How to Build a Time Machine (英語) ペーパーバック – 2003/3/25
What if it were possible to build a machine that could transport a human being through time?
Is that credible?
A hundred years ago, few people believed it possible for humans to travel through outer space. Time travel, like space travel, was merely science fiction. Today, spaceflight is almost commonplace. Might time travel one day become commonplace too?
Traveling in time is certainly easy to envisage. You step into the time machine, press a few buttons, and step out again, not just somewhere else, but somewhen else-another time altogether. Writers of science fiction have exploited this theme again and again since H. G. Wells blazed the trail with his famous 1895 story The Time Machine. British audiences (the author included) thrilled to the adventures of the time lord Doctor Who and his attractive lady accomplices. Hollywood movies such as Back to the Future and books such as Timeline make it all seem so easy.
So can it really be done? Is time travel a scientific possibility?
A moment's thought uncovers some tricky questions. Where exactly are the past and future? Surely the past has disappeared and cannot be re-trieved, while the future hasn't yet come into being. How can a person go to a world that doesn't exist? Sidestepping that, what about the inevitable paradoxes that come from visiting the past and changing it? What does that do to the present? And if time travel were feasible, where are all the time tourists from the future, coming back to peer curiously at twenty-first-century society?
There is no doubt that time travel poses some serious problems, even for physicists used to thinking about outlandish concepts like antimatter and black holes. But maybe that is because we are looking at time in the wrong way. After all, our view of time has changed dramatically over the years. In ancient cultures it was associated with process and change, and rooted in the cycles and rhythms of nature. Later, Sir Isaac Newton took a more abstract and mechanistic view. "Absolute, true and mathematical time, flowing equably without relation to anything external" was the way he expressed it, and this became the accepted notion among scientists for two hundred years.
Everyone assumed without question that, whatever one's preferred definition, time is the same everywhere and for everybody. In other words, it is absolute and universal. True, we might feel time passing differently according to our moods, but time itself is simply time. The purpose of a clock is to circumvent mental distortions and record, objectively, the time. Implicit in this view is that time can be chopped up into three parts: past, present, and future. The present-now-is supposed to be the fleeting moment of true reality, with the past banished to history-mere shadowy memory-and the future still hazy and unformed. And that all-important now is taken to be the same moment throughout the universe: your now and my now are identical wherever we are and whatever we are doing.
Such is the commonsense picture of time, the one we use in daily life. Few people think about time any differently. But it's wrong-deeply and seriously wrong.
That it couldn't be right became apparent about the turn of the twentieth century. The credit for exposing the flaws in the everyday notion of time is largely associated with the name of Albert Einstein and the theory of relativity. At a stroke, Einstein's work demolished Newton's view of both space and time, rendered meaningless the universal division of time into past, present, and future, and paved the way for time travel. The theory of relativity is nearly a century old. Following publication of the so-called special theory of relativity in 1905, it was accepted by physicists almost immediately. Over the decades it has been exhaustively tested in many experiments. Today, the scientific community is unanimous that "time is relative" and the commonsense notion of an absolute time with a universal "now" is a fiction. Yet among the general public, the relativity of time still comes as something of a shock. Many people seem not to have heard about it at all. Some of them refuse flatly to believe it when told, in spite of the clear experimental evidence.
In the coming chapters we shall see how the theory of relativity implies that a limited form of time travel is certainly possible, while unrestricted time travel-to any epoch, past or future-might just be possible too. If this seems hard to swallow, remind yourself of J. B. S. Haldane's famous dictum: "The universe is not only queerer than we think, it is queerer than we can think."
1. How to Visit the Future
In an obvious sense we are all time travelers. Do nothing, and you will be conveyed inexorably into the future at the stately pace of one second per second. But this is of limited interest. A true time traveler needs to leap forward dramatically in time and reach the future sooner than everyone else.
Can it be done?
Indeed it can. Scientists have no doubt whatever that it is possible to build a time machine to visit the future. And they've known the formula for nearly a century.
[ Time and Motion
It was in 1905 that Albert Einstein first demonstrated the possibility of time travel. He did this by first demolishing the commonsense picture of time dating back to Newton and replacing it with his own concept of relative time.
Einstein was twenty-six when he published his special theory of relativity. He was then not the pipe-smoking disheveled sage with tousled gray hair who provided the role model for many a fictional nutty professor, but a dapper young man in a suit working at the Swiss patent office. In his spare time, the young Einstein was studying the way light moves. In doing so, he noticed an inconsistency between the motion of light and that of material objects. Using only high-school mathematics, he demonstrated that if light behaves the way that physicists supposed, Newton's straightforward idea of time must be flawed.
The trail of reasoning that leads from the motion of light to this startling conclusion about time has been discussed thoroughly elsewhere and need not concern us here. What matters for our purposes is the central claim of the special theory of relativity, which is that Time is elastic. It can be stretched and shrunk. How? Simply by moving very fast.
What precisely do I mean by "stretching time"? Let me state it more carefully. According to the special theory of relativity, the exact duration of time between two specified events will depend on how the observer is moving. The interval between successive chimes on my clock might be one hour when I am sitting still in my living room, but it will be less than one hour if I spend that time moving about.
To express the same thing in a more practical manner, suppose I board an airplane in New York and fly to Rio and back while you stay at Kennedy Airport. Then the duration of the journey according to me isn't the same as the duration according to you. In fact, it is a bit less for me.
Two points need to be made at the outset. First, I'm not talking about the apparent duration of the journey. Your experience of being bored at the airport with the hours seeming to drag by, while I am happily occupied watching airline movies, is not the effect being discussed here. Mental time is a fascinating topic in psychology, but my concern is with physical time, the sort measured by mindless clocks. The second point is that the time discrepancy for the example given is minuscule-only a few hundred-millionths of a second-far too small to be noticed by a human being; however, it is measurable by modern clocks.
That is pretty much what the physicists Joe Hafele and Richard Keating did in 1971. They put highly accurate atomic clocks into airplanes, flew them around the world, and compared their readings with identical clocks left on the ground. The results were unmistakable: time ran more slowly in the airplane than in the laboratory, so that when the experiment was over the airborne clocks were fifty-nine nanoseconds slow relative to the grounded clocks-exactly the amount predicted in Einstein's theory.
Because your time and my time get out of step if we move differently, there can obviously be no universal, absolute time, as Newton assumed. Talk of the time is meaningless. The physicist is bound to ask: Whose time?
Significant though the Hafele-Keating experiment may be historically, it is hardly the stuff of science fiction: a timewarp of fifty-nine nanoseconds doesn't make for an adventure. To get a really big effect you have to move very fast. The benchmark here is the speed of light, a dizzying 300,000 kilometers per second. The closer to the speed of light you travel, the bigger the timewarp gets.
Physicists call the slowing of time by motion the time dilation effect. Think of a speed. Divide by the speed of light. Square it. Subtract from 1. Take the square root. The answer is . . . Einstein's time dilation factor! This is a graph of the "slowdown factor." Notice how the graph shows the dilation factor as a function of speed and starts out fairly flat, but plummets as light speed is approached. At half the speed of light, time is about 13 percent slowed; at 99 percent, it is seven times slower-1 minute is reduced to about 8.5 seconds.
Technically, the timewarp becomes infinite when the speed of light is reached. This is a sign of trouble. In fact, it tells us that a normal material body can't reach the speed of light. There is a "light barrier" that can never be breached. The no-faster-than-light rule is a key result of the theory of relativity:
Nothing can break the light barrier.
This includes not just material bodies but waves, field disturbances-physical influences of any sort. It spoils a lot of science fiction because, fast though it goes, light still takes a long time to cover interstellar distances. The nearest star, for example, is over four light-years away, which means it takes light over four years to get there from Earth. The Milky Way galaxy is about 100,000 light-years across. Administering a galactic empire would be a slow process.
However, there is some compensation. Because time is stretched by speed, interstellar journeys would seem quicker for the astronauts than for those left on Earth at mission control. In a spaceship traveling at 99 percent of the speed of light, a trip across the galaxy would be completed in only 14,000 years. At 99.99 percent of the speed of light, the gain is even more spectacular: the trip lasts a mere 1,400 years. If you could reach 99.999999 percent of the speed of light, the trip could be completed in a human lifetime. Speeds like this are far beyond current spacecraft technology. (Our best spacecraft reach a paltry 0.01 percent of the speed of light.) But there are objects that travel very close to the speed of light. These are subatomic particles, such as cosmic rays and atomic fragments emitted in radioactive decays, or purposely accelerated in giant "atom smashers." It's possible to observe very large time dilations by using these particles as simple clocks. The particle accelerator known as the Large Electron Positron (LEP) collider at the Centre Européenne pour la Recherche Nucléaire (CERN) laboratory near Geneva could propel electrons to 99.999999999 percent of the speed of light. This is so fast it falls short of the speed of light by a literal snail's pace. At this speed, timewarp factors approaching a million were achieved. Even this pales into insignificance conpared to timewarp factors of billions experienced by some cosmic ray particles.
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 when muons were moving inside the accelerator at 99.7 percent of the speed of light, their average lifetime was extended by a factor of twelve.
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 percent of the speed of light to a nearby star situated ten 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 of her journey to be just over twenty Earth years. But Sally experiences time differently. For her, the journey has taken less than three years, so when she gets back to Earth she finds that the date there is 2021 and Sam is now seventeen years older than she is. Sally and Sam are no longer twins of the same age. In effect, Sally has been transported seventeen 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 six months by traveling at 99.99999 percent of the speed of light.
Traveling through time works the opposite way from traveling through space. The shortest distance between two points is a straight line, so in daily life you get from A to B most quickly by following a direct route. But when it comes to time travel, it is stay-at-home Sam who ages more; that is, he takes longer 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 maneuvers 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 (there being six years' round-trip travel time after departure) this way, in order to reequalize her age with Sam's. If she reverses her trajectory, she will succeed only in leaping another seventeen 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 equation shows that the Earth's gravity causes clocks to lose one micro-second every three hundred years. This leads to the curious prediction that
Time runs faster
But not so much that astronauts notice. (You would gain just a couple of milliseconds by spending six 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 one-tenth 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 meters high. A slowing effect of 0.000000000000257 percent 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 a 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 when the ball is shrunk to about the size of a pea.
Of course, squashing all that matter into a cubic centimeter 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 Manhattan, yet containing masses greater than the Sun (about two thousand trillion trillion tons). The gravity of these collapsed stars is so great that even their atoms are crushed to form neutrons, so they are known as "neutron stars." One such object lies in the constellation of Taurus, deep within a ragged cloud of expanding gas called the Crab Nebula. The nebula contains the shattered remains of a giant star that was seen to explode in 1054 by Chinese chroniclers.
Astronomers have discovered many more such objects and determined that the gravity at their surfaces is large enough to cause substantial timewarps. A clock on a typical neutron star would tick about 30 percent 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 ten 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 are 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 aging and delicate grandfather clock that I put 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 would 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; that is, energy has mass and 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 1 percent 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 fifty 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-that is, 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; if the particle could get there, this would imply that 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 ten years before Einstein's special theory of relativity, H. G. Wells realized 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 that 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 nonphysicists 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 the same moment? Einstein insisted that 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 seven-hundreths of a second for voice messages to traverse the globe in optical fibers. (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 twenty 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, owing to the time dilation effect. So opinions will differ, depending on whom you consult, on how much delay has elapsed while light (or radio) signals are traveling between A and B. An astronaut rushing past 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
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.
This doesn't imply that the order of cause and effect can be reversed simply by traveling fast. Let me explain why. Events have an 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 was 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, causality would be in trouble, and past and future would become jumbled. 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 around the world, but also because human beings don't move at more than a tiny fraction of the speed of light anyway. However, that is incidental. The crucial 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. Ultrahigh speed is not a problem in principle, merely a practical difficulty that may be overcome someday. The major drawback is the energy cost. To accelerate a ten-ton payload to 99.9 percent of the speed of light requires an energy expenditure of ten 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 be used only 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.
- 出版社 : Penguin Books; Reprint版 (2003/3/25)
- 発売日 : 2003/3/25
- 言語 : 英語
- ペーパーバック : 144ページ
- ISBN-10 : 0142001864
- ISBN-13 : 978-0142001868
- 対象読者年齢 : 18歳歳以上
- 寸法 : 12.93 x 1.02 x 19.66 cm
- Amazon 売れ筋ランキング: - 905,009位洋書 (の売れ筋ランキングを見る洋書)
Super zu lesen, gut zu verstehen und hochgradig interessant. Ja, es gibt Wormholes und ja man könnte – rein theoretisch durch sie reisen. Dazu braucht man allerding einige Vorkehrungen, Antimaterie und alle Energie des Universums. Was soll’s, allein die Auseinandersetzung mit dem Thema ist spannend und Davis der Autor dafür, das Geschehen einem näher zu bringen.
The 2nd star has been removed because the author, like many who write at this level, suddenly make vast leaps of imagination right where your own non PHD understanding on the subject starts to fail... so they basically cover the stuff you know well and then suddenly just blurt out something without any explanation.
For instance, ageing one end of a worm hole near a dense body, and then being able to travel into the past by traversing the worm hole. Really? Does that even work? I don't doubt time passes more slowly near dense bodies, but does the actual exit of the worm hole exist in the past? Or is it merely younger? I just felt some explanation around such suggestions would have been valuable as that is exactly where I struggle with these concepts. There must be maths to support it, but no mention of it at all is made etc.
A great idea, but in my view, just like Brian Cox on TV, they tell you all the stuff you possibly know already with lots of nice analogies, but then when it really matters, they quickly gloss over things in a single sentence.
Though there are many Philosophical problems with time travel, which Davies lucidly present, yet it has not been possible to find plausible physical constraints other than by ad hoc paraphrasing of prohibitions. Davies lucidly presents many of these constraints thereby also introducing his readers to many areas of physics. He appears to believe that surely one of these ad hoc principles will eventually acquire some physical plausibility.
On the other hand to appreciate what Godel, the man of few words, might have had in mind consider the following. Godel's universe does not allow for a universal time coordinate. The set of events only allows partial time orderings i.e. ordering along the path of any observer. To appreciate the consequences we may consider the following parable.
Our time traveler wishing for whatever reason to painlessly end his life and being an avid science fiction reader, aware of the Grandfather paradox but not wanting to harm his brother or sister, he decides to return to the time of his childhood to shoot his childhood self. However, the only effect of the shot is a small recoil since Locally, even in Godel's universe, Newtonian physics holds. I.e. there is no Newtonian way for him to disappear.
Unfortunately, Nature's Laws aren't the only Laws applicable here. Society's Laws dictate that our traveler will spend the rest of his life behind bars for killing a child and, thus, unable to return to the 21st Century as Godel's universe would allow.
We will assume that our time traveler presents a negligible perturbertion to the large scale structure of the Godel universe. Though these events our traveler encounters on his trip share Godel coordinates with events he recalls from his past they are New Events. To our traveler they occur in the 21st Century. To those whom our traveler has met on his journey the events occur in the 20th Century. ( Likewise, if our traveler were to return to an earlier time in the 21st Century than when he left, his memories of the intervening period will not be shared by those greeting him; nor would he share the memories of those who saw him off on his journey. ) Only events along a particular path are relevant. Such events are time ordered w.r.t. the particular path. As Godel said, there is No Paradox!
* R. Ruker, "Infinity and the Mind", pp.170 - 181, Bantum Books, 1983 ISBN 0-553-23433-1