The Labyrinths of Time

by Peter Cowlam

A marine organism in unfathomable ocean depths receives light from a star a light year away, and responds, with a tiny twitch, the merest throb. By definition, the light the organism is influenced by has taken a year to reach it, as a staggered simultaneity, asking us to reconcile an apparent contradiction. But is it reconcilable, when the star as it appears now is not as the star now is, and that ‘now’ is not an absolute? Or do we leave it at that, when our ideas of ‘now’ and ‘nowness’ are inscrutable, problematic?

Or to take another instance, with Einstein’s thought experiment and the traveller on the tram. He sees a clock whose hands are showing nine o’clock, and recedes from it at the speed of light. If by some miracle of optics he were still able to see the clock, as he moves from it at light speed, he would only ever see the hands as he saw them when he left, fixed at nine o’clock. Conversely people on the ground will note time recorded much as they expect, with the minute hand moving continually through the minutes. Does this mean that for the traveller moving at the speed of light the hands are actually pointing at nine o’clock, while for those left grounded they move to a minute past, to two minutes past, to three minutes past etc?

This is just one curious aspect of the dissemination of information over enormous distances, and the behaviour of matter at very high velocity, as is put in mathematical terms by Jacob Bronowski—

Even the point about clocks running slow was singled out at last by an inexorable fate. In 1905 Einstein had written a slightly comic prescription for an ideal experiment to test it.

If there are two synchronised clocks at A and if one of these is moved along a closed curve with constant velocity v until it returns to A, which we suppose to take t seconds, then the latter clock on arriving at A will have lost ½t(v/c)2 seconds by comparison with the clock which has remained stationary. We conclude from this that a clock fixed at the Earth’s equator will run slower by a very small amount than an identical clock fixed at one of the Earth’s poles.

Einstein died in 1955, fifty years after the great 1905 paper. By then one could measure time to a thousand millionth of a second. And therefore it was possible to look at that odd proposal to ‘think of two men on earth, one at the North Pole and one at the Equator. The one at the Equator is going round faster than the one at the North Pole; therefore his watch will lose.’ And that is just how it turned out.

The experiment was done by a young man called H. J. Hay at Harwell. He imagined the earth squashed flat into a plate, so that the North Pole is at the centre and the equator runs round the rim. He put a radio-active clock on the rim and another at the centre of the plate and let it turn. The clocks measure time statistically by counting the number of radio-active atoms that decay. And sure enough, the clock at the rim of Hay’s plate keeps time more slowly than the clock at the centre. That goes on in every spinning plate, on every turntable. At this moment, in every revolving gramophone disc, the centre is ageing faster than the rim with every turn. [1]

This raises questions as to what exactly is a clock, and what it is a clock measures. Might it be something other than time? Does, for example, Jeremy Bernstein’s following ‘definition’ of a clock merely confuse the issue, or does its internal life, once it’s set in motion, really tell us anything about the phenomenon we call time?

First, we give a qualitative argument to show that the rate of moving clocks is slower than rest clocks. To this end, imagine a particularly simple form of clock. Consider two mirrors separated by a certain distance and imagine we have set off a light signal between the mirrors. The light will now bounce back and forth between the mirrors at a regular rate, since the speed of light is constant. (We can always imagine that the mirrors are in vacuum.) In principle this is a perfectly fine clock and we can make it as accurate as we like by decreasing the distance between the mirrors. Now suppose we attach the mirrors to the walls of something that can move so that the mirrors are in the vertical direction but we move the whole system in the horizontal at right angles to the line between the mirrors. Now we view this somewhat bizarre apparatus from the rest frame. Suppose the light starts off from the lower mirror. If the apparatus were at rest, then to hit the upper mirror the light would simply have to follow a straight-line path at right angles to the lower mirror. However, when the mirrors are in motion with respect to us, we will observe the light start off at an angle from the lower mirror to catch the upper one, which is moving. In fact, to make the round trip, as we view it from the rest frame, the light will have to follow a triangular path which is, evidently, longer than the path if the system is at rest with respect to us. Since according to the principle of constancy the speed of light is the same in both frames, we would say that the round trip is longer for the ‘clock’ that is in motion. Hence we would argue that the period of the light clock is longer when the clock is moving than when it is at rest. [2]

This of course presupposes that the speed of light is finite. But, supposing it has limits imposed on it only by virtue of the medium it is travelling through. Would it then be true to say that time permeates different media – different parts of the universe – at varying rates? Stephen Hawking thought it does—

Another prediction of general relativity is that time should appear to run slower near a massive body like the earth. This is because there is a relation between the energy of light and its frequency (that is, the number of waves of light per second): the greater the energy, the higher the frequency. As light travels upward in the earth’s gravitational field, it loses energy, and so its frequency goes down. (This means that the length of time between one wave crest and the next goes up.) To someone high up, it would appear that everything down below was taking longer to happen. This prediction was tested in 1962, using a pair of very accurate clocks mounted at the top and bottom of a water tower. The clock at the bottom, which was nearer the earth, was found to run slower, in exact agreement with general relativity. The difference in the speed of clocks at different heights above the earth is now of considerable practical importance, with the advent of very accurate navigation systems based on signals from satellites. If one ignored the predictions of general relativity, the position that one calculated would be wrong by several miles! [3]

Perhaps the central problem lies in what we think of as time. In the Hawking example, the two timepieces are doing something, and whatever it is they’re doing, they’re doing differently. The question is, are they really measuring time? In any disagreement with accepted science one would have to explain what it is they are doing. The difficulty with diverging from science’s established canon is that the only other realms we have are philosophy and metaphysics.

J. W. Dunne’s An Experiment With Time, first published in 1927, links precognitive dreams with a wholly different theory of time. From dreams of a predictive nature that Dunne himself had experienced he concluded it was the dreaming subject and not the surrounding train of events that intimated future personal experiences. For Dunne the moment of ‘now’ was not adequately described by science, which merely sectionalises time as a fourth dimension. In Dunne’s conception an endless sequence of higher dimensions of time measures our passage through the one, lone tier our physicality inhabits, the lowest. Each of time’s successive higher levels is accompanied, accordingly, by a higher level of consciousness. At the summit is the ultimate observer, whose view must necessarily be of eternity, with everything in it whole, singular, co-contemporaneous. The demands of our waking life prevent us from exceeding the present moment, though when we dream we enter a form of consciousness revealing to us more than is usual of our timeline, in connecting fragments of our future with memories of our past.

The novelist and lepidopterist Vladimir Nabokov, who through these two main disciplines outlined his belief in an underlying pattern to the cosmos, nevertheless declined to suggest a supreme intelligence responsible for that design. But he was taken enough with Dunne’s proposals that, from October 1964, he indulged over two months in recording his dreams. The data he gathered were used to test the proposition that time to some degree operates in reverse, to the extent that a post or future event can leave its trace in a current dream. Nabokov was a lifelong insomniac, and the results of his inquiries were published in 2018. [4]

An important criticism of Dunne is in his layers of time, one stacked on another, and the reduction of meaning to an infinite regress, with reality always subject to one more term in the series of knowability.

Nabokov was also much influenced by Bergson, for whom time is a motive force, and is counter to Darwin’s evolutionary natural selection. For Bergson evolution springs from an élan vital, or in human terms the creative impulse, present from the beginning (ontologically speaking), and now bifurcated as intuition and intelligence, a manifestation unrecognisable without the action of time, and not necessitating environmental pressures. But what is the ‘action’ of time?

Time is the dimension of change, a fact which distinguishes it from the three dimensions of space. But how does genuine temporal change differ from mere variation as exhibited in space? When a road is said to change in breadth along its length, ‘change’ is being used only metaphorically, in contrast to its literal use when a child is said to change in height as it becomes older. Some theories of time and change do not really accommodate this distinction, and as such are sometimes accused of ‘spatializing’ time or denying the reality of temporal ‘becoming’. Some philosophers believe, indeed, that developments in physics connected with the theory of relativity necessitate this denial, because they seem to demonstrate that the notion of an absolute ‘now’ must be abandoned along with the Newtonian notion of the absoluteness of simultaneity. Events deemed ‘past’ in one frame of reference must be deemed ‘future’ in other frames, apparently indicating that the distinction between past and future is only a subjective, experientially based one rather than reflecting a genuine ontological divide. Philosophers of this persuasion adopt what is commonly called a ‘static’ view of time, thus partaking in a tradition stretching back to Parmenides and Zeno, who held the appearance of temporal change to be an illusion.

In opposition to the ‘static’ view stands the ‘dynamic’ view of time, traceable back to Aristotle and before him Heraclitus. By this account the future lacks the reality of the past and present, and indeed reality is continually being added to as time passes. The objection mentioned earlier is not difficult to overcome, since even the theory of relativity acknowledges that some events are past and others future, no matter which frame of reference is selected, and these may be said to lie in the absolute past or future. The relativity of simultaneity only requires us to revise our conception of the present, allowing it to embrace all events not causally connected to us by a physical signal. A more serious challenge to the dynamic view of time comes from J. M. E. McTaggart, who claimed that the notion of temporal becoming (bound up with the A-series of past, present, and future) leads to contradiction. But it seems fair to protest that McTaggart’s argument demonstrates not so much the absurdity of the notion of temporal becoming as the incoherence of his representation of that phenomenon. According to McTaggart, the phenomenon supposedly consists in future events ‘becoming present’ and then ‘receding into the past’, whence it apparently follows, absurdly, that all events are past, present, and future. But the lesson is just that we should not think of ‘the present’ as somehow ‘moving’ along the sequence of events from past to future. In denying the reality of the future, we may appeal to the fact that not all future-tensed statements appear to be determinately true or false.

The asymmetry of time is perhaps its most striking feature and the most difficult to explain. The fundamental laws of physics are time-reversible, and yet complex macroscopic processes like the growth of a tree or the breaking of glass could not happen in reverse save by a miracle. This is often supposed to be explicable by reference to the second law of thermodynamics, which implies that closed systems tend to evolve from conditions of less to greater disorder, or ‘entropy’. But why should the universe have been created in a particularly low state of entropy – or was this just an accident without which time might have been isotropic? And how does the asymmetry of time as we know it relate to the apparent non-existence of phenomena involving ‘backwards’ causation, such as time-travel? These are problems which are still very little understood by either metaphysicians or physicists. [5]

McTaggart’s ‘A series’ corresponds to our everyday experience of past, present, and future, the series of instances running from the far past, through the near past, to the present, and from the present to the near future and the far future. That is opposed to the ‘B series’, where instances are ordered earlier-than, later-than. In the ‘A series’, to the observer in temporal movement, events in time are in a moving relation, future to present to past. In the ‘B series’ time events are ordered in fixed relations to each other. McTaggart argued that the ‘A series’ was necessary to a complete theory of time, since only in the ‘A series’ does change occur. He added that it is also self-contradictory, and that our perception of time passing is, therefore, an illusion.

The Argentine writer J. L. Borges, in his essay ‘A New Refutation of Time’, [6] does not overlook the antinomy inherent in that title. He invokes Berkeley, who denied the existence of matter, explaining the world of appearance as only the construct of our senses, a set of images and impressions present only in our minds, changing from one instant to another. Hume later contended that there was no necessary connection between one event and another. For example, if I have always observed event A followed by event B, according to him it does not automatically follow that that will always be the case. If one can call into question event B always following event A, there are grounds also for suspecting that there is no sequential relationship between them, and that the two events are independent of time, which is to say that like matter time doesn’t exist. If matter exists only in the mind, then the changes matter undergoes also exist only in the mind, as too does the time taken for change to take place. That said, for all its argumentation, ‘A New Refutation of Time’ succeeds endlessly in undermining its own negations, with its author concluding that ‘The world, unfortunately, is real; I, unfortunately, am Borges.’

Perhaps more contentious than all these questions is the view of physicist James Barbour, who introduces quantum physics into the argument (which, it is well known, Einstein grappled with unsuccessfully in reconciling with relativity)—

Einstein’s theory of general relativity easily admits…a pluralistic notion of time. This is after all why it is called the theory of relativity. One can use any clock one pleases to measure the evolution of the universe. In the end no question about what really happened will depend on which one you choose.

The key question we face now is whether such a pluralistic conception of time can be realized in the quantum theory. So far, no one has found a way to do this. People have, with great effort, managed to make formulations of quantum gravity in which time is defined by one of the clocks in the system. But it turns out that the answers to questions about what really happened all seem to depend on which clock one uses to define time in the quantum theory.

One of the ways this problem arises comes from trying to describe what happens to the quantum state when an observer makes a measurement. Quantum theory tells us that we must change the state of the system we are observing at the moment that an observation has been made. But if different observers use different clocks to label when measurements are made, they are going to believe they are talking about different quantum states.

This suggests that a theory that allows all possible clocks must be a pluralistic quantum theory…. Disagreements about the evolution of the different quantum states may in this way become simply an aspect of the fact that different observers hold different information, which is represented in different quantum states. The challenge, as before, is to make sure sense can be made of the relationship between the views held by all the different observers, so that the world retains a sufficient coherence, and that to some approximation it can still be described in the language of classical space and time.

It is too early to tell if a proposal like this is going to succeed. But let me stress that it can work only if the world has the right balance of complexity and order. There must be sufficient complexity to ensure that different observers are completely distinguished from each other by their having different views of the universe. But there must be sufficient order to ensure that the different observers can agree that they are speaking about the same universe. Thus we are led once again to the notion that a quantum universe must be a self-organized world balanced between order and variety.

The consistent-histories formulation may also be able to express such a pluralistic approach to time, as different sets of consistent histories may be chosen that correspond to how the world would seem to evolve according to time as measured by different clocks. This is a strength of this kind of approach. The fact that the interpretation is built around a notion of histories means that time and change are built into the language of the theory. The key issues here again are the balance of complexity and order that the world must have if the pluralistic description of time in general relativity is to be recovered from the quantum theory.

All these approaches posit that time, as measured by clocks, is fundamental. But if there is a possibility that the theory must describe universes that contain no clocks, this may not be the most basic language to describe the world. One may then ask if there is available a language for the interpretation of quantum cosmology that does not presume that time and change have meaning.

Such an approach to the problem of time has been developed by Julian Barbour, who for the last several years has been arguing that the notion that time is what is measured by a clock cannot work in a quantum theory of gravity. Instead, he has proposed a radical view of quantum cosmology in which time has no fundamental meaning at all. The proposal is simplicity itself. According to it, what exists – the universe – is nothing but a great collection of moments. Each moment is a snapshot of the universe, a simple configuration of things. He calls the collection of all of these moments the heap. The heap contains a great many moments. But there is no sense in which the different moments can be ordered in time. They just simply are. Period. The quantum state of the universe serves only one function, which is to give the probability that any given moment may be found in this collection.

In this conception, all of physical law reduces to one kind of question. Some godlike being reaches into the heap and pulls out a moment. What is the probability that such a randomly selected moment will have some particular characteristic? To describe this, we need no notion of time or change. Nothing is changing in time because there is no time – the whole heap just is, period, and it is all that is.

Why then, do we have an impression that there is time, that we are changing, that you and I were here five minutes ago, and so on? According to Barbour’s idea, each moment – say, this one – is an entity in itself, and does not change. We believe in time, because our world is structured in a very special way. Each moment is structured so as to give us the impression that other moments also exist. We have memories and we see all around us evidence that can only be construed as telling us about other moments that we might like to say happened in the past. [7]

In essence, Barbour conceives of a universe giving rise to its entire stock of moments simultaneously, and what we call time is the approximation of those moments in a sequencing process that we ourselves perform.

At this point, the problem stretches beyond my powers of elucidation, though I cannot help but cling to a possible future where a solution is to be found.

Notes

[1] Bronowski, J., The Ascent of Man, BBC (London, 1974), pp 254–55

[2] Bernstein, Jeremy, Einstein, Fontana/Collins (Glasgow, 1976), pp 59–60

[3] Hawking, Stephen W., A Brief History of Time, Guild Publishing (London, 1990), pp 32–33

[4] Barabtarlo, Gennady (ed), Insomniac Dreams: Experiments With Time by Valdimir Nabokov, Princeton and Oxford (New Jersey and Woodstock, 2018), passim

[5] Lowe, E. J., ‘Time’ in The Oxford Companion to Philosophy (ed Honderich), OUP (Oxford, 1995), pp 875–76

[6] Borges, Jorge Luis, ‘A New Refutation of Time’, in Labyrinths, Penguin Modern Classics (Harmondsworth, 1986), p 252

[7] Smolin, Lee, The Life of the Cosmos, Weidenfeld and Nicolson (London, 1997), pp 288–89


Peter Cowlam is a poet, novelist and playwright. As novelist, he has won the Quagga Prize for Literary Fiction twice, most recently in 2018 for his novel New King Palmers, which is at the intersection of old, crumbling empires and new, digital agglomerates. The Quagga Prize is awarded for independently published works of fiction. He has had plays performed at the Barbican Theatre, Plymouth, and by the Dartington Playgoers, and has had readings at the State University of New York and for the Theatre West 100 Plays project in Bristol, England. He has had four collections of haikuesque poems published (one in collaboration with Kathryn Kopple), also independently, and as poet and writer of fiction his work has appeared in En Bloc, The Battersea Review, The San Francisco Review of Books, The Blue Nib, The Galway Review, Easy Street, Literary Matters, Eunoia Review, The Brown Boat, Valparaiso Fiction Review, The Four Quarters Magazine, Ink, Sweat & Tears, The Liberal, the Criterion, and others. Peter Cowlam is the Literary Editor at Ars Notoria (arsnotoria.com).