Seeing Further

by Bill Bryson

  Combining these two assumptions generates the equations of his Special Theory of Relativity. It has astonishing consequences. Moving objects experience a slower passage of time. This is known as time dilation. These transformations are only valid for two frames at constant relative velocity. Naïvely applying them to other situations gives rise to such puzzles as the famous twin paradox.

  This is a thought experiment in special relativity, in which a twin makes a journey into space in a fast rocket, returning home to find he has aged less than his identical twin, who stayed on Earth. This result appears puzzling because the laws of physics should exhibit symmetry. Since either twin sees the other twin as travelling, each should see the other ageing more slowly. How can an absolute effect (one twin really does age less) come from a relative motion? Hence it is called a paradox.

  But there is no paradox, because there is no symmetry. Only one twin accelerates and decelerates, so this differentiates the two cases. Since we each experience minor accelerations, whether on horseback or in a jet plane, we each carry around our own personal scale of time. These are undetectable in ordinary life, but real.

  When time stretches, space shrinks. When you rush to catch an aeroplane, the wall clock you see runs a tiny bit slower than your wristwatch. Compensating for the time, the distance to the aeroplane’s gate looks closer to you. Time is pricey, though – a second of time difference translates to 300,000 kilometres of space.

  The stretching of space and time occurs because they are wired together. More fundamentally, Einstein’s work implied that time runs slower the stronger is the gravitational field (and hence the observer’s local acceleration). His general relativity theory sees gravity not as a force but as a distortion of space-time.

  The rates of clocks on Earth then depend on whether they are on a mountain or in a valley; the valley clock runs slower. This is somewhat like the slowing of clocks as they move past us at high velocity. This gravitational effect is unlike that of the smoothly moving observers on, say, two trains moving by each other, each of whom thinks the other’s clock runs slowly. In a gravitational field, the clocks experience different accelerations if they are not at the same altitude. But observers both in the valley and on the mountain agree that the mountain clock runs faster. Experiments checked these results and found complete agreement. Further, particle acceleration experiments and cosmic ray evidence confirmed the predictions of time dilation, where moving particles decay slower than their less energetic counterparts. Gravitational time changes give rise to the phenomenon of gravitational ‘redshift’, which means that light loses energy as it rises against gravity. There are also well-documented delays in signal travel time near massive objects like the Sun. Today, the Global Positioning System must adjust signals to account for this effect, so the theory has even practical effects.

  In empty space, the shortest distance between two points is a straight line. In space-time, this is called a ‘world line’ that forms the shortest curve between two events. If gravitation curves a space-time, then the straight line becomes a curve, which is the shortest space-time distance between two points. That curvature we see as the curve of a ball when thrown into the distance, a parabola.

  This linked with a radical view, pushed by Hermann Minkowski, that neither space nor time is truly fundamental. In relativity, both are mere shadows, and only a union of the two exists in the underlying reality. Minkowski had called Einstein a ‘lazy dog’ when Einstein was his student. But while reading Einstein’s first paper on relativity, he had a brilliant idea, and so laid the foundations for the next great insight. Minkowski’s invention was space-time, a joint entity. Einstein later used his intuition to propose that mass curves space-time, and we sense this curvature as gravity.

  The fundamental idea of space-time played out in many ways. Time runs faster in space than on a star, because gravity warps space-time. This leads to timewarps that can become severe, when a star implodes and time grinds to a halt. Stars a few times larger than our own can do this, capturing their own light and plunging into an infinitesimal speck we call a black hole. Its gravitation remains with us, though, a timewarp imprinted on empty space. Anyone falling along with the star will see the external world pass through all of eternity, while gravity pulls him into a spaghetti strand. The singularity where all ends up is a ‘nowhen’ and ‘nowhere’, signifying that the physical universe as we understand it ceases.

  Einstein’s singular geometric and kinematic intuition motivated his theory. He assumed that every point in the universe can be treated as a ‘centre’, whether it is deep in a gravitational well (such as where we live) or in empty space, far from curvatures in space-time induced by gravity. Correspondingly, he reasoned, physics must act the same in all reference frames. This simple and elegant assumption led, after much labour, to a theory showing that time is relative to both where you are and how you are moving. Newton’s laws hold well enough in a particular local geometry. They work in different circumstances, though they must be modified for the environment. Still, this fact can be expressed in the theory itself. This leads to the principle that there is no ‘universal clock’. To get things right, we must perform some act of synchronisation between two systems, at the very least.

  There is another victim of his intuition. Not only is there not a universal present moment, but also there is no simple division between past, present and future in general – that is, everywhere in the universe. Locally, they do mean something, but not necessarily to those far from us, in a universe that continually expands.

  Though you and I on Earth may agree about what ‘now’ means on the nearest star, Proxima Centauri, an astronaut moving quickly through the solar system who asks this same question when we do will refer to a different moment on Proxima Centauri.

  Does this mean that only the present moment ‘really’ exists? But one person’s past can be another’s future, so past, present and future must exist in a physical sense, and so be equally real.

  Einstein said of the death of an old friend, within months of his own death, ‘Now he has departed from this strange world a little ahead of me. That means nothing. People like us, who believe in physics, know that the distinction between past, present and future is only a stubbornly persistent illusion.’

  In physics, time is not a sequence of happenings, but a chain that is just there, embedded in space-time. Our lives move along that chain, like a train on a track. Observers differ over whether a given event occurs at a particular time, but there is no universal Now. Instead, an event belongs to a multitude of Nows, depending on others’ states of motion or position. Time stretches away into past and future, as we see them, just as space extends away from any place. This is the interwoven thing we call space-time, and it is more fundamental than our particular sense of our local world.

  Even more odd possibilities come from these ideas. General relativity allows time travel of a sort, in special circumstances. These may be disallowed by a more fundamental theory, but for now, some puzzling paradoxes emerge from our understanding of time. Presumably events may not happen before their cause, but proving this in general has so far eluded us.

  TIME’S MOMENTUM

  Time goes, you say? Ah no!

  Alas, time stays, we go.

  – Henry Austin Dobson, The Paradox of Time, 1877

  Why do we think that time moves, instead of the fixed, eternal space-time that theory suggests? Because evolution has not selected us to see it that way. Time’s flow is a simple way to order the world effectively; that does not mean it is fundamental. Space-time is simple and elegant, but that does not mean it plays well in the rough scramble of life. During a seminar at Princeton University, Einstein remarked that the laws of physics should be simple. Someone asked, ‘What if they aren’t?’ Einstein replied that if so, he was not interested in them.

  Yet simplicity may not be the best way to regard time. Time seems to flow because that flow is a holistic concept, not reducible to simple systems like
a collision of atoms. In this sense, the paradox of time’s flow is an aspect of our minds. We can see time as moving, bringing events to us, or the reverse: we flow through time, sensing a moving moment.

  This interlaces with the findings of Sadi Carnot in 1824, when he carefully analysed steam engines with his Carnot cycle, an abstract model of how an engine works. He and Rudolf Clausius noted that disorder, or entropy, steadily increases as machines operate. This means the amount of ‘free energy’ available continually decreases.

  This is the second law of thermodynamics. The continual march of time then defines an arrow of time, defined by the growth of entropy. It is easy enough to observe the arrow by mixing a little milk into your coffee. Try as you might, you can’t reverse it. In the nineteenth century entropy’s increase took its place beside other definitions of time’s momentum. Another definition is the psychological arrow of time, whereby we see an inexorable flow, dominating our intuitions. The third view, a cosmological arrow of time, emerged when we discovered the expansion of the universe in the twentieth century.

  This dramatic time asymmetry seems to offer a clue to something deeper, hinting at the ultimate workings of space-time. For example, suppose gravity acts on matter – what is the maximum entropy nature can pack into a volume? There is a clean answer: a black hole. In the 1970s Stephen Hawking of Cambridge University, holding the chair Newton had, showed that black holes fit neatly into the second law. Originally the second law described hot objects like steam engines. Applied to black holes, that can also emit radiation and have entropy, the second law shows that a three-million-solar-mass black hole, such as the one at the centre of our galaxy, has a hundred times the entropy of all the ordinary particles in the observable universe. This is astonishing. Collapsed objects are giant repositories of disorder, and thus sinks of the productions of time itself.

  These ideas spread throughout science, with varying results. Entropy inevitably increases in thermodynamics, but that seems to fly in the face of our own world, which flourishes with new life forms and increasing order. In contrast to the physical view of time, biologists pointed out that life depends on a ‘negative entropy flow’ which is local, driven by a larger decrease elsewhere. For us, this ‘elsewhere’ is the Sun, which supports our entire natural world. The Sun will expand and engulf the Earth in about five billion years. By then we may have a fix for that problem, if we are still around as humans. But then the stars themselves will die out, having burned their core fuels, this will take several tens of billions of years more, and thereafter the universe will indeed cool and entropy will rise throughout.

  Increasing entropy implies a ‘heat death’ as our universe expands. This means the end of time will be cold and dark.

  So biological systems do not refute the arrow of time; they define it well during our present, early state of the universe. These realisations ran in parallel through the nineteenth and twentieth centuries, promoting fruitful scientific dialogue.

  DEEP TIME REVISITED

  The human perception of time has ramified through many sciences. Such fundamental changes in a basic view always echo through culture.

  The enormous expansion of our perceptions of time has altered the way we think of ourselves, framed in nature. Palaeontologists track the extinction of whole genera, and in the random progressions of evolution feel the pace of change that looks beyond the level of mere species such as ours. Geologists had told them of vast spans of time, but even that did not seem to be enough to generate the order we see on Earth.

  The Darwin–Wallace theory explains our Earthly order as arising from evolution through natural selection. As perhaps the greatest intellectual event of the nineteenth century, it invokes cumulative changes that add up. The fossil record showed that mammals, for example, can take millions of decades to alter significantly. Our own evolution has tuned our sense of probabilities to work within a narrow lifetime, blinding us to the slow sway of long biological time. (And to the fundamental physical space-time, as we discussed.)

  This may well be why the theory of evolution came so recently, in an era when our horizons were already quickly expanding; it conjures up spans of time far beyond our intuition. On the creative scale of the great, slow and blunt Darwinnowings, such as we see in the fossil record, no human monument can endure. But our neophyte primate species can now bring extinction to many, and no matter what the clock, extinction is for ever. We live in hurrying times.

  Yet we dwell among contrasts between our intuitions and the timescape of the sciences. In their careers, astronomers discern the grand gyre of worlds. But planning, building, flying and analysing a single mission to the outer solar system commands the better part of a professional life. Future technologies beyond the chemical rocket may change this, but there are vaster spaces beckoning beyond which can still consume a career. A mission scientist invests the kernel of his most productive life in a single gesture toward the infinite.

  Those who study stars blithely discuss stellar lifetimes encompassing billions of years. In measuring the phases of stellar mortality they employ the many examples, young and old, that hang in the sky. We see suns in snapshot, a tiny sliver of their grand and gravid lives caught in our telescopes. Cosmologists peer at distant galaxies whose light is reddened by the universal expansion, and see them as they were before Earth existed. Observers measure the microwave emission that is relic radiation from the earliest detectable signal of the universe’s hot birth. Studying this energetic emergence of all that we can know surely imbues (and perhaps afflicts) astronomers with a perception of how like mayflies we are.

  No human enterprise can stand well in the glare of such wild perspectives. Perhaps this is why for some science comes freighted with coldness, a foreboding implication that we are truly tiny and insignificant on the scale of such eternities. Yet as a species we are young, and promise much. We may yet come to be true denizens of Deep Time.

  COSMOLOGICAL TIME

  Through the twentieth century’s developing understanding of stellar evolution, astronomy outpaced even the growing expanses of biological time by dating the age of stars. These lifetimes were several billion years, a fact some found alarming. In the mid-twentieth century some globular clusters of stars even seemed to be older than the universe, a puzzle that better measurement resolved.

  However, a still grander canvas awaited. Perhaps the most fundamental aspect of time lies in our description of how it all began, along with the universe itself: cosmology.

  There were many ‘origin stories’ of earlier cultures, but these gave little thought to how the universe came to be, beyond simple stories. Ancient times, until the nineteenth century, preferred eternity to process. As the Bhagavad Gita says, ‘There never was a time when I was not … there will never be a time when I will cease to be.’ Since time and space began together – as both St Augustine and the big bang attest – the Bhagavad Gita has a point. The chicken and the egg arrived at the same time.

  Yet Newton thought that the universe had to be eternally tuned by God’s hand, or else gravitation would cause it to collapse. This view held fairly well until a new theory of gravity and time arrived.

  When Einstein developed his theory of general relativity in 1915, physicists believed in a perfectly static universe without beginning or end, like Newton. Though he had a theory of curved space-time, and so could consider all the universe, Einstein inherited this bias. He attempted the first true cosmology – that is, a complete description of the universe’s lifetime, from simple assumptions – under the influence of the ancients.

  To make his early equations describe a universe unchanging in time, he added a cosmological constant to his theory to enforce a static universe. It had matter in it, which he knew meant that gravitation favoured collapse – but he demanded that it be a time-independent, eternal universe. Analysis soon showed that Einstein’s static universe is unstable. A small ripple in space-time or in the mass it contained would make the universe either expand or contract. E
instein had brought his own concepts of time to the issue, and so missed predicting the expanding universe. Soon enough, astronomers’ observations showed that our universe is expanding from an earlier, smaller event. After this era, cosmological ideas of time moved beyond him.

  Modern cosmology developed along parallel observational and theoretical tracks in the twentieth century. Correct cosmological solutions of general relativity emerged, and astronomers found that distant galaxies were apparently moving away from us. This comes from the expansion of space-time itself, not because we are uniquely abhorrent. Tracking this expansion backward gave a time when space-time approached zero. St Augustine had proposed that God made both space and time, and the big bang told us when that was.

  Through the twentieth century, observations of how fast distant galaxies seemed to rush away from us have pushed the age of the universe back to the currently accepted number of 13.7 billion years. By then relativity had altered and even negated our understanding of Intuitive Time, so cosmology’s enormous extension of Deep Time only added to the startling changes.

  Now astronomers observe that the universal expansion is accelerating, perhaps because of the unknown effects represented by Einstein’s added cosmological constant. We now seem to occupy an unusual niche in the long history of this universe, living beyond the early, hot era, yet well before the accelerating expansion will isolate galaxies from each other, then stars, and finally may wrench apart all of matter as space-time stretches ever-faster. Time seems then like a judge, not a mere clock.