Thrice Upon a Time
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"The world gets tinier," Elizabeth agreed. "Anyway, where was I? To cut a long story short, we ended up by deriving a set of mathematical expressions that interrelated entropy functions, quantum energy-states, and space-time coordinates of quantum events. In particular, certain variables that could be interpreted as time and energy turned out to be covariant."

"You mean there was some kind of equivalence relationship?" Lee asked, sounding surprised.

"Not quite. But you could almost think of it that way It meant that the universe could be represented by an ensemble of events, each characterized by a set of energy states and space-time numbers; nothing more. And in such a representation of the universe, conservation of mass-energy did not hold; it was replaced by a conservation of the product of that quantity with space-time. It was possible to transform one universe into another in which either quantity varied inversely with the other. If you made all the spatial variables constant, the space-time functions reduced to pure time; so you could transform energy to time or vice versa. We had no idea what that meant, but it was fun playing games with the equations."

"I've never heard of anything like that," Lee said. "They don t seem similar in any respect at all. There just isn't anything in common."

"That was why I said it wasn't really correct to call it an equivalence relationship," Elizabeth said. "What it seemed to say was that energy could be extracted from the universe, which is where conventional conservation breaks down, and injected into another version of that universe in which the time coordinates of all the events were shifted by some amount. The more energy you transformed, the greater the time shift would be." She looked around the table and shook her head in wonder. "If that was interpreted as taking place within the same universe, it seemed to say that energy could be transferred through time. We couldn't see any physical significance in it and dismissed the whole thing as a theoretical curiosity like tachyons and negative mass. And that s what I've always believed until I saw the machine downstairs."

"Elizabeth showed me some of the mathematics a while ago," Charles commented. "I realized then that some of the expressions could be identified with parts of my own work. That was why I thought she'd be rather interested in what we re doing."

"Rather interested!" Elizabeth echoed. "Charles, that must be the biggest understatement to date in this century. I'm overwhelmed, fascinated. . . completely hooked, to use our guests' parlance. In fact I'm even presumptuous enough to assume that I m part of the team now. I am, aren't I, Charles? You wouldn't keep me in the dark about what happens next now that you've shown me this much. You wouldn't dare."

"Och, you don t have to tell me that," Charles replied, raising his eyebrows. "It would be more than my life s worth and I know it." He stopped eating and placed his knife and fork down. His expression at once became more serious. "Of course you re part of the team now, Liz. I m certain you could be a big help in making sense out of this whole thing. I m assuming we'll be seeing a lot more of you down here now, whenever you can find some free time."

"Well, I m glad we see eye to eye on that, Charlie Ross. You d have been in trouble if you d said anything else." Elizabeth paused to let her mood adjust to Charles's tone, then went on, "Very well, where do we go from here? What are your thoughts, Charles? Don t tell me you haven t been turning a few speculations over in your head in the last week."

Charles took a sip from his wine glass and nodded as if he had been waiting for the question. The others watched him expectantly. "We must conclude that past and present versions of the universe in which we live exist and are equally real," Charles told them. "We thus have a continuum of some kind. I think we re all agreed that it can't be of the popular infinitely branching, parallel variety; that would introduce too many impossible complications. In any case, it isn't supported by the data we've seen." He looked around to invite comment, but the others just nodded silently. "Neither can it be of the simple serial variety that we considered initially; in such a model it would be impossible to affect the present by manipulating a past, and again our results seem to indicate that this is not the case. The only model I can think of that could be consistent with what we've seen is a more complex serial one in which altering the events in a past universe does affect not only the future of that particular universe as it evolves in time, but also the presents of all the other universes that lie ahead of it. In other words there is some mechanism of causal connection through the continuum that the simple serial model doesn't take account of."

"You mean like with the jar," Lee said. "That one message changed what happened in all the universes involved, not just in the one universe where the message was received."

"Precisely that," Charles confirmed. "To be anywhere near the reality at all, the model will have to possess a mechanism that explains such evident facts."

"Any ideas?" Cartland asked.

I think maybe I have," Charles replied. "Everything we have discovered so far seems to add up to two things: First, the universe that we see around us and form part of is simply one of many, equally real universes that appear to be strung sequentially along a single timeline; second, events that happen in this universe affect not only its future, but the situations in all the other universes that lie ahead of it. That, of course, suggests a continuity throughout the system; the future universes ahead of us form a progression of states that are evolving from the present state. We need to ask ourselves what the mechanism is that provides that continuity. That same mechanism will turn out to be, unless I m very much mistaken, the same mechanism that enables events in one universe to alter what happens in another. Obviously we re talking about a causal influence that must be propagated by some means."

"Agreed, but I don t think you'll find you have to look very far," Cartland said with a shrug. "The continuity follows from the fact that objects don t suddenly just appear and vanish; they endure in time. So a universe an hour, say, ahead of this one will contain the same objects. They provide the continuity."

"Objects?" Charles repeated in a mildly challenging tone. "A candle, such as the one on the table there? A mayfly? A cigarette? They'll endure in time?"

"Oh, all right," Cartland conceded. "I used the wrong word. Molecules then. Atoms, if you like."

"The candle, the mayfly, and the cigarette are breaking down molecules all the time," Charles pointed out. "And they all contain carbon fourteen; atoms come apart too."

"Oh, you know what I mean, Charles," Cartland said, sounding a little surprised. "Protons, neutrons, and electrons if you like. Or quarks and photons whatever you'll accept as the basic mass-energy quanta. They don t change."

"They don t," Charles agreed at last. "But they do rearrange. Bundles of them may come together and remain attached for a while to form a tree, and then fall apart again and disperse when the tree dies and decays. But as you say, Ted, the basic entities endure. They rearrange into different patterns to produce the changes that we call time, and they provide the continuity that enables one universe to evolve from another."

"But you said all the universes were equally real," Elizabeth said, looking slightly puzzled. "How can the same quarks and things be in all of them at once?" She thought for a moment, and her expression changed suddenly. "Oh, wait a minute. I think I can see what you re getting at. You're saying that the continuity between universes in the time dimension is just as physically real as the spatial continuity inside a universe. Every particle has a real extension in time, just as tangible as its extension in space. Right?"

"Exactly!" Charles declared. "So if you alter the arrangement of particles in one universe, you alter the arrangement of them in all subsequent universes as well by virtue of that continuity." He sat back, sipping his wine, to allow time for the others to reflect on what had been said. Eventually Cartland shook his head and frowned.

"Sorry, not quite with you," he confessed. "Are you saying that the whole universe is just a part of some bigger continuum, and that things like particles somehow extend right through the whole thing? The objects we see are only really parts of what they are completely?"

"Yes," Charles replied. He pointed toward the center of the table. "That candle has burned about a quarter of the way down, but in the universe that s an hour or so behind us, it's still intact; in a universe that's a few hours ahead, it probably doesn't exist as such at all. The whole candle is the sum of all those, and all the points between. But all we see is the part of it that exists in the particular universe that we happen to be part of. The real candle is all of them put together."

"I hear what you re saying," Cartland murmured slowly. "It s a bit difficult to visualize though."

"Try thinking of a two-dimensional analogy," Murdoch suggested. "Imagine that the universe is flat, and that everything it contains is flat. It's a plane, okay? Now form a solid continuum by stacking an infinite number of zero-thickness planes like that together, like the pages of an infinitely thick book. Every page is a universe. The basic particles are ink particles, and they form character shapes, that is, objects. But unlike in an ordinary book, where all the pages are different, the ink particles continue through like 'threads, so the patterns they form can only change gradually, not abruptly. Also all the pages move together in one direction along the threads as they slide down the entropy slope that Elizabeth talked about earlier. So anybody inside one of those universes, us for example, will see the patterns changing sequentially. That's what he calls time."

"Ah Cartland nodded and pulled his moustache. "Yes ... now I see what you re driving at." Morna and Robert entered at that point to clear the dishes and prepare the table for the next course. The conversation reverted to small-talk for a while, mainly among Murdoch, Charles, and Lee. Cartland picked up Murdoch s sketch and examined it silently while Elizabeth stared thoughtfully at the center of the table. Cartland looked up just as Morna was about to leave the room behind Robert. "Compliments to Mrs. Paisley," he called out. "Tell her the duck was splendid." Morna nodded, smiled, and closed the door.

"Okay," Lee said. "We've explained how they're all real and how they're connected. So how about events in one universe affecting events in universes ahead of it? I can see how causal influences can move forward in time and affect the future. That's everyday experience. But now you sound as if you're saying that causes can run on ahead and get into other universes that lie in front. The patterns that exist in all the future universes can get rearranged into something different."

"Yes," Murdoch said simply.

"Wait a minute." Cartland broke in, raising a hand. "What are we saying now? Is this how the universe in which the jar was broken managed to get 'erased,' as Charles put it?"

"Yes," Murdoch said again. "A universe existed in which the objects and inhabitants formed by the thread patterns included a broken jar. It broke because of causes that lay behind it, in the past. Then a signal was sent back that eliminated those causes. The pattern from that point onward was re-formed into a new one representing a different sequence of events."

"But what about the people in the lab who did break the jar?" Cartland demanded. Where are they now? Do you mean that these threads . . . 'jumped' somehow into a new arrangement when the signal was received? The people who broke the jar were . . . 'reset' into us, who didn't?"

"That's just what I mean," Murdoch said, nodding emphatically. Everything that formed any part of the original pattern was reset. Hence our memories and records are consistent with the new pattern that now exists. On the timeline as it exists now, no jar was ever broken. Yes, it's preposterous, but it accounts for the facts."

"It accounts for a lot of other things we've seen too," Charles added after a while, speaking slowly and seriously. "It would explain, for example, how we could receive a signal and then fail to send it later on. A universe existed that contained in a tiny part of itself a couple of inhabitants who had no record of any signal having been received at some point in the past. They sent a signal to that point. In doing so, they rearranged the threads that constituted themselves, their memories, and their instruments into new patterns that did include memories and records of the event. The fact that they failed to send the signal later wouldn't matter at all, since the people who did send the signal would already have ceased to exist as such anyhow."

"And here s a sobering thought," Murdoch added. "The same mechanism explains why we always see records of other selves in the future who tried aiming signals back at points where they d never received any, but we never get around to trying the same thing ourselves: If we did, we'd join the list of the ones who had been reset."

"Good God!" Cartland exclaimed. "That means we've already been through it every one of us here at this table."

"Seems that way," Murdoch agreed. He made an effort to keep his voice nonchalant as he spoke, just to enjoy the expression on Cartland s face.

Cartland s eyes widened, and his moustache seemed suddenly to bristle of its own accord. His throat convulsed soundlessly for a moment while he struggled to regain his voice. "Good grief," he managed eventually.

"This is all very hypothetical at this stage," Charles told them. "The first thing on the priority list is to see if we can devise some way of trying to test the theory more thoroughly."

Lee had been finishing his dessert and listening. When a short silence descended, he placed his spoon in his empty dish, looked up, and said, "You re saying it s like an old newspaper picture that s made up out of dots. The dots are really the ends of a bundle of threads that has been cut across. The plane of the cut is a universe."

"That s a good enough analogy," Murdoch agreed.

Lee nodded. "Fine. Now the threads are suddenly rearranged. But those cross sections are material particles. To rearrange their pattern, they have to move perpendicular to the time axis. That means they have to move through space in all of the plane universes they pass through. How could they do that instantaneously?"

"We've never said anything about the process being instantaneous," Charles pointed out. "There could be a finite propagation delay along the continuum that we haven't any data on yet that would enable us to measure it. Alternatively, the basic entities that constitute the threads may be more fundamental than quarks or photons. If a quark comes apart into something simpler, the attributes that define mass may disappear in the process. Hence you could find that it s possible to decompose mass at one point into components that themselves do not possess mass individually but only when they're combined together, transport those components to some other point without a relativistic restriction, and reconstitute the property of mass there. But that takes us right out on the fringe of the whole business, and there's a lot of work to be done there yet. In fact this is something I'd like to talk to Elizabeth about while she's here." He turned toward her as he spoke. "You haven t been saying very much for a while, Lizzie. What's your opinion?"

Elizabeth had been listening intently throughout with her fingers pointed together in front of her mouth and her dessert standing untouched before her. "Opinion on what, Charles?" she asked. "Your last point or the whole business?"

"The whole 'reset model that we've been discussing," Charles replied.

Elizabeth brought her arms down to her sides and paused for a moment to collect her words. "I think you re on the right track," she said at last. "As you say that explanation does account for the observed facts, as extraordinary as it sounds, and for the time being at least I'd be completely at a loss to suggest even the beginnings of any alternative. However, there are two things that bother me about it as it stands.

"The first is that the model is static-at least if we forget for the moment about being able to send signals up and down the continuum. By that I mean that future events are predefined by the patterns that exist in the threads. The future is already determined but unknown, and is just waiting to be consciously experienced. There s no scope for human decision, free will, and chance. I don't like that. I believe that those things are real and important."

"I agree," Lee tossed in. "I can t buy that they re just illusions either."

"But I never said that," Charles protested. "Take the incident with the jar. That was something that had every appearance of chance about it, and the event was changed. That says to me very clearly that such things are not unalterably predetermined."

"I know," Elizabeth said. "But the model doesn't explain it. According to the model you described, that event was always written into the timeline until the signal was sent back to change it, which means that only a machine like yours can alter the thread pattern. So was the whole of human history and evolution before that simply a playing out of a fixed script? I can't believe that, Charles. The model has to show how such things as chance could operate before you built your machine, and at present it doesn't."

"I agree with you," Charles said at once. "And I've no answer to give. What's your second problem?"

"Maybe another way of saying the same thing," Elizabeth said. "The experiment with the jar, for example, seemed to indicate that the people in a particular universe did manage to alter their own past. But the model still doesn't explain that fully; it only half explains it."

"How s that?" Murdoch asked, looking surprised. "I thought we covered it okay."

Elizabeth shook her head. "Let's imagine somebody decides to change something in his past, in other words something he remembers," she said. "So he sends a signal back that resets the timeline and remains imprinted upon the fabric of the new timeline that it creates instead. Because of information contained in the signal, the something that was to be changed is changed, and the new somebody who is formed on that timeline perceives nothing that requires changing. Hence our original premise that he began by deciding to change something becomes untenable. So how and when did the signal ever come to be sent to begin with? Or to be a little more specific, how did the people who sent the signal about the jar manage not to receive the signal when they were at the time you were at when you received it? Either a signal was or was not received at that time. If it was, why didn't they receive it; if it wasn't, how did you?"

Murdoch swung his head round to look at Charles. Charles thought for a while and nodded slowly. "She s right," he murmured.

"In the model, causes and effects remain as we would normally define them," Elizabeth went on. "But instead of being simply related in sequence along a unidirectional timeline, they exist on a complicated loop that takes place in time. The loop makes the whole thing an impossible situation, at least it does if the loop is postulated as a permanent feature of the model, like the threads. It can't be always there, but the model doesn't explain how it can come and go.

"You mean the model needs to be dynamic," Cartland said.

Elizabeth nodded decisively. "Yes, dynamic." She picked up her spoon at last and looked at Charles before returning her attention to her meal. "As I said, I think you're on the right track. But we need to add something that will give free will and random influences a chance to operate something that injects an element of uncertainty into the whole process. The loops must be allowed to appear and disappear dynamically."

"Something like a quantum dynamics of space-time," Murdoch remarked.

"Yes, something very much like that," Elizabeth agreed. "We need to extend quantum uncertainty, or something very like it, throughout the whole continuum of universes. When the model includes that, I think it will be getting extremely close indeed."

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