The physics of 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.

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.

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.

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:

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.

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.

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.