero to the critical density (but no more). This should be enough to make everybody happy. Indeed, the biggest problem now is that the vocabulary of cosmology doesn’t quite seem adequate to the task of describing all this activity.

The term Universe, with the capital “U”, is usually used for everything that we can ever have knowledge of, the entire span of space and time accessible to our instruments, now and in the future. This may seem like a fairly comprehensive definition, and in the past it has traditionally been regarded as synonymous with the entirety of everything that exists. But the development of ideas such as inflation suggests that there may be something else beyond the boundaries of the observable Universe — regions of space and time that are unobservable in principle, not just because light from them has not yet had time to reach us, or because our telescopes are not sensitive enough to detect their light.

This has led to some ambiguity in the use of the term “Universe”. Some people restrict it to the observable Universe, while others argue that it should be used to refer to all of space and time. If we use “Universe” as the name for our own expanding bubble of spacetime, everything that is in principle visible to our telescopes, then maybe the term “Cosmos” can be used to refer to the entirety of space and time, within which (if the inflationary scenario is correct) there may be an indefinitely large number of other expanding bubbles of spacetime, other universes with which we can never communicate. Cosmologists ought to be happy with the suggestion, since it makes their subject infinitely bigger and therefore infinitely more important!

Further reading: John Gribbin, Companion to the Cosmos, Weidenfeld & Nicolson, London, 1996.

In praise of Whigs

My fellow blogger Jim Grozier ( recently had some interesting things to say about the history of science, and the way historians think about science.  This prompted me to dig out the Preface to the Folio Society edition of my own history of science, in their edition known as a History of Western Science but originally published by Penguin as Science: A History.  In both cases, “a” history, not “the” history, for obvious (I hope) reasons.

In Praise of Whigs
I have been interested in history for as long as I can remember, and writing about science for nearly as long; but it was only well into my career that I realised I was also writing about history. My writing career began with journalism, where stories had to have immediate impact, dealing almost exclusively with things that were ‘new’ and this week’s ‘breakthrough’ – which often became last week’s out-of-date idea. Even when I started writing books, at first I concentrated on so-called cutting-edge research, which made for some excited scurrying to get the stories into print before they became out of date, but didn’t always result in books with a long shelf life. The change came when I decided to write a book about quantum physics, consciously intended as the book I wished someone else had written for my benefit. Lacking the cutting-edge immediacy of its predecessors, it was turned down by eight publishers
before seeing life in 1984 as In Search of Schrödinger’s Cat, and has remained in print ever since. Even then, it only slowly dawned on me, thanks to correspondence from readers, that what Ihad written was a history of how quantum physics developed in
the twentieth century, and who the people were who developed it. Readers, I learned, were fascinated to discover that people they knew of only as names on laws (such as Heisenberg, of uncertainty principle fame) were human beings with human frailties (in this case, among other things, severe hay fever, which played a part in his discovery of some key features of the quantum world).

Gradually, my books became more focused on scientific history and biography (which, after all, is a kind of history), until Stefan McGrath, my editor at Penguin, suggested that I should do the job properly, and write a history of the development of Western science. The result was the book you now see. And once again, after it was published I learned that I had written something that wasn’t entirely what I thought I was writing.

One of the reviews of the Allen Lane edition of this book referred to it sneeringly as a ‘Whig view of history’. Never having trained as a historian, I was only vaguely aware of the existence of factions among professional historians with different views on the
interpretation of history, but it was clear from the context that this was not intended as a complimentary remark. Intrigued, I checked up on what, exactly, the term means. As I had suspected, I discovered that Thomas Babington Macaulay was the archetypal ‘Whig historian’, but (as I had also anticipated) that the term is almost exclusively used as one of derision, so that very few historians, past or present, describe themselves as ‘Whigs’. From John Warren, author of History and the Historians, I learned that ‘most people interested in non-academic history enjoy a good, sweeping narrative and appreciate the way in which Whig-style history gives them straightforward explanations’, which certainly fits what I was trying to do. I also learned that the term was coined by Herbert Butterfield, and that his influential writings helped to push British academic history ‘towards narrow PhD style
research and books which had little or no appeal to a general
readership’ – certainly not my scene.

Macaulay’s great-nephew George Macaulay Trevelyan, following the family tradition, wrote in an autobiographical essay that:
The poetry of history lies in the quasi-miraculous fact that once,
on this earth, once, on this familiar spot of ground, walked
other men and women, as actual as we are today, thinking their
own thoughts, swayed by their own passions, but now all gone,
one generation vanishing after another, gone as utterly as we
shall shortly be gone . . .

I prefer to emphasise the continuity rather than the vanishing, theway the torch of, in this case, scientific progress is passed on from one generation to the next; but I agree with Trevelyan about the poetry. And I would emphasise that in the history of science, whatever the situation may be in the broader historical context, we are talking about progress. Albert Einstein did come up with an objectively better description of the Universe than Isaac Newton did, not because he was any more clever than Newton, but because of all the things that had been discovered in the centuries between Newton’s death and Einstein’s birth.

In his biography of Trevelyan, David Cannadine summed up the success of his Whig approach to history as ‘in evoking the past, in unfolding a narrative, and in capturing the imagination of a broad general public’. Adding this to the comments already quoted, to paraphrase Tom Lehrer, ‘It makes a fellow proud to be a Whig.’ My sneering critic precisely hit the nail on the head, and helped me to understand what I was doing in writing this book – my aim is indeed to evoke the past, to unfold a narrative, and to capture the imagination of a broad general public; and I am flattered to be mentioned in the same breath as Macaulay and Trevelyan.

But in the light of such criticism, in case any other professional historians of a non-Whiggish persuasion should stumble upon this book, there is one relevant point that I would like to make crystal clear. History is inevitably about people, because it is people who make history. But I am firmly convinced that individuals do not play a great part in determining the way history develops (at least, not in terms of the history of science), because if one individual had not made a particular discovery, or come up with a particular law, someone else would have at about the same time. The reason why science has progressed in the way it has since the ball started rolling in the middle of the sixteenth century (why it started rolling then is perhaps another story) is that one thing builds on another, and that science and technology go hand in hand. To take a simple example, Galileo Galilei could not have discovered the moons of Jupiter before the telescope was invented, and the discovery of the moons of Jupiter helped to spur both Galileo and other telescope makers to develop better instruments for observing the heavens.

There is room to debate whether or not the influence of a single individual such as Napoleon or Mohammed can change the way history is developing in the broader sense; but there is very little room for speculation that the course of science over the past few centuries would have been radically different if Newton, or Einstein, or any of the other people whose work is described in this book had not existed.
So if you are looking for a narrow PhD-style book, you have come to the wrong place. But if you have Whiggish tendencies and want a sweeping narrative with plenty of stories about real people doing out-of-the-ordinary things, you are just the kind of person I hope to be able to please.

Snarks, boojums and redshifts

Another pet hate — people who think that the cosmological redshift is a Doppler/velocity effect.  It ain’t.  But that doesn’t reduce its importance; if anything, the opposite.

Edwin Hubble made the two most important discoveries in cosmology.  First he proved that many “nebulae” are other “island universes” beyond the boundaries of the Milky Way.  Then, he discovered that the galaxies, as these nebulae are now known, are moving apart from one another – that the Universe is expanding.  But he didn’t make the second discovery on his own; the astronomer who actually carried out most of the painstaking observational work was Hubble’s colleague at the Mount Wilson Observatory, Milton Humason.  Hubble, the more senior astronomer, chose Humason as his partner because Humason was, quite simply, the best observer in the world in the 1920s, able to push the abilities of what was then the best telescope on Earth, the 100-inch (2.54 m) reflector at Mount Wilson, to the limit.
From the perspective of the 21st century, it’s worth taking stock of what those measurements involved.  Humason had to spend long hours in the cold of an unheated telescope dome, open to the sky, on a mountain top at night, keeping the telescope trained on particular patch of the sky while light from a distant galaxy was focussed on to a glass photographic plate.  The dome had to be unheated, because convection currents from any heater would disturb the air and distort the image; and observations were best made in winter, when the air was still and the nights were long.  Often, the galaxy being studied would be so faint that at the end of one night’s observing the photographic plate would have to be packed away, in the dark, in a light-proof box, then taken out the next night and used to build up a brighter image of the distant galaxy.  And then the plate had to be developed by hand before its image could be analysed.  All this required enormous patience, a quality Humason had in abundance but Hubble did not, as well as great skill.  A far cry from modern techniques, where telescopes can be operated by remote control from air-conditioned rooms, and the light is gathered on photographic chips, with photons (particles of light) being counted by computers.
In the second half of the decade of the 1920s, Hubble was still primarily interested in measuring the distances to galaxies.  He was intrigued by a discovery that had been made in the previous decade by Vesto Slipher, an astronomer working at the Lowell Observatory in Flagstaff, Arizona.  Slipher had been working with a 24-inch refracting telescope which had a new instrument called a spectrograph attached to it.  This could make photographs of the spectra of faint astronomical objects, by adding up the light over several nights if necessary.  Among the objects Slipher studied in this way were several of the family still known as nebulae, which Hubble was about to prove were actually external galaxies.  By 1925, just when Hubble was beginning to measure distances to galaxies, Slipher had measured 41 of these spectra, and found that just two of them (including the Andromeda Nebula) showed blueshifts, while 39 showed redshifts.  This was the limit of what he could do with the 24-inch telescope, but the evidence hinted that the galaxies that looked bigger and brighter had smaller redshifts.  The obvious inference was that galaxies that look bigger and brighter galaxies are closer to us – so Hubble guessed that measuring redshifts might be a way of measuring distances to galaxies, and roped Humason in to test the idea with the 100-inch telescope.  Humason measured the redshifts, while Hubble estimated the distances to the same galaxies, using other techniques.
By the beginning of the 1930s, Hubble and Humason had made enough observations to show that the relationship between redshift and distance is about as straightforward as it could possibly be: the redshift is proportional to the distance – or, putting it the way round that mattered to Hubble, distance is proportional to redshift.  This is now known as Hubble’s law.  It means that if one galaxy has twice the redshift of another it is twice as far away, and so on.  Once the distances to a few nearby galaxies had been measured by other means, the rule could be calibrated, and distances to other galaxies, much farther away across the Universe, could be measured simply by measuring their redshifts.  In fact, this simple law only applies accurately to relatively nearby galaxies, and a more subtle relationship applies farther out across the Universe, but this does not detract from the importance of Hubble’s discovery.
Hubble himself wasn’t interested in why the light from galaxies showed redshifts.  All he cared about was how the redshift (whatever its cause) could be used to measure distances.  But the natural guess people made at first was that the redshifts are caused by the Doppler Effect.  If so, it meant that just two external galaxies (including Andromeda) are moving towards us, and all the rest are moving away – not as individuals, but as members of clusters like the Virgo Cluster.  It was soon realised, however, that this recession of the galaxies is not caused by galaxies and clusters moving through space.  Albert Einstein’s general theory of relativity, which he had completed in 1915, described how space itself could be bent by the presence of matter, like a stretched rubber sheet with a heavy weight on it.  The equations also described how space as a whole could stretch, but in 1915 nebulae hadn’t even been identified as external galaxies, and Einstein had dismissed this as a trick of the mathematics with no physical significance.  After the discovery of the redshift-distance relationship, Einstein and other mathematicians realised that this was exactly what his equations described – space itself stretching and carrying clusters of galaxies along with it.  This was the beginning of modern cosmology.
The cosmological redshift is not a Doppler Effect.  It is not caused by galaxies moving through space, but by the space between the galaxies stretching during the time it takes light to get from one galaxy to another, and stretching the light to longer wavelengths.  Galaxies do move through space, producing Doppler Effects in their spectra, but these are simply added to or subtracted from the cosmological redshift – which is why, for example, Andromeda shows a blueshift.  It is moving towards us through space faster than the space between us and Andromeda is expanding.  But for all except the nearest galaxies, the cosmological redshift dominates.

How to build a time machine

And by special request:

A Do-it-Yourself Time Machine
Traditionally, writers of “hard” Sf are supposed to work within the framework of the known laws of physics as far as possible, but are allowed to make use of two “impossible” assumptions. One is space travel at speeds faster than that of light, which is forbidden by the equations of relativity theory, and which no scientist believes to be possible. The other is, or was, time travel, which flies in the face of common sense, and is “obviously” impossible. But in recent years, relativists have been forced to the uncomfortable conclusion that, in fact, time travel is not ruled out by Einstein’s equations.
Here is the English language version of an article of mine which first appeared in Italian in the sober pages of the science fact magazine l’Astronomia. The bottom line is that there is nothing in the laws of physics which forbids time travel, with all that that implies. The safety net favoured by relativists in our location is that actually constructing such a machine would involve very advanced technology. But that is a far cry from it being scientifically impossible (like travelling at a speed faster than that of light), and as Arthur C. Clarke once said (not Fred Hoyle, in our version of reality), any sufficiently advanced technology is indistinguishable from magic.
Scientific understanding of the way the Universe works, in the form of the general theory of relativity, has now progressed to the point where it is possible to provide you with the following simple instructions for building a time machine. This is now a practicable possibility, limited only by the available technology; we can accept no responsibility, however, for any paradoxes caused by the operation of such a machine.
First, catch your black hole. Do not try to find a black hole in the container in which you received these instructions. The black hole is not supplied with the instructions, and is not included in the price.
A black hole is an object which has such a strong gravitational pull that it wraps spacetime around itself, like a soap bubble, cutting off the inside of the hole from the rest of the Universe. To give you some idea of what this involves, imagine turning our Sun into a black hole. The Sun is about a million times bigger, in terms of volume, than the Earth. But in order to turn it into a black hole, it would have to be squeezed into a sphere only a few kilometers across—about the size of Mount Everest, or the Isle of Wight.
Nevertheless, astronomers are sure that black holes like this do exist. They can detect them by their gravitational influence on nearby stars—if you see a star being tugged sideways by something that isn’t there, the chances are that the invisible something is not the infamous cat Macavity, but a black hole.
As you are no doubt aware from your study of Einstein’s equations, every black hole has two ends, and is properly regarded as a “wormhole”, linking two different locations in spacetime by a tunnel through hyperspace. We suggest that in order to avoid problems with spaghettification (see below), the black hole should have a minimum mass of about 100 times the mass of our Sun. This will make it very easy to tow the hole to a convenient location (such as the back yard of the Solar System, between the orbits of Mars and Jupiter) by dangling a moderate sized planet (you may find Jupiter convenient for this task) in front of it and moving the planet. The gravitational attraction between the planet and the black hole will then bring the hole along behind like a donkey following a carrot.
If you do not have a spacecraft capable of towing planets, we refer you to our leaflet “Build Your Own Spaceship”, available from the usual address.
It is now necessary to ensure that both ends of the black hole are in the same place, but at different times. This is achieved by driving your spaceship into the black hole, and out of the other end of the tunnel. After identifying your location from the star maps provided, tow the other end of the hole back to the Solar System.
You can now adjust the time machine to your own specification using the relativistic time dilation procedure. This involves whirling the second end of the black hole round in a circle, at a speed of approximately half the speed of light (that is, 150 million kilometers per second) for an appropriate period. The relativistic time dilation effect will ensure that a time difference builds up between the two ends of the hole. After checking the time difference from the usual geological indicators, to ensure just the amount required, you may then bring the hole to a halt, and your time machine is ready to use.
WARNING: We can take no responsibility for difficulties caused by careless use of the time machine. Before attempting to use the time machine, please read the following historical background and explanation of the granny paradox:
When astronomer Carl Sagan decided to write a science fiction novel, he needed a fictional device that would allow his characters to travel great distances across the Universe. He knew, of course, that it is impossible to travel faster than light; and he also knew that there was a common convention in science fiction that allowed writers to use the gimmick of a shortcut through “hyperspace” as a means around this problem. But, being a scientist, Sagan wanted something that would seem to be more substantial than a conventional gimmick for his story. Was there any way to dress up the mumbo-jumbo of Sf hyperspace in a cloak of respectable sounding science? Sagan didn’t know. He isn’t an expert on general relativity—his background specialty is planetary studies. But he knew just the man to turn to for some advice on how to make the obviously impossible idea of hyperspace connections through spacetime sound a bit more scientifically plausible in his book Contact.
The man Sagan turned to for advice, in the summer of 1985, was Kip Thorne, at CalTech. Thorne was sufficiently intrigued to set two of his PhD students, Michael Morris and Ulvi Yurtsever, the task of working out some details of the physical behaviour of what the relativists call “wormholes”—tunnels through spacetime. At that time, in the mid-1980s, relativists had long been aware that the equations of the general theory provided for the possibility of such hyperspace connections. But before Sagan set the ball rolling again, it had seemed that such hyperspace connections had no physical significance and could never, even in principle, be used as shortcuts to travel from one part of the Universe to another.
Morris and Yurtsever found that this widely held belief was wrong. By starting out from the mathematical end of the problem, they constructed a set of equations that matched Sagan’s requirement of a wormhole that could be physically traversed by human beings. Then they investigated the physics, to see if there was any way in which the known laws of physics could conspire to produce the required geometry. To their own surprise, and the delight of Sagan, they found that there is. To be sure, the physical requirements seem rather contrived and implausible. But that isn’t the point. What matters is that it seems that there is nothing in the laws of physics that forbids travel through wormholes. The science fiction writers were right—hyperspace connections do, at least in theory, provide a means to travel to far distant regions of the Universe without spending thousands of years pottering along through ordinary flat space at less than the speed of light.
The conclusions reached by the CalTech team duly appeared as the scientifically accurate window dressing in Sagan’s novel when it was published in 1986, although few readers can have appreciated that most of the “mumbo-jumbo” was soundly based on the latest discoveries made by mathematical relativists. And then, like a cartoon character smiting himself on the head as the penny dropped, the relativists realised that this isn’t the end of the story.
The point is that these tunnels, or wormholes, go through spacetime, not just space. Einstein taught us that space and time are inextricably linked, in a four-dimensional entity called spacetime. You can’t, in the words of the old song, have one without the other. It follows that a tunnel through space is also a tunnel through time. The kind of hyperspace connections described in Contact, and based on real physics, could indeed also be used for time travel.
The CalTech researchers have shown how two black holes like this could lie at opposite ends of a wormhole through hyperspace. And the two black holes can lie not just in different places, but at different times—or even at the same place but in different times. Jump in one hole, and you would pop out of the other at a different time, either in the past or the future. Jump back in to the hole you popped out of, and you would be sent back to your starting point in space and time.
The time tunnel you haver constructed using the above instructions always has the end that has been whirled around at half the speed of light in the future compared with the “stationary” end. Jump in the mouth that has been moved, and you emerge from the stationary mouth at the time corresponding to the clocks attached to the moving mouth—in the past, compared with where you started. You can set the interval of the time difference to be anything you like, using the time dilation effect, but you can never go back into the past to an earlier time than the moment at which you completed the time machine. In order to do that—for example, to go back in time to watch the 1966 World Cup Final—you need to find a naturally occurring time machine, or one built by an ancient civilization and left in orbit around a convenient star (see our leaflet, Locating Alien Civilizations The Easy Way). One obvious possibility would be to take a naturally occurring microscopic wormhole, and expand it to the required size using cosmic string.
Cosmic string, of course, is the material left over from the Big Bang of creation, which stretches across the Universe but has a width much narrower than that of an atom. Among its other interesting properties, cosmic string experiences negative tension—if you stretch a piece, instead of trying to snap back into its original shape, it stretches more. Any experienced do-it-yourself enthusiast will appreciate that this offers a useful means to hold the throat of a wormhole open.
HAZARDS: Please read the following section before entering the black hole:
1. Spaghettification
The kind of black hole astronomers are familiar with, containing as much mass as our Sun, would have a very strong tidal pull. What this means is that as you fell into it feet first, your feet would get pulled harder than your head, so your body would stretch. At the same time, tidal forces would squeeze you sideways. The relativists have a technical term for the resulting effect; they call it “spaghettification”. In order to avoid spaghettification, the black holes that provide the entrances and exits to hyperspace should ideally contain about a million times as much mass as our Sun, and be about as big across as our entire Solar System. This is impractical at the present state of technology, but the hundred solar mass black holes we recommend can be navigated successfully, avoiding spaghettification, if care is taken to avoid the central singularity. We accept no responsibility for injuries caused by reckless driving.
2. The granny paradox
BE CAREFUL who you bring back from the future with you, and what activities they get up to while visiting your time. Suppose you use the time machine to go forward in time a few decades, and bring back a young man to visit his granny when she was a young girl, before his mother was born. The traveller from the future may, either by accident or design, cause the death of his granny as a young girl. Now, if granny died before his mother was born, obviously he never existed. So you never brought him back in time, and granny was never killed. So you did bring him back in time … and so on. WE DO NOT ACCEPT RESPONSIBILITY for paradoxes caused by careless use of the time machine.
As well as the paradoxes, time travel opens up the possibility of strange loops in which cause and effect get thoroughly mixed up. In his story “All You Zombies”, Robert Heinlein describes how a young orphan girl is seduced by a man who turns out to be a time traveller, and has a baby daughter which is left for adoption. As a result of complications uncovered by the birth, “she” has a sex change operation, and becomes a man. “Her” seducer recruits “her” into the time service, and reveals that he is in fact “her” older self. The baby, which the older version has meanwhile taken back in time to the original orphanage, is a younger version of both of them. The closed loop is delightful, and, we are now told, violates no known laws of physics—although the biology involved is decidedly implausible. WE DO NOT ACCEPT RESPONSIBILITY for travellers stuck in time loops.
And now, you are ready to enjoy decades of harmless amusement with your time machine. In the event of difficulties, please do not hesitate to contact our customer service department, which is located at the usual address, and in the year 4242 AD.
DEEP SCIENCE: Readers interested in the scientific theory underlying time machine construction, rather than just the practical aspects, may be interested to know something of current black hole research. Quite apart from the large black holes you would need to build a working time machine, the equations say that the Universe may be full of absolutely tiny black holes, each much smaller than an atom. These black holes might make up the very structure of “empty space” itself. Because they are so small, nothing material could ever fall in to such a “microscopic” black hole—if your mouth is smaller than an atom, there is very little you can feed on. But if the theory is right, these microscopic wormholes may provide a network of hyperspace connections which links every point in space and time with every other point in space and time.
This could be very useful, because one of the deep mysteries of the Universe is how every bit of the Universe knows what the laws of physics are. Consider an electron. All electrons have exactly the same mass, and exactly the same electric charge. This is true of electrons here on Earth, and studies of the spectrum of light from distant stars show that it is also true of electrons in galaxies millions of light years away, on the other side of the Universe. But how do all these electrons “know” what charge and mass they ought to have? If no signal can travel faster than light (which is certainly true, many experiments have confirmed, in ordinary space), how do electrons here on Earth and those in distant galaxies relate to each other and make sure they all have identical properties?
The answer may lie in all those myriads of microscopic black holes and tiny wormhole connections through hyperspace. Nothing material can travel through a microscopic wormhole—but maybe information (the laws of physics) can leak through the wormholes, spreading instantaneously to every part of the universe and every point in time to ensure that all the electrons, all the atoms and everything that they are made of and that they make up obeys the same physical laws.
And there you have the ultimate paradox. It may be that we only actually have universal laws of physics because time travel is possible. In which case, it is hardly surprising that the laws of physics permit time travel.
John Gribbin

For more about black holes in general, cosmic string, and time travel in particular, see:
John Gribbin, In Search of the Edge of Time (US title Unveiling the Edge of Time), Penguin, London and Harmony, New York.
John and Mary Gribbin, Time & Space, Dorling Kindersley, London.
Kip Thorne, Black Holes and Time Warps, Norton, New York, and Picador, London.

Let it snow

Another golden oldie from my archive, but topical still.


Douglas Lin, of the University of California, Santa Cruz, has looked in detail at what happens to the solid chunks of material that build up in the disc around a young star like the Sun. One crucial feature of his calculations is the way the solid objects interact with the gas that is still present in the disc during the early stages of planet formation. Because of the interaction between pressure, gravity and rotation, the gas at any chosen distance from the central star moves around the star slightly more slowly than the speed with which the particles and lumps of material are moving in their orbits. This means that the particles are overtaking the gas; in effect, as Lin puts it, ‘running into a headwind that slows them down and causes them to spiral inward, toward the star’. A piece of material a metre across can halve its distance from the star in this way in just a thousand years, and the bigger the pieces grow the faster they move inwards – up to a point.
    That point is picturesquely dubbed the ‘snowline’. It is the distance from the star where frozen water, ammonia and other volatile substances evaporate; in the case of the Sun at a distance of between 2 AU and 4 AU, between the orbits of Mars and Jupiter. This is why the boundary between the rocky planets and the icy objects in our Solar System lies where it does.
    At the snowline, water vapour released by the icy grains as they evaporate changes the properties of the gas in such a way that it now rotates faster than the solid grains, giving them a boost which tends to make them move outwards in their orbits. So material piles up at the snowline, where grains are packed closer together and can quickly grow into larger lumps. Within a million years of the formation of the Sun, many of these lumps are a kilometre or so across and very little dust remains. As they grow, and as gas is being dissipated from the inner part of the disc by the heat of the Sun, the planetisimals, as they now are, are less influenced by interactions with the gas, and many of them migrate inwards towards the Sun, into the region where rocky planets are found today. The exact positions that the planets end up in when this migration stops depends on many factors, including the temperature in different regions of the disc and the size of the planet, but the overall picture is clear from many computer simulations.
    Planetisimals gather up the remaining dust gravitationally and collide and merge with one another, with the survivors settling into roughly circular orbits which have been swept clean of debris. Chunks of material left over from these collisions may still be with us, in the form of some of the asteroids. Because there is more dust to feed on farther out from the Sun, embryonic planets grow bigger farther out. According to Lin’s calculations, at a distance of 1 AU from the Sun a planetary embryo can grow to one tenth of the mass of the Earth within 100,000 years, but then all the available dust is gone; at a distance of 5 AU, there is more dust and an embryo can continue to grow for a few million years, reaching a size of about four Earth masses. But this isn’t the end of the story. Interestingly, Lin points out that there is no room for any more planets in our Solar System today – the planets we have are as close together as the complex interaction of gravitational forces between them will allow. It is very likely that more planets formed when the Solar System was young, but that the surplus were ejected from unstable orbits before the present stable pattern was established.
    It cannot be a coincidence that Jupiter, the largest planet in our Solar System, lies just beyond the snowline; but astronomers are still not able to explain just how a Jupiter-sized planet ended up in a stable orbit there. Interactions between an embryonic planet in the outer part of the Solar System and the gas in the disc, still significant that far from the Sun, explain why the embryonic Jupiter ended up close to the snowline, and accumulated a great deal of gas from the material available there. But what stopped it spiralling inwards into an orbit like those of the many ‘hot Jupiters’ that have now been discovered? If it had done so, it would have pushed any rocky planets in the inner Solar System into the Sun ahead of it.
    Once Jupiter had formed, it helped the other giant planets to form by stopping the inward flow of material in the disc and by disturbing the orbit of planetisimals so that many of them migrated to the outer part of the Solar System. The first effect aided the formation of the second gas giant, Saturn; the second effect provided enough frozen chunks to make the massive cores of the ice giants, Uranus and Neptune. All of this, prior to the processes which sent the giant planets into their present orbits and disturbed the Kuiper Belt, only took about 10 million years after the formation of the Sun. But the formation of the Earth took a lot longer.