by Paul Davies
It sounds fanciful, but according to the theory of relativity, such a thing is not impossible. One way to travel through time I’ve already mentioned – exploiting the effects of gravity, which slows time. If you were to take a vacation somewhere with a big gravitational field (close to a black hole, say) you could twiddle your thumbs for a few moments while Earth-time fast-forwarded to your desired future date. Admittedly, hanging out next to a black hole is not a very practicable suggestion, but the theory of relativity provides another way to leap into the future, and it’s much easier. Not only gravity, but speed, has the effect of slowing time, as Einstein noted in his original 1905 paper. You can reach the future quicker simply by travelling fast. Unfortunately, that means very fast. To give you a feel for the numbers, on a long-haul flight, a clock on an aeroplane typically changes by a few nanoseconds relative to an identical clock left at the airport, which, in terms of human experience, means the passengers age (very slightly) less.
Nanoseconds hardly make for a Doctor Who-style adventure. Far bigger time warps require extremely high speeds: the closer the speed gets to that of light, the bigger the warp factor. When the LHC propels protons to 99.9999 per cent of the speed of light, it generates a time warp so big that one second of proton time corresponds to about two hours in the lab. Cosmic ray protons are even more out of temporal rhythm with Earth. The highest energy cosmic ray so far discovered was found at the Pierre Auger Observatory – an array of particle detectors scattered over the pampas in Argentina. With an energy 2 million times greater than anything produced at the LHC, it was dubbed the ‘Oh-My-God’ particle because its energy is off the scale. It was moving so close to the speed of light that in its own reference frame, it could theoretically have crossed the galaxy in a few minutes, compared to the 100,000 years we on Earth would estimate that it took. Going that quickly, a person could fast-forward to Earth year 3000 in a mere 2 seconds! I’m ignoring the cost, the dangers and the effects of starting and stopping, but the basic physics is sound enough.
Unfortunately, it’s not possible to use warp speed to go to the future and then come back again to now by the same means, because that would entail going both forward and backward in time. And the physics of visiting the past turns out to be far more problematic than going to the future. It is certainly philosophically problematic because of the well-known paradoxes it entails, the most famous being the so-called ‘grandfather paradox’. What happens if a time traveller goes back a few decades and murders his own grandfather as a youngster? Then the time traveller would never be born. How, then, could the murder happen? But, if it didn’t happen, the time traveller would be born, and so could have carried out the murder. Either way, the narrative is inconsistent. This is called a causal loop paradox. By intermingling past and future events, the normal causal chain – that effects follow causes – is messed up, and chaos looms.
Of course, it is those very paradoxes that make time-travel stories such compelling science fiction, ever since H. G. Wells blazed the trail in the 1890s with his book The Time Machine. Though authors often fail to resolve the paradoxes, it is possible to have consistent causal loops. For example, imagine a story in which a time traveller visits the past and prevents a murder, and the rescued individual goes on to become the time traveller’s grandfather. That narrative hangs together well enough, but it implies that the time traveller cannot be free to kill his grandfather, which some people find absurd. Yet the laws of physics restrict our freedom in many ways we accept unthinkingly: I’m not free to walk upside down on the ceiling, for example, however much I may wish to do so.
Even if there are ways around the philosophical paradoxes, there remains the question of whether travel into the past is in fact physically possible. And this is where things get a bit murky. When Einstein formulated his theory of relativity, he accepted that it predicted strange time-warping effects but he hoped it wouldn’t permit a person or an object to loop back into the past. In fact, merely signalling the past, as in Benford’s Timescape, unleashes causal paradoxes, because if someone is informed of the future they can act to change it. But Einstein was unable to rule out such things because nothing in his theory of relativity said it couldn’t be done.
The nagging doubt lay like an embarrassing secret in the foundations of general relativity for some decades. By then, Einstein was living in Princeton and working at the Institute for Advanced Study. At this stage of his career he was a living legend, but his research was drifting and he sometimes said the only reason he went to work was to walk home with Kurt Gödel, a logician also employed at the Institute. Gödel worked on foundational aspects of mathematics, but he also took the trouble to learn Einstein’s general theory of relativity, and in 1948 he produced a solution of Einstein’s equations describing a universe that did indeed allow observers to travel into their own past. Although physically possible, Gödel’s example was peculiar inasmuch as it needed the whole universe to be rotating. At that time astronomers lacked the means to rule out a slowly spinning universe, but we now know that if it was rotating, even at a snail’s pace, it would show up in the cosmic microwave background.
Unrealistic though it was, Gödel’s solution served to demonstrate that general relativity does indeed allow causality-busting time loops in principle. Over the years, other scenarios have been discovered that permit backward-in-time travel, the most well-known of which is the wormhole in space. Wormholes are like tunnels or stargates linking distant places to form a shortcut – similar to a black hole, but possessing a way out as well as a way in. Both black holes and wormholes have powerful gravitational fields that warp time, but whereas a black hole is a one-way journey to nowhere, an astronaut could traverse a wormhole and come out in another part of the galaxy, a scenario imaginatively depicted in the science-fiction movie Contact. If the intrepid astronaut then dashed home the conventional way – by crossing the space between the stars – she could complete a loop in space that would also be a loop in time, thus becoming a temponaut astronaut.
Although black holes are common, nobody has ever detected a wormhole and it could be they don’t exist, or, more relevantly, cannot exist. Even though general relativity doesn’t outlaw wormholes or time travel, quantum physics might, for example by creating an instability in the quantum vacuum (see p. 56). Stephen Hawking once proposed what he called a Chronology Protection Hypothesis, stating that, in practice, time loops could never form – ‘making the world safe for historians,’ he quipped. To date, however, nobody has proved chronology protection, and the disturbing possibility of time loops remains on the ‘maybe’ list.
16. What is the Source of Time’s Puzzling Arrow?
Our fascination with time-travel stories stems largely from a natural desire we all have to undo the wrongs of the past so we can make better lives for ourselves and our fellow humans in the present. However, in the absence of time travel we have to confront the reality that the past is a done deal: a car can’t be un-crashed, a failed exam remains a fail, a life lost cannot be recovered. But here’s the curious thing: the future remains open, and we retain the power to shape it. What, then, is the source of this asymmetry between past and future, this ‘arrow of time’?
I first became interested in the subject after a lecture given by Fred Hoyle at the Royal Society in London in 1968 on why radio broadcasts are heard after they are transmitted and not before. (In truth, it was a bit more scientific than that, but the asymmetry of radio waves captures the gist of it.) Later I wrote a whole book on time asymmetry, intending it to be the last word on the subject. That was in the mid-1970s and was the reason why Greg Benford came to see me. All these decades later, somewhat shockingly, there remains widespread confusion – and many more books – about the arrow of time.
Boiled down to its essentials, the issue with time’s arrow is this. Imagine taking a movie of an everyday incident and playing it in reverse to an audience. Everybody laughs because it looks so preposterous. People walking backwards, rivers flowing uph
ill, sandcastles washed into shape by retreating waves. But in physics a laugh test isn’t enough. What exactly gives the game away? Here’s a clue. Open a new pack of cards. The manufacturers arrange them in numerical order by suit. Shuffle the cards. The sequence will now be jumbled. If a magician shuffled a pack of jumbled cards and gave them to you in numerical order, you’d know you were being duped. While it’s not impossible for jumbled cards to be randomly shuffled into order, it’s exceedingly improbable. The arrow of time here is clear: random disruption turns order into disorder.
Scientists zeroed in on this basic property in the middle of the nineteenth century. The Austrian physicist Ludwig Boltzmann considered how gas molecules rush around randomly, banging into each other and spreading heat energy around. He analysed this natural shuffling mathematically and identified something called entropy, a precisely defined quantity that measures the degree of disorder in the gas. Then he used Newton’s laws of mechanics, plus an averaging assumption, to prove that entropy would never go down. The rise and rise of entropy is one expression of the so-called second law of thermodynamics, perhaps the most inclusive law in all of physics. Because what’s true of gases is true of everything: all systems have a natural tendency to grow messier, to degenerate and decay (see Figure 12). Readers with teenage children will understand: for ‘system’ read ‘bedroom’. And, of course, children know that when it comes to bedrooms they are much easier to mess up than tidy up. Understanding the cosmic implications of all this, the British physicist Lord Kelvin delivered a lecture in 1852 famous for what has to be the most depressing prediction in the history of science. The entire universe, claimed Kelvin, is dying, slowly choking on its own entropy. Gradually, inexorably, cosmos is turning into chaos.
If the relentless march of disorder defines the arrow of time, then the universe must have been more ordered in the past. And indeed it was. As I have been at pains to point out, the universe that emerged from the big bang was astonishingly, bafflingly, extremely highly ordered. Had it been exactly ordered, the arrow of time would have stalled, because perfection persists. It would be a case of blandness for ever: gravity would have nothing to get its teeth into. But, of course, the nascent universe wasn’t 100 per cent perfect. There were those ever so slight, wispy splodges found by COBE, a mere 0.001 per cent variation in temperature, far below what human senses would register. The splodges betray a minute departure from orderly perfection, a palette of almost imperceptible density perturbations in the primordial plasma.
Gravity set to work on the splodges: the over-dense regions pulled more strongly, drawing in the surrounding material and amplifying the density contrast, generating large-scale complexity – clusters of galaxies, churning clouds of gas and meandering stars. Clumping is gravity’s gift to the cosmos. Without clumping we wouldn’t be here, for gravity sculpts the element-forming stars, the habitable planets, the orderly structure of the solar system. But, like a petulant god, the creator is also the destroyer. Gravity is remorseless, tirelessly awaiting its next victim, as Chandrasekhar foretold. The sun’s life-sustaining stability is the result of a temporary hang-up, a multi-billion-year quiescent interlude in which fuel is squandered to combat the crushing effects of gravity, a titanic tussle that gravity will ultimately win.
Figure 12. An everyday kitchen phenomenon. It’s not hard to tell which picture was taken earlier and which later.
Being irreversible, gravitational clumping, like the flow of heat from hot to cold, represents a type of entropy increase. The end point of gravity’s tendency to pull things together is the black hole. Paradoxically, black holes are at one and the same time perfectly ordered and perfectly disordered. Their geometry is extremely simple and symmetric. On the other hand, they swallow and obliterate everything that comes their way. Black holes seemingly eat all forms of order, erasing its memory. If Earth and its human cargo were sucked into a black hole, the only record of our erstwhile existence would be the increase in the black hole’s mass. The fire of Alexandria at least left the ashes of the books. If the big bang had coughed out black holes instead of smooth gas, there would have been no cosmic order, no life, no library of Alexandria.
Thus it is that gravity, the incubator and annihilator of habitable order, is also the source of time’s pervasive arrow. The time asymmetry that distinguishes yesterday from tomorrow, memories from anticipation, birth from death, can be traced back to the birth of the universe itself and, specifically, to its extraordinary degree of primordial smoothness. But where did that smoothness come from in the first place? Do we just accept it as an unexplained initial condition? A Big Fix?
One possible explanation is an appeal to the tiny violation of time-reversal symmetry in certain hard-to-discern particle processes touched on in Chapter 12. Did the very particles of the universe themselves come with their own inbuilt arrow, which somehow projected itself on to the entire cosmos in the torrid aftermath of the big bang? Maybe, but in my view not very likely. Far and away the most popular explanation for the smooth start to the universe is the inflationary scenario that we looked at in Chapter 9. A burst of antigravity-propelled expansion in the first split second creates precisely that almost, though not quite perfect, uniformity. But that’s still not the end of the trail, because the universe has to get itself into an inflationary state at the outset. How did that come about? The scientific community is still very far from reaching a consensus on these thorny issues. All that can be said for certain is that one of the most fundamental properties of the physical world – that tomorrow is different from yesterday – still lacks a full explanation, and it lies high on my own list of essential, unanswered big questions.
17. The Black Hole Paradox
During my career, I must have attended thousands of lectures, and very few of them stand out as historic. But one such occurred in January 1975 at the Rutherford Appleton Laboratory near Oxford. The lecture was given by Stephen Hawking, and it has been dramatically portrayed in films and documentaries. I have a vivid memory of the event, sitting near the back of the lecture theatre, straining to follow Hawking’s distorted speech and trying to make sense of the mathematics.
At that time, Hawking was a familiar figure in the theoretical physics community, but he was far from being a public celebrity. All that changed, however, with this lecture, for it was on that occasion that he explained how quantum effects fundamentally alter the nature of black holes. In a nutshell, according to Hawking, black holes are not in fact totally black but glow with radiant heat, as a result of which they slowly shrink, and finally explode out of existence in a shower of subatomic debris. It was a sensational claim.
I have to admit that I was initially very sceptical of Hawking’s prediction. I had myself been working on the quantum theory of black holes, using the celebrated solution to Einstein’s gravitational field equations discovered by Karl Schwarzschild in 1916 – the one that, all along, contained a description of a black hole. My own work indicated the existence of a cloud of quantum energy around the event horizon, but because Schwarzschild’s solution describes an eternally existing black hole, it is symmetric in time: nothing distinguishes past from future, because nothing changes. As a result, the cloud of energy around the black hole is static; it does not flow away from the hole in the form of radiation in the manner that Hawking suggested.
Figure 13. Headstone in Westminster Abbey commemorating Stephen Hawking, featuring his formula for the temperature of a black hole.
I put in some arduous work to get to the bottom of this discrepancy. The key to Hawking’s result lies in the brief phase at the outset, when a ball of matter (e.g. a star) undergoes a convulsion and collapses to produce the black hole. The death of the star – abrupt, catastrophic, near-instantaneous – marks the birth of the black hole, but a subtle record of the star’s sudden demise lingers on, engraved into the quantum vacuum, disrupting it to produce a continuous flux of energy that lasts for as long as it takes for the black hole itself to die. And black holes take an u
nconscionable time a-dying: an object born in a microsecond might take a billion trillion trillion trillion trillion trillion years to evaporate away completely.
With the benefit of hindsight, all that was there in Hawking’s lecture if I hadn’t been too stupid to see it. What finally convinced me that Hawking was right was a simple calculation I made to describe an observer who accelerates through empty space, in the absence of any gravitational field. Because acceleration mimics a gravitational force, constant acceleration represents an analogue of a black hole, but with simpler mathematics. What I found was striking: an accelerating observer would perceive a bath of heat around herself, closely analogous to the Hawking radiation around a black hole. That result was confirmed the following year in an elegant calculation made by William Unruh, who showed that a particle detector accelerating through a quantum vacuum would indeed absorb energy as if immersed in heat radiation.
Hawking’s lecture had an energizing effect on the physics community. Previously, only a handful of physicists were interested in quantum effects induced by gravitational fields, which were generally deemed to be too small to make much difference to anything, but it would quickly become one of the most intensively studied topics in theoretical physics. It’s true that ‘the Hawking effect’, as the evaporation of black holes soon became known, is exceedingly weak. But the real significance of his result lay in its unexpected combination of simplicity and depth: the equation for the temperature of a black hole, like Dirac’s formula for the electron, contained very few symbols but nevertheless opened a whole new window on reality. And, as with Dirac, Hawking’s equation may be found in Westminster Abbey (see Figure 13).
Although nobody has ever detected radiation from a black hole, the conceptual ramifications of the prediction soon proved both vexing and profound. One immediate puzzle concerned the source of heat energy, which must ultimately come from the mass (= energy) of the black hole. Since nothing can get out of a black hole, the quanta of heat radiation have to be created outside the event horizon. But then how does their energy derive from the interior of the hole? It seemed paradoxical.