“How… how old was I, do you think?”
Helias turned, and found the professor seated on the step next to him.
“Who can say? I don’t even know how old you are now…. Let’s say a dozen years older.”
“What would you say, was Nudeliev right when he said there was nobody on the other shuttle?”
The professor had the air of a frightened child who, faced with big questions and lacking the courage to find his own answers, was looking for comfort and confirmation from an adult. But Helias was too tired to accept that role. The only thing he was able to say was “You’re the expert….”
Then he handed the card to the professor.
“Part of it is here. You ought to be able to find the rest in the computer back there.”
On taking the card, the professor perked up and hurried off towards the lab. Now he had something that would help him find the answers he was looking for.
Helias got to his feet too. And slowly began to secure Petersen’s hands, though the man still showed no signs of coming to.
© Springer International Publishing AG 2017
Massimo VillataThe Dark Arrow of TimeScience and Fictionhttps://doi.org/10.1007/978-3-319-67486-5_18
18. Everything Had Ended Well
Massimo Villata1
(1)Osservatorio Astrofisico di Torino, INAF, Pino Torinese (TO), Italy
Massimo Villata
Email: [email protected]
Everything had ended well. Almost everything. At least as far as this present of theirs was concerned. The future, or their possible futures, was something they’d deal with when the time came.
In the meantime, the professor, who had copied everything copiable from Nudeliev’s computers, was passing his days picking through the information in those files, analyzing it all, with brief pauses for spartan meals, and holding his remaining appetite in check with dutiful trips to the gym, emerging sweaty but smiling, and thumbing his nose at the scales.
Helias had finally been reunited with his parents, to his great joy. But there was no trace of Kathia. Something, someone, had slipped through the net that had closed around Nudeliev’s secret project. And Kathia’s disappearance was part of this something.
All they could do was wait for Mattheus to recover completely. Perhaps, among the information he had collected while he was held captive, they would find the end of the tangled skein that, unraveled, would lead them to Kathia.
Helias’s parents were under considerable strain. On the one hand, there was the relief of regaining their freedom and the happiness of finding their son again; one the other, all the doubts about their future, since they still had very little idea of what to do with themselves. Whether to return to Earth or go to Alkenia as earthlings, or stay on Thaýma as Thaymites. Whatever they did, they would have felt lost, cut loose and rootless, without a past that could guide them in planning a future. But it was only a question of time, as Helias knew, they would soon find their way, a new way.
Helias, for his part, had no doubts. He knew where to go. To the only possible place. Where he would still be able to feel her presence.
And that evening, at dusk, seated on the rock surrounded by snowy mountains, it was as if he could see her emerge from the lake again, dripping and heedless of the cold, as if a warm sun still shone on those shores.
And for a moment, had the sensation of hearing her voice. But he couldn’t make out the words.
Helias lay back on the rock. And saw Nasymil, already sparkling in the sky.
Then he closed his eyes.
It was as if a hand had stroked his forehead.
Or maybe it was only the evening breeze, gently caressing his face.
Appendix: The Science Behind the Fiction
The concept of time travel has always fascinated scientists and writers, as well as philosophers and the lay public. There is an enormous literature about it, starting with ancient myths and legends, sacred Hindu and Buddhist texts, down to modern science fiction novels and movies.
From the scientific standpoint, whether time travel is possible is a question that has sparked a great deal of debate. Often the possibility is ruled out a priori, if only because of the logical and physical paradoxes that traveling in the past would entail. Of the various kinds of “time machine” that have been suggested, those that make use of general relativity concepts and space-time warps (at times together with quantum physics), like closed timelike curves and wormholes, are currently popular. Of the many studies in this field, mention should be made of the seminal paper by Morris, Thorne and Yurtsever. 1 Here, our idea of time travel is very different from those that are now in vogue, and relies on elements of classical and quantum relativistic physics and electrodynamics. Like any other time machine, it would be very difficult, if not indeed impossible, to actually construct. But it is a useful, instructive and intriguing thought experiment that enables us to probe the effective possibility of traveling in time, with all its contradictions and paradoxes. Among other things, our theoretical vision also permits “instantaneous” interplanetary trips, despite all the well-known difficulties—especially in terms of time and energy—that such trips could involve, and that science fiction writers have always struggled with, often inventing highly imaginative solutions. But let’s take one thing at a time, beginning… from the beginning.
Traveling in space means moving from one spatial position to another. Similarly, time travel hinges on the idea that we can do the same thing from one time period to another. Obviously, there are major differences. For example, moving in space takes a certain amount of time, from which we can deduce the speed of movement (space/time): the higher the speed, the less time will be taken. Time, though, flows on its own, independently of our will and our actions, unstoppable. We cannot stand still in time. Indeed, our existence is a continual trip in time, but a trip whose “speed” we cannot change. Or rather, we have nothing to compare it to, nothing we can use to gauge the “speed” at which we are moving through time. All we can say is that we are traveling in time at a rate of one second per second.
Actually, this is not entirely true. We know from special (and general) relativity that time does not flow in the same way in all reference frames. Because of the so-called “time dilation”, a clock will be slower if it is located in a reference frame that is moving relative to the one where we are observing. There, everything slows down. And so we can, in fact, compare the time passing there with the time that passes here, and say, for example, that time is running at half a second per second there, and that our twin there is aging more slowly than we are. Obviously, our twin can say the exact same thing about us, since the situation is perfectly symmetrical. This is the famous “twin paradox”, where each of the two twins should be younger than the other. The paradox can be resolved through general relativity, which deals not only with inertial reference frames but also with those affected by acceleration or subject to gravitational fields. Thus, if we want to really compare the age of the two twins after a certain period of time, we have to bring them into the same reference frame—the Earth, say, which is a quasi-inertial frame. One twin remained there, while the other left on a spaceship that accelerated at a very high speed, comparable to that of light. Then, with other velocity variations (slowing and reversing), he returned to his twin brother on Earth. The brother has aged thirty years, while only three have gone by for the astronaut—apparently because he underwent accelerations but the other didn’t. As general relativity tells us, acceleration and gravity are equivalent. In fact, time dilation can also take place in an intense gravitational field, as exists near a black hole. Like in the movie “Interstellar”, where the characters who approach a black hole for a few hours return to the spaceship to find that their companion has been waiting for them for more than twenty years…
And so, an astronaut can return to the starting point after experiencing a different flow of time, and find everything older than would normally be the case. In theory, he can �
��travel” as he likes in the future of the place he started from, but only thanks to the accelerations, gravitational or not, he undergoes.
But then, there’s nothing really very strange in all this. After all, the theory of relativity has given us over a century to get used to the idea that time can pass in different ways under different conditions, and so “trips” forward in time don’t frighten us. Trips backward in time, on the other hand, seem much more intriguing, with all their logical and physical paradoxes.
But again, we’ll take one step at a time, following the logical sequence used in this novel.
The question is: is there a limit speed, that can’t be exceeded, for a trip in space? Many people would answer: yes, certainly, it’s the speed of light! Right… But now we’ll change the question: what is the minimum time it takes to cover that distance? Some people would answer: the time taken by light! Wrong… It all depends on who measures the time taken and the space—the distance—covered.
Suppose we want to go to a planet 20 light-years away from Earth. At non-relativistic speeds, say, less than 1/20 of the speed of light (which from now on we’ll call c , as all physicists do, and which is around 299,800 km/s), it would take us more than 20 times the time it takes light, or in other words over 400 years. As we increase the speed, however, the relativistic effects of length contraction and time dilation begin to make themselves felt. For an astronaut traveling at extremely high speeds, near that of light (but which can’t be reached with today’s technologies), 0.995 c for example, the distance from Earth to the planet would be reduced by around a factor of 10, and he would thus take around 2 years to get to it. On Earth, we can calculate that the trip ought to take a little over 20 years. “Earth” years. So why do the two calculations give such wildly different results? Because time dilation means that time on the spaceship runs around 10 times more slowly than it does on Earth, and so the astronaut will reach the planet after only 2 of “his” years.
So what happens if we increase speed further, up to a limit tending (as mathematicians say) to c ? Well, that’s easy: all the distances tend to zero. And so the time taken by any trip also tends to zero. Seen from this impossible spaceship, any trip, even if it crosses half the Universe, goes by in a flash, an instant. And in fact we would “calculate” that the hands of the clock on board, during those billions of years that the trip lasts from our point of view, won’t even budge.
One thing is certain: a spaceship like this will never exist. But we know that there is something that can (and indeed must) travel at speed c : an electromagnetic wave in vacuum, or rather, its quantum correspondent, the photon, or any other hypothetical particle with null mass. The main difference between the photon and the impossible spaceship is that the latter, as speed increases, would continue to gain inertial mass (by the same factor as the time dilation), which tends to infinity as speed tends to c . That’s why this spaceship is also theoretically impossible. The massless photon, by contrast, must travel at speed c , whatever the reference frame. It’s compelled to do so. And so it’s usually said that there’s no such thing as a reference frame where the photon is at rest. True or not, such a “system” certainly wouldn’t have much physical meaning: in addition to hosting a massless particle at rest, all distances would be reduced to zero—no space, in other words. We know, moreover, that the photon’s “proper time” is null, just like its mass—and so no time. (In any case, why would a photon need time if it doesn’t have anywhere to go?) It would be a “system” we can save only by a little sleight of hand with zeroes and infinities. Since speed equals space/time, it would be 0/0 for the photon at rest, or in other words indeterminate and thus compatible with c , as it must be in any reference frame. Seen from a “normal” reference frame, the distance in space covered by the photon and the time it takes would both be 0 multiplied by infinity (the usual conversion factor, called the Lorentz factor, becomes infinite) and both would in turn be compatible with any finite value. Consequently, their ratio can indeed be equal to c , as required.
Be that as it may, in any case, if you travel at speed c , distances shrink to zero and time doesn’t exist. But you have to have null mass, otherwise it can’t be done.
And so, as the novel asks, “How could Helias Kadler and the other travelers, with the whole spaceship and its far from negligible mass, ‘ride the light’?” The question arises because the novel features interplanetary trips at speed c , complete with passengers for whom time doesn’t pass and who arrive at their destination in a “flash”.
The answer is fairly simple. Let’s take the particle-antiparticle “annihilation”, with an electron and a positron, for example. They both exist up to the moment of the “collision”, after which they disappear and in their place high-energy electromagnetic radiation is released, typically two photons, which obviously travel at speed c . So all you need do is have the spaceship interact with an equal amount of antimatter, and presto chango: as a product of the annihilation, you’ll have radiation directed at speed c towards the chosen destination. Upon arrival, you “simply” use what’s known as pair creation, where two photons produce a particle-antiparticle pair, to separate matter and antimatter, and abracadabra, you have your spaceship and passengers again, safe and sound at their destination. Naturally, this assumes that you’ve got a technology that can restore the original organization of the individual particles. Or that in reality true annihilation doesn’t take place, but matter and antimatter, however conjoined, maintain their identity during the null time that the trip lasts.
All of this, if it could be done, would make it possible to “transmit” passengers over arbitrarily large distances in literally no time at all. But for observers on Earth the trip lasted, in our case, twenty years. If Helias Kadler were to decide to come right back to Earth, he’d find everyone had aged forty years, just as in the twin paradox. Isn’t there any way to get around this problem? Indeed, there is, “There’s the trick”, as Mattheus Bodieur laconically remarks in the first chapter of the story. “What trick?” asks Helias Kadler, and we join him in asking.
Let’s consider a different, alternative, interpretation of antimatter: antimatter is nothing other than ordinary matter going backward in time. This was being said as early as the 1940s, by Stueckelberg 2 during the war and Feynman 3 , 4 a few years after, but it attracted relatively little notice, perhaps because physicists then were more concerned with nuclear questions, the atomic bomb first and then the H-bomb. The concept has recently been taken up again in order to explain some of the fundamental mysteries arising from the observation of the cosmos, and “dark energy” 5 , 6 , 7 in particular. The scientific arguments presented from this point on, however, are largely the fruit of the author’s own heretical mind, or otherwise depart from the views held by mainstream physics. But to paraphrase T.H. Huxley’s famous observation, “Every new theory begins as heresy, then becomes doctrine, and ends as superstition.”
The physical process that describes electron-positron annihilation, mentioned earlier, is part of quantum electrodynamics (QED), which is a very complicated business. One of Feynman’s great merits was that of representing the complex (and largely incomprehensible) formulas for these quantum interactions in simple and instructive pictorial form, called, unsurprisingly, Feynman diagrams. 8 In the case of electron-positron annihilation, the simplest Feynman diagram is as shown in Fig. 1 .
Fig. 1 Feynman diagram of electron-positron annihilation ( https://en.wikipedia.org/wiki/Feynman_diagram#/media/File:Feynman_EP_Annihilation.svg )
In the initial state (bottom), we have one electron (e − ) and one positron (e + ) which approach, and then interact and disappear, with two photons (γ) appearing in their place. This is the common interpretation. But following the path indicated by the red (gray in the printed version) arrow, the alternative interpretation tells us that there is only one electron, coming from the left, which by emitting two photons inverts its “course” in time, so that it
can be observed at earlier times as a positron, while simultaneously, as an electron, it was going forward in time.
To visualize the process of electron-positron pair creation, all we have to do is invert the direction of the time axis (putting the past at the top and the future at the bottom) or turn the diagram upside down, exchanging e − and e + (or inverting the red arrow). In this case, the alternative interpretation tells us that there is an electron coming from the future (and thus observed as an e + ), which by absorbing two photons performs a time inversion and goes back toward the future.
And all this is in agreement with the CPT theorem in relativistic quantum physics, which states that if we apply simultaneous transformations of charge conjugation C (a particle becomes its antiparticle and vice versa), parity P (inversion of the spatial axes) and time reversal T to a physical process, we obtain another physically possible process, or in other words one which obeys the same physical laws. This CPT transformation is what we did to pass from annihilation to pair creation.
But perhaps there’s a more subtle meaning in the CPT transformation. If the laws of physics must be invariant for CPT (the so-called CPT symmetry of physical laws), and we consider a physical system consisting only of matter and the equations governing its behavior (electrodynamic or gravitational, for example), what does applying CPT transformations to this system in these equations mean? It means describing the behavior of the corresponding system of antimatter as observed from a completely inverted space-time.
The fact that CPT symmetry is the only universally valid symmetry (according to our current physical knowledge), or in other words valid for all types of interaction, including strong and weak nuclear interactions, tells us that these three operations cannot be separated, but must always take place together. So dealing with antimatter also means that we are observing a system that evolves in an upside-down space-time.
The Dark Arrow of Time Page 23