Time Travel Paradoxes

By David Lewis

TIME travel, I maintain, is possible. The paradoxes of time travel are oddities, not impossibilities. They prove only this much, which few would have doubted: that a possible world where time travel took place would be a most strange world, different in fundamental ways from the world we think is ours. I shall be concerned here with the sort of time travel that is recounted in science fiction. Not all science fiction writers are clear-headed, to be sure, and inconsistent time travel stories have often been written. But some writers have thought the problems through with great care, and their stories are perfectly consistent.

If I can defend the consistency of some science fiction stories of time travel, then I suppose parallel defenses might be given of some controversial physical hypotheses, such as the hypothesis that time is circular or the hypothesis that there are particles that travel faster than light. But I shall not explore these parallels here. What is time travel? Inevitably, it involves a discrepancy between time and time. Any traveler departs and then arrives at his destination; the time elapsed from departure to arrival (positive, or perhaps zero) is the duration of the journey. But if he is a time traveler, the separation in time between departure and arrival does not equal the duration of his journey. He departs; he travels for an hour, let us say; then he arrives. The time he reaches is not the time one hour after his departure. It is later, if he has traveled toward the future; earlier, if he has traveled toward the past. If he has traveled far toward the past, it is earlier even than his departure. How can it be that the same two events, his departure and his arrival, are separated by two unequal amounts of time? It is tempting to reply that there must be two independent time dimensions; that for time travel to be possible, time must be not a line but a plane.2 Then a pair of events may have two unequal separations if they are separated more in one of the time dimensions than in the other. The lives of common people occupy straight diagonal lines across the plane of time, sloping at a rate of exactly one hour of time1 per hour of time. The life of the time traveler occupies a bent path, of varying slope.

On closer inspection, however, this account seems not to give us time travel as we know it from the stories. When the traveler revisits the days of his childhood, will his playmates be there to meet him? No; he has not reached the part of the plane of time where they are. He is no longer separated from them along one of the two dimensions of time, but he is still separated from them along the other. I do not say that two-dimensional time is impossible, or that there is no way to square it with the usual conception of what time travel would be like. Nevertheless I shall say no more about two-dimensional time. Let us set it aside, and see how time travel is possible even in one-dimensional time.

The world—the time traveler’s world, or ours—is a four-dimensional manifold of events. Time is one dimension of the four, like the spatial dimensions except that the prevailing laws of nature discriminate between time and the others—or rather, perhaps, between various timelike dimensions and various spacelike dimensions. (Time remains one-dimensional, since no two timelike dimensions are orthogonal.) Enduring things are timelike streaks: wholes composed of temporal parts, or stages, located at various times and places. Change is qualitative difference between different stages—different temporal parts—of some enduring thing, just as a “change” in scenery from east to west is a qualitative difference between the eastern and western spatial parts of the landscape. If this paper should change your mind about the possibility of time travel, there will be a difference of opinion between two different temporal parts of you, the stage that started reading and the subsequent stage that finishes. If change is qualitative difference between temporal parts of something, then what doesn’t have temporal parts can’t change. For instance, numbers can’t change; nor can the events of any moment of time, since they cannot be subdivided into dissimilar temporal parts. (We have set aside the case of two-dimensional time, and hence the possibility that an event might be momentary along one time dimension but divisible along the other.) It is essential to distinguish change from “Cambridge change,” which can befall anything. Even a number can “change” from being to not being the rate of exchange between pounds and dollars. Even a momentary event can “change” from being a year ago to being a year and a day ago, or from being forgotten to being remembered. But these are not genuine changes. Not just any old reversal in truth value of a time-sensitive sentence about something makes a change in the thing itself.

A time traveler, like anyone else, is a streak through the manifold of space-time, a whole composed of stages located at various times and places. But he is not a streak like other streaks. If he travels toward the past he is a zig-zag streak, doubling back on himself. If he travels toward the future, he is a stretched-out streak. And if he travels either way instantaneously, so that there are no intermediate stages between the stage that departs and the stage that arrives and his journey has zero duration, then he is a broken streak. I asked how it could be that the same two events were separated by two unequal amounts of time, and I set aside the reply that time might have two independent dimensions. Instead I reply by distinguishing time itself, external time as I shall also call it, from the personal time of a particular time traveler: roughly, that which is measured by his wristwatch. His journey takes an hour of his personal time, let us say; his wristwatch reads an hour later at arrival than at departure. But the arrival is more than an hour after the departure in external time, if he travels toward the future; or the arrival is before the departure in external time (or less than an hour after), if he travels toward the past. That is only rough. I do not wish to define personal time operationally, making wristwatches infallible by definition. That which is measured by my own wristwatch often disagrees with external time, yet I am no time traveler; what my misregulated wristwatch measures is neither time itself nor my personal time. Instead of an operational definition, we need a functional definition of personal time; it is that which occupies a certain role in the pattern of events that comprise the time traveler’s life. If you take the stages of a common person, they manifest certain regularities with respect to external time. Properties change continuously as you go along, for the most part, and in familiar ways. First come infantile stages. Last come senile ones. Memories accumulate. Food digests. Hair grows. Wristwatch hands move.

If you take the stages of a time traveler instead, they do not manifest the common regularities with respect to external time. But there is one way to assign coordinates to the time traveler’s stages, and one way only (apart from the arbitrary choice of a zero point), so that the regularities that hold with respect to this assignment match those that commonly hold with respect to external time. With respect to the correct assignment properties change continuously as you go along, for the most part, and in familiar ways. First come infantile stages. Last come senile ones. Memories accumulate. Food digests. Hair grows. Wristwatch hands move. The assignment of coordinates that yields this match is the time traveler’s personal time. It isn’t really time, but it plays the role in his life that time plays in the life of a common person. It’s enough like time so that we can—with due caution— transplant our temporal vocabulary to it in discussing his affairs. We can say without contradiction, as the time traveler prepares to set out, “Soon he will be in the past.”

 

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We mean that a stage of him is slightly later in his personal time, but much earlier in external time, than the stage of him that is present as we say the sentence. We may assign locations in the time traveler’s personal time not only to his stages themselves but also to the events that go on around him. Soon Caesar will die, long ago; that is, a stage slightly later in the time traveler’s personal time than his present stage, but long ago in external time, is simultaneous with Caesar’s death. We could even extend the assignment of personal time to events that are not part of the time traveler’s life, and not simultaneous with any of his stages. If his funeral in ancient Egypt is separated from his death by three days of external time and his death is separated from his birth by three score years and ten of his personal time, then we may add the two intervals and say that his funeral follows his birth by three score years and ten and three days of extended personal time. Likewise a bystander might truly say, three years after the last departure of another famous time traveler, that “he may even now—if I may use the phrase—be wandering on some plesiosaurus- haunted oolitic coral reef, or beside the lonely saline seas of the Triassic Age.” If the time traveler does wander on an oolitic coral reef three years after his departure in his personal time, then it is no mistake to say with respect to his extended personal time that the wandering is taking place “even now”. We may liken intervals of external time to distances as the crow flies, and intervals of personal time to distances along a winding path. The time traveler’s life is like a mountain railway. The place two miles due east of here may also be nine miles down the line, in the westbound direction. Clearly we are not dealing here with two independent dimensions. Just as distance along the railway is not a fourth spatial dimension, so a time traveler’s personal time is not a second dimension of How far down the line some place is depends on its location in three-dimensional space, and likewise the locations of events in personal time depend on their locations in one-dimensional external time. Five miles down the line from here is a place where the line goes under a trestle; two miles further is a place where the line goes over a trestle; these places are one and the same. The trestle by which the line crosses over itself has two different locations along the line, five miles down from here and also seven. In the same way, an event in a time traveler’s life may have more than one location in his personal time. If he doubles back toward the past, but not too far, he may be able to talk to himself. The conversation involves two of his stages, separated in his personal time but simultaneous in external time. The location of the conversation in personal time should be the location of the stage involved in it. But there are two such stages; to share the locations of both, the conversation must be assigned two different locations in personal time.

The more we extend the assignment of personal time outwards from the time traveler’s stages to the surrounding events, the more will such events acquire multiple locations. It may happen also, as we have already seen, that events that are not simultaneous in external time will be assigned the same location in personal time—or rather, that at least one of the locations of one will be the same as at least one of the locations of the other. So extension must not be carried too far, lest the location of events in extended personal time lose its utility as a means of keeping track of their roles in the time traveler’s history. A time traveler who talks to himself, on the telephone perhaps, looks for all the world like two different people talking to each other. It isn’t quite right to say that the whole of him is in two places at once, since neither of the two stages involved in the conversation is the whole of him, or even the whole of the part of him that is located at the (external) time of the conversation. What’s true is that he, unlike the rest of us, has two different complete stages located at the same time at different places. What reason have I, then, to regard him as one person and not two? What unites his stages, including the simultaneous ones, into a single person?

The problem of personal identity is especially acute if he is the sort of time traveler whose journeys are instantaneous, a broken streak consisting of several unconnected segments. Then the natural way to regard him as more than one person is to take each segment as a different person. No one of them is a time traveler, and the peculiarity of the situation comes to this: all but one of these several people vanish into thin air, all but another one appear out of thin air, and there are remarkable resemblances between one at his appearance and another at his vanishing. Why isn’t that at least as good a description as the one I gave, on which the several segments are all parts of one time traveler? I answer that what unites the stages (or segments) of a time traveler is the same sort of mental, or mostly mental, continuity and connectedness that unites anyone else. The only difference is that whereas a common person is connected and continuous with respect to external time, the time traveler is connected and continuous only with respect to his own personal time. Taking the stages in order, mental (and bodily) change is mostly gradual rather than sudden, and at no point is there sudden change in too many different respects all at once. (We can include position in external time among the respects we keep track of, if we like. It may change discontinuously with respect to personal time if not too much else changes discontinuously along with it.) Moreover, there is not too much change altogether. Plenty of traits and traces last a lifetime. Finally, the connectedness and the continuity are not accidental. They are explicable; and further, they are explained by the fact that the properties of each stage depend causally on those of the stages just before in personal time, the dependence being such as tends to keep things the same. To see the purpose of my final requirement of causal continuity, let us see how it excludes a case of counterfeit time travel. Fred was created out of thin air, as if in the midst of life; he lived a while, then died. He was created by a demon, and the demon had chosen at random what Fred was to be like at the moment of his creation. Much later someone else, Sam, came to resemble Fred as he was when first created. At the very moment when the resemblance became perfect, the demon destroyed Sam.

Fred and Sam together are very much like a single person: a time traveler whose personal time starts at Sam’s birth, goes on to Sam’s destruction and Fred’s creation, and goes on from there to Fred’s death. Taken in this order, the stages of Fred-cum Sam have the proper connectedness and continuity. But they lack causal continuity, so Fred-cum-Sam is not one person and not a time traveler. Perhaps it was pure coincidence that Fred at his creation and Sam at his destruction were exactly alike; then the connectedness and continuity of Fred-cum-Sam across the crucial point are accidental. Perhaps instead the demon remembered what Fred was like, guided Sam toward perfect resemblance, watched his progress, and destroyed him at the right moment. Then the connectedness and continuity of Fred-cum-Sam has a causal explanation, but of the wrong sort. Either way, Fred’s first stages do not depend causally for their properties on Sam’s last stages. So the case of Fred and Sam is rightly disqualified as a case of personal identity and as a case of time travel.

We might expect that when a time traveler visits the past there will be reversals of causation. You may punch his face before he leaves, causing his eye to blacken centuries ago. Indeed, travel into the past necessarily involves reversed causation. For time travel requires personal identity—he who arrives must be the same person who departed. That requires causal continuity, in which causation runs from earlier to later stages in the order of personal time. But the orders of personal and external time disagree at some point, and there we have causation that runs from later to earlier stages in the order of external time. Elsewhere I have given an analysis of causation in terms of chains of counterfactual dependence, and I took care that my analysis would not rule out casual reversal a priori. I think I can argue (but not here) that under my analysis the direction of counterfactual dependence and causation is governed by the direction of other de facto asymmetries of time. If so, then reversed causation and time travel are not excluded altogether, but can occur only where there are local exceptions to these asymmetries. As I said at the outset, the time traveler’s world would be a most strange one. Stranger still, if there are local—but only local causal reversals, then there may also be causal loops: closed causal chains in which some of the causal links are normal in direction and others are reversed. (Perhaps there must be loops if there is reversal: I am not sure.) Each event on the loop has a causal explanation, being caused by events elsewhere on the loop. That is not to say that the loop as a whole is caused or explicable. It may not be. Its inexplicability is especially remarkable if it is made up of the sort of causal processes that transmit information. Recall the time traveler who talked to himself. He talked to himself about time travel, and in the course of the conversation his older self told his younger self how to build a time machine. That information was available in no other way. His older self knew how because his younger self had been told and the information had been preserved by the causal processes that constitute recording, storage, and retrieval of memory traces. His younger self knew, after the conversation, because his older self had known and the information had been preserved by the causal processes that constitute telling.

But where did the information come from in the first place? Why did the whole affair happen? There is simply no answer. The parts of the loop are explicable, the whole of it is not. Strange! But not impossible, and not too different from inexplicabilities we are already inured to. Almost everyone agrees that God, or the Big Bang, or the entire infinite past of the universe, or the decay of a tritium atom, is uncaused and inexplicable. Then if these are possible, why not also the inexplicable causal loops that arise in the time travel? I have committed a circularity in order not to talk about too much at once, and this is a good place to set it right. In explaining personal time, I presupposed that we were entitled to regard certain stages as comprising a single person. Then in explaining what united the stages into a single person, I presupposed that we were given a personal time order for them. The proper way to proceed is to define personhood and personal time simultaneously, as follows. Suppose given a pair of an aggregate of persona-stages, regarded as a candidate for personhood, and an assignment of coordinates to those stages, regarded as a candidate for his personal time. If the stages satisfy the conditions given in my circular explanation with respect to the assignment of coordinates, then both candidates succeed: the stages do comprise a person and the assignment is his personal time.

I have argued so far that what goes on in a time travel story may be a possible pattern of events in four dimensional space-time with no extra time dimension; that it may be correct to regard the scattered stages of the alleged time traveler as comprising a single person; and that we may legitimately assign to those stages and their surroundings a personal time order that disagrees sometimes with their order in external time. Some might concede all this, but protest that the impossibility of time travel is revealed after all when we ask not what the time traveler does, but what he could do. Could a time traveler change the past? It seems not: the events of a past moment could no more change than numbers could. Yet it seems that he would be as able as anyone to do things that would change the past if he did them. If a time traveler visiting the past both could and couldn’t do something that would change it, then there cannot possibly be such a time traveler. Consider Tim. He detests his grandfather, whose success in the munitions trade built the family fortune that paid for Tim’s time machine. Tim would like nothing so much as to kill Grandfather, but alas he is too late. Grandfather died in his bed in 1957, while Tim was a young boy. But when Tim has built his time machine and traveled to 1920, suddenly he realizes that he is not too late after all. He buys a rifle; he spends long hours in target practice; he shadows Grandfather to learn the route of his daily walk to the munitions works; he rents a room along the route; and there he lurks, one winter day in 1921, rifle loaded, hate in his heart, as Grandfather walks closer, closer,. . . .

Tim can kill Grandfather. He has what it takes. Conditions are perfect in every way: the best rifle money could buy, Grandfather an easy target only twenty yards away, not a breeze, door securely locked against intruders. Tim a good shot to begin with and now at the peak of training, and so on. What’s to stop him? The forces of logic will not stay his hand! No powerful chaperone stands by to defend the past from interference. (To imagine such a chaperone, as some authors do, is a boring evasion, not needed to make Tim’s story consistent.) In short, Tim is as much able to kill Grandfather as anyone ever is to kill anyone. Suppose that down the street another sniper, Tom, lurks waiting for another victim, Grandfather’s partner. Tom is not a time traveler, but otherwise he is just like Tim: same make of rifle, same murderous intent, same everything. We can even suppose that Tom, like Tim, believes himself to be a time traveler. Someone has gone to a lot of trouble to deceive Tom into thinking so. There’s no doubt that Tom can kill his victim; and Tim has everything going for him that Tom does. By any ordinary standards of ability, Tim can kill Grandfather. Tim cannot kill Grandfather. Grandfather lived, so to kill him would be to change the past. But the events of a past moment are not subdivisible into temporal parts and therefore cannot change. Either the events of 1921 timelessly do include Tim’s killing of Grandfather, or else they timelessly don’t. We may be tempted to speak of the “original” 1921 that lies in Tim’s personal past, many years before his birth, in which Grandfather lived; and of the “new” 1921 in which Tim now finds himself waiting in ambush to kill Grandfather. But if we do speak so, we merely confer two names on one thing. The events of 1921 are doubly located in Tim’s (extended) personal time, like the trestle on the railway, but the “original” 1921 and the “new” 1921 are one and the same.

If Tim did not kill Grandfather in the “original” 1921, then if he does kill Grandfather in the “new” 1921, he must both kill and not kill Grandfather in 1921—in the one and only 1921, which is both the “new” and the “original” 1921. It is logically impossible that Tim should change the past by killing Grandfather in 1921. So Tim cannot kill Grandfather. Not that past moments are special; no more can anyone change the present or the future. Present and future momentary events no more have temporal parts than past ones do. You cannot change a present or future event from what it was originally to what it is after you change it. What you can do is to change the present or the future from the unactualized way they would have been without some action of yours to the way they actually are. But that is not an actual change: not a difference between two successive actualities. And Tim can certainly do as much; he changes the past from the unactualized way it would have been without him to the one and only way it actually is. To “change” the past in this way, Tim need not do anything momentous; it is enough just to be there, however unobtrusively. You know, of course, roughly how the story of Tim must go on if it is to be consistent: he somehow fails. Since Tim didn’t kill Grandfather in the “original” 1921, consistency demands that neither does he kill Grandfather in the “new” 1921. Why not? For some commonplace reason.

Perhaps some noise distracts him at the last moment, perhaps he misses despite all his target practice, perhaps his nerve fails, perhaps he even feels a pang of unaccustomed mercy. His failure by no means proves that he was not really able to kill Grandfather. We often try and fail to do what we are able to do. Success at some tasks requires not only ability but also luck, and lack of luck is not a temporary lack of ability. Suppose our other sniper, Tom, fails to kill Grandfather’s partner for the same reason, whatever it is, that Tim fails to kill Grandfather. It does not follow that Tom was unable to. No more does it follow in Tim’s case that he was unable to do what he did not succeed in doing. We have this seeming contradiction: “Tim doesn’t, but can, because he has what it takes” versus “Tim doesn’t, and can’t, because it’s logically impossible to change the past.” I reply that there is no contradiction. Both conclusions are true, and for the reasons given. They are compatible because “can” is equivocal. To say that something can happen means that its happening is compossible with certain facts. Which facts? That is determined, but sometimes not determined well enough, by context. An ape can’t speak a human language— say, Finnish—but I can. Facts about the anatomy and operation of the ape’s larynx and nervous system are not compossible with his speaking Finnish.

The corresponding facts about my larynx and nervous system are compossible with my speaking Finnish. But don’t take me along to Helsinki as your interpreter: I can’t speak Finnish. My speaking Finnish is compossible with the facts considered so far, but not with further facts about my lack of training. What I can do, relative to one set of facts, I cannot do, relative to another, more inclusive, set. Whenever the context leaves it open which facts are to count as relevant, it is possible to equivocate about whether I can speak Finnish. It is likewise possible to equivocate about whether it is possible for me to speak Finnish, or whether I am able to, or whether I have the ability or capacity or power or potentiality to. Our many words for much the same thing are little help since they do not seem to correspond to different fixed delineations of the relevant facts.

Tim’s killing Grandfather that day in 1921 is compossible with a fairly rich set of facts: the facts about his rifle, his skill and training, the unobstructed line of fire, the locked door and the absence of any chaperone to defend the past, and so on. Indeed it is compossible with all the facts of the sorts we would ordinarily count as relevant is saying what someone can do. It is compossible with all the facts corresponding to those we deem relevant in Tom’s case. Relative to these facts, Tim can kill Grandfather. But his killing Grandfather is not compossible with another, more inclusive set of facts. There is the simple fact that Grandfather was not killed. Also there are various other facts about Grandfather’s doings after 1921 and their effects: Grandfather begat Father in 1922 and Father begat Tim in 1949. Relative to these facts, Tim cannot kill Grandfather. He can and he can’t, but under different delineations of the relevant facts. You can reasonably choose the narrower delineation, and say that he can; or the wider delineation, and say that he can’t. But choose. What you mustn’t do is waver, say in the same breath that he both can and can’t, and then claim that this contradiction proves that time travel is impossible. Exactly the same goes for Tom’s parallel failure.

For Tom to kill Grandfather’s partner also is compossible with all facts of the sorts we ordinarily count as relevant, but not compossible with a larger set including, for instance, the fact that the intended victim lived until 1934. In Tom’s case we are not puzzled. We say without hesitation that he can do it, because we see at once that the facts that are not compossible with his success are facts about the future of the time in question and therefore not the sort of facts we count as relevant in saying what Tom can do. In Tim’s case it is harder to keep track of which facts are relevant. We are accustomed to exclude facts about the future of the time in question, but to include some facts about its past. Our standards do not apply unequivocally to the crucial facts in this special case: Tim’s failure, Grandfather’s survival, and his subsequent doings. If we have foremost in mind that they lie in the external future of that moment in 1921 when Tim is almost ready to shoot, then we exclude them just as we exclude the parallel facts in Tom’s case. But if we have foremost in mind that they precede that moment in Tim’s extended personal time, then we tend to include them. To make the latter be foremost in your mind, I chose to tell Tim’s story in the order of his personal time, rather than in the order of external time. The fact of Grandfather’s survival until 1957 had already been told before I got to the part of the story about Tim lurking in ambush to kill him in 1921. We must decide, if we can, whether to treat these personally past and externally future facts as if they were straightforwardly past or as if they were straightforwardly future.

Fatalists—the best of them—are philosophers who take facts we count as irrelevant in saying what someone can do, disguise them somehow as facts of a different sort that we count as relevant, and thereby argue that we can do less than we think—indeed, that there is nothing at all that we don’t do but can. I am not going to vote Republican next fall. The fatalist argues that, strange to say, I not only won’t but can’t; for my voting Republican is not compossible with the fact that it was true already in the year 1548 that I was not going to vote Republican 428 years later. My rejoinder is that this is a fact, sure enough; however, it is an irrelevant fact about the future masquerading as a relevant fact about the past, and so should be left out of account in saying what, in any ordinary sense, I can do. We are unlikely to be fooled by the fatalist’s methods of disguise in this case, or other ordinary cases. But in cases of time travel, precognition, or the like, we’re on less familiar ground, so it may take less of a disguise to fool us. Also, new methods of disguise are available, thanks to the device of personal time.

Here’s another bit of fatalist trickery. Tim, as he lurks, already knows that he will fail. At least he has the wherewithal to know it if he thinks, he knows it implicitly. For he remembers that Grandfather was alive when he was a boy, he knows that those who are killed are thereafter not alive, he knows (let us suppose) that he is a time traveler who has reached the same 1921 that lies in his personal past, and he ought to understand—as we do— why a time traveler cannot change the past. What is known cannot be false. So his success is not only not compossible with facts that belong to the external future and his personal past, but also is not compossible with the present fact of his knowledge that he will fail. I reply that the fact of his foreknowledge, at the moment while he waits to shoot, is not a fact entirely about that moment. It may be divided into two parts. There is the fact that he then believes (perhaps only implicitly) that he will fail; and there is the further fact that his belief is correct, and correct not at all by accident, and hence qualifies as an item of knowledge. It is only the latter fact that is not compossible with his success, but it is only the former that is entirely about the moment in question. In calling Tim’s state at that moment knowledge, not just belief, facts about personally earlier but externally later moments were smuggled into consideration. I have argued that Tim’s case and Tom’s are alike, except that in Tim’s case we are more tempted than usual— and with reason—to opt for a semi-fatalist mode of speech. But perhaps they differ in another way. In Tom’s case, we can expect a perfectly consistent answer to the counterfactual question: what if Tom had killed Grandfather’s partner? Tim’s case is more difficult. If Tim had killed Grandfather, it seems offhand that contradictions would have been true. The killing both would and wouldn’t have occurred. No Grandfather, no Father; no Father, no Tim; no Tim, no killing. And for good measure: no Grandfather, no family fortune; no fortune, no time machine; no time machine, no killing. So the supposition that Tim killed Grandfather seems impossible in more than the semi-fatalistic sense already granted. If you suppose Tim to kill Grandfather and hold all the rest of his story fixed, of course you get a contradiction. But likewise if you suppose Tom to kill Grandfather’s partner and hold the rest of his story fixed—including the part that told of his failure—you get a contradiction. If you make any counterfactual supposition and hold all else fixed you get a contradiction. The thing to do is rather to make the counterfactual supposition and hold all else as close to fixed as you consistently can. That procedure will yield perfectly consistent answers to the question: what if Tim had not killed Grandfather?

In that case, some of the story I told would not have been true. Perhaps Tim might have been the time-traveling grandson of someone else. Perhaps he might have been the grandson of a man killed in 1921 and miraculously resurrected. Perhaps he might have been not a time traveler at all, but rather someone created out of nothing in 1920 equipped with false memories of a personal past that never was. It is hard to say what is the least revision of Tim’s story to make it true that Tim kills Grandfather, but certainly the contradictory story in which the killing both does and doesn’t occur is not the least revision. Hence it is false (according to the unrevised story) that if Tim had killed Grandfather then contradictions would have been true. What difference would it make if Tim travels in branching time?

Suppose that at the possible world of Tim’s story the space-time manifold branches; the branches are separated not in time, and not in space, but in some other way. Tim travels not only in time but also from one branch to another. In one branch Tim is absent from the events of 1921; Grandfather lives; Tim is born, grows up, and vanishes in his time machine. The other branch diverges from the first when Tim turns up in 1920; there Tim kills Grandfather and Grandfather leaves no descendants and no fortune; the events of the two branches differ more and more from that time on. Certainly this is a consistent story; it is a story in which Grandfather both is and isn’t killed in 1921 (in the different branches); and it is a story in which Tim, by killing Grandfather, succeeds in preventing his own birth (in one of the branches). But it is not a story in which Tim’s killing of Grandfather both does occur and doesn’t: it simply does, though it is located in one branch and not the other. And it is not a story in which Tim changes the past. 1921 and later years contain the events of both branches, coexisting somehow without interaction. It remains true at all the personal times of Tim’s life, even after the killing, that Grandfather lives in one branch and dies in the other.

[Credit: David Lewis]
[PDF version of article: Time Travel Paradoxes by David Lewis]

Chronology Protection Conjecture: Where are They?

“Where are they?” It becomes necessary to ponder about time travellers if you are going to discuss time travel. Well, if time travel is possible, where are the time travellers from future? What if a time machine is handled over you? Where would you like to go first in time dimension? Of course, your answer would be ‘in the past’!! As you know quantum physics allows time travel with given circumstances.[See, Time Travel]

I have already peer reviewed a lot of research paper in regards to time travel. Consider, if our civilization might have been survived for next six centuries and fore, we would have reached to the stage of post singularity and tending to become a typeII civilization. Since every time travelling trick acquire highly risky and pesky technologies like traversable wormholes, tipler cylinder, closed time like curve,macroscopic casimir effect(filled with high negative energy densities) so it is fairly reasonable to assume that building a time machine is just a engineering problem. I bet if we have ensured our survival to the next ten centuries, we would have all such technologies which are today viewed as the challenge. So I’ll assume that our future descendents have such technology which would allow them to travel back and forth in time. Now, a obvious question which knock down our brain is-“where are they?”
Well explanation can be offered in two ways:
1.Chronology Protection Conjecture(CPC):This was first proposed by Pro. Hawking in 1992. Well CPC is nothing but a metaphorical device which prevents the macroscopic time travel. The idea of chronology protection gained considerable currency during the 1990’s when it became clear that traversable wormholes,which are not too objectionable in their own right seem almost generically to lead to the creation of time machines. Why CPC is a key issue? In Newtonian physics, and even in special relativity or flat-space quantum field theory, notions of chronology and causality are so fundamental that they are simply built into the theory ab initio. Violation of normal chronology (for instance, an eect preceding its cause)is so objectionable an occurrence that any such theory would immediately be rejected as unphysical. Unfortunately, in general relativity one can’t simply assert that chronology is preserved, and causality respected, without doing considerable ad-ditional work. The essence of the problem lies in the fact that the Einstein equations of general relativity are local equations, relating some aspects of the spacetime curvature at a point to the presence of stress-energy at that point. Additionally, one also has local chronology protection, inherited from the fact that the spacetime is locally Minkowskian(the Einstein Equivalence Principle), and so in the small general relativity respects all of the causality constraints of special relativity. There is quantum like thingy known as Cauchy horizon problem which prevent the formation of closed time like curve but that could be easily overrun by Casimir effect(exception of Cauchy horizon problem). One side of the horizon contains closed space-like geodesics and the other side contains closed time-like geodesics. When waves traveling in Misner space pass through the identification world line. As this happens infinitely many times while approaching the horizon, the stress-energy tensor diverges at the horizon. Presumably, this prevents space time from developing closed time-like curve ts that would otherwise be feasible. Thus, CPC is protected.
2.Multiverse Theory: This could also be proposed as a possible strategy to explain the paradox. There are infinite universes having every single possibility. So, it is possible that indeed, time travellers from future might be lurking into the past enjoying dinosaur riding but in a different parallel universe. Thusly, it resolves the paradox.

3.No Time Machine can be engineered: Probably this is the simplest solution to the paradox. The parody with time travel is that it always involves something that is way beyond our technology or even rhetorical ideas. General requirements of a time machine are tipler cylinders, black holes, warp drives, wormholes, Kerr Neumann black holes, BPS black holes etc. which won’t seem feasible by any means of technology. Perhaps, which is why there are no time traveller intruding into the past to get better resources, appaling Homo Sapiens.

Video: The Time Traveller, Real Time Machine and True Story of Philadelphia Experiment

Ever got fascinated to time travel? If not, be now! Here is a man who claims that he is a time traveller and he had evidence of time travel. Watch this video:

Well, I don’t find anything credible enough to prove him time traveller.
Now come to the reality. Possibly we would have a quantum time machine in near future. By warping space-time fabric using cris-cross of high intensity laser beams, could make teleportation of a elementary particle into the past, possible. Watch it.

Probably you know about secret Philadelphia experiment conducted in 1943 on a ship named U.S.S. Enridge. It is said that ship was teleported using tesla coils which generated a very high electro-magnetic field and warped space time fabric, a special manifestation of relativity theory unknown yet. See the reality!…?




Wormhole Engineering

By John Gribbin

There is still one problem with wormholes for any hyperspace engineers to take careful account of. The simplest calculations suggest that whatever may be going on in the universe outside, the attempted passage of a spaceship through the hole ought to make the star gate slam shut. The problem is that an accelerating object, according to the general theory of relativity, generates those ripples in the fabric of spacetime itself known as gravitational waves. Gravitational radiation itself, travelling ahead of the spaceship and into the black hole at the speed of light, could be amplified to infinite energy as it approaches the singularity inside the black hole, warping spacetime around itself and shutting the door on the advancing spaceship. Even if a natural traversable wormhole exists, it seems to be unstable to the slightest perturbation, including the disturbance caused by any attempt to pass through it.

But Thorne’s team found an answer to that for Sagan. After all, the wormholes in Contact are definitely not natural, they are engineered. One of his characters explains:

There is an interior tunnel in the exact Kerr solution of the Einstein Field Equations, but it’s unstable. The slightest perturbation would seal it off and convert the tunnel into a physical singularity through which nothing can pass. I have tried to imagine a superior civilization that would control the internal structure of a collapsing star to keep the interior tunnel stable. This is very difficult. The civilization would have to monitor and stabilize the tunnel forever.

But the point is that the trick, although it may be very difficult, is not impossible. It could operate by a process known as negative feedback, in which any disturbance in the spacetime structure of the wormhole creates another disturbance which cancels out the first disturbance. This is the opposite of the familiar positive feedback effect, which leads to a howl from loudspeakers if a microphone that is plugged in to those speakers through an amplifier is placed in front of them. In that case, the noise from the speakers goes into the microphone, gets amplified, comes out of the speakers louder than it was before, gets amplified . . . and so on. Imagine, instead, that the noise coming out of the speakers and into the microphone is analysed by a computer that then produces a sound wave with exactly the opposite characteristics from a second speaker. The two waves would cancel out, producing total silence.

For simple sound waves, this trick can actually be carried out, here on Earth, in the 1990s. Cancelling out more complex noise, like the roar of a football crowd, is not yet possible, but might very well be in a few years time. So it may not be completely farfetched to imagine Sagan’s “superior civilization” building a gravitational wave receiver/transmitter system that sits in the throat of a wormhole and can record the disturbances caused by the passage of the spaceship through the wormhole, “playing back” a set of gravitational waves that will exactly cancel out the disturbance, before it can destroy the tunnel.

But where do the wormholes come from in the first place? The way Morris, Yurtsever and Thorne set about the problem posed by Sagan was the opposite of the way everyone before them had thought about black holes. Instead of considering some sort of known object in the Universe, like a dead massive star, or a quasar, and trying to work out what would happen to it, they started out by constructing the mathematical description of a geometry that described a traversable wormhole, and then used the equations of the general theory of relativity to work out what kinds of matter and energy would be associated with such a spacetime. What they found is almost (with hindsight) common sense. Gravity, an attractive force pulling matter together, tends to create singularities and to pinch off the throat of a wormhole. The equations said that in order for an artificial wormhole to be held open, its throat must be threaded by some form of matter, or some form of field, that exerts negative pressure, and has antigravity associated with it.

Now, you might think, remembering your school physics, that this completely rules out the possibility of constructing traversable wormholes. Negative pressure is not something we encounter in everyday life (imagine blowing negative pressure stuff in to a balloon and seeing the balloon deflate as a result). Surely exotic matter cannot exist in the real Universe? But you may be wrong.

Making  Antigravity

The key to antigravity was found by a Dutch physicist, Hendrik Casimir, as long ago as 1948. Casimir, who was born in The Hague in 1909, worked from 1942 onwards in the research laboratories of the electrical giant Philips, and it was while working there that he suggested what became known as the Casimir effect.

The simplest way to understand the Casimir effect is in terms of two parallel metal plates, placed very close together with nothing in between them (Figure 6). The quantum vacuum is not like the kind of “nothing” physicists imagined the vacuum to be before the quantum era. It seethes with activity, with particle-antiparticle pairs constantly being produced and annihilating one another. Among the particles popping in and out of existence in the quantum vacuum there will be many photons, the particles which carry the electromagnetic force, some of which are the particles of light. Indeed, it is particularly easy for the vacuum to produce virtual photons, partly because a photon is its own antiparticle, and partly because photons have no “rest mass” to worry about, so all the energy that has to be borrowed from quantum uncertainty is the energy of the wave associated with the particular photon. Photons with different energies are associated with electromagnetic waves of different wavelengths, with shorter wavelengths corresponding to greater energy; so another way to think of this electromagnetic aspect of the quantum vacuum is that empty space is filled with an ephemeral sea of electromagnetic waves, with all wavelengths represented.

This irreducible vacuum activity gives the vacuum an energy, but this energy is the same everywhere, and so it cannot be detected or used. Energy can only be used to do work, and thereby make its presence known, if there is a difference in energy from one place to another.

Between two electrically conducting plates, Casimir pointed out, electromagnetic waves would only be able to form certain stable patterns. Waves bouncing around between the two plates would behave like the waves on a plucked guitar string. Such a string can only vibrate in certain ways, to make certain notes — ones for which the vibrations of the string fit the length of the string in such a way that there are no vibrations at the fixed ends of the string. The allowed vibrations are the fundamental note for a particular length of string, and its harmonics, or overtones. In the same way, only certain wavelengths of radiation can fit into the gap between the two plates of a Casimir experiment . In particular, no photon corresponding to a wavelength greater than the separation between the plates can fit in to the gap. This means that some of the activity of the vacuum is suppressed in the gap between the plates, while the usual activity goes on outside. The result is that in each cubic centimetre of space there are fewer virtual photons bouncing around between the plates than there are outside, and so the plates feel a force pushing them together. It may sound bizarre, but it is real. Several experiments have been carried out to measure the strength of the Casimir force between two plates, using both flat and curved plates made of various kinds of material. The force has been measured for a range of plate gaps from 1.4 nanometers to 15 nanometers (one nanometer is one billionth of a metre) and exactly matches Casimir’s prediction.

In a paper they published in 1987, Morris and Thorne drew attention to such possibilities, and also pointed out that even a straightforward electric or magnetic field threading the wormhole “is right on the borderline of being exotic; if its tension were infinitesimally larger . . . it would satisfy our wormhole-building needs.” In the same paper, they concluded that “one should not blithely assume the impossibility of the exotic material that is required for the throat of a traversable wormhole.” The two CalTech researchers make the important point that most physicists suffer a failure of imagination when it comes to considering the equations that describe matter and energy under conditions far more extreme than those we encounter here on Earth. They highlight this by the example of a course for beginners in general relativity, taught at CalTech in the autumn of 1985, after the first phase of work stimulated by Sagan’s enquiry, but before any of this was common knowledge, even among relativists. The students involved were not taught anything specific about wormholes, but they were taught to explore the physical meaning of spacetime metrics. In their exam, they were set a question which led them, step by step, through the mathematical description of the metric corresponding to a wormhole. “It was startling,” said Morris and Thorne, “to see how hidebound were the students’ imaginations. Most could decipher detailed properties of the metric, but very few actually recognised that it represents a traversable wormhole connecting two different universes.”

For those with less hidebound imaginations, there are two remaining problems — to find a way to make a wormhole large enough for people (and spaceships) to travel through, and to keep the exotic matter out of contact with any such spacefarers. Any prospect of building such a device is far beyond our present capabilities. But, as Morris and Thorne stress, it is not impossible and “we correspondingly cannot now rule out traversable wormholes.” It seems to me that there’s an analogy here that sets the work of such dreamers as Thorne and Visser in a context that is both helpful and intriguing. Almost exactly 500 years ago, Leonardo da Vinci speculated about the possibility of flying machines. He designed both helicopters and aircraft with wings, and modern aeronautical engineers say that aircraft built to his designs probably could have flown if Leonardo had had modern engines with which to power them — even though there was no way in which any engineer of his time could have constructed a powered flying machine capable of carrying a human up into the air. Leonardo could not even dream about the possibilities of jet engines and routine passenger flights at supersonic speeds. Yet Concorde and the jumbo jets operate on the same basic physical principles as the flying machines he designed. In just half a millennium, all his wildest dreams have not only come true, but been surpassed. It might take even more than half a millennium for designs for a traversable wormhole to leave the drawing board; but the laws of physics say that it is possible — and as Sagan speculates, something like it may already have been done by a civilization more advanced than our own.

Hyperluminal Spaceship, Tachyons and Time Travel

Einsteins theory of relativity suggests that none can have hyperluminal speed. Negative mass or tachyon are the particles which always travel at superluminal speed and had a negative time frame means time run backward for them. What if a spaceship is travelling at hyper light speed? Would time run backward for that space ship? These are questions which are to be solved here by Earnst L Wall.

By Earnst L Wall

To depart somewhat from a pure state machine argument for a moment, we will consider a more general discussion of the argument that an object that moves faster than the speed of light would experience time reversal.  For example,  the space ship Enterprise, in moving away from Earth at hyperluminal velocities, would overtake the light that was emitted by events that occurred while it was still on the earth.  It would then see the events unfold in reverse time order as it progressed on its path.  This phenomena would be, in effect, a review of the record of a portion of the Earth=s history in the same manner that one views a sequence of events on a VCR as the tape is run backwards.  But this does not mean that the hyperluminal spacecraft or the universe is actually going backwards in time anymore than a viewer watching the VCR running in reverse is moving backwards in time.

Further, it must be asked what would happen to the universe itself under these circumstances.  To illustrate this, suppose a colony were established on Neptune.  Knowing the distance to Neptune, it would be trivial, even with today’s technology, to synchronize the clocks on Earth and Neptune so that they kept the same absolute time to within microseconds or better.  Next, suppose that the Enterprise left Earth at a hyperluminal velocity for a trip to Neptune.  When the crew and passengers of the Enterprise arrive at Neptune, say 3 minutes later in Earth time, it is unlikely that the clocks on Neptune would be particularly awed or even impressed by the arrival of the travelers. When the Enterprise arrives at Neptune, it would get there 3 minutes later in terms of the time as measured on both Neptune and Earth, regardless of how long its internal clocks indicated that the trip was.  Neither the Enterprise nor its passengers would have moved backwards in time as measured on earth or Neptune.

The hands of a clock inside the Enterprise, as simulated by a state machine, would not be compelled to reverse themselves just because it is moving at a hyperluminal velocity.  This is because the universal state machine is still increasing its time count, not reversing it.  Nor would any molecule that is not in, or near the trajectory of the space ship, be affected insofar as time is concerned, provided it does not actually collide with the space ship.

In the scheme above, reverse time travel will not occur merely because an object is traveling at hyperluminal velocities.  Depending on the details of the simulation, hyperluminal travel may cause the local time sequencing to slow down, but a simulated, aging movie queen who is traveling in a hyperluminal spacecraft will not regain her lost youth.  Simulated infants will not reenter their mother’s wombs.  Simulated dinosaurs will not be made to reappear.  A simulated hyperluminal spacecraft cannot go back in time retrieve objects and bring them back to the present.  Nor would any of the objects in the real universe go backward in time as a result of the passage of the hyperluminal spacecraft.

The mere hyperluminal transmission of information or signals from point to point, nor objects traveling at hyperluminal velocities from point to point, does not cause a  change in the direction of the time count at the point of departure nor at the point of arrival of these hyperluminal entities, nor at any point in between.

Based on concepts derived from modern computer science, we have developed a new method of studying the flow of time.  It is different from the classical statistical mechanical method of viewing continuous time flow in that we have described a hypothetical simulation of the universe by means of a gigantic digital state machine implemented in a gigantic computer.  This machine has the capability of mirroring the general  non-deterministic, microscopic behavior of the real universe

Based on these concepts, we have developed a new definition of absolute time as a measure of the count of discrete states of the universe that occurred from the beginning of the universe to some later time that might be under consideration.   In the real universe, we would use a high energy gamma ray as a clock to time the states, these states being determined by regular measurements of an object’s parameters by analog-to-digital samples taken at the clock frequency.

And based on this definition of time, it is clear that, without the physical universe to regularly change state, time has no meaning whatsoever.  That is, matter in the physical universe is necessary for time to exist. In empty space, or an eternal void, time would have utterly no meaning

This definition of time and its use in the simulation has permitted us to explore the nature of time flow in a statistical, non-determinate universe. This exploration included a consideration of the possibility of reverse time travel.  But by using the concept of a digital state machine as the basis of a thought experiment, we show clearly that to move backward in time, you would have to reverse the state count on the universal clock, which would have the effect of reversing the velocity of the objects. But this velocity includes the not only the velocity of the individual objects, but the composite velocities of all objects composing a macroscopic body. As a result, this macroscopic body would also reverse its velocity, providing the state was specified with sufficient precision.

But if you merely counted backward and obtained a reversal of motion, at best you could only move back to some probable past because of the indeterminate nature of the process.  You could not go back to some exact point in the past that is exactly the way it was.   In fact, after a short time, the process would be come so random that there would be no real visit to the past.  A traveler would be unable to determine if he was going back in time, or forward in time.  Entropy would continue to increase.

But doing even this in the real universe, of course, would present a problem because you would need naturally occurring, synchronized, discrete states (outside of quantized states, which are random and not universally synchronized).  You would need to be able to control a universal clock that counts these transitions, and further, cause it to go back to previous states simultaneously over the entire universe.   Modern physics has not found evidence of naturally occurring universal synchronized states, nor such an object as a naturally occurring clock that controls them.  And even if the clock were found, causing the clock to reverse the state transition sequence would be rather difficult.

Without these capabilities, it would seem impossible to envision time reversal by means of rewinding the universe.  This would not seem to be a possibility even in a microscopic portion of the universe, let alone time reversal over the entire universe.

But aside from those difficulties, if you wished to go back to an exact point in the past, the randomness of time travel by rewind requires need an alternative to rewinding the universe.  This is true for the simulated universe, and a hypothetical rewind of the real universe.  Therefore, the only way to visit an exact point in the past is to have a record of the entire past set of all states of the universe, from the point in the past that you wish to visit onward to the present.  This record must be stored somewhere, and a means of accessing this record, visiting it, becoming assimilated in it, and then allowing time to move forward from there must be available.  And, while all of this is happening in the past, the traveler’s departure point at the present state count, or time, must mover forward in time while the traveler takes his journey.

Even jumping back in time because of a wormhole transit would require that a record of the past be stored somewhere.  And, of course, the wormhole would need the technology to access these records, to place the traveler into the record and then to allow him to be assimilated there.  This would seem to be a rather difficult problem.

This then, is the problem with time travel to an exact point in the past in the real universe.  Where would the records be stored?  How would you access them in order just to read them?  And even more difficult, how would you be able to enter this record of the universe, become assimilated into this time period, and then and have your body begin to move forward in time.  At a very minimum our time traveler would have to have answers to these questions.

Still another conundrum is how the copy of the past universe would merge with the real universe at the traveler’s point of departure.  And then, if he had caused any changes that affected his departure point, they would have to be incorporated into that part of the universal record that is the future from his point of departure, and these changes would then have to be propagated forward to the real universe itself and incorporated into it.  This is assuming that the record is separate from the universe itself.

But if this hypothetical record of the universe were part of the universe itself,  or even the universe itself, then that would imply that all states of the entire universe, past, present, and future, exist in that record. This would further imply that we, as macroscopic objects in the universe, have no free will and are merely stepped along from state to state, and are condemned to carry out actions that we have no control over whatsoever.

In such a universe, if our traveler had access to the record, he might be able to travel in time.  But he were to be able to alter the record and affect the subsequent flow of time, he would have to have free will, which would seem to contradict the condition described above.  We obviously would be presented with endless recursive sequences that defy rationality in all of the above.

This is all interesting philosophy, but it seems to be improbable physics.

Therefore, in a real universe, and based on our present knowledge of physics, it would seem that time travel is highly unlikely, if not downright impossible.

We do not deny the usefulness of time reversal as a mathematical artifact in the calculation of subatomic particle phenomena.  However,  it does not seem possible even for particles to actually go backwards in time and influence the past and cause consequential changes to the present.

Further, there is no reason to believe that exceeding the speed of light would cause time reversal in either an individual particle or in a macroscopic body.  Therefore, any objections to tachyon models that are based merely on causality considerations have little merit.

For the sake of completeness, it should be commented that the construction of a computer that would accomplish the above feats exactly would require that the computer itself be part of the state machine. This could add some rather interesting problems in recursion that should be of interest to computer scientists.  And, it is obvious that the construction of such a machine would be rather substantial boon to the semiconductor industry.

We already know from classical statistical mechanics that increasing entropy dictates that the arrow of time can only move in the forward direction .  We have not only reaffirmed this principle here, but have gone considerably beyond it. These concepts would be extremely difficult, if not impossible, to develop with an analog, or continuous statistical mechanical model of the universe.

We have defined time on the basis of a state count based on the fastest changing object in the universe.  But it is interesting to note that modern day time is based on photons from atomic transitions, and is no longer based on the motion of the earth.  Conceptually, however, it is still an extension of earth based time.

But finally, history is filled with instances of individuals who have stated that various phenomena are impossible, only later to be proven wrong, and even ridiculous. Most of the technology that we take for granted today would have been thought to be impossible several hundred years ago, and some of it would have been thought impossible only decades ago.  Therefore, it is emphasized here that we do not say that time travel is absolutely impossible.  We will merely take a rather weak stance on the matter and simply say that, based on physics as we know it today, there are some substantial difficulties that must be overcome before time travel becomes a reality.

Sublight Travel And Galactic Exploration Through Wormholes

Though it seems impossible to colonize galaxy at sub-light speed but without FTL travel we can still colonise the universe at sub-light velocities[ using self replicating probes and Bioprograms which I’ve discussed recently], but the resulting colonies are separated from each other by the vastness of interstellar space. In the past trading empires have coped with time delays on commerce routes of the order of a few years at most. This suggests that economic zones would find it difficult to encompass more than one star system. Travelling beyond this would require significant re-orientation upon return, catching up with cultural changes etc. It’s unlikely people would routinely travel much beyond this and return.

Nanotechnology only exacerbates the situation. We expect full- nanotech, uploading, AIs etc to arrive before interstellar travel becomes practical. Assume we keep the same dimensions for our bodies and brains as at the moment. Once we are uploaded onto a decent nanotech platform our mental speeds can be expected to exceed our present rates by the same factor as electrical impulses exceed the speed of our neurochemical impulses – about a million. Subjective time would speed up by this factor. Taking a couple of subjective-years as the limit beyond which people would be reluctant to routinely travel this defines the size of a typical trade zone / culture as not exceeding a couple of light minutes. Even single stellar systems would be unable to form a single culture/trade zone. The closest planet then would seem further away than the nearest star today.

With full nanotech there will be little need to transfer matter. Trade in the distant future is likely to consist of mostly information. Design plans for new products, assembled on receipt. Patterns of uploaded consciousness of intrepid travellers. Gossip and news. But with communication delays to Alpha Centauri of the order of millions of subjective years two-way exchanges are difficult to imagine – even when we are enjoying unlimited life spans.

[Image credit: TheMarginal]

Communication and exploration would be, essentially, a one-way process. If you had a yen to travel to the Alpha Centauri you could. Squirt your encoded engrams down an interstellar modem and arrive decode at Alpha. Assuming the receiving station hasn’t shut in the intervening millions of years of subjective cultural change. You could leave a copy behind as redundancy or if you wanted to explore both regions, but I suspect many of us will not find this completely satisfactory. The speed of light barrier would limit us and cramp our style us much more than it does at present.

A wormhole could be constructed, by confining exotic matter to narrow regions to form the edges of three-dimensional space like a cube. The faces of the cube would resemble mirrors, except that the image is of the view from the other end of the wormhole. Although there is only one cube of material, it appears at two locations to the external observer. The cube links two ‘ends’ of a wormhole together. A traveller, avoiding the edges and crossing through a face of one of the cubes, experiences no stresses and emerges from the corresponding face of the other cube. The cube has no interior but merely facilitates passage from ‘one’ cube to the ‘other’.

The exotic nature of the edge material requires negative energy density and tension/pressure. But the laws of physics do not forbid such materials. The energy density of the vacuum may be negative, as is the Casimir field between two narrow conductors. Negative pressure fields, according to standard astrophysics, drove the expansion of the universe during its ‘inflationary’ phase. Cosmic string (another astrophysical speculation) has negative tension. The mass of negative energy the wormhole needs is just the amount to form a black hole if it were positive, normal energy. A traversable wormhole can be thought of as the negative energy counterpart to a black hole, and so justifies the appellation ‘white’ hole. The amount of negative energy required for a traversable wormhole scales with the linear dimensions of the wormhole mouth. A one meter cube entrance requires a negative mass of roughly 10^27 kg.

Wormholes can be regarded as communication channels with enormous bandwidth. The wormhole will collapse when the amount of mass passing through it approaches the same order as the amount of negative mass confined to its edges. According to some scientists information has a minimum energy of  kTlog2 associated with it. For 1- meter radius cube this implies a potential bandwidth of over 10^60 bits/sec. Even very small nano-scale wormholes have bandwidths of the order > 10^50 bits/sec. This suggests it will usually be more economic to squirt the design of an object down a channel rather than the object itself.

Construction of such cubes is, of course, far, far beyond our present day abilities. With AIs and nanotech combined we expect the limits on intelligences to be governed by physics, not biology. Our brains’ processing capacity lies somewhere between 10^15 – 10^18 bit/sec. A comparably sized nanoelectronic brain would have power of 10^32 – 10^36 bit/sec. Assuming a factor of million is lost for the speedup still leaves 8 – 12 orders of magnitude expansion in the complexity, or depth of thought, of our brains as we switch from biology to nanotechnology. So we should not assume construction and manipulation of the materials required will long remain beyond the grasp of future civilisations, populated by such super-intelligences. The remainder of the article will assume the mass production of wormholes is economically achievable. Wormholes enable travel from one mouth to the other. To travel to distant parts of the universe one wormhole end stays at home and the other is carted away, at sublight velocities, to the destination.

Problems begin when the distant wormhole end turns about and returns home. According to the twin paradox the traveller returns aged less than the stay-at-home twin (their clocks are no longer in step). Travelling through the wormhole from the stay-at-home end to the go- away-and-come-back end transports you forward in time. Travelling in the reverse direction transports you back in time. Wormholes allow time travel. This conclusion was realised soon after the first articles on traversable wormholes were published. Depending on your view of the plausibility of time travel this is either, if you believe time travel possible, very exciting or, if you scoff at time travel, proof that traversable wormhole can’t exist. No general consensus emerged in the pages of various physics journals as the subject was batted back and forth. Elaborate and very interesting papers reconciled time travel with quantum theory, whilst others (like Hawking ) proposed a Chronological Protection Conjecture[CPC], which says the Universe Shalt Not Allow Time Travel.

A space probe with a wormhole could be powered from base. The fuel is uploaded through the wormhole from base to the in-flight ship. There would an energetically very strong potential hill for the fuel to climb to reach the ship. For a ship moving at relativistic speeds most of the energy of the fuel would be lost in the climb. This suggests that the ship would be stripped to the bare minimum, just modern rockets are. [ref: Time Travel Research Center]

The probe remains in contact with the home base, throughout the trip. As a drop point approaches another wormhole plus deceleration rig would be loaded through to detach itself from the mother craft. Deceleration would likely be quicker and less expensive than acceleration because the daughter craft could brake itself against interstellar/galactic gas, dust and magnetic fields. For energy cost reasons it is not likely that transfer of colonists would begin until deceleration is complete.

The colonists transfer through this hole, whilst the main probe continues its outward voyage. One of the first activities of colonists would be to secure the connections with home by increasing the wormhole capacity and numbers. Transport of manufacturing plants, more wormholes etc would continue until local nanotech factories become locally more competitive than transport of finished product via wormholes. After this point the wormholes would be increasingly used for communications rather than materials transport.

An analogy with the cloud chamber spring to mind here. Charged particles are tracked through cloud chambers. Each particle is invisible, but its presence is deduced from the trail of growing droplets left behind. Similarly the space probe is all but invisible, lost in the immensity of the dark of space. The burgeoning colonies left behind mark its passage. The colonies send out further wormholes probes. From a distance the whole affair would resemble a growing 3-D snowflake.

Road, sea and air routes let commerce draw on the whole earth’s resources and the telecommunications highways keep us in contact with each other. Wormhole connections laid down by space probes enable a space-faring civilisation to remain a single economic entity, with all the social and material benefits that follow. Wormholes connections enable the region colonised to stay interconnected as civilisation expands through the universe.

Wormholes do have one major trick up their sleeves. We have seen that wormholes don’t permit time travel. But they do exhibit some very strange effects. Consider a colonist stepping through the home wormhole to transfer to the landing ship. Ship time and home time are running in synchronisation. If I wait 15 years at home after launch before stepping through then I appear at the travelling end at the point when the probe passes Andromeda. In crossing 2,250,000 light years of conventional space I travel 2,250,015 million years into the future. So, Wormholes could help us in colonization of galaxy and universe and may be possible we could colonize parallel universes[assuming they exists].

Teleportation: Impossible?

Ever since its invention in the 1920s, quantum physics has given rise to countless discussions about its meaning and about how to interpret the theory correctly. These discussions focus on issues like the Einstein-Podolsky-Rosen paradox, quantum non-locality and the role of measurement in quantum physics. In recent years, however, research into the very foundations of quantum mechanics has also led to a new field – quantum information technology. The use of quantum physics could revolutionize the way we communicate and process information.

The important new observation is that information is not independent of the physical laws used to store and processes it (see Landauer in further reading). Although modern computers rely on quantum mechanics to operate, the information itself is still encoded classically. A new approach is to treat information as a quantum concept and to ask what new insights can be gained by encoding this information in individual quantum systems. In other words, what happens when both the transmission and processing of information are governed by quantum laws?

The elementary quantity of information is the bit, which can take on one of two values – usually “0” and “1”. Therefore, any physical realization of a bit needs a system with two well defined states, for example a switch where off represents “0” and on represents “1”. A bit can also be represented by, for example, a certain voltage level in a logical circuit, a pit in a compact disc, a pulse of light in a glass fibre or the magnetization on a magnetic tape. In classical systems it is desirable to have the two states separated by a large energy barrier so that the value of the bit cannot change spontaneously.

Two-state systems are also used to encode information in quantum systems and it is traditional to call the two quantum states 0ñ and 1ñ. The really novel feature of quantum information technology is that a quantum system can be in a superposition of different states. In a sense, the quantum bit can be in both the 0ñ state and the 1ñ state at the same time. This new feature has no parallel in classical information theory and in 1995 Ben Schuhmacher of Kenyon College in the US coined the word “qubit” to describe a quantum bit.

A well known example of quantum superposition is the double-slit experiment in which a beam of particles passes through a double slit and forms a wave-like interference pattern on a screen on the far side. The essential feature of quantum interference is that an interference pattern can be formed when there is only one particle in the apparatus at any one time. A necessary condition for quantum interference is that the experiment must be performed in such a way that there is no way of knowing, not even in principle, which of the two slits the particle passed through on its way to the screen.

Single-particle quantum interference

Quantum interference can be explained by saying that the particle is in a superposition of the two experimental paths: passage through the upper slitñ and passage through the lower slitñ. Similarly a quantum bit can be in a superposition of 0ñ and 1ñ. Experiments in quantum information processing tend to use interferometers rather than double slits but the principle is the same (see right). So far single-particle quantum interference has been observed with photons, electrons, neutrons and atoms.

Beyond the bit

Any quantum mechanical system can be used as a qubit providing that it is possible to define one of its states as 0ñ and another as 1ñ. From a practical point of view it is useful to have states that are clearly distinguishable. Furthermore, it is desirable to have states that have reasonably long lifetimes (on the scale of the experiment) so that the quantum information is not lost to the environment through decoherence. Photons, electrons, atoms, quantum dots and so on can all be used as qubits. It is also possible to use both internal states, such as the energy levels in an atom, and external states, such as the direction of propagation of a particle, as qubits (see table).

The fact that quantum uncertainty comes into play in quantum information might seem to imply a loss of information. However, superposition is actually an asset, as can be seen when we consider systems of more than one qubit. What happens if we try to encode two bits of information onto two quantum particles? The straightforward approach would be to code one bit of information onto each qubit separately. This leads to four possibilities – 0ñ1 0ñ2 0ñ1 1ñ2 1ñ1 0ñ2 and 1ñ1 1ñ2 – where 0ñ1 1ñ2 describes the situation where the first qubit has the value “0” and second qubit has the value “1”, and so on. This approach corresponds exactly to a classical coding scheme in which these four possibilities would represent “00”, “01”, “10” and “11”.

However, quantum mechanics offers a completely different way of encoding information onto two qubits. In principle it is possible to construct any superposition of the four states described above. A widely used choice of superpositions is the so-called Bell states. A key feature of these states is that they are “entangled” (see box). Entanglement describes correlations between quantum systems that are much stronger than any classical correlations.

As in classical coding, four different possibilities can be represented by the four Bell states, so the total amount of information that can be encoded onto the two qubits is still two bits. But now the information is encoded in such a way that neither of the two qubits carries any well defined information on its own: all of the information is encoded in their joint properties. Such entanglement is one of the really counterintuitive features of quantum mechanics and leads to most of the paradoxes and other mysteries of quantum mechanics (seeBell’s inequality and quantum non-locality).

It is evident that if we wish to encode more bits onto quantum systems, we have to use more qubits. This results in entanglements in higher dimensions, for example the so-called Greenberger-Horne-Zeilinger (GHZ) states, which are entangled superpositions of three qubits (see further reading). In the state 1/2( 000ñ + 111ñ), for instance, all three qubits are either “0” or “1” but none of the qubits has a well defined value on its own. Measurement of any one qubit will immediately result in the other two qubits attaining the same value.

Although it was shown that GHZ states lead to violent contradictions between a local realistic view of the world and quantum mechanics, it recently turned out that such states are significant in many quantum-information and quantum-computation schemes. For example, if we consider 000 and 111 to be the binary representations of “0” and “7”, respectively, the GHZ state simply represents the coherent superposition (1/Ö2)( “0”ñ + “7”ñ). If a linear quantum computer has such a state as its input, it will process the superposition such that its output will be the superposition of the results for each input. This is what leads to the potentially massive parallelism of quantum computers.

It is evident that the basis chosen for encoding the quantum information, and the states chosen to represent 0ñ and 1ñ, are both arbitrary. For example, let us assume that we have chosen polarization measured in a given direction as our basis, and that we have agreed to identify the horizontal polarization of a photon with “0” and its vertical polarization with “1”. However, we could equally well rotate the plane in which we measure the polarization by 45º. The states in this new “conjugate” basis, 0´ñ and 1´ñ, are related to the previous states by a 45º rotation in Hilbert space

ñ = (1/Ö2)( 0ñ + 1ñ)

ñ = (1/Ö2)( 0ñ – 1ñ)

This rotation is known in information science as a Hadamard transformation. When spin is used to encode information in an experiment we can change the basis by a simple polarization rotation; when the directions of propagation are used, a beam splitter will suffice. It is important to note that conjugate bases cannot be used at the same time in an experiment, although the possibility of switching between various bases during an experiment – most notably between conjugate bases – is the foundation of the single-photon method of quantum cryptography.

Quantum dense coding

Entangled states permit a completely new way of encoding information, as first suggested by Charles Bennett of the IBM Research Division in Yorktown Heights, New York, and Stephen Wiesner of Brookline, Massachusetts, in 1992. Consider the four Bell states: it is clear that one can switch from any one of the four states to any other one by simply performing an operation on just one of the two qubits. For example, one can switch from Y+ñ to Yñ by simply applying a phase shift to the second qubit when it is “0” (i.e. 0ñ ® – 0ñ, 1ñ ® 1ñ). The state f+ñ can be obtained by “flipping” the second qubit, while the state fñ can be obtained by the combination of a phase shift and flipping.

All three of the operations are unitary and they do not change the total probability of finding the system in the states 0ñ and 1ñ. In working with Bell states it is common to refer to four unitary operations: the phase shift, the bit flip, the combined phase-shift/bit-flip, and the identity operator, which does not change the state on which it operates. All four operations are relatively easy to perform in experiments with photons, atoms and ions.

Quantum dense coding

To understand what this means, imagine that Bob wants to send some information to Alice. (The characters in quantum information technology are always called Alice and Bob.) Entanglement means that, in theory, Bob can send two bits of information to Alice using just one photon, providing that Alice has access to both qubits and is able to determine which of the four Bell states they are in (see left).

This scheme has been put into practice by my group in Innsbruck using polarization-entangled photons (see Mattle et al . in further reading). The experiment relies on the process of spontaneous parametric down-conversion in a crystal to produce entangled states of very high quality and intensity. The nonlinear properties of the crystal convert a single ultraviolet photon into a pair of infrared photons with entangled polarizations.


How to entangle photons

The experiment used quarter- and half-wave polarization plates (plates that shift the phase between the two polarization states of a photon by l/4 and l/2, respectively) to make the unitary transformations between the Bell states. In fact it is possible to identify only the Y+ñ and Yñ states uniquely using linear elements such as wave plates and mirrors. However, by being able to discriminate between three different possibilities – Y+ñYñ and f±ñ – Bob could send one “trit” of information with just one photon, even though the photon had only two distinguishable polarization states. It has been shown that a nonlinear quantum gate will be needed to distinguish between all four Bell states. Such a gate would depend on a nonlinear interaction between the two photons and various theoretical and experimental groups are working on this challenge.

Quantum teleportation

Quantum dense coding was the first experimental demonstration of the basic concepts of quantum communication. An even more interesting example is quantum teleportation.

Suppose Alice has an object that she wants Bob to have. Besides sending the object itself, she could, at least in classical physics, scan all of the information contained in the object and transmit that information to Bob who, with suitable technology, could then reconstitute the object. Unfortunately, such a strategy is not possible because quantum mechanics prohibits complete knowledge of the state of any object.

There is, fortunately, another strategy that will work. What we have to do is to guarantee that Bob’s object has the same properties as Alice’s original. And most importantly, we do not need to know the properties of the original. In 1993 Bennett and co-workers in Canada, France, Israel and the US showed that quantum entanglement provides a natural solution for the problem (see further reading).

Teleportation theory

In this scheme Alice wants to teleport an unknown quantum state  to Bob (see left). They both agree to share an entangled pair of qubits, known as the ancillary pair. Alice then performs a joint Bell-state measurement on the teleportee (the photon she wants to teleport) and one of the ancillary photons, and randomly obtains one of the four possible Bell results. This measurement projects the other ancillary photon into a quantum state uniquely related to the original. Alice then transmits the result of her measurement to Bob classically, and he performs one of the four unitary operations to obtain the original state and complete the teleportation.

It is essential to understand that the Bell-state measurement performed by Alice projects the teleportee qubit and her ancillary photon into a state that does not contain any information about the initial state of the teleportee. In fact, the measurement projects the two particles into a state where only relative information between the two qubits is defined and known. No information whatsoever is revealed about . Similarly, the initial preparation of the ancillary photons in an entangled state provides only a statement of their relative properties. However, there is a very clear relation between the ancillary photon sent to Bob and the teleportee photon. In fact, Bob’s photon is in a state that is related to Alice’s original photon by a simple unitary transformation.

Consider a simple case. If Alice’s Bell-state measurement results in exactly the same state as that used to prepare the ancillary photons (which will happen one time in four), Bob’s ancillary photon immediately turns into the same state as . Since Bob has to do nothing to his photon to obtain , it might seem as if information has been transferred instantly – which would violate special relativity. However, although Bob’s photon does collapse into the state  when Alice makes her measurement, Bob does not know that he has to do nothing until Alice tells him. And since Alice’s message can only arrive at the speed of light, relativity remains intact.

In the other three possible cases, Bob has to perform a unitary operation on his particle to obtain the original state, . It is important to note, however, that this operation does not depend at all on any properties of .


Quantum statistics

The main challenge in our experiment was to perform a Bell-state measurement on two particles that were generated independent of each other (see Bouwmeester et al. in further reading). Since a Bell-state measurement probes the collective or relative properties of two quantum particles, it is essential that the particles “forget” any information about where they were generated. To achieve this we must perform the experiment in such a way that we are unable, even in principle, to gain any path information. We do this by directing the two photons – the teleportee and Alice’s ancillary – through a semitransparent beam splitter from opposite sides (see right). We then ask a simple question: if the two particles are incident at the same time, how will they be distributed between the two output directions?

Since photons were used in the experiment, one might naively have expected that both photons would emerge in the same output beam. This feature, called “bunching”, is well known for bosons (particles with integer spin such as photons) and was demonstrated with optical beam splitters for the first time in 1987 by Leonard Mandel’s group at the University of Rochester in the US. Surprisingly, perhaps, bunching only happens for three of the Bell states. In contrast, for the Yñ state , the photons always leave in different beams. In other words, the photons “anti-bunch” and behave as if they were fermions. This is a direct consequence of interference.

This means that for the Yñ state we have no way of knowing which way the photons reached the detectors: both photons could have been transmitted by the beam splitter, or both could have been reflected. By adding various polarizers it is also possible to identify photons in the Y+ñ state. As with dense coding, however, quantum gates will be needed to make the experiment work with the f+ñ and fñ states.


Teleportation experiment

In the actual experiment the teleportee photon was also made using parametric down-conversion (see left). This provides an additional photon that can be used as a trigger informing us that the teleportee photon is “ready”. The experiment itself involved preparing the teleportee photon in various different polarization states – horizontal, vertical, +45º, -45º and right-hand circular – and proving that Bob’s photon actually acquired the state into which the teleportee photon was prepared. The teleportation distance was about 1 metre. Since the experiment was set up to identify only the Yñ state, the maximum success rate for teleportation was, in theory, 25%, and the measured success rate was much lower.

A related experiment was recently performed at the University of Rome La Sapienza (see Boschi et al . in further reading) using only one entangled pair of photons. In this experiment Alice was able to prepare Bob’s particle at a distance, again to within an unitary transformation. By essentially performing a Bell-state measurement on two properties of the same photon, the Rome group was able to distinguish between all four Bell states simultaneously.

The entanglement of photons over distances as great as 10 km has now been demonstrated at the University of Geneva, so teleportation is expected to work over similar distances. The teleportation of atoms should also be possible following a recent experiment at the Ecole Normale Supérieure in Paris that demonstrated that pairs of rubidium atoms could be entangled over distances of centimetres (see Hagley et al . in further reading).

Entanglement swapping

As mentioned above, an important feature is that teleportation provides no information whatsoever about the state being teleported. This means that any quantum state can be teleported. In fact, the quantum state does not have to be well defined; indeed, it could even be entangled with another photon. This means that a Bell-state measurement of two of the photons – one each from two pairs of entangled photons – results in the remaining two photons becoming entangled, even though they have never interacted with each other in the past (see right). Alternatively, one can interpret this “entanglement swapping” as the teleportation of a completely undefined quantum state (see Bose et al. in further reading). In a recent experiment in Innsbruck, we have shown that the other two photons from the two pairs are clearly entangled.

Quantum outlooks

We conclude by noting that, amazingly, the conceptual puzzles posed by quantum mechanics – and discussed for more than sixty years – have recently led to completely novel ideas that might even result in applications. These applications could include quantum communication, cryptography and computation. In return, these technological considerations lead to a better intuitive understanding of basic issues such as entanglement and the meaning of information on the quantum level. The whole field of quantum information technology is a classic example of basic physics and potential applications working hand in hand.

How to entangle photons
When an ultraviolet laser beam strikes a crystal of beta barium borate, a material with nonlinear optical properties, there is a small probability that one of the photons will spontaneously decay into a pair of photons with longer wavelengths (to conserve energy). The photons are emitted in two cones and propagate in directions symmetric to the direction of the original UV photon (to conserve momentum). In so-called type II parametric down-conversion, one of the photons is polarized horizontally and the other is polarized vertically. It is possible to arrange the experiment so that the cones overlap (see photograph). In this geometry the photons carry no individual polarizations  all we know is that the polarizations are different. This is an entangled state. (P G Kwiat et al. 1995 Phys. Rev. Lett75 4337)
Quantum dense coding
Bob can send two bits of information to Alice with a single photon if they share a pair of entangled photons. To begin, one photon each is sent to Alice and Bob. The photons are in one of the four Bell states. Bob then performs either one of the three unitary transformations on his photon, transferring the pair into another Bell state, or simply does nothing  the fourth option. He then sends the photon to Alice who measures the state of the pair. Since there are four possible outcomes of this measurement, Bob has sent twice as much information as can be sent classically with a two-state particle.
Quantum statistics
When two particles are incident symmetrically on a 50/50 beam splitter it is possible for both to emerge in either the same beam (left) or in different beams (right). In general, bosons (e.g. photons) emerge in the same beam, while fermions (e.g. electrons) emerge in different beams. The situation is more complex for entangled states, however, and two photons in the Bell state |Yñemerge in different beams. Therefore, if detectors placed in the two outward directions register photons at the same time, the experimenter knows that they were in a |Yñ state. Moreover, because we do not know the paths followed by the photons, they remained entangled.
Single-particle quantum interference
Interference fringes can be observed in a two-path interferometer if there is no way of knowing, not even in principle, which path the particle takes. In a Mach Zehnder interferometer a quantum particle strikes a beam splitter and has a 50/50 chance of being transmitted or reflected. Mirrors reflect both paths so that they meet at a second 50/50 beam splitter, and the numbers of particles transmitted/reflected by this beam splitter are counted. If no information about the path is available, the particle is in a superposition of the upper and lower paths. To observe interference one customarily varies the length of one of the paths (e.g. with a variable wave plate) and counts single clicks at the detectors as a function of this phase.
Teleportation theory
The scheme of Bennett et al. Alice wishes to teleport an unknown quantum state | (the “teleportee”) to Bob. They agree to share an entangled pair of “ancillary” photons. Alice then performs a Bell-state measurement on the teleportee and her ancillary photon, and obtains one of the four possible Bell results. This measurement also projects Bob’s ancillary photon into a well defined quantum state. Alice then transmits her result to Bob, who performs one of four unitary operations to obtain the original state.
Teleportation experiment
In the experiment a pulse from a mode-locked Ti:sapphire laser (not shown) is frequency doubled, and the resulting UV pulse is used to create the entangled pair of “ancillary” photons in a nonlinear crystal. The UV pulse is then reflected back through the crystal to produce a second pair of photons: one is used as the teleportee while the other acts as a “trigger”. Polarizers are used to prepare the teleportee photon in a well defined state, while various filters ensure that no path information is available about Alice’s photons. Coincident photons detections at f1 and f2 project the photons onto a |Yñ state (in which they have different polarizations). And since Alice’s ancillary and Bob’s photon are also entangled, this detection collapses Bob’s photon into an identical replica of the original.

[resource: Time Travel Research Center]

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