Inflation for Beginners

I was prompted to add this by recent debate about the cosmic background radiation. From my book Companion to the Cosmos.

inflation: 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 in a small fraction of a second. This process would smooth out spacetime to make the Universe flat (see flatness problem), and would also resolve the horizon problem.
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, 15 to 20 billion years ago. 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 Planck length (10-35 m), when the density was not infinite but “only” some 1094 grams per cubic centimetre. 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 (see free lunch Universe).
Other problems with the Big Bang theory before the development of inflationary models involve the extreme flatness of spacetime (which means that the expansion of the Universe is balanced against the tug of gravity so that it sits precisely on the dividing line between expanding forever and one day recollapsing in a Big Crunch; see density prameter), and its appearance of extreme homogeneity and isotropy, most clearly indicated by the uniformity of the background radiation.
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 force by about 10-35 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 10-32 of a second there were 100 doublings. This 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 10-33 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.
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 10-10 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 10-33 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 (Physical Review, volume D23 page 347, January 1981). 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. Although there were obvious flaws with the specific details of Guth’s original model (which he acknowledged at the time), 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 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 realisation 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 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 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 “”. “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 10-25 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 10-30 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.
Further reading: John Gribbin, In the Beginning.


The First Scientist

I was prompted to post this partly in response to the posting yesterday by Thecuriousastronomer about Galileo.


William Gilbert of Colchester deserves pride of place in any account of the scientific revolution of the seventeenth century, because he was the first person to set out clearly in print the essence of the scientific method – the testing of hypotheses by rigorous experiments – and to put that method into action.  He did so to such effect that his discoveries in the field of magnetism were unsurpassed for two centuries; and by a happy calendrical coincidence, his great book on magnetism was published at the dawn of the new century, in 1600.
     To put Gilbert’s life and work in an historical perspective, in 1600 Elizabeth I was nearing the end of her long reign.  The Spanish Armada had been defeated just twelve years earlier, and although the first attempt to plant an English colony in North America (at Roanoke Island, in what is now North Carolina) had failed in the mid-1580s, the successful attempt at establishing a permanent settlement in Jamestown, Virginia, would take place in 1606.  In 1600, William Shakespeare was at the height of his creative powers, and in the 1599-1600 season the plays performed at his Globe Theatre in London were Julius Caesar, Twelfth Night, and As You Like It, while Hamlet and the Merry Wives of Windsor followed the next year.  London  itself was a city of some 75,000 inhabitants, with twice that number in the rapidly growing suburbs sprawling outside the city walls.  It was filthy, smelly and unhygienic; bubonic plague spread by the fleas that lived on rats often broke out in summer, when those that could afford to retreated to the countryside.  The poor had no such option.
      Unfortunately, we know only the outlines of Gilbert’s own life, because of two disasters that occurred later in the seventeenth century.  Many of his papers and experimental equipment were left to the Royal College of Physicians when he died, and both their building and Gilbert’s own former house in London were destroyed in the Great Fire of 1666.  Any other material that might have been of interest to historians would have been at his house in Colchester,  but that was in a part of the town destroyed during the English Civil War, at what became known as the Second Siege of Colchester, in 1648. There is a manuscript in the Bodleian Library in Oxford which gives an actual birth date, 24 May 1544.  We also know that Gilbert went up to Cambridge in 1558, and 14 would be about the right age for a scholar to enter the university in those days.
     Once Gilbert arrived in Cambridge, he began to leave traces which have survived to the present day.  He stayed in residence at the university for eleven years, gaining both his BA (1560) and MA (1564), qualifying as a doctor (1569) and becoming a Senior Fellow (all at St John’s College).  There is no record of his activities between 1569 and 1573, and this has led to fanciful accounts that he may have traveled widely in Europe, perhaps even meeting Galileo.  Since Galileo was only born in 1564, however, it seems unlikely that any such meeting occurred!  But the most likely explanation of Gilbert’s activities during these years after leaving Cambridge and before setting up as a physician in London in 1573 is that it was just at this time that he became seriously interested in magnetism and carried out his early experiments; but the work certainly wasn’t completed then.

    Our first clue to Gilbert’s approach comes from the book itself.  The preface to the book also mentions that it describes work that had been essentially complete some 18 years before it was published.
     It is an intriguing coincidence (if it is only a coincidence) that Gilbert first took an important office in the Royal College of Physicians, as Censor, in 1581; and it is hard to see how the successful and busy physician that Gilbert became after that time could have found time for much scientific work,  If Gilbert began his key magnetic experiments (perhaps in Colchester) in the four years ending in 1573, then spent a decade using his spare time to refine his results, that places the key experiments, the first true application of what became the scientific method, in the early 1570s, in England, before Galileo was even ten years old, and dates the completed work to the early 1580s, when Galileo was a medical student in Pisa.
     The evidence that Gilbert started his medical practice in 1573 comes from references after his death (in 1603) that he had been a London physician for thirty years; but the first direct documentary evidence of his life in London dates from 1581, with that appointment as Censor, when he was already a member of the Royal College of Physicians.  Throughout the rest of the century, Gilbert was a prominent member of the College, holding several offices including that of Treasurer from 1587 to 1594 and from 1597 to 1599, and being elected President in 1600.
    His career as a physician was crowned by the appointment as one of the Queen’s doctors in 1601, and this too has been the subject of exaggerated interpretation down the years.  Gilbert was just one of the royal panel of physicians, not singled out in any way, and he received the usual stipend of one hundred pounds a year (referred to as a “pension”) for his services.  This has grown in the telling so that he is sometimes referred to as the Queen’s Chief Physician (or her Personal Physician), and the pension becomes a mythical personal bequest in the Queen’s Will.  None of this is true.  But it is true that although Gilbert was confirmed in his post of Royal Physician when James I (in whose honour the first American colony was named) succeeded Elizabeth in 1603, he died later that year, almost certainly of plague.  His lasting memorial is the book, De Magnete, published in 1600.

    Naturally occurring magnetic rocks, or lodestones, had been known since ancient times, both in China and in the Eastern Mediterranean.  Our name “magnet” comes from the old term lithos magnetis, or “magnesian stone,” which may have referred to lodestones found near the town of Magnesia, in Greece, although this is no more than a supposition.  But although lodestones were known in ancient times, their properties were not investigated scientifically, and they were surrounded by superstition (as in the belief that they could cure illnesses) and exaggeration, as when Pliny tells us that:
Near the river Indus there are two mountains, one of which attracts iron and one repels it.  A man with iron nails in his shoes cannot raise his feet from the one or put them down on the other.
There was also considerable confusion in ancient times about the relationship between what we now call electricity and magnetism.  The Ancient Greeks valued amber, which they called elektron, and is actually the fossilised remains of resin from a variety of trees. They knew that when it was rubbed, it gained the power of attracting straws, small pieces of sticks, and even thinly beaten pieces of copper or iron.  But they thought that the effect was a result of the amber being heated by friction when it was rubbed, This was not a completely mad idea.  The Greeks had noticed that small pieces of straw and so on are “attracted” to a fire (we now know, because of convection currents set up in the air) and thought that something similar might be happening with the amber, and although they noticed that amber could attract all kinds of small objects, while lodestone could only attract iron, it still seemed to them that the attractive power of amber was essentially the same as the attractive power of the lodestone.

     Nothing new was discovered about magnetism until the eleventh century AD, when suddenly we find references to the use of magnetic compasses in navigation.  The origins of the discovery of this pointing property of magnets are lost, and it is clear that whoever first made the discovery realised its enormous commercial and military value, and kept it secret as long as possible.  The discovery seems to have been made first in China, and a little later in Europe, assuming that the knowledge did not spread from China westward.  One reason to think that the discoveries may have been independent of one another is that from the earliest references Chinese compasses are designed to point south, while European compasses are designed to point north.
     In the centuries that followed, a great deal of information, misinformation and superstition grew up as a result of interest in the compass.  As it became appreciated that the lodestone had two special points, just as the heavenly sphere has two special poles, even before it was widely understood that the Earth is round it was common to make lodestones round, to mimic the shape of the heavenly sphere.  Such a sphere has two magnetic poles, one of which points north and the other south.
     It was known that with two such lodestones opposite poles attract and similar poles repel one another, and that if a lodestone is cut in half  between the two poles, two new poles appear at the cut, each the opposite of the original pole in that half of the lodestone.  It was even understood that you could find the poles of a spherical lodestone by laying bits of iron wire on the surface of the sphere and seeing how they align to point to the magnetic poles.  But there was confusion about why a compass needle should point north – was it because it was attracted by the Pole Star, or was it because there was a magnetic island far to the north of Europe?  Or was it just because it was in the nature of magnetic needles to point north?  And although a magnetised needle would point to the north, it did not try to move to the north, even though it would both point to and move towards a lodestone placed near it.  Magnetism was also still seen as having medicinal properties, and a supposed cure for gout, for example, was to bandage a piece of magnetic material tightly up against the affected limb.  This at least had the merit, unlike some Medieval medical treatments, of doing no harm to the patient.

     Yet another key property of the compass needle, the way it dips to point slightly below the horizontal, was only discovered in the sixteenth century, just about in Gilbert’s lifetime.  Although the dip was mentioned in a letter written by the German Georg Hartmann in 1544, this was not published at the time, and the first report of the discovery to reach a wide audience came from the London-based instrument maker Robert Norman, in 1581.  This discovery essentially completed the package of information about magnetism (and electricity) that Gilbert set out to explain and understand through his experiments, and to describe in his great book.
     I don’t intend to take you through all of Gilbert’s work, because the important point I wish to emphasise is not what he discovered, but how he discovered it.

  The full title of his masterwork is usually translated as On the Loadstone and Magnetic Bodies and on the Great Magnet the Earth.  Gilbert sets out his stall as the practitioner of a new kind of investigation of the world in the preface of his book, pulling no punches as he kicks off with the assertion that:

In the discovery of hidden things and in the investigation of hidden causes, stronger reasons are obtained from sure experiments and demonstrated arguments than from probable conjectures and the opinions of philosophical speculators of the common sort

at once distancing himself from the school of natural philosophy, dating back to the Ancient Greeks, which attempted to unravel the mysteries of the Universe solely by thinking about them, without actually carrying out experiments.  It’s worth quoting extensively from that preface, to make it clear that not only was Gilbert doing something new, he was well aware of the revolutionary nature of his new style of investigation:

Every day, in our experiments, novel, unheard-of properties came to light  .  .  .
   But why should I, in so vast an ocean of books whereby the minds of the studious are bemuddled and vexed – of books of the more stupid sort whereby the common herd and fellows without a spark of talent are made intoxicated, crazy, puffed up; and are led to write numerous books and to profess themselves philosophers, physicians, mathematicians, and astrologers, the while ignoring and contemning men of learning – why, I say, should I add aught further to this confused world of writings, or why should I submit this noble and (as comprising many things before unheard of) this new and inadmissible philosophy to the judgment of men who have taken oath to follow the opinions of others, to the most senseless corrupters of the arts, to lettered clowns, grammatists, sophists, spouters, and the wrong-headed rabble, to be denounced, torn to tatters and heaped with contumely.
  To you alone, true philosophers, ingenuous minds, who not only in books but in things themselves look for knowledge, have I dedicated these foundations of magnetic science – a new style of philosophizing.  But if any see fit not to agree with the opinions here expressed and not to accept certain of my paradoxes, still let them note the great multitude of experiments and discoveries – these it is chiefly that cause all philosophy to flourish; and we have dug them up and demonstrated them with much pains and sleepless nights and great money expense.  Enjoy them you, and, if ye can, employ them for better purposes.  I know how hard it is to impart the air of newness to what is old, trimness to what is gone out of fashion; to lighten what is dark; to make that grateful which excites disgust; to win belief for things doubtful; but far more difficult is it to win any standing for or to establish doctrines that are novel, unheard-of, and opposed to everybody’s opinions.  We care naught, for that, as we have held that philosophy is for the few.
     Gilbert’s first objective is to draw a distinction between magnetism and the amber effect (for which he introduces the term electricity) in order to clear the air before moving on to his study of magnetism itself.  In order to do this, he has to carry out a thorough investigation of electricity, and to help him he invents the first electroscope (he called it a versorium), in the form of a light needle, made of metal, “three or four fingers long” and “poised on a sharp point after the manner of a magnetic pointer” (that is, a compass needle).

  When a piece of rubbed amber, or other suitable material, is brought near to one end of the needle, the pointer revolves.  Using this sensitive detector, Gilbert set out to investigate the properties of electricity.  The Greeks had speculated that the attraction might be caused by the warmth of rubbed amber, and in all the time since them this had remained a possible explanation of the phenomenon.  It was Gilbert who took what seems to us the obvious step of warming amber by other means, and finding that this does not produce an attraction (nor, as he pointed out, do other warm objects display electric attraction).  It was the rubbing, not the warmth, that mattered. In the same spirit, Gilbert later tests the old wives’ tale that garlic will demagnetise iron or a lodestone by actually rubbing them with garlic and showing that there is no effect.  But this didn’t stop the old wives’ tale persisting through the seventeenth century!
    Gilbert suggested that the rubbing removed a “humour” from the body, and left behind an “effluvium” surrounding the rubbed object; if you replace these terms by, respectively, “charge” and “electric field,” this is essentially the modern view of what is going on.
     Above all, though, Gilbert appreciated the need for careful, repeatable experiments.

We have set over against our discoveries larger and smaller asterisks according to their importance and their subtility.  Let whosoever would make the same experiments handle the bodies carefully, skillfully, and deftly, not heedlessly and bunglingly; when an experiment fails, let him not in his ignorance condemn our discoveries, for there is naught in these books that has not been investigated and again and again done and repeated under our eyes.  Many things in our reasonings and our hypotheses will perhaps seem hard to accept, being at variance with the general opinion; but I have no doubt that hereafter they will win authoritativeness from the demonstrations themselves  .  .  .
   This natural philosophy (physiologia) is almost a new thing, unheard of before; a very few writers have simply published some meagre accounts of certain magnetic forces.  Therefore we do not quote the ancients and the Greeks as our supporters, for neither can paltry Greek argumentation demonstrate the truth more subtilly nor Greek terms more effectively, nor can both elucidate it better  .  .  .
To those men of early times and, as it were, first parents of philosophy, to Aristotle, Theophrastus, Ptolemy, Hippocrates, Galen, be due honour rendered ever, for from them has knowledge descended to those that have come after them: but our age has discovered and brought to light very many things which they too, were they among the living, would cheerfully adopt.  Wherefore we have had no hesitation in setting forth, in hypotheses that are provable, the things that we have through a long experience discovered.

     In all, there are 33 discoveries denoted by asterisks in the chapter of De Magnete on electricity, indicating that Gilbert had carried out all these experiments for himself.  Although some of these discoveries might have predated him, there is no surviving record of any earlier work on any of the 33 discoveries, which range from the discovery that a wide variety of other materials (such as sapphire, sulphur, and sealing-wax) attract light objects when rubbed to the fact that solar heat concentrated on to amber with a concave mirror does not result in attraction, to the fact that an electric object attracts small pieces of material towards itself in a straight line.  And, of course, the electric force, as we would now call it, attracts a wide variety of materials, not just iron.  In all this work, and his theoretical explanations of the things he observed, Gilbert single-handedly established electricity as a new branch of science, distinct from magnetism.  Virtually nothing was added to his work in the seventeenth century, so that it provided the jumping off point for the eighteenth-century work which led to the concept of electric charge.
     In his work on magnetism, Gilbert used the spherical lodestones that I have already described, which he called terrellae, meaning “little Earths.”
     It was at the very heart of his magnetic philosophy that he regarded these as models of the Earth itself, and that he thought of the Earth as a giant spherical magnet.  This is an important distinction.  Earlier investigators made their lodestones spherical in order to mimic the shape of the heavens; Gilbert made his spherical in order to mimic the shape of the Earth.  The nature of the magnetic influence of a terrella was investigated using a magnetised compass needle, which would align itself to point to the poles of the terrella just as the terrella would align itself to point to the poles of the Earth, with no need to invoke magnetic islands to the north of Europe, or some influence from the Pole Star.

     In these experiments, Gilbert was the first person to appreciate that, because magnetic opposites attract, it is the south pole of a magnet that points to the north pole of the Earth; in modern language, we sometimes refer to the “north-seeking” pole of a compass needle to make the point clear.  As Gilbert puts it:

All who hitherto have written about the poles of the loadstone, all instrument-makers, and navigators, are egregiously mistaken in taking for the north pole of the loadstone the part of the stone that inclines to the north, and for the south pole the part that looks to the south: this we will hereafter prove to be an error.  So ill-cultivated is the whole philosophy of the magnet still, even as regards its elementary principles.

This is not just some matter of hair-splitting semantics, or a cheap gibe at his predecessors.  The point is that Gilbert recognises that it is the same process that makes a magnet that is free to move orient itself relative to a fixed magnet that makes a compass needle orient itself with respect to the Earth’s magnetism.  The Earth is a magnet, and therefore understanding magnetism will help us to understand the Earth.  This is the first example of trying to understand global (ultimately, universal) forces by carrying out experiments on a laboratory scale.  And, as Gilbert appreciates, magnetism can then be used to provide information about what is going on deep inside the Earth, in regions we can never see.
     The other aspect of Gilbert’s work that I particularly want to draw attention to takes us in the other direction – not inwards to probe the structure of the Earth, but out into space.  Gilbert was among the first to appreciate that there is something more to magnetism than an attractive influence, or force; and he was the first to set out clearly just what that “something” seemed to be.  In doing so, he came very close to the modern idea of a field, suggesting that the magnetic effect surrounded the Earth (and, by implication, other planets) in a sphere of influence.
    This work jumped off from the investigation of magnetic dip.  This was first fully described in print by Robert Norman, in a little book called The New Attractive, which he published in 1581, several years after what seems to have been Gilbert’s most productive experimental period.  Since Gilbert repeated some of Norman’s experiments and described their results in De Magnete, he must have found some time during his busy life in the 1580s to do at least a little scientific work; it is also possible that some of his experiments on dip pre-dated Norman’s work, although they were not published until 1600.  We shall never know, and it doesn’t really matter.
     Norman tells us that he began to investigate magnetic dip (he called it “declination,” but that term has a quite different meaning today) when he got angry at the problems it caused him when he was manufacturing compasses.  It was well known by then that a magnetised needle suspended from its mid-point would not lie horizontally, but with the north-seeking end pointing downwards, below the horizon. (In the Northern Hemisphere, of course.  In the south, it is the south-seeking end that dips below the horizon.)
     In order to compensate for this, instrument makers such as Norman had to snip a little piece off the north-seeking end of the needle so that it would balance perfectly on its pivot and make the compass usable for navigation.  Norman  became so cross when he spoiled a particularly fine compass by cutting too much off the needle that he decided to find out just why the magnetised needles behaved in this way, and to do so he invented a new kind of  compass, the dip circle.

     In a dip circle, a graduated circular rim (like the tyre of a bicycle wheel) is set up vertically, and a compass needle is supported on an axle in the middle of the wheel so that it can rotate freely in the vertical plane.  Norman  found that needles set up in this way always pointed downward at the same angle, 67 degrees, in London, and he conjectured that the angle of dip might be related to latitude.
     But his great insight, the idea that Gilbert picked up on and developed, was that the magnetic needle is not being attracted towards the North Pole; it simply points to the North Pole, indicating the direction of something (which we would now call the magnetic field) in the vicinity of, in this case, London.  He said that “In my judgment [the point attractive] ought rather to be called the point respective.” He reinforced this conclusion with a particularly subtle experiment, which Gilbert repeated and described in De Magnete.  He took a piece of iron or steel a couple of inches long, and thrust it through a piece of cork.  He then filled a glass vessel with water, and by painstakingly carving away at the cork little by little, made the needle float horizontally in the water, a few inches below the surface, suspended by the buoyancy of the cork, “like to the beam of a pair of balances being equally poised at both ends.”  Then:

Take out the same wire without moving the cork, and touch with the [lodestone], the one end with the south of the Stone, and the other end with the north, and then set it again in the water, and you shall see it presently turn upon his own centre, showing the aforesaid declining property, without descending to the bottom, as by reason it should, if there were any attraction downwards.

So the needle is lining up with what we would now call the magnetic field, but which Norman refers to as a “virtue.”  He says “I am of opinion, that if this virtue could by any means be made visible to the eye of man, it would be found in a spherical form extending round the Stone.”

     Gilbert was able to go further, by investigating the way dip varied around his terrellae – remember that it is a key contribution to scientific thinking that he regarded these models as miniature Earths, and that he could therefore extrapolate from their behaviour to the behaviour of the real Earth.  He was able to show that the angle of dip does indeed vary with latitude, and he found another way of showing that what is being measured is a direction, not an attraction, by demonstrating that for a spherical terrella the dip was always the same at any particular latitude, whatever the strength of the lodestone.  If the dip were due to an attraction, you would expect it to be more pronounced if the magnetism of the stone were stronger, but this is not the case.  The needle takes up its orientation relative to the terrella (or the Earth) as a whole, not because of the strength of an attraction towards the pole.  “This movement,” says Gilbert, “is produced not by any motion away from the horizon towards the earth’s centre, but by the turning of the whole magnetic body to the whole of the earth.”

     This idea of the Earth extending an influence out into space around itself links with Gilbert’s speculations about the nature of the Universe itself and the place of the Earth within it.  In doing so, he makes another conceptual leap.  Having used terrellae as models for the Earth, he now uses the Earth as a model for other objects in the Universe.  Copernicus had published  his De Revolutionibus only in 1543, the year before Gilbert was born, and as the fate of Galileo highlights, in Gilbert’s lifetime it was still far from being received wisdom that the Earth is just a planet orbiting the Sun, unsuspended in the void.  Indeed, it was still a matter of debate whether the Earth rotated on its axis, or the heavens revolved around the Earth – although Gilbert left his readers in no doubt about where he stood on that question.  
     As Gilbert pointed out, “either the earth whirls in  daily motion from west to east, or the whole heavens and the rest of the universe of things necessarily speeds about from east to west.”  But the stars are so distant from us that they would have to travel at enormous speeds to complete the circuit in 24 hours.  He dismissed the idea of the “adamantine spheres” out of hand – “what structure  .  .  .  can be imagined so strong, so tough, that it would not be wrecked and shattered to pieces by such mad and immeasurable velocity?”
     This is a question that simply would not have occurred to his predecessors.  They regarded the heavens as something mystical, not subject to the same rules as solid objects here on Earth.  But here is Gilbert, almost a century before Newton, implicitly assuming that the same laws of physics apply to the most distant stars as to a lump of matter on Earth.  Science is encroaching on what used to be the territory of religion, with dire consequences for some scientists in some parts of Europe.  It was still possible to be burned at the stake for expressing such views in Catholic countries; in England, you might get burned for being a Catholic, but not for offering a scientific opinion about the nature of the Universe.  So Gilbert is free to say that “the space above the earth’s exhalations is a vacuum,” and that “the entire terrestrial globe, with all its appurtenances, revolves placidly and meets no resistance” in that vacuum.
     This is an implicit recognition of something studied in more detail by both Galileo and Newton – the idea of inertia, that an object once set in motion will continue to move as long as it is not affected by external forces (such as friction).  Gilbert does not explicitly say that the Earth also moves around the Sun, but he refers approvingly to the work of Copernicus (“a man most worthy of the praise of scholarship”) in the context of the motion of the other planets round the Sun.
     De Magnete summarises a body of work which marks the beginning of the application of the scientific method of investigating the world, and pointed the way for Galileo, Newton, and the other seventeenth century pioneers. Most of all, though, it explained clearly for the first time the nature of the experimental scientific method.

Oh yes — and we know from his correspondence that Galileo read and admired De Magnete.


Adapted from my book Science: A History.