Born in 1894 in Charleroi in Belgium, Lemaître was educated at a Jesuit school and went to university to study civil engineering. World War I interrupted his studies; he became an artillery officer and received the Belgian Croix de Guerre for his valour.

Back at university after the war, he studied physics and mathematics – along with training for the priesthood; and he made progress on all fronts. In 1923 he was ordained as a priest, and in that same year he went to Cambridge as a graduate astronomy student, where he worked for a year with Sir Arthur Eddington. He spent the following year at the Harvard College Observatory, where Harlow Shapley was now director.

From Shapley he learned about the various features of spiral nebulae, including their speed of recession from us. Back in Belgium in 1925, he became a part-time lecturer at the Catholic University of Louvain and began work on a paper that was published in 1927 whose title sums up its content: ‘A homogeneous universe of constant mass and growing radius accounting for the radial velocity of extragalactic nebulae’.

He showed from Einstein’s equations of general relativity that the universe was expanding, as Alexander Friedmann had done, five years before. Lemaître did so independently, as Friedmann’s work was little known outside Russia. But Lemaître went further, and linked the expansion to the observed redshift of the galaxies. He argued that the speed of expansion increased with distance so that the galaxies which are furthest away from us are fastest to recede and so have the greatest redshift in their spectra.

This relationship between distance and speed of recession would become known as Hubble’s Law – which leads us to Edwin Hubble, who two years after Lemaître’s paper published observational evidence for the expansion of the universe.

Hubble, born in Marshfield, Missouri, in 1889, was noted at school for his athletic prowess in track and field events; he was also keen on basketball, boxing, dry-fly fishing – and astronomy. Indeed he went on to study astronomy at the University of Chicago, along with mathematics and philosophy. He did well, and won a Rhodes Scholarship to Oxford; and there, at the request of his father, he made a major change in his studies and took up law. He later added literature and Spanish for a master’s degree.

Back in the US in 1913, he taught for some months at a high school in Indiana (and coached the basketball team), and practiced law for a time in Kentucky. But his heart was in astronomy, and in 1914 he reshaped his life by returning to the University of Chicago to study astronomy at the Yerkes Observatory. In 1917 he completed his PhD and was offered a post at the Mount Wilson Observatory.

But now the US joined World War I, and Hubble enlisted in the infantry and rose to the rank of major. Back in the US in 1919 he went to take up the position at Mount Wilson and stayed there for the rest of his life.

Hubble arrived at Mount Wilson at the time when the 100-inch Hooker Telescope was completed, and he was able to use this to probe much further than anyone else had done before. He looked at the spiral nebulae and studied their speed of recession – and also their distance.

The technique for finding the distance of stars had been developed by Harlow Shapley. He used stars called Cepheid variables. These were stars which, as the name suggests, varied in their brightness, and one of the first of them was in the constellation Cepheus – Delta Cephei. They are much more luminous than the Sun – up to 100,000 times so.

Cepheid variables have two very strange features. Firstly, their brightness varies in a steady pulsed pattern. And secondly, their overall brightness and their pulsation period are directly related. It is like having a lighthouse flashing amongst the stars. All you have to do is count the flashes and you have a measure of the absolute brightness of one of these stars. With that absolute brightness, you have a yardstick. It is like having two friends with similar torches. If one torch looks fainter than the other, than you know that the friend carrying it is further away.

This remarkable relationship between the luminosity and the pulsation period of the Cepheid variables was discovered by Henrietta Swan Leavitt, one of a group of women hired by Shapley’s predecessor at the Harvard Observatory, Edward Charles Pickering, to process astronomical data.

Also in the group was Williamina Fleming from Dundee who was initially working as a maid in Pickering’s house; she went on to catalogue more than 10,000 stars and to become Harvard’s curator of astronomical photographs. She was the first woman in such a post. She had literally hundreds of discoveries – stars and variables stars, nebulae and novae, one of the nebulae being the Horsehead in Orion.

Henrietta Swan Leavitt’s discovery of the significance of Cepheid variables enabled Harlow Shapley to calculate the size of the Milky Way and identify our position within it. His belief that the spiral nebulae were also within the Milky Way was refuted when Hubble found a faint Cepheid variable in the Andromeda nebula – and found that the faintness was due to the star being a great distance from us – nearly a million light-years away. That was far outside the Milky Way, so far that the Andromeda nebula could only be a galaxy in its own right, hence we refer to it today as the Andromeda Galaxy. (The distance has since been revised to an even higher one, around 2 million light-years.)

Hubble, with the power of the new telescope at Mount Wilson, was able to compile two sets of data and put them together. One was for the distances, using the Cepheid variables, and the other for speed relative to us, using redshift. He had data from Vesto Slipher, as well as his own, for which he had the help of a very talented assistant, Milton Humason.

Humason had no academic qualifications, having dropped out of school when he was 14. He loved the mountains, and got a job driving mule teams taking materials and equipment up Mount Wilson for the building of the observatory, and then a position as janitor. He volunteered to be a night assistant, and showed such technical skill that he was taken on as a full-time staff member. He achieved much and played a major role in Hubble’s work.

In 1929 Hubble published his classic paper which showed that that the universe is expanding, with the furthest-away galaxies receding fastest. Up till that time Einstein had not accepted the findings of Friedmann and Lemaître, but after Hubble he publicly endorsed Lemaître’s work.

Now if the universe is expanding today, and the expansion is fastest in its most remote regions, that strongly suggests that in the past the universe was smaller and not expanding so fast. And if we can run the imaginary film back wards, there must have been a stage when the universe was compressed into a tiny space – until the box was opened and the contents somehow burst out. Lemaître called it the ‘primeval atom’. This is the concept of the Big Bang.

An issue that came to the fore around 1920 was the question of the nature of a particular group of nebulae – spiral nebulae.

It was know that a number of these spiral nebulae were moving away from us, at a significant speed. It was possible to find this out by using a property of waves called the Doppler effect.

This effect is familiar in sound waves, when we hear a rise in the pitch of the siren of a car heading toward us, and then the pitch starts to fall as the car overtakes us and fades away into the distance ahead.

The same effect happens with light, where the equivalent of a sound’s pitch is the colour of light – its position in the spectrum that runs between blue at one end and red at the other. If a light-source is moving towards us, there is a shift towards the red end of the spectrum; and if it is moving away, then the shift is toward the blue.

What we actually see with distant stars are absorption lines, where some of the light pouring out from the star’s core has been absorbed in its outer gaseous layers during the first part of its journey towards us. A particular absorption line tells us that a particular colour in the light has been absorbed by a corresponding chemical element. This is how we can tell what stars are made of, by looking for which colour lines are missing from the light they send to us. And similarly, if there was a planet orbiting the star, we could learn about its atmosphere from the absorption lines of the starlight passing through it.

The clue to the motion of the star comes from the position of these absorption lines in the spectrum. If they are shifted towards the red, as compared with a star of similar composition, then we deduce that the star moving away from us.

The explanation of the effect came in 1842 from the Austrian Christian Doppler. Six years later Hippolyte Fizeau in France found the first spectral lines to show a redshift, and in 1864 the English astronomer Sir William Huggins made the first calculation of a speed.

Huggins worked at home in South London, in his own private observatory, assisted by his wife Margaret, an able researcher in her own right. Huggins was a skilled photographer, the first to use the new dry plate process, and he was fortunate to have a professor of chemistry – William A. Miller – as a neighbour, to help identify the elements in the spectra. They found two main types of spectra. Some of the misty patches in the sky (like the Orion Nebula) had pure emission spectra, the hallmark of a gas; while others (such as the spiral nebula M31 in Andromeda) had the type of spectra that is characteristic of stars.

In 1912 Vesto Slipher at the Lowell Observatory at Flagstaff, Arizona, measured the redshifts of the spectrum of 15 spiral nebulae and found that all but three are receding from us.

Slipher’s finding opened up the debate about the nature of the spiral nebulae. Huggins had shown that they had the spectra of stars, and now it was clear that some of them were receding from us at immense speeds. The explanation which we have today is that these nebulae are complete galaxies, and the mistiness is due to the myriad of stars of which they are composed; and today we speak of spiral galaxies and reserve the word ‘nebula’ for the real mist-like objects, the clouds of dust and gas that drift in space.

But at the time there was an argument, with some astronomers maintaining that everything was contained within our own galaxy, the Milky Way.

One of the leading proponents of this latter view was Harlow Shapley, working at Mount Wilson Observatory in California. Shapley’s track record on galaxies was a good one, as he was the first man to show that our galaxy, the Milky Way, was much larger than had been previously believed – and that the sun was far from the centre of the Milky Way. (We will find out how he demonstrated this in the next part of this series.)

Shapley had found his way into astronomy by a rather indirect route. Born on a farm in Missouri, he dropped out of school and studied at home, and then got a job as a newspaper reporter covering crime stories. He decided to catch up with his school education, and did so rapidly. He planned to go to the University of Missouri to study jourmalism, but found that the opening of the university’s School of Journalism had been postponed. So he looked for another subject. The first one in the course directory was Archaeology, which he later said that he found difficult to pronounce – so he opted instead for the subject after that; which was Astronomy. A brilliant career followed, taking him to Princeton and then Mount Wilson.

In 1920 Shapley debated the nature of spiral nebulae with Heber D. Curtis, who had been studying nebulae at the Lick Observatory for eighteen years. The Great Debate was held at the Smithsonian Museum of Natural History in Washington, DC. Curtis argued that objects like the nebula in Andromeda were ‘island universes’ (a term originally coined by the philosopher Immanuel Kant, who had himself believed that the nebula lay beyond the Milky Way). Curtis won, and today we speak of the Andromeda Galaxy, one amongst a vast number of such island universes.

But Shapley had already a success that nothing could tarnish. He had discovered the nature of our galaxy, and our place within it. And a further success that would highlight his name in the history of astronomy was that another aspect of his work was – as we shall see – of key importance for Edwin Hubble.

The one strand is the observational work of astronomers, developing techniques to measure the distance of stars and galaxies – and also their relative speed. The discovery – published by Edwin Hubble in 1929 – that the galaxies are receding from us, with the speed of recession growing with distance, is the basis of the belief of an expanding universe.

A parallel strand of investigation involves purely pencil and paper, and at the heart of this is Albert Einstein’s theory of general relativity, published in 1915. This provides a deep insight into the nature of gravity, showing that what we see as gravity’s ‘pull’ is in fact the bending of space and time by matter. Material objects such as the Sun change the very geometry of time and space around them. In that distorted landscape, other material objects, such as the planets, find their paths are not straight lines but orbits around the Sun.

These two strands, of theory and of observation, meet in the work of Sir Arthur Eddington who in 1919 provided the first confirmation of Einstein’s theory. He travelled to west Africa to measure the bending of starlight by the Sun’s gravitational field, something that could be seen directly during a solar eclipse.

Eddington’s observation confirmed the power of general relativity. The Sun had been fed into Einstein’s equations and the bending of starlight had come out. What then if we decide to take an even bigger unit of matter and see what happens? What indeed if we go so far as to take the entire universe and feed it into the equations of general relativity?

Einstein tried this; but the first result was not encouraging. It simply showed that all the matter in the universe would clump together under the effects of gravity – as we might possibly have expected. But general relativity was much too beautiful a theory to jettison just because it didn’t seem to be giving the right answer in this case. So Einstein persevered; and he suggested that in order to produce the universe we see, there had to be some kind of force of expansion to counter the gravitational attraction – a kind of a push to counter the universal gravitational pull.

Einstein could not say what this proposed new force was, just that it must somehow reside in empty space. It appeared in his equations in the form of a number called the cosmological constant – a number whose value had to be carefully selected to give the desired push-pull balance.

But this balance was so delicate that the model was unstable. It was, commented Eddington, on a knife-edge between runaway expansion and runaway contraction.

However, more theorists were coming up to tackle the problem, and the first in was the Russian physicist and mathematician Alexander Friedmann. Born in 1888 in St Petersburg, where his father was a composer and ballet dancer and his mother a pianist, he had been a pilot in World War I and was awarded the Cross of St George for bravery. Following the Russian Revolution of 1917, he was made head of an aircraft factory. After the war he became a university professor – and also a balloonist, setting a record for an ascent; and he died in 1927 of typhoid, when only 37.

Friedmann’s mathematical skills were focused in particular on meteorology, forecasting weather and looking at the dynamics of a fluid such as air. General relativity became an additional interest, and in 1922 – the same year that Stalin took power in Russia – he came up with a new solution to Einstein’s equations. He showed that if you assume that the universe is evenly filled with matter, there are three possibilities. One is Einstein’s static model, where the push and the pull balance, but there can also be two other outcomes – one for a contracting universe, and the other for an expanding one. This was something radical and extraordinary – a dynamic universe, in an immense process of change.

‘As Copernicus made the Earth go round the Sun, so Friedmann made the Universe expand,’ said the authors of a later book on his life and work. At the time, not many people read his paper. Einstein did, and first of all called it ‘suspicious.’ Friedmann wrote to him right away to explain further, and six months later Einstein announced that he had revised his opinion. ‘My criticism,’ he said, ‘was based on an error in my calculations. I consider that Mr Friedmann’s results are correct and shed new light.’

It would be seven years before the theory was confirmed, but even in 1922 there were developments in observational astronomy which were opening up questions about the scale of the universe, and the next part of the story involves the study of nebulae.

The Burning of the Clavie on January 11 in Burghead marks the start of the new year – it’s the old date of New Year’s Eve, Hogmanay, before the change to the Gregorian calendar in 1752. The barrel filled with tar and pieces of wood, and specially shaped for being carried by a single bearer, is taken round the village by the Clavie king and the Clavie crew, and then set up on the Doorie Hill for its fiery end. The embers are given to the various households to bring good luck for the new year ahead.

Burghead is also notable for the images of a bull which were found when the harbour of today was built in 1805. The bulls are inscribed in Pictish style, and are the only such bulls from that period to be found in Scotland. There are inscriptions of bovine animals at other sites, but they are cows. Around 30 of the bulls were found when the present-day fishing harbour of Burghead was developed, two centuries ago, and today only six remain, four locally in Burghead and Elgin, one in Edinburgh, and one in the British Museum.

There are stories of bulls being sacrificed in one or two other parts of the Highlands of Scotland on special occasions, and from the Western Isles a tradition of someone dressed in the hide of a bull going round at Hogmanay. At each house he would singe his tail at the hearth fire and hold it out for each member of the household to sniff, for good luck for the coming year.

And around 25 miles to the south of Burghead, at Inveravon, the Kirk Session records for 1714 reveal ‘ane act against clavies’, and Marian McNeill, who quotes the story, suggests that the word ‘clavie’ may come from the Gaelic cliabh, meaning a basket.

However, given that the New Year traditions for Scotland are generally strong, mentions of a bull and an association with fire are really only found in fragments. These fragments are so few that they may not necessarily be the remnants of an ancient custom across the whole country; they could also be something local that has happened to spread to one or two other areas.

The bull in the sky

There is however an example of a tradition of a bull and the journey of torchbearers which could have reached Burghead around eighteen hundred years ago; this is the Roman cult of Mithras.

The classic analysis of the cult has been carried out in recent years by Prof. David Ulansey in books such as The Origin of the Mithraic Mysteries and articles in journals including Scientific American. David Ulansey is Professor Emeritus of Philosophy and Religion at the California Institute of Integral Studies in San Francisco, and specialises in the religions snd cosmologies of the ancient Mediterranean world.

The Mithras cult, which reached its peak in the 3rd century AD, involved activities in an underground temple, meant to replicate the underground cave where it was said that the god Mithras killed a bull. The cult was particularly popular amongst soldiers, and it had administrators and merchants as well. The greatest concentrations of Mithraic temples are found in Rome itself, and also notably in those parts of the Empire – often on the most distant frontiers – where Roman soldiers were stationed.

Previously the cult had been regarded as coming from Iran, and the ancient god Mithra. However, there are no accounts in Iranian mythology of Mithra killing a bull. David Ulansey looked instead at the pictures of Mithras killing the bull – and how there would be particular other animals in the images, four in all – a dog, a snake, a raven, and a scorpion. Dog, snake and scorpion are beautifully shown in this picture from the Vatican Museums taken by Canadian photographer Gregory Melle.

David Ulansey noted a point made by two earlier scholars (the German K.B. Stark and the Canadian Roger Beck): that the Mithraic scenes are pervaded by astronomical imagery – the zodiac, planets, sun, moon and stars. So suppose, he said, that this whole cult is about astronomy; that the bull at the heart of it is the constellation Taurus; that the dog is Canis Major, the snake Hydra, the raven Corvus, and the scorpion Scorpio. All five constellations are located in a continuous band in the sky.

What then is the significance of the core image, the death of the bull? Ulansey says that this refers to the precession of the equinoxes, whereby the direction of the axis of the earth’s rotation slowly changes over a period of approximately 26,000 years. This wobble means that the polar point in the sky, the axial point about which the whole sky seems to turn, changes very slowly over time. This polar point today coincides with the location of the star Polaris, and indeed gives the star its name. In the past its location was slightly different, and over a period of around 26,000 years it will describe a little circle in the sky.

When we look up at the night sky, we see the stars turning around the fixed axial point, a bit like a giant mill, with the band around the mill – the celestial equator – holding the great structure together. There is a second band in the sky, formed by the earth’s orbit around the sun. As the year progresses, the rising-place of the sun makes a journey through the sky, its course going through the zodiac.

The two bands are bound together, meeting at two points – the spring and the autumn equinoxes. They mark the times of balance, when the sun’s journey through the constellation of the zodiac crosses the band in the sky formed by the earth’s rotation. We might think of these two crossing-points as riveting the framework that holds the universe together.

The wobble in the direction of the earth’s axis means a very slow and gradual move of the band of the celestial equator, and hence a very slow and gradual change in the crossing-points of the celestial equator with the zodiac – and this is the precession of the equinoxes.

The spring equinox today is in the constellation of Aquarius – hence the song about the dawning of the Age of Aquarius. For the previous two thousand years or so, it was in the constellation of Pisces, the Fish. For two thousand years or so before that, from around 2000 BC onwards, it was in Aries the Ram. And for two thousand years or so further back, it was in Taurus the Bull.

The journey of the torchbearer

Now in the year 128 BC, the Greek astronomer Hipparchus is said to have discovered the precession of the equinoxes. There are reasons for thinking that this was in fact a rediscovery, in that the phenomenon was known in more ancient times, but what matters in the present context is that the concept came to the fore in the 1st century BC. The discovery of powerful forces of change in the heavens had huge significance for people on the earth below, since the sky was regarded as the place where the human soul journeys after death.

‘A new force had been detected capable of shifting the cosmic sphere,’ he says. ‘Was it not likely that this new force was a sign of the activity of a new god, a god so powerful that he was capable of moving the entire universe?’

It is this god, given the name of Mithras, who was seen to have taken the spring equinox away from the Bull – and hence to have overcome his great power: to have slain him.

And that, says Ulansey, was exactly the way in which the worshippers of Mithras regarded him. One example is a scene showing the young Mithras holding a sphere in one hand and rotating a circle with the other – this will be the circle of the zodiac.

There is also an image of Mithras in the role of the god Atlas, supporting the world on his shoulder, as Atlas traditionally does.

And there is one more aspect of Mithras that is worth noting. There are a number of scenes of his birth, in which he is said to have sprung to life out of a rock. In almost all of these scenes, he is shown as carrying a torch.

Two torchbearers were part of the Mithras ritual. A bull was killed in an underground pit, and two attendants held flaming torches, one turned up and the other pointing down.

What does the torch represent? In the ancient world, the sun was often depicted as a torchbearer, and one of the ancient Greek cults includes a torchbearer who is said to be the sun. David Ulansey suggests that the torch pointing up is the spring equinox in Taurus the Bull, and the torch pointing down is the autumn equinox in Scorpio.

So a torchbearer travelling round a fixed route is to the fore in the Mithras cult – associated with a bull and the passage of the seasons.

But how could a Mithras cult from Rome have ever reached Burghead? That is what we will look at in the second part of this story.

Hallaig by Sorley MacLean is on one level about the clearance of people from the land of which they were a part. At another level it is a poem about the nature of Time.

‘Tha tìm, am fiadh, an coille Hallaig’
‘Time, the deer is in the Wood of Hallaig.’

Tha bùird is tàirnean air an uinneig
trom faca mi an Àird an Iar
’s tha mo ghaol aig Allt Hallaig
’na craoibh bheithe, ’s bha i riamh

The window is nailed and boarded
Through which I saw the West
And my love is at the Burn of Hallaig
A birch tree, and she has always been

eadar an t-Inbhir ’s Poll a’ Bhainne,
thall ’s a bhos mu Bhaile Chùirn:
tha i ’na beithe, ’na calltainn,
’na caorann dhìrich sheang ùir.

Between Inver and Milk Hollow,
Here and there about Baile-churn:
She is a birch, a hazel,
A straight slended young rowan.

This is a remarkable poem – that goes without saying, and much has been written about its background in the Highland Clearances. But it is a poem on several levels, and the power of its central image is so deep that it takes us into the territory of philosophy and physics – and gives us insight into areas on the very frontier.

Time as a mill, Time as a river

Much in physics stems from our choice of an image of Time. The ancient Greeks had two alternatives. One was a picture of Time as a turning millstone – slowly and inexorably making its round like the starry sphere of the sky. That image turns up in some unusual places, for instance in the story of the king who had a magic mill that could grind out whatever he desired, a mill which ended up at the bottom of the Pentland Firth. It could grind out gold or salt – two substances connected with Time, gold being impervious to Time and salt making everything it touches immune to decay.

That image of Time is cyclic and rather rigid, but a freer alternative is of Time as a river. Here we have something linear, but also dynamic – and a bit more unpredictable, with the swirl and flux of the flowing water.

Now both these images are rather ‘un-alive’. The turning millstone is man-made and predictable, the river natural but still inorganic. Can we get something more alive?

The answer is yes. In various mythologies around the world, we images such as that of Time as a reed. You can see why, with the plant’s linear growth, gradually upward through the passage of time. Just as a burning candle bore the destructive marks of time for the monks of the Middle Ages, so does a growing reed show time flowing forward for people living amidst the natural world.

And in some other cultures we find Time as a snake. Again you can see how, with the snake swallowing its prey which is slowly transformed by the digestive system that it is gradually passed through. The snake represents Time as a process that changes everything with which it comes into contact.

The Deer and the Wood

So now let us look in more detail at Sorley MacLean’s poem – and we can see images of Time as something alive – and not only one image, but two. There is the time of the deer flitting through the Wood of Hallaig – and the time of the Wood itself.

We can see the two processes of life, operating in different direction. Vertically there is the slow – ever-so-slow – growth of the trees, the birch and the hazel and the rowan; and the growth of the trees – which are compared to the growth of humans:

tha i ’na beithe, ’na calltainn,
’na caorann dhìrich sheang ùir.

She is a birch, a hazel,
A straight slended young rowan.

And then on a horizontal axis there is a different type of time – the time of the deer, a much faster and more elusive time, slipping past amongst them.

‘Tha tìm, am fiadh, an coille Hallaig’
‘Time, the deer is in the Wood of Hallaig.’

A second dimension of time

Physics today has a problem, which increasingly is being recognised as to do with the nature of Time – or the way in which picture Time. The two great pillars of modern physics, quantum theory and relativity, are incompatible when it comes to picturing Time, and for more than eighty years physicists have wrestled unsuccessfully with the problem.

Relativity operates within an existing framework of time. Time and space together form the platform on which matter moves. But quantum theory seems to require time to be somehow more fluid and spontaneous, to emerge along with matter out of the deep. Immense efforts have been made to fit the two theories together, with outcomes that have opened up new vistas – for instance of the first moments of the universe; but the fit is not yet seamless. And it looks as if the fundamental incompatibility may only be completely resolved when we develop a more comprehensive picture of time out of which the time of relativity and the time of quantum theory can each emerge in their own particular situations.

Now one promising theory has been for two-way time – to suggest that at the quantum level there may be two opposing flows of time that interact like two currents of the sea, and where the current meet and the waves break we may find the world of matter surfacing out of the underlying flux.

This picture of two flows of time meeting is an extraordinary one which we will look at in more detail in another of these sessions. Its origins are deep within the Schrödinger wave equation, which turns out to contain a description of not one wave but two. One of these waves comes from the past, and this is the wave that we normally select for study, since this is the flow of time that we are familiar with. But the Schrödinger equation also contains a description of a second wave, coming from the future. The waves themselves are deep below the surface, so deep that we do not perceive them. But the combination of the two of them gives us the world around us.

With this picture, we have a single dimension, but two different directions to travel through it.

But there is a second picture that is even more appropriate to the two-dimensional image of Hallaig – and this picture is one of two-dimensional time.

Sir Arthur Eddington, the man whose observations of the planet Mercury confirmed Einstein’s theory of general relativity, tried out some different mathematical forms of relativity. In one of these he made a modification to the familiar picture of three dimensions of space and one of time, to switch instead to a combination of two space dimensions and two time ones. He said that a world of two-dimensional time would ‘defy imagination’; but he continued to investigate the format, and moved on to a version in which three-dimensional particles could exist in a two-dimensional time.

Two dimensions from six

Eddington was a brilliantly gifted man, with the ability to combine mathematical skill with philosophical depth, but his investigation into two-dimensional time was eventually forgotten. But in 2007 Itzhak Bars of the University of Southern California in Los Angeles came up with a situation which two-dimensional time could solve.

He noted that in quantum theory there seems to be a deep link between position and momentum – in fact the two are linked in the uncertainty relationship which tells us that the more precisely we know the one, the less sure we can be about the other.

So he thought that to express quantum theory in the most natural way, we need a mathematics in which the two are on a completely equal footing. He looked for this; and he found that the only way he could get there was to add in two extra dimensions. One of the extra dimensions was of space, and the other one was of time. In a six-dimensional universe, with a total of four dimensions of space and two of time, he could get the deep underlying symmetry between position and momentum that he needed.

And strangely enough, this six-dimensional universe with its two dimensions of time was not so much beyond experience as we might have feared. The various rules of symmetry kept it quite close to ‘normal’. The two dimensions of time did not lead to time travel or any bizarre paradoxes.

He used a beautiful image to depict this six-dimensional world and its relation to us. The situation, he says, is rather like what happens when we hold our hand up by a lamp and see a two-dimensional shadow on the wall. Bars says that the six-dimensional world is the underlying one, and that it throws up a variety of forms of four-dimensional ‘shadows’ – of which our universe is one.

We live then in a Shadowland, a four-dimensional world which is rich and varied – but which is still only a slice of the bigger picture.

So here indeed is a strange new world to explore – first of all mathematically, and then by experiment, if suitable predictions can be made that we can try to test. And we have an image from the world of poetry to help us think about the new possibilities – a picture of time in two different dimensions, the time of the Wood of Hallaig and the time of the deer flitting through it.

And the words of the poet echo in our minds, as in a film made by Neil Kempsell with the voice of Sorley MacLean himself and music by the late and richly talented Martyn Bennett.

‘Tha tìm, am fiadh, an coille Hallaig’
‘Time, the deer is in the Wood of Hallaig.’

Back to OISF

There are two fundamentally different ways of picturing the world around us. One is as a collection of objects – and we learn from our earliest moments that we are surrounded by things that we pick up or bump into.

But an alternative approach is to see the world as formed out of processes – actions and experiences. We switch focus from the food we pick up to the process of eating, from the chairs we bump into to the process of exploring the room.

In our modern material Western world, objects are to the fore, and we look to the world to be solid and stable and as unchanging as possible. But for older societies, who live by hunting and gathering, change is an integral part of life. The world is a continuous flux, and the picture of the world is in terms of processes.

So for a situation in which we might say, ‘It is a dripping spring’ – the Apache language would take a word for ‘being white’, a word for ‘moving downwards’ and a word for ‘to’, to get something like ‘whiteness moves downward’.

We can see that this is a fresher and more vivid description, coming from a time when people lived much more in the flux of the natural world than we do.

We, by contrast, turn the abstract processes of our mind into things. We ask if a friend ‘grasps’ an idea, as if it were a bottle of beer that we pass across the table. We say that we have a ‘point of view’ – like a place where we sit to watch the sun go down. We even see someone else’s point of view, just as we see a picture on the wall.

We speak of Time in the same way. It is a highly abstract concept, so abstract that debate has continued for several thousand years as to its nature. But that doesn’t prevent us from ‘saving’ it like money in the bank, or ‘giving’ it to people like sweets from a bag.

A dialogue in Alice in Wonderland warns us to take care with this kind of language.

‘I don’t know what you mean,’ said Alice.

‘Of course you don’t!’ the Hatter said, tossing his head contemptuously. ‘I dare say you never even spoke to Time!’

‘Perhaps not,’ Alice cautiously replied: ‘but I know I have to beat time when I learn music.’

‘Ah! that accounts for it,’ said the Hatter. ‘He won’t stand beating. Now, if you only kept on good terms with him, he’d do almost anything you liked with the clock. For instance, suppose it were nine o’clock in the morning, just time to begin lessons: you’d only have to whisper a hint to Time, and round goes the clock in a twinkling! Half-past one, time for dinner!’

(‘I only wish it was,’ the March Hare said to itself in a whisper.)

Verbs and nouns

We have a fundamental grammatical difference in our Western languages between objects and processes. Objects are nouns and processes are verbs. These grammatical structures have been with us for a long time, and people have been writing about them since the Greek philosopher Plato first highlighted them 2500 years ago.

The rigidity of our language contrasts with the fluidity with which we develop science, and sometimes language and science can be out of step. For instance, we regard light as a thing. We say that ‘it’ flashes. That’s not very good physics, since we currently understand light to be a process, a dynamic interaction of electric and magnetic fields that spreads rapidly through space. You can’t pick ‘it’ up like a dropped sweet, indeed you can’t give it a push to make ‘it’ travel faster. As far as the knowledge goes that has been gained over the centuries about light, the appropriate way to refer to light is definitely not as ‘it’. But of course, that way of speaking locked into our day-to-day language.

The Hopi people handle the situation better than us. In their language, the word ‘light’ is a verb – as is ‘wave’, ‘flame’, and indeed also ‘meteor’.

The Nootka people of Vancouver Island go even further. In their language, all words seem to have verb-nature. They would say that ‘a house occurs’ rather than speak of a thing called a house. And if we think over a long enough timescale, we can see that a house is indeed a process, one that starts with building and ends with demolition. In fact, we can see ourselves as a process from birth to death, a process of change in which any single photograph is not the totality of ‘me’ but simply a single frozen slice of the flow.

The Celtic languages

Now when we come to the Celtic languages, there are nouns and verbs, as in English – but their relative importance is different. The verb comes at the start of the sentence. Gaelic would say:

Tha an cat mor
(Is the cat big)
The cat is big

Tha mi a’ dol
(Am I a-coming)
I am coming, I come

Tha mi a’ tighinn
(Am I a-going)
I am going, I go

We of course in English turn the word-order round and start with the verb when we have a question to ask, but this Gaelic form is for the basic structure of a statement.

The same pattern is there in Welsh:

Yr wyf i yn mynd
(There be I a-going)
I am going, I go

Yr wyf i yn canu
(There be I a-singing)
I am singing, I sing

So while physics has been moving to a process-based picture of the world about us – a picture which is built in to various older languages – Western languages have been moving away from it. We in the West like to think and speak in terms of a world of solid objects. Could this mindset be at the root of our conceptual difficulties with areas of modern physics like quantum theory which picture the world in terms of processes rather than things?

Back to OISF

There was the first Penguin book from 1935, a biography of Shelley by André Maurois; and Penguin number 3, Poet’s Pub by Eric Linklater. And there was also a book on cosmology, published in Pelican Books in 1940. The wartime paper is thin and the pages became dog-eared, but it was kept with care.

In The Expanding Universe, Sir Arthur Eddington described the new picture of the cosmos. He described the measurement of the distances of spiral nebulae and the red-shift of the light which shows that they are moving away from us, and he explained how the theories of Albert Einstein and Willem de Sitter had produced a model which fitted the observations.

Seeking deeper

Throughout his life GMB was in general not often impressed by the explanations of popular science. Too often, he thought, they did ‘nothing to satisfy the perennial human hunger for what is true and good and beautiful’, failing to go deep into the great mysteries such as Time.

He sought something more than that, something with more of the sense and exploration that he found at the age of eight when he read science fiction stories in the Wizard and wrote his own ones. The story of these and much else can be found in the finest introduction to his life and work, Interrogation of Silence by Rowena Murray and Brian Murray. Coming through the book, clearly and lyrically, is a picture of how he saw life as a journey in search of something – insight, experience, illumination.

Lux Perpetua
By such glimmers we seek you

he wrote in the collection Following a Lark, which appeared in print just days after his death in April 1996.

‘I have picked up a few curious things from the shore of the great ocean of time,’ says a character in one of his novels.

Eddington understood that quest. On the closing page of The Expanding Universe he wrote:

‘A slight reddening of the light of distant galaxies, an adventure of the mathematical imagination in spherical space, reflections on the underlying principles implied in all measurement, nature’s curious choice of certain numbers such as 137 in her scheme – these and many other scraps have come together and formed a vision. As when the voyager sights a distant shore, we strain our eyes to catch the vision. Later we may more fully resolve its meaning. It changes in the mist; sometimes we seem to focus the substance of it, sometimes it is rather a vista leading on and on till we wonder whether aught can be final.’

Elsewhere he wrote: ‘Wherever a way opens we are impelled to seek, conscious that in this activity of mind we are obeying the light that is in our nature.’

Eddington had a remarkable combination of skills. He could focus on specifics with great lucidity, explaining radical new developments in physics in language that was clear and simple and went to the heart of a concept. And at the same time he did not shrink back from the wider implications of the ideas. The territory that he took the reader into could verge on the mystic, but the steps there were disciplined and scientific.

‘For the truth of the conclusions of physical science, observation is the supreme Court of Appeal,’ he wrote.

Cumbria and Cambridge

He was born in 1882 in Kendal, Cumbria, and he was not yet three when his father died during a typhoid epidemic. His mother had to bring up her two children with little income, but by the time he was sixteen Eddington had won a scholarship to the college that would become the University of Manchester. He went on to further study at Cambridge and employment at the Royal Observatory at Greenwich. In 1913 he became professor of astronomy at Cambridge.

Eddington was the first person to develop a real understanding of what goes on in the heart of a star. He built on Karl Schwarzschild’s model of a star as a gas held in a balance between the attractive force of gravity and the heat bursting outwards. He calculated the pressure and density of this stellar gas – and its temperature, which he showed was millions of degrees. For the source of this colossal heat, he turned to the new developments in nuclear physics of the time, in particular nuclear fusion.

His name became well-known in 1919 when he jointly organised the expedition to West Africa that provided the first experimental proof for Einstein’s theory of general relativity. The co-organiser was the Astronomer Royal, Frank Watson Dyson (the man who introduced the BBC’s Greenwich time signal, the ‘pips’). The aim in travelling to the island of Principe was to observe the solar eclipse of 29 May, to measure the extent to which the path of starlight was bent by the sun’s gravitational field. The confirmation catapulted Einstein to global fame. Eddington summed it up in an adaptation of a poem by an earlier astronomer, Omar Khayyam:

Oh leave the Wise our measures to collate
One thing at least is certain, LIGHT has WEIGHT
One thing is certain, and the rest debate –
Light-rays, when near the Sun, DO NOT GO STRAIGHT.

Eddington and Einstein

Eddington had been early to recognise the significance of general relativity, which had been published in 1915 at a time when many other British astronomers were arguing that links with German colleagues should be broken. Eddington, whose parents were Quakers, was a pacifist and repeatedly called for British scientists to keep up pre-war friendships and scientific contact. He was also a conscientious objector, and indeed it was only the intervention of the Astronomer Royal and others that kept him out of prison in 1918.

He was widely regarded as the best exponent of relativity, and Einstein reckoned that his book The Mathematical Theory of Relativity (1923) was ‘the finest presentation of the subject in any language’.

A number of his concepts and phrases have become part of our culture, among them ‘time’s arrow’ for our one-way experience of the passage of time from past to future. It was also Eddington who popularised the French mathematician Émile Borel’s concept of the infinite number of monkeys on typewriters producing a library of books.

‘If I let my fingers wander idly over the keys of a typewriter it might happen that my screed made an intelligible sentence. If an army of monkeys were strumming on typewriters they might write all the books in the British Museum. The chance of their doing so is decidedly more favourable than the chance of the molecules returning to one half of the vessel.’

This influenced many people, from the Argentinian writer Jorge Luis Borges, who developed the concept into a universal library, to the American comedian Bob Newhart, who observed that the monkeys would type out a lot of gibberish too:

‘So they would have to hire guys to check the monkeys to see if they were turning out anything worthwhile. … Look, I’ve got something: “To be or not to be … that is the gezortenblatt …” ’

Eddington himself, a keen cyclist who once covered the 122 miles from Doncaster to Cambridge, devised the Eddington number which records the number of days in your life on which you have cycled at least the same number. His own E number the year before he died was 77. (In other words, on 77 days he had cycled more than 77 miles).

More roads to travel

Some of the territory he explored still needs further investigation, in particularly the work on what he called ‘fundamental theory’, an attempt to unify quantum theory, relativity, cosmology and gravitation. The work was uncompleted at the time of his death in 1944, but a book Fundamental Theory was published posthumously.

This readiness to explore was a defining feature. ‘I think that science would never have achieved much progress if it had always imagined unknown obstacles hidden round every corner,’ he wrote. ‘At least we may peer gingerly round the corner, and perhaps we shall find there is nothing very formidable after all.’

This exploration took him forward into deep questions about the nature of reality.

‘The universe is of the nature of a thought or sensation in a universal Mind,’ he wrote in The Nature of the Physical World (1928). ‘To put the conclusion crudely – the stuff of the world is mind-stuff. As is often the way with crude statements, I shall have to explain that by “mind” I do not exactly mean mind and by “stuff” I do not at all mean stuff. Still that is about as near as we can get to the idea in a simple phrase.’

And to find out what that stuff of the world was, he said, part of a shared quest.

‘Whether in the intellectual pursuits of science or in the mystical pursuits of the spirit, the light beckons ahead, and the purpose surging in our nature responds.’

Masterly

In an obituary, Time magazine which had featured him on a 1934 cover, spoke of him as ‘one of mankind’s most reassuring cosmic thinkers’.

‘Shy, neat, reed-nosed Sir Arthur looked precisely like the British university don he was, and he discoursed on his cosmic subject with a wit and clarity rare among scientists. He set down in brook-clear language a masterly simplification of Einstein’s theory of relativity.’

For a poetic epitaph, part of George Mackay Brown’s ‘A Song for Winter’ might apply:

He gave his songs
To the striking of a road through high snows,
To star configurations,
To talk with eagles and goatherds

Back to OISF

It was the year of the Six-Day War in the Middle East and the military coup in Greece. It was the year when North Sea gas came ashore in Britain, when the Beatles issued Sergeant Pepper, and when Celtic won the European Cup. Nicole Kidman was born, Elvis Presley got married, and Woody Guthrie died.

Dr Christiaan Barnard carried out the first heart transplant and Jocelyn Bell discovered pulsars.

And two physicists, working independently, applied the Higgs mechanism to unite electromagnetism and the weak interaction into a single overall structure. Twelve years later, they would share the Nobel Prize.

The two men were very different in background. Steven Weinberg, born in New York City, is an atheist and a strong supporter of the state of Israel. He takes a view of nature which can sometimes seem quite bleak.

Abdus Salam, born in Jhang, Punjab, was a Muslim who quoted the Quran in support of the scientific quest for knowledge. He had a particular interest in symmetry.

‘That may come from my Islamic heritage for that is the way we consider the universe created by Allah with ideas of beauty and symmetry and harmony, with regularity and without chaos.’

But the two also had much in common, including a deep concern to act on global issues. Weinberg has written, spoken and campaigned strongly on the dangers of nuclear weapons, and continues to do so. For a time in the early 1970s he was a consultant to the U.S. Arms Control and Disarmament Agency, ACDA, providing them with technical background for the SALT arms reduction talks with the Soviet Union. Salam established the International Centre for Theoretical Physics in Trieste as a place where physicists in developing countries could go for periods of creative stimulation, enabling them to keep at the forefront of their subject without joining a brain-drain to America and Europe.

And in physics, both were clear about the need to pursue the task of seeking structure and using the techniques of symmetry and of quantum field theory – and if necessary to opt out of the tide of fashion and choose their own direction.

Salam had studied mathematics at the University of the Punjab and then won a scholarship to Cambridge, where he was a research student of Nicholas Kemmer. When Kemmer moved to Edinburgh, Salam was appointed in his stead, and then in 1957 became professor at Imperial College London where he built up a brilliantly talented team, among them Tom Kibble who told him about the Higgs mechanism.

Weinberg had been in the same class at high school as Sheldon Glashow, and had gone on to study at Cornell and Princeton, and to become professor of physics at the University of California in Berkeley. in 1966 he took leave from his post at Berkeley to go to Massachusetts, so that his wife could study at Harvard Law School; today she is Professor of Law at the University of Texas at Austin. In Massachusetts Weinberg spent time at Harvard with Schwinger, who he would later succeed there, and at MIT. In 1967 he was working on the strong interaction, trying to apply the Higgs mechanism to it and getting conflicting results – and then realised that his model was in fact telling him about the weak interaction instead.

Turning the key

‘When I started doing research in early 1950s,’ Weinberg observed recently, ‘physics seemed to be in a dismal state.’ The problem was the proliferation of all kinds of particles and forces.

‘Nature, like an enemy, seemed intent on concealing from us its master plan.

‘At the same time, we did have a valuable key to nature’s secrets. The laws of nature evidently obeyed certain principles of symmetry, whose consequences we could work out and compare with observation, even without a detailed theory of particles and forces… It was like having a spy in the enemy’s high command.’

Both Weinberg and Salam realised that the Higgs mechanism provided a means of keeping the symmetry of the electroweak interaction and at the same time breaking it sufficiently for the pulses of the weak force to be concentrated in particles with a non-zero mass.

Their papers predicted three such particles – and in 1983 all three were found by the Super Proton Synchrotron at CERN. The team leaders, Carlo Rubbia and Simon van der Meer, were awarded the Nobel prize the following year for the discovery.

The new particles were the W⁺ and the W^-, and the neutral Z⁰. They are very massive, with the W about 80 times the mass of a proton, and the Z just over 90 times. By comparison, the mass of an iron atom is around 55 times the proton’s mass.

With such a large mass, their lifetime is very short indeed, and they only travel an incredible short distance before vanishing.

The Weinberg and Salam papers also predicted a fourth particle – one that was a kind of leftover after all the necessary weak particles had been put in place. This additional particle was the Higgs, and so its discovery puts one large additional piece of support for Weinberg and Salam’s work.

In addition to the experimental support, a strong theoretical underpinning came from two Dutch physicists, Martinus Veltman and his student Gerardus t’Hooft. They showed that mathematically the theory held together so well that it had none of the infinities that had plagued so much of field theory for so long. That work earned them the Nobel Prize for Physics in 1999.

The Standard Model

The momentum from the success with the electroweak interaction carried forward to the strong interaction, using the idea of SU(3) symmetry and quarks, with various physicists playing a part in developing what is now called the Standard Model.

But the aim of science is always to press on to get closer to the truth, and it is clear that the Standard Model is not the final stage. The big unresolved challenge is to reconcile it, the theory of the very small, with general relativity, the theory of the very large, and that seems a long way from completion. The Standard Model encompasses the strong, weak and electromagnetic forces, but not gravitation.

And indeed although the Higgs particle consolidates the Standard Model, it also provides deep and perhaps unsettling philosophical challenges.

First of all, it finally removes any hope of a material base to physics. That hope was really lost in 1926 when Schrodinger produced his wave theory of matter, picturing an unknown substance in motion – its unknown nature was why he gave it the mathematical symbol psi – out of which matter somehow formed as the waves on the ocean. In the Schrodinger picture we see the wave and can model it and calculate its shape, but we know nothing of the deep sea beneath.

The Schrodinger picture was countered by Heisenberg, who insisted that we could still have particles, while not needing to look at their deeper nature. We could not zoom too closely in on their direct moments of contact, he said, but instead we much stand back at a distance and simply correlate the measurements of what went in and what comes out.

Heisenberg’s approach meant that physicists could avoid the issue of what matter is and simply talk about how it behaves. So they could continue to talk about particles in fairly familiar – and fairly material – language.

The concept of the Higgs field means that this approach is no longer good enough. It tells us that what makes matter the way it is – is something quite specific but also quite non-material, a field. We start with something fundamental, whose essence we do not know, namely light. We add in something even more non-material, the concept of symmetry. And we add in something else non-material, the Higgs field. And the outcome of these various insubstantial and non-material entities is – the stuff that builds up through atoms and molecules into lumps of iron and concrete.

2500 years of argument

The old debate amongst the Greeks was between Aristotle and Plato, who argued about what was the primary factor of existence. Plato said that it was form and Aristotle said that it was substance. Plato said that the fundamental essence was a set of patterns – universal templates or archetypes – which created the real world when they were somehow stamped onto a formless kind of clay.

Aristotle said that the clay was the essence, and that forms were secondary, being the patterns which we notice. He gave the example of the concept of a snub nose. Could we say that snubness somehow existence as a form and was imposed on the various noses of the world? He asked. No, was his reply, snubness is a concept that we create to enable us to better catalogue the noses around us.

The debate was one by Aristotle and he and the Greeks set us off down a trail of substance. This was why they developed the concept of an atom as something fundamental – it was part of a picture in which substance was primary.

But now we have a theory in which substance is not primary, but created out of light, mathematics and a field. A field is simply a form – a kind of abstract structure in space – indeed if an atom is an example of pure substance, then a field might be seen as a case of pure form.

That in turn leads to the question of whether or not we should be talking about particles, or whether we should use the language of waves.

And deep under the surface is the question of order. Symmetry is now invoked to impose order on nature – but where does symmetry come from? And how does it ‘impose’ itself?

So in one way the Higgs discovery reinforces a remarkable theory that took its present shape in the early 1970s. In another way it undermines a worldview that formed 2,500 years ago – and thus points the way forward to the next development in physics, whatever it might be, with as many questions as answers. These are good reasons for physicists to be cheerful – and to burst into song.

Back to OISF

The reasoning came from symmetry. When the electroweak field was looked at from one perspective it appeared as electromagnetism. When viewed from another perspective, it appeared as the weak interaction which causes radioactivity.

But because the weak interaction in the world is very different from the electromagnetic one, the symmetry could not be complete. So somehow the symmetry had to be broken.

Can we somehow keep symmetry and yet break it? The answer at first might seem to be no, if we think of symmetry as something like a vase which we break when we drop it. But we don’t have to go that far in the concept of breaking things. We could think of the symmetry of a circle or a five-pointed star and allow it to break a little – and get a rose. The original symmetry is still there, but with edges that are somehow ‘softer’.

The problem was that Goldstone’s theorem seemed to force the choice to be between a perfect vase or a smashed one, ie no vase at all. But Philip Anderson’s 1963 paper had suggested that in superconductivity a similar problem was in fact resolved by a process of condensation. Particles in a crystal had their behaviour shaped by the lattice of the crystal.

That suggestion from Anderson was enough to encourage physicists at three centres to take up the challenge anew – and each independently to come up with a solution.

Breaking it gently

The way to resolve the problem is to invoke a new field which fills all of space – today called the Higgs field. This field obeys the rules of symmetry, just as does the existing field of the electroweak theory. But it somehow condenses into a single state – in the same way as the theory of a bar magnet tells us that the jumbled-up magnetic domains drop down into place in a single direction which locks in. Or in the way in which the electrons in a superconductor lock in to a single coordinated structure.

So the field itself is symmetric – but the fact that it condenses into a single fixed state breaks the symmetry.

And it is this field that provides the mass. It links with the Yang-Mills field (the field which has to exist to maintain gauge symmetry) and the particles of the Yang-Mills field acquire mass as a result. The outcome is not only the photon for electromagnetism but no less than four other particles. Three of these are concentrations of the weak interaction, now given mass by the condensing of the Higgs field. And there is a fourth, a kind of by-product of the process, something new – the particle which has become known as the Higgs.

In Brussels

The first to publish were at the Free University of Brussels – Francois Englert and Robert Brout.

Englert’s first degree had been in engineering, but he switched to physics and went to work at Cornell as Brout’s research assistant. They found that their approaches to physics were so similar that when the time came for Englert to go back to Belgium, Brout decided to move there with his family, and went on to acquire Belgian citizenship and to play a big part in the further development of physics in the country, up till his death last year.

One of the features that Englert and Brout shared was a readiness to look afresh at any problem, and that, says Englert today, is how they made their breakthrough with what has come to be known as the Higgs particle.

‘The generality of our results is largely attributable to the use of quantum field theory, which at the time was largely ignored in elementary-particle physics. Its use in deriving the mechanism was no accident. Driven by his unusual faculty to translate abstract concepts into tangible intuitive images, Robert always conspicuously disregarded academic knowledge and favored entering any subject from scratch. For him, the fact that he was no expert on particle physics was an advantage: He could easily free himself from fashionable trends in the quest for a consistent theory of short-range fundamental forces.’

At Imperial

Imperial College London was the base of Tom Kibble, who had taken his physics degree and doctorate at Edinburgh. He was of Scots descent and born in Madras in India, where his grandfather had been a medical officer and his grandmother, Helen Bannerman, had become a well-known writer of children’s books. Working with him at Imperial were two visiting Americans, Gerry Guralnik and Dick Hagen, who had both attended lecture courses by Julian Schwinger during their earlier studies.

The paper written by the three was just being put in the post for publication when the papers by Englert and Brout and by Peter Higgs arrived.

In Edinburgh

Meanwhile at Edinburgh Peter Higgs had been following the arguments about Anderson’s work on superconductivity. In particularly, he noted a criticism made by Wally Gilbert, a remarkable man who started out as a physicist but switched to biology after meeting the James Watson (of double helix fame) and went on to win the Nobel Prize for his work in sequencing DNA. Today in retirement, he is an artist-photographer whose work is exhibited in galleries across the US, with the images including an Orkney series.

In 1964 Gilbert had argued that there was a fault in the argument that symmetry-breaking could lead to mass. Peter Higgs thought at first that this was indeed the end of any hope of a way forward, but then realised that a method developed by Julian Schwinger could be applied to show Gilbert was wrong. He sent a letter accordingly to the journal Physics Letters which is published at CERN, the particle accelerator centre near Geneva.

He then worked on a second paper, to put together the actual way in which the symmetry-breaking occurs, using the Higgs field. He sent off this paper to Physics Letters as well – only to have it returned as not suitable for publication. It turned out afterwards that the editor of the journal had thought the paper ‘not to have any relevance to particle physics’.

‘I was rather shocked,’ he says. ‘I did not see why they would accept a paper that said this is a possible way to evade the Goldstone theorem, and then reject a paper that showed how you actually do it.’

So during August he revised the paper and with the encouragement of one of his colleagues, Euan Squires, added on a paragraph that drew attention to the fact that the theory had practical experimental consequences – that it predicted a new particle which could be looked for. This emphasis was one of the factors that associated Peter Higgs’s name with the search for the particle.

He sent the paper to the editor of another journal, Physical Review Letters, who confirmed that he would accept it and mentioned the paper by Englert and Brout which he was also about to publish.

The Edinburgh connection

Peter Higgs had come to Edinburgh four years before to take up a lecturing post in the Tait Institute of Mathematical Physics. Its graduates include Sir David Wallace (seen above on the left with Peter Higgs) who subsequently became President of the Institute of Physics and Master of Churchill College, Cambridge, and Dennis Canavan, who went on to become first a teacher and then one of Scotland’s most highly regarded political figures.

The Institute took its name from James Clerk Maxwell’s friend and colleague, Peter Guthrie Tait, and was housed in Roxburgh Street, just across the road from the Physics Department.

The Tait Chair in Natural Philosophy had been established in 1922, with the aim of developing the study of mathematical physics, and its first incumbent was Sir Charles G. Darwin, the physicist grandson of the great naturalist. After him came Max Born, one of the founding fathers of quantum theory, who won the Nobel Prize for the probabilistic interpretation.

Born had begun his career at Göttingen as assistant to the mathematician David Hilbert and his own assistants included Werner Heisenberg, Wolfgang Pauli and Enrico Fermi.

In 1953 Born was succeeded by one of his former students, Nicholas Kemmer, who established the Tait Institute itself. Kemmer, born in St Petersburg, had been educated in Germany when his family moved there after the Russian Revolution. He had worked in Zurich as Pauli’s assistant, then on wartime atomic energy research, and after the war at Cambridge. His own research had developed the use of symmetry for protons, neutrons and mesons, and was a first stage in the developments that would grow into a core concept in particle physics today. At Cambridge, he gave priority to his teaching work, for which he was in much demand, with his students including Ron Shaw and Freeman Dyson, who speaks of the high quality of Kemmer’s teaching of quantum field theory.

And indeed it was another one of Kemmer’s Cambridge research students – Abdus Salam – who along with Steven Weinberg took the step of using the Higgs approach to solve the problem of electroweak theory.

Back to OISF

The technique that seemed to be the most powerful one was the use of symmetry, and the use of Lie groups enabled a classification to be made that brought the weak interaction into a possible unification with the electromagnetic one. That was truly amazing. The long-distance electromagnetic field that gives us light and radio waves was somehow linked at a deep level with the weak interaction which we only know through its by-products in processes at the quantum level like radioactive decay.

A second application of the treatment involved another type of symmetry, gauge symmetry, which required the existence of a new type of field, the Yang-Mills-Shaw field, which brought the weak interactions even closer, by giving them a new particle of their own to complement the electromagnetic one (the photon).

But – damn and blast – the predicted ‘weak photon’ was massless, which could not be the case in reality. And – damn and blast three times over – Goldstone’s theorem showed that there was no way in which you could generate a mass-possessing weak particle without destroying the symmetry completely.

For those few people who refused to abandon the problem, if they had any request from Father Christmas it would be for a symmetry-breaking kit – something that would break the symmetry while preserving it.

The situation required the kind of ingenuity of an Orcadian student from Birsay who had happily stuck photos of his native islands on the wall of his Edinburgh digs with Copydex, which at the time was regarded as proof against just about anything – a problem which his landlady encountered when she decided that the pictures infringed the rules of the house. She tried to haul them off the wall and took off a quantity of wallpaper with them, and irately confronted him for his misdeeds. Without the slightest appearance of a pause for thought, he said with a kind of calm authority: ‘Oh, what a pity that you didn’t ask me for the Copydex remover.’

Something this was needed with the electroweak interaction – to remove some of the picture-equivalents off the wall without at the same time taking the wallpaper with them.

The equivalent of the Copydex remover came indeed not from looking at a wall but from things that are much bigger and solider than the world of very small particles. There were three situations in solid state physics that produced the clues.

Situation number 1

When atoms join up to form a crystal, their outer electrons loosen and begin to drift. Having lost these outer electrons, the previously electrically-neutral atoms have a net positive charge. The electrons stay in the crystal, not attached to any particular atom, and an electric field can start them moving in a particular direction – this is what forms an electric current. However, the effect of the positive lattice with the little pulls of the various atoms in the structure can be to slow down the electrons – and make them appear to be more sluggish and massive than they would otherwise have been.

So one way for a particle to behave as if it has more mass is to put it in some kind of external lattice like this.

Situation number 2

A magnetic substance is formed out of many little units which are themselves magnetic – they are called domains. When the substance is very hot, the domains will move around and point in a random mix of ways and from the outside we would never know that there was the potential for magnetism there. But if we let the temperature drop, there comes a point where suddenly the domains click together into pointing in a single direction. Somehow each lines up with its neighbour, but not in a one-by-one fashion but all an overall ‘decision’. We have no way of knowing in advance which direction they will happen to lie along.

The reason why they line up in this way is because this is the most stable form they can take. It is as if they have dropped down to the lowest point they can reach. It is a bit analogous to us filling a jar with sugar and tapping it from time to time – to see the level sink as the sugar grains start to fit together better and better. In the case of the magnetic substance, there is no tapping process, and the alignment happens almost in an instant. But there is a parallel in that in each case the little units – whether domains or grains – ‘find’ that by aligning themselves closely a stable ground-state is reached.

The magnetic substance when it was hot was very symmetric in that we could turn it around in as many ways as we would like, and in terms of magnetism each direction looked the same. But after we cooled it, we had this sudden transition of the domains into an overall direction. So the individual units still retained their own internal symmetry while the collective result was to make a break.

Situation number 3

This is in a very strange world, the interior of a superconductor. Here electrons can travel through the crystal lattice so smoothly that nothing slows them down in any way and they can travel forever. Here something has happened which is a kind of parallel to the magnet in that there has been a process of internal ordering. The electrons have a kind of overall link between them that enables them to get through the lattice without bumping into any of the lattice atoms.

It is a bit like dancing the conga. If a group of people are in a crowded room and all try to make for the door on their own, their will be a lot of bumping into others and an ever-slowing rate of progress, but if they line up in conga formation they can negotiate their way round in a coordinated way and avoid touching anyone.

Where does this get us? Well, from situation 1 we see that some kind of background lattice can cause particles within it to slow down and behave as if they have become more massive. So maybe we need to find some kind of background lattice encompassing the whole of space, so that it can somehow interact with the particles we have been studying and cause them to behave ‘massively’. We need in fact a background lattice that consists purely of forces – and that is just a definition of something that we have already become familiar with, a field.

So we need an additional field to interact with the field that we already have, in particular the Yang-Mills field.

But how will this field get round the constraints of Goldstone’s theorem? – which the Yang-Mills field on its own could not get beyond.

Here is where situations 2 and 3 come in. This new background field has to have the various symmetries, otherwise we have broken them completely, but since it is a brand-new field with only one task, to help us out of our problem, we do not need to allow it to have all the myriad of options that the more familiar fields do. Indeed, it only requires to have one option, just like the magnetic bar does, and just like the electrons in the superconductor do. There is one single position that the choice of options locks in to – so to that extent it has broken the symmetry – but the break is not so bad that we have lost the symmetry completely.

Superconductor superstructure

In 1963 Philip Anderson looked closely at what happens inside a superconductor and said that there was something important for particle physicists to be aware of. Anderson was a specialist in the solid state, and went on to share the Nobel Prize in 1977 for his work on the electron interactions in phenomena like magnetism and superconductivity. His studies at Harvard had been interrupted by the war, in which he had been deployed in research on building radio antennas, and after going back to Harvard to complete his training (and where his fellow-students included Tom Lehrer) he went to work at Bell Laboratories, joining a glittering array of researchers there. He found that the sophisticated mathematical techniques of quantum field theory that he had learned from Schwinger at Harvard had practical applications in the advanced radio work. In his background there are professors on both sides of the family, together with a love of the outdoors, and from a sabbatical year in Japan there is a deep interest in Japanese culture and he is a first-degree master of the game of Go.

The paper that Philip Anderson wrote in 1963 showed that in a superconductor the ordered cloud of electrons acts like a single quantum system which can be energised, and that the bursts of energy look like particles. The presence of an electromagnetic field affects these excitations in a way that makes them behave as if they had acquired a mass. So, he noted, symmetry was being broken but yet mass was being generated, and so the blocking effect of Goldstone’s theorem had been overcome. The Goldstone difficulty was, he said – ‘not a serious one’. It was this paper that opened the way for the breakthrough of Peter Higgs.

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