by Paul Davies
In a series of careful experiments carried out at CERN in 1966, particles called ‘muons’ were circulated inside a small accelerator to test Einstein's time dilation equation to high precision. Muons are unstable, and decay with a known half-life. A muon sitting on your desktop would decay on average in about two microseconds. But moving inside the accelerator at 99.7 per cent of the speed of light, the average muon lifetime was extended by a factor of 12.
The twins effect
The effect of motion on time is often discussed using the parable of the twins. It goes something like this. Sally and Sam decide to test Einstein's theory, so Sally boards a rocket ship in 2001 and zooms off at 99 per cent of the speed of light to a nearby star situated 10 light years away. Sam stays at home. On reaching her destination, Sally immediately turns around and heads home at the same speed. Sam observes the duration tion of her journey to be just over 20 Earth years. But Sally experiences time differently. For her, the journey has taken less than 3 years, so when she gets back to Earth she finds that the date there is 2021 and Sam is now 17 years older than she is. Sally and Sam are no longer twins of the same age. In effect, Sally has been transported 17 years into Sam's future. With a high enough speed, you could ‘jump’ to any date in the future you like. The year 3000 could be reached in less than 6 months by travelling at 99.99999 per cent of the speed of light.
Travelling through time works the opposite way to travelling through space. The shortest distance between two points is a straight line, so in daily life you get from A to B quickest by following a direct route. But when it comes to time travel, it is stay-at-home Sam who ages most, i.e. he takes the longest to reach year 2021. By zooming about, Sally dramatically shortens the time difference between the two events ‘Earth year 2001’ and ‘Earth year 2021’. In fact, the more she zooms this way and that, the shorter the time difference between these two events becomes.
Some people find the twins effect paradoxical, because from Sally's point of view, she is at rest in the rocket ship while the Earth flies away. However, there is no paradox because the situation for Sally and Sam is not symmetrical. Sally is the one who accelerates away by firing the rocket motors, then manoeuvres around the star, and finally decelerates to land on Earth. These changes in motion single her out as the one to age less.
Note that Sally cannot ‘get back’ to Earth year 2007 this way, in order to re-equalize her age with Sam's. If she reverses her trajectory, she will only succeed in leaping another 17 years into Sam's future. High-speed motion is a one-way journey into the future.
How to use gravity to travel into the future
Speed is only one method of warping time. Another is gravity. As early as 1908 Einstein began extending his special theory of relativity to include the effects of gravity. Using another ingenious argument concerning light, he came to the remarkable conclusion that:
Gravity slows time.
He didn't clinch the argument until 1915, when he presented his so-called general theory of relativity. This work extended the special theory published in 1905 to include the effects of gravitational fields on time, and on space, too.
Putting the numbers into Einstein's theory shows that the Earth's gravity causes clocks to lose one microsecond every 300 years. This leads to the curious prediction that:
Time runs faster in space.
But not so much that astronauts notice. (You would gain just a couple of milliseconds by spending 6 months aboard the International Space Station.) However, physicists can readily measure the effect using accurate clocks. In 1976, Robert Vessot and Martin Levine flew a hydrogen maser clock into space from West Virginia and monitored it carefully from the ground. Sure enough, the rocket-borne clock gained about 0.1 of a microsecond before crashing into the Atlantic Ocean a couple of hours later.
There is even a tiny time difference between the bottom and top of a building. In 1959 an experiment was carried out at Harvard University to measure the timewarp factor up a tower 22.5 metres high. A slowing effect of 0.000000000000257 per cent was detected by using an extremely accurate nuclear process. Small it may be, but the measured value confirmed Einstein's prediction. Nobody was really surprised at this result, as physicists had long accepted gravity's effect on time.
If you could magically squash the Earth to half its diameter (retaining all its mass), its surface gravity would be twice as big, and so would be the timewarp. Go on compressing, and the effect rises. When the radius reaches the critical value of 0.9 cm, time ‘stands still’. Nothing can escape! The graph shows the ‘slowdown factor’ for a clock on the surface of the contracting ball. Notice how the timewarp becomes infinite (i.e. time slows to zero) when the ball is shrunk to about the size of a pea.
(see Gravitational timewarp on page 22)
Of course, squashing all that matter into a cubic centimetre is a pretty fanciful notion. But stupendous compressions do occur in astrophysics. For example, when stars run out of fuel they shrink spectacularly under their own weight, ending up a tiny fraction of their original size. Some large stars actually implode, quite suddenly, and form spinning balls not much bigger than London, yet containing masses greater than the sun (about 2,000 trillion trillion tonnes). The gravity of these collapsed stars is so great that even their atoms are crushed to form neutrons, so they are called ‘neutron stars’. One such object lies in the constellation of Taurus, deep within a ragged cloud of expanding gas known as the crab nebula. The nebula contains the shattered remains of a giant star that was seen to explode in 1054 by Chinese chroniclers.
(see The crab nebula on page 25)
Astronomers have discovered many more such objects, and determined that the gravity at their surfaces is large enough to
Caption
Gravitational timewarp
cause substantial timewarps. A clock on a typical neutron star would tick about 30 per cent slower than one on Earth. So take up residence near a neutron star (admittedly not a very practical proposition), and you have a ready-made time machine for journeying into the future. Seven years spent there would correspond to 10 years passing by on Earth.
If you could look back at Earth from the surface of a neutron star, you would see terrestrial events speeded up, like a fast-forward video show. Events in your immediate vicinity would seem normal, though. It wouldn't feel as if you were living in a high-speed world, or that mental time was disconcertingly whizzing by.
Is all this true? Yes, it is. There is a pair of neutron stars in the constellation of Aquila that cavort about each other, emitting regular radio bleeps, enabling astronomers to confirm with great precision the timewarping effects that Einstein's general theory of relativity predicts.
Is it really time that slows?
Some people object that the theory of relativity merely describes how clocks are affected by motion and gravitation, not time itself. This is a misunderstanding. Clocks measure time. If all clocks (including the human brain, which governs our personal perception of time) are slowed equally, then it is correct to say that time itself has slowed, for there is no duration of time other than what can be measured by clocks (of some sort). Similarly, if all distances were shrunk in length by the same factor, it would be true to say that space had shrunk.
To make this point clear, suppose I have an ageing and delicate grandfather clock that I stick on a jet plane to test the time dilation effect. If the clock falls to bits as the plane roars down the runway, it would be wrong to conclude that time stands still on board the plane because the clock is no longer ticking. To make sense of time dilation, the effects of acceleration on the clock mechanism must be factored out before concluding anything about time itself. Time dilation is the pure time phenomenon that remains. Note that during smooth motion, such as uniform flight in an airplane, there are no mechanical effects on clocks anyway. (Galileo long ago taught us that uniform motion is only relative.) A constant velocity does not lead to any forces that would affect a clock, otherwise we'd have to worry about how the clock woul
d depend on the speed of Earth through space.
E = mc2: Einstein's famous equation
Even those with no scientific education will be familiar with Einstein's famous equation E = mc2. It will play a crucial role in the discussion of time travel. The symbols here stand for energy, E, mass, m, and the speed of light, c. The theory tells us that mass and energy are related, i.e. energy has mass and
Caption
The crab nebula
mass is a form of energy. In the diagram the swinging pendulum is very slightly heavier than the static one, all else being equal, because the kinetic energy of the pendulum has mass. The conversion factor c2 is a very big number because the speed of light is so great. This means a little bit of mass is worth an awful lot of energy. For example, one gram of matter, converted into electricity, could power an entire city for several days. Nuclear reactions of the sort used in power stations convert about one per cent of the mass of the fuel into energy, a much higher yield than chemical reactions. Conversely, familiar quantities of energy don't have much mass. The heat energy needed to boil a kettle dry would weigh a measly 50 picograms.
Energy enters the time machine story via gravitation. Mass is a source of gravity. As energy has mass, it must gravitate too. The heat energy inside the Earth, for example, contributes a few nanograms to your body weight.
Einstein derived his equation from the special theory of relativity. One way to glimpse the link is to reflect on the fact that material bodies cannot go faster than light. So what happens if you just go ahead and try to accelerate a particle of matter through the light barrier? This is precisely the sort of thing that physicists working with subatomic particles do with their giant accelerator machines. The result is that as the particle gets nearer the speed of light, it becomes heavier, i.e. puts on mass. (An electron whirling around inside the LEP accelerator, for example, weighed about 200,000 times an electron at rest.) This makes the particle harder and harder to speed up. More and more of the energy goes to making the particle heavier, less and less to increasing its speed. The speed of light is the final barrier at which, if the particle could get there, would imply its mass is infinite. To make it go any faster would therefore require an infinite force, which is impossible.
The future is out there
Although he wrote 10 years before Einstein's special theory of relativity, H. G. Wells spotted that time could be thought of as the fourth dimension. He surmised that just as we can move through the three dimensions of space, so it might be possible to move through the time dimension, too. But this beguiling idea tacitly assumes the past and future are ‘out there’ somewhere, so it's not merely the present that is real. Physicists do, indeed, think of all time as equally existent – making up an extended ‘timescape’. To be sure, the concepts of past, present and future are convenient linguistic devices in the realm of human affairs, but they have no absolute physical significance. Einstein himself expressed it bluntly in a letter to a friend. ‘The distinction between past, present and future,’ he wrote, ‘is only an illusion, even if a stubborn one.’
This often strikes non-physicists as crazy. How can the past and future exist alongside the present? Einstein gave the following argument for why we can't dissect time neatly into past, present and future in a way that all observers would agree on. Start by asking: How do we know that ‘now’ in one place is the same as ‘now’ in another? Think about this. Suppose it is 6 p.m. where you are. What events are happening on the other side of the world at that same moment? Einstein insisted there was no proper answer to such a simple question.
Why, you might wonder? Can't we just phone somebody and do a blow-by-blow comparison? Well, the problem is that it takes time for telephone signals to travel, even at the speed of light. In fact, it takes about 0.07 second for voice messages to traverse the globe in optical fibres. (The delay is not quite noticeable to the human ear.) So the news from the other side of the world always arrives a bit late. (Not much, granted, but I am making a point of principle. If your friend was on Mars you might wait 20 minutes to learn what was happening.) Since it is a fundamental principle of physics that no signal can travel faster than light, some delay is inevitable.
In itself, the delay is no problem in trying to establish simultaneity; you could simply compensate by subtracting the requisite time interval needed for the signal to arrive. The real difficulty lies in the fact that observers who move differently disagree on the value of this compensating factor. That is because their clocks tick differently due to the time dilation effect. So opinions will differ, depending on who you consult, on how much delay has elapsed while light (or radio) signals are travelling between A and B. An astronaut rushing past the Earth at half the speed of light would be seriously at odds with an earthbound observer in deciding on the precise delay time for a round-the-world signal.
As a result of such mismatches, there is no unique event on the other side of the world, or on Mars, or generally at any other point in space apart from where you are located, that is exactly simultaneous with your ‘now’. There will be a range of such events at distant places. Which particular event is judged to be happening at the same moment as ‘6 p.m. at home’ will depend on just how the observer is moving. The ambiguity isn't much when restricted to Earth (just a fraction of a second this way or that), but the range of contending nows grows with distance. For Mars it is some minutes. For a star on the other side of the galaxy, events happening at the same moment as an event on Earth today might lie anywhere in a time span of 100,000 years.
The upshot is there can't be a single present moment that is the same for everybody everywhere. To spell it out:
There is no universal ‘now’.
We have to accept that time at a faraway place must extend somewhat into our perceived past and future. And by symmetry, distant observers will regard time on Earth as extending into their past and future. There is no other way to make sense of the facts. Obviously, then, it's wrong to think of only the present as real, right across the cosmos. Some events that you judge to be in the past will be regarded by someone else as lying in his or her future, or present – and vice versa.
To take a concrete example, Earth has a definite history, and so does a hypothetical Planet X situated 5,000 light years away. Attempts to compare dates of specific events on the two planets are pointless because the alignment of the respective timelines is ambiguous over a span of thousands of years.
(see What time is it now? on page 32)
This doesn't imply that the order of cause and effect can be reversed simply by travelling fast. Let me explain why. Events have ambiguous time order only if light doesn't have long enough to pass between them. For example, if I fire a gun on Earth and an astronaut fires a gun on Mars one second later (by my reckoning), an observer in a speeding rocket ship might well judge the Mars gun as having been discharged first. But if the Mars gun goes off a week after mine, everyone agrees on which fired first, as a week is easily long enough for light to travel between Earth and Mars. If no physical influence can exceed the speed of light, ambiguously time-ordered events can never affect each other, so causality isn't threatened. Notice, however, that if the no-faster-than-light rule was wrong,
Caption
What time is it now?
causality would be in trouble, and past and future would become scrambled. As we shall see, this little clue will turn out to be highly significant for the construction of a general-purpose time machine.
There is never any ambiguity about the time order of a sequence of events happening at one place; nobody claims that the battle of Hastings came after the battle of Waterloo. The quibbling comes only when events here and now are compared with events there and now – where ‘there’ is a long way away. Even then, the discrepancies are too small to notice on Earth itself, partly because light takes so little time to travel round the world, but also because human beings don't move more than a tiny fraction of the speed of light anyway. However, that is incidental. The cr
ucial point is that there can be no absolute meaning assigned to ‘the same moment’ at two different places.
So the future is out there all right, and it can be visited. All you need as an effective time machine is a spaceship that can travel very close to the speed of light or withstand the lethal conditions near a neutron star. Ultra-high speed is not a problem in principle, merely a practical difficulty that may be overcome some day. The major drawback is the energy cost. To accelerate a 10 tonne payload to 99.9 per cent of the speed of light requires an energy expenditure of 10 billion billion joules, equivalent to humanity's entire power output for several months. And the energy needed grows in direct proportion to the timewarp factor: halving the clock rate demands twice the energy. With these costs, nobody is going to take a great leap forward in time using rocket technology. If a way could be found to tap natural sources of energy in space, near-light travel might one day be achievable. Then the future would lie within our grasp.
What about coming back from the future?
High-speed travel and gravitational time dilation can only be used to go forward in time. But just as the future is surely out there, so is the past. It's there for the visiting. The trick is to figure out a way to reach it.
2 How to visit the past
* * *
There was a young lady named Bright
Who travelled much faster than light,
She started one day
In the relative way,
And returned on the previous night.
Punch, 19 December 1923
The first hint that certain gravitational fields might permit travel backwards as well as forwards in time came in 1937, with a little-known paper by W. J. van Stockum published in a Scottish scientific journal. Van Stockum used Einstein's general theory of relativity to predict what would happen if an observer went into orbit around a rotating cylinder. He found that if the cylinder spins fast enough, the observer could return to her starting point before she left. In other words, a closed loop in space could also become a loop in time. Nobody got excited because, to simplify the mathematics, van Stockum had assumed, unrealistically, that the cylinder was infinitely long. Nevertheless, this result served to show that the general theory of relativity did not explicitly forbid travel into the past. Another 50 years were to pass before physicists found a more realistic way to make a time machine.