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  Relativistic time travel is a great scientific tool for the science fiction toolbox. When the science in fiction is accurate, characters traveling at high velocities through space should be experiencing (suffering from, really) time dilation. Two examples of relativistic time travel in science fiction stand out. The first is Forever War by Joe Haldeman;4 the second is Orson Scott Card's Ender series (known as the Ender Quintet).5

  In Forever War, time dilation pops in when troops travel to military encounters on different planets. Each battle takes our hero William Manella centuries farther from the earth he knows. When eventually he returns home, he is so socially displaced that his language is archaic and his heterosexuality is repulsive. Imagine two races fighting each other hindered by time dilation, unaware of the enemy's stage of development when they next engage. It really is all relative!

  The Ender series takes place over centuries, which are merely decades to Ender who travels at relativistic speeds. Much of the Ender universe revolves around a relativistic war with aliens that humans have charmingly named “buggers.” A hero from an earlier confrontation with the buggers has been stashed away in the spaceship (eighty years before the book's setting). He is sent on a journey at near light speed that will return him to Earth when the humans have their fleet ready for the final battle against the buggers who have also been taking advantage of time dilation on their (relatively) long journey into human space.

  EINSTEIN CONSIDERS THE GRAVITY OF HIS IDEAS

  When we add gravity to our relativity soup, we get something that tastes a bit different than special relativity. This is Einstein's theory of general relativity.

  Imagine you are in an elevator that is descending very quickly but not terminally. You should feel lighter, as if less gravity was pushing down on you (yes, that's right, pushing; we'll get to why later). Einstein used complex geometry to show how gravity and acceleration are equivalent.

  Consider twins named Alice and Betty who both volunteer to be blindfolded and gently knocked out for science. Don't ask. I can't explain their motives.

  Anyway, Alice wakes up in a spaceship accelerating from the planet at a rate of one unit of Earth gravity (1g), while Betty wakes up in an empty back room of a Starbucks in Flushing, New York. They both push themselves up and are asked if they know whether they are in a spaceship or on Earth. Neither will know for sure, except Betty thinks she smells coffee. They don't know because they feel an equivalent amount of force pushing down on them. Einstein concluded that the reason we feel gravity is because we are always accelerating.

  Quick fact: the gravity of Earth (g) = 9.8 meters per second every second = 32 feet per second every second.

  It might help if we bring general relativity down a couple of dimensions. Imagine a two-dimensional sheet pulled taut with a bowling ball sitting at its center. The weight of the ball curves the sheet around it. The area closer to the ball will have a steeper dip than areas farther away. Objects such as marbles will tend to roll toward the dip and then circle around the bowling ball.

  Fig. 1.1. Illustration of a big ball on a sheet of graph paper. (iStock Photo/koya79.)

  Even light, like a marble on our sheet, will roll around massive stellar objects. General relativity teaches us that masses don't pull on each other. Instead, the force makes mass fall along curves. I believe physicist John Wheeler summed up the geometric nature of general relativity best when he said, “Spacetime tells matter how to move, but matter tells spacetime how to curve.”6

  Technical note: The sheet metaphor is incomplete because the fabric of spacetime is not a flat stretched sheet. It is shaped in such a way that the earth presses on it from all directions. This is some complicated geometry.

  To me, the most striking consequence of rolling in these curves is gravitational time dilation. In our four-dimensional universe, massive objects such as planets or stars not only stretch and dent space, they also stretch time. Yes: the steeper the curve in spacetime, the slower time flows.

  This is consistent with special relativity. As gravity increases, you fall faster (acceleration). When stuff accelerates, time slows (time dilation). The larger the mass, the more stretched and warped spacetime becomes, and the slower time flows for anyone near the surface. Therefore time does not pass at the same rate everywhere. It is flexible. Our modern satellites use Einstein's field equations to compensate for this. Otherwise the GPS for our cars and smartphones wouldn't be accurate.7

  Did you know that the earth's core is about two and a half years younger than its surface? General relativity explains this too. Gravity at the earth's core is greater than on the surface, meaning that clocks will tick a bit slower down below. Over the 4.5 billion years of the earth's existence, the lag between the surface and core clocks have added up to about two and a half years.8

  Something to ponder: do you need gravity to have time?

  A movie example is Interstellar, which was based on exchanges between physicist Kip Thorne and producer Lynda Obst. This movie is a love letter to anyone who loves hard science. Tons of time dilation problems need to be overcome in this movie. Oh, and a lot of general relativity is included as a bonus. If you ask me, gravity is a supporting character. Joseph Cooper, the main character, spends a short time (relatively speaking) in the gravity well of a black hole. Eighty years have passed on Earth by the time he returns. Oops.

  MASS IS ENERGY, AND SOMETIMES IT MAKES HOLES

  In addition to the gravity-acceleration equivalency principle, Einstein's general relativity equations show that the geometry of spacetime is equal to the energy of all the stuff in it. The stuff in this context can be either mass or energy. In fact according to Einstein, gravity moving matter (and energy) along curves is what embodied spacetime.9

  I'll let you in on something that isn't a secret: mass and energy are different forms of the same type of stuff. Einstein proved this when he derived his famous equation, E=mc2 (energy equals mass multiplied by the speed of light squared). In non-math language, this means that the mass of an object is the measure of its energy content. A lot of energy is trapped in the mass of your body. (In a chapter bonus, I'll tell you how much.)

  Because of the energy-mass equivalency, as an object accelerates, its mass increases. How? The answer is special relativity. As an object increases velocity relative to an observer, the amount of energy it carries also increases so it will appear more massive to the observer. In fact, the energy (mass) it would take to accelerate a single particle to the speed of light approaches infinity. You can thank the properties of spacetime for the speed of light limit.

  If we push general relativity to its extreme, we arrive at a black hole, a location in spacetime that is infinitely warped by a singularity. A singularity is an infinitely small and dense point, something that is not clearly defined in physics.

  In fact, this is where physics ends because infinity is not a number. It is an idea. As such, it can't be used in mathematical operations. And yet, black holes exist. Their gravity is so intense that, according to general relativity, time must slow to a stop. Black holes are covered in more depth in chapter 4.

  NO WITNESSES…YET

  Here is a question I imagine you desperately (I have a big imagination) want to ask: if, according to general relativity, time travel is theoretically allowed, then outside of science fiction, why haven't we met time travelers?

  Think of time travel as a journey along a two-lane highway that contains many on- and off-ramps. As a time traveler, you can't visit an earlier era unless an exit ramp to that era exists. This gives us the following scientific rule of time travel: it is impossible to travel back to a time before time machines exist. This rule comes from the equations for general relativity where solutions for the continuum must exist at both ends, no matter whether we are talking about location or time.

  But, for the sake of argument, if an alien race invented a time machine, say, a thousand years ago, and we got our greedy hands on the machine, it might be possible to travel a thousand year
s into our past. Sorry, Back to the Future, but your DeLorean time jump isn't sufficiently scientific for me. That didn't stop me from watching it three times.

  TWO SCIENTIFICALLY PLAUSIBLE WAYS TO SURF SPACETIME WAVES

  1. WORMHOLES (HYPERSPACE IN 4-D SPACETIME)

  The idea of wormholes in space emerges from Einstein's theory that gravity arises from objects warping space. Wormholes are sometimes called Einstein-Rosen bridges because the idea of shared interiors was first fleshed out in a 1935 paper cowritten by Albert Einstein and Nathan Rosen. They showed that it was theoretically possible that the inward path of a black hole could be matched to a path that merged outward again at some different neighborhood of spacetime.10

  It is not unimaginable to consider the possibility of two extreme local distortions warping space at different locations. If these bulges were to connect, you'd get a wormhole, a connection between the two distant locations. The series Stargate SG-1 revolves around an Einstein-Rosen bridge portal device.

  As any Trekie will happily remind you, a stable wormhole is the raison d’être of the television series Star Trek: Deep Space Nine. In the series, a stable wormhole connects the Alpha Quadrant, the location of the mainline characters, with the Gamma Quadrant—the home of a lot of unknown aliens.

  The young adult (YA) story “The Outpost,” written by Paige Daniels for Brave New Girls: Tales of Girls and Gadgets, takes place in a well-defined fictional universe where a group of profiteers known as Keepers control access to wormholes. This elite group controls access to interstellar travel, granting them control on all colony trade.11 Who will stand up to them? There you go: plot plus science.

  What if I want a wormhole that also integrates time travel? It is theoretically possible to use a wormhole as a time machine. Of course, it is a whole lot easier with the help of fiction than in real life because it involves moving one end of a wormhole.

  Fig. 1.2. Illustration of a wormhole. (iStock Photo/eugendobric.)

  First, we'd need a starship that can generate a gravity field strong enough to attract one end of a wormhole (remember: energy is connected to mass that is connected to gravity). Next, we'd have to drag the end along at speeds approaching the speed of light. As we know from special relativity, the clocks at the end we are dragging would run slower compared to the nonaccelerating end. Thus, we create a connection between two time zones where one end leads to the future and the other to the past.

  Okay, let me combine a few ideas and add a dash of Doctor Who science to build a time and space machine. Of course, I'd have to come from a race that developed a time machine very early on because I can't violate the whole “not traveling farther back than the first time machine” rule.

  To begin, I would need a black hole and the technology to manipulate its gravitational waves. Gravitational waves as predicted by general relativity are ripples in spacetime that spread out from accelerated mass. We will go more in-depth on gravitational waves and black holes in future chapters, where they will take up both space and time.

  Anyway, this setup would allow me to bend the on- and off-ramps of my time tunnel. Maybe, to make my life easier, I would lock a few fixed points into time for reference. Next, because it would take a lot of space to store my equipment, time rotors, power source, and so on, I'd need some sort of container to put all of this in.

  Why don't I stow it in a higher-dimension tesseract? A tesseract is to a cube what the cube is to a square. It is folded space, dimensions within dimensions. This would allow me to store a lot of stuff inside something with a small volume (i.e., a container that is bigger on the inside than on the outside). Let's say my tesseract is the size of a box large enough to walk into. And why not paint it blue and call it a TARDIS?

  In Madeleine L'Engle's A Wrinkle in Time, a tesseract is a time and space machine that is a “wrinkle” in space and time.12 This is a fantasy device used to explain travel through space and time rather than explaining hard science, but it's a cool enough idea to mention. Come on, in what other fictional world can you travel by tessing?

  2. COSMIC STRINGS

  This is a weaker theory than wormholes but still workable for science fiction. I once used it in a story to explain interstellar travel after I got a little bored with wormholes.

  A cosmic string is a long, thin, and nearly infinitely dense theoretical remnant of the big bang. Consider it a long-line singularity. To build a space and time machine with them, you need to set two of these strings in parallel. Their relative motion, along with the geometry of spacetime, would allow for a closed time curve, allowing for backward time travel. However, as physicist Stephen Hawking has pointed out, most likely this system would collapse into a black hole.13

  In the Star Trek: The Next Generation episode “The Loss,” the Enterprise encounters a two-dimensional string.14 Guess what? Mayhem ensues.

  PARTING COMMENTS

  We live in four-dimensional spacetime composed of three spatial dimensions (length, width, and height) and one dimension of time. The speed of light is the galactic speed limit of light, gravity, and time.

  Time is not absolute, and it doesn't flow uniformly. Einstein showed us that time is woven into the fabric of space. His theories united space with time, matter with energy, and everything to gravity. From special relativity we learn that time is flexible and that mass has energy content. From general relativity we learn that gravity is not about pulling, but it is about falling, and if you add stuff to spacetime, you will change its geometry and fall differently (faster).

  Fortunately for both scientists and producers of good science fiction, Einstein's theories left a lot of low-hanging fruit with space travel, time travel, wormholes, cosmic strings, and the existence of black holes all providing nibbles.

  Something to ponder: In many scientific theories, time appears to emerge from the physical laws of our universe. Simply, our universe may bring time along for the ride as it expands. What about universes formed under different conditions? Do they have time?

  CHAPTER 1 BONUS MATERIALS

  BONUS 1: A SPECIAL RELATIVITY PARADOX

  A paradox is defined as a statement or a collection of statements that might sound true but that lead to contradictions that defy intuition. Personally, I'm not convinced that paradoxes exist outside the rocky marriage of philosophy and mathematics that we call logic. Most of the paradoxes you'll come across are self-referential statements such as, “I always lie. Well? Did I or didn't I just tell the truth?” A paradox most likely means that something is wrong with the assumptions.

  Nevertheless, we're going to fool around with things and ask one question: what do you get when you mix a sibling paradox with time travel? A wicked brew, I tell you. It is called the twin paradox.

  I hope you remember the twins Alice and Betty because they're back. One day, Betty decides to board a rocket for a round-trip journey to Gliese 581, a star in the Libra constellation. Except for short periods of acceleration and deceleration near Earth and the star, Betty will travel at a constant velocity close to the speed of light. Gliese 581 is approximately twenty light-years away, so Betty's round-trip journey will take a little over forty years to complete.

  Earth-homebody Alice knows all about special relativity (the faster through space, the slower through time), so she recognizes that time will run more slowly for Betty during her voyage. Alice calculates that Betty will actually have aged only four years when she returns.

  It is all relative, so I will now retell the story from Betty's perspective. This is where a paradox (might) creep in. From Betty's point of view, she's the one remaining stationary, and it's Earth and Alice who move away at a rapid velocity and a later return. So, using the same logic as before, it's Betty who experiences forty years of time and Alice is the one who has experienced only four years.

  When the twins are finally reunited, who has aged forty years and who has aged four years? If they are both right, you have a paradox.

  Luckily for our sanity, there is a flaw in this tho
ught experiment. The paradox relies on the assumption that the journeys taken by the twins are equivalent. They aren't. The difference comes down to acceleration. Whereas Alice remained relativity stationary on Earth, Betty undergoes three periods of rapid acceleration: the beginning, the middle (at the U-turn), and at the end of her journey. During each period of acceleration, she jumped to a different inertial time frame. Each jump took her farther from her sister's time frame.

  The correct result is that Alice has aged forty years and Betty has aged only four years. No paradox.

  BONUS 2: HOW MUCH ENERGY IS CONTAINED WITHIN THE MATTER OF YOUR BODY?

  E=mc2 shows that the mass (m) of an object is really the measure of its energy (E) content in terms of the speed of light (c). This equation is a result of special relativity, and it shows how much energy is contained in matter.

  Consider a person who weighs 150 pounds. For this, I'm going to have to go metric on you. Physics is much easier using metrics. One hundred fifty pounds is about sixty-eight kilograms. Using Einstein's equation, this person has 6.12 x 1018 (the little number hanging near the 10 is called an exponent, and it is shorthand for how many zeros to add to the end of the number; in this case 1018 is shorthand for 10 followed by 18 zeros) joules of energy (68 kg x 300,000,000 meters/second). This amounts to 1.7 x 1015 watt-hours or 1.7 x 1012 kilowatt-hours or 1,700,000 billion kilowatt-hours.

  That is a lot of energy. According to the US Energy Information Administration, in 2016 the United States produced, from all sources, a mere 4,079 billion kilowatt-hours.15 So this 150-pound person contains more than 417 years of US energy production.

  BONUS 3: MUTANTS