The Big Bang and before 3: Lemaître’s universe, Hubble’s law

Georges Lemaître was a devout priest and a brilliant physicist who found Hubble’s Law in theory two years before Hubble did in practice. He took Einstein’s equations of general relativity and showed that they had a solution in which the universe expands, with the speed of expansion increasing as time goes on – just as Hubble had observed in his study of distance and speed of recession of the spiral nebulae.

scientists_lemaitreBorn 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.

Williamina Fleming

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.

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The Big Bang and before 2: A shift in the mist

The Latin word nebula means ‘mist’, and originally a nebula was any sort of misty patch in the sky. Today it is more precise, referring to an interstellar cloud of dust and gas; and we shall see in a moment why the name evolved.

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.

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The Big Bang and before 1: The first ideas

The story of the development of the idea of the Big Bang has two separate strands, and we have to switch back and fore between them.

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.

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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.

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The clavie and the stars

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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.

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The physics of the Wood of Hallaig

Time, the deer is in the Wood of Hallaig.

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.’

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Processes and objects

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?

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Eddington’s universe

Whenever the poet George Mackay Brown reorganised his library, getting rid of some of the overspill, some books from younger years would always remain.

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.’


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

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