Similar to time dilation, the amount of physical contraction gets much more pronounced as the moving object approaches the speed of light. The equation for the Lorentz Contraction is:
Again, this is best elucidated by example. The Final Five Cylons are escaping the nuclear fires of Dead Earth and heading to the Twelve Colonies. Since their ship was not jump-capable, but was capable of traveling at relativistic speeds, they have time on their hands. A lot of time. Since they are all scientists, there are many discussions and debates along the way. Along the way, Galen and Saul get into a spirited debate about how their speed is affecting the passage of time and the length of their ship. So when they stop briefly at the Algae Planet to stock up on a few things (and build a temple), they decide to do a quick experiment. Tory will accelerate the ship up to a predetermined speed. At a set time (and knowing this group, we’re assuming that there was another long debate on how this would be accomplished), Tyrol would measure the length of their ship, whose rest length is 100 m, while onboard. Tigh would be stationed in a shuttle and would measure the length of the ship as it passed by. We’ll assume that the ship’s top speed was 0.999c. After six trials at six different speeds, Tyrol and Tigh compared their measurements.
Lorentz contraction as a function of relative speed
Velocity as a fraction of c Lrest (Tyrol) Lmoving (Tigh)
0.1 100m 99m
0.5 100 m 87 m
0.75 100m 66m
0.9 100 m 43 m
0.99 100m 14m
0.999 100 m 4.5 m
Tigh sees the ship successively shorter the higher the relative speed. Recall that motion is meaningful only relative to a given reference frame. Anders, who was doing an experiment of his own, also noted that Tigh’s ship was shortened by the exact same fraction.
Let’s return to our example with Starbuck and Apollo. Assume that when they passed at 0.75c, not only did they observe each other’s clocks, but they measured the length of each other’s Vipers. Lee says that Kara’s Viper was relativistically shortened, and Kara says that Lee’s Viper was. From each other’s point of view, both Vipers were compressed to 66 percent of their length at rest. (The same percentage by which their clocks slowed down, notice.)
The effects of Special Relativity seem irrational simply because humans don’t travel at relativistic speeds yet. These effects may not be intuitive, but they do describe the way the universe works on a large scale. In fact, if the implications of Special Relativity seem like something from The Twilight Zone, things are about to get weirder as we turn our attention to gravity and General Relativity.
CHAPTER 12
General Relativity and Real Gravity (or the Lack Thereof)
Nearly all spacecraft on TV or in the movies have some form of artificial gravity. This type of artificial gravity, built not around physics but economics, was invented around the turn of the last century by a French stage magician named Georges Méliès. Méliès left the theater to become a trailblazer in the then-new medium of motion pictures, and in 1902 he produced the science fiction classic Le Voyage dans la Lune. The film portrayed a Jules Vernean voyage by a group of crazy wizard-scientists (aided by a bevy of pretty girls) launched by rocket cannon from Earth to the Moon.
The excessive G forces involved with launching people from a cannon—which should have flattened them into a puree—apparently didn’t affect these intrepid voyageurs. When Méliès’s astronauts land on the Moon, they are clearly not jumping around under the diminished influence of lunar gravity. Like many subsequent movie producers, Méliès either didn’t know, or didn’t care, about the changes in the magnitude of gravity that take place when one leaves the surface of Earth. And in nearly every science fiction film that followed, from the Flash Gordon serials to Duck Dodgers in the 24½th Century, cosmic travelers kept their feet firmly planted on the deck of their spaceships. If anyone bothered to ask, “artificial gravity” became the easy way out for movie producers who didn’t want to spend hundreds of thousands of dollars rigging wires, using other complicated special effects, or renting a special NASA low-gravity-simulator aircraft, nicknamed the “vomit comet,” to give the illusion that their actors were weightless. Simply turn on the “artificial gravity” and presto—actors could walk around a soundstage in Hollywood and not have to explain to the audience why they weren’t experiencing the near-zero-gravity environment of outer space.
Why do real-life astronauts, working on the flight deck of the space shuttle or within the modules of the International Space Station, float? What is weightlessness anyway? For that matter, what is gravity? For that answer, we turn to both Sir Isaac Newton and Albert Einstein.
In 1687 Sir Isaac Newton published his best-known work, his Philosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), often known simply as The Principia. It was in the Principia that Newton first published his Law of Universal Gravitation, which dictated the gravitational force between any two objects. The Law of Universal Gravitation is one of the most famous equations in physics:
In this equation, F represents the gravitational force between the two objects, G is the universal gravitational constant,1 m1 and m2 are the masses of each object, and r is the distance between the two objects. Simply stated, any two objects in the universe that possess mass attract each other via the force of gravity. Even the book in your hands exerts a small gravitational pull. The more massive the objects are, the greater their mutual gravitational attraction.
The force of gravity between two objects decreases dramatically as the distance between them increases, in what we call an inverse-square relationship. For example, Saturn is approximately twice as far from the Sun as Jupiter. Since the force of gravity decreases as 1/r2 , Saturn feels about one-quarter the gravitational attraction from the Sun as does Jupiter. Neptune, thirty times farther from the Sun than Earth, feels 1/900 the gravitational pull of the Sun that Earth does. An important thing to note is that Newton’s Law of Universal Gravitation is not time-dependent. In other words, if Newton’s equations were correct, were the star Sirius to disappear right now, you would instantly stop feeling its gravitational attraction
Chief Galen Tyrol and Sharon "Boomer" Valerii.
Chief Galen Tyrol and Sharon "Boomer" Valerii.
Newton’s Law of Universal Gravitation has not been entirely abandoned, and still has wide application in physics and engineering today (like planning the trajectories of spacecraft to other planets). In fact, it will come in very useful in our subsequent discussion of artificial gravity later in this chapter. In the years following Newton’s Principia, however, it became obvious that his law was not a complete description of gravity.
When Special Relativity arrived on the scene in 1905, there were apparent contradictions to Newton’s Universal Law of Gravitation. So in 1915, and again in 1916, Einstein published two papers expounding upon the General Theory of Relativity (GR) to reconcile the two theories. The fundamental principle behind General Relativity initially seems to be so straightforward as to be child’s play, but anything studied in sufficient detail becomes amazingly complex, and the implications of GR are profound.
According to Einstein’s first postulate of General Relativity, there is no difference between gravity and a uniformly accelerated reference frame. That’s it. This is easily elucidated by example. Captain Louanne “Kat” Katraine sits in her Viper, preparing to launch. Over the wireless she hears the voice of the catapult officer as he finishes his checklist, “Nav con green. Thrust steady and positive. Mag cat engaged. Good hunting, Kat.” The magnetic catapult engages and rockets her Viper down the launch tube, the forward acceleration slamming her back against the ejection seat. Now let’s say that on a subsequent launch Kat’s crew chief covered her Viper canopy with duct tape so she can see nothing but the inside of her cockpit. Let’s also assume that, upon launch, she is typically thrust back into her seat with a force equivalent to the force of gravity, or 1 G. With no external reference, Kat would not be
able to tell if she had been shot down the launch tube, or if her maintenance crew had pulled a prank and simply tipped the Viper up onto its engines and she was forced into the seat by gravity. A person with no outside frame of reference has absolutely no way of distinguishing one from the other,be and the universe sees the two situations as synonymous. The force you feel from gravity is the same as the force of uniform acceleration.
Why was this such a ground-breaking concept? Let’s examine the implications. Imagine that we have a super-high-tech elevator, one that is capable of accelerating upward very rapidly (see the figure below). We fire a single photon (see chapter 13, “The Wonderful World of Radiation”) into the elevator at the very instant the elevator shoots upward. It will follow a curved trajectory relative to the elevator. Because the force of gravity is equivalent to uniform acceleration, if the elevator had been sitting on the ground the massless photon we fired into it would still have a curved trajectory, this time due to gravity rather than acceleration.
A single photon shot into our high-speed elevator.
According to General Relativity, the force of gravity is not really a force at all, but is instead a warp or curve in the very fabric of space-time. Any object that has mass warps space-time—more mass means more of a warp. Another nearby object in space (and time) will feel that warping of space—as well as creating its own gravity warp—and the two objects will be accelerated toward each other. Therefore, if a large mass like a star warps space-time, then anything passing by the star—including light—would be subject to its gravitational influence and have its trajectory altered.
The predicted bending of light, in particular starlight, was experimentally verified in 1919 by Sir Arthur Stanley Eddington. On an island off the west coast of Africa, Eddington photographed a total solar eclipse. Before the eclipse he also photographed the stars that should be in the line of sight of the Sun during the eclipse. The apparent positions of the stars near the Sun were shifted by the amount predicted by General Relativity, which revealed that the path of starlight had been gravitationally bent. Similar to the bending of starlight, when NASA spacecraft send data to Earth, they must aim their communications antennae in such a way to account for the curvature of the radio signal due to the gravitational effect from the Sun.
An enlightening way to visualize gravity is to imagine a perfectly taut, perfectly flat trampoline. Place a marble on the edge of the trampoline—it will make a very slight, nearly imperceptible, indentation on the trampoline. You could roll your marble from one side of the trampoline to the other with a mere flick of your thumb. The marble will travel straight and true, and will be slowed, or deflected, only a small amount due to friction with the surface of the trampoline.
How the warping of space-time by our Sun affects spacecraft communications.
Now place a bowling ball in the center of the trampoline. It will cause a sizable indentation. The depth of the indentation depends on the mass of the bowling ball—a 10-pound ball will make a medium sized impression, while a maximum regulation 16-pound ball will make a much deeper “warp” in the trampoline surface. The indentation of the bowling ball in the surface of the trampoline is similar to the way any object with mass distorts the region of space-time around it. The more mass, the greater the distortion.
With the addition of the bowling ball, your marble-shooting game becomes significantly more challenging. Instead of shooting marbles from one side to the other in a straight line, you’ve now got to deal with this giant frakking indentation in the middle of the trampoline. Any marble rolled across the trampoline no longer travels in a straight line. Instead all marbles curve to varying degrees toward the indentation created by the bowling ball. Some marbles, launched far away from the bowling ball, are deflected hardly at all. Other marbles, launched with great speed nearer to the ball, are deflected slightly—they make it to the other side, but their paths always curve in the direction of the bowling ball. Marbles traveling at a much slower speed are pulled into the bowling ball completely and never make it to the other side.
Sometimes, with practice or by luck, you can launch a marble at just the right speed and at just the right medium distance from the bowling ball that it travels across the trampoline in ways that would be impossible without the influence of the bowling ball. You can launch a marble in such a way that it curves 90 degrees around the bowling ball. You can even launch a marble so that it travels completely around the bowling ball and returns back to you without bouncing off any other obstacle.
Massive objects (like stars and planets) warp the fabric of spacetime like the bowling ball does to the trampoline. More mass means a greater warp. Say we have a Raptor traveling in interstellar space far from any massive object. If the Raptor does not fire any thrusters, it will travel in what seems to be a straight line.bf That Raptor will find its path deflected as it approaches a star or planet. The Raptor will travel faster and faster and its path will be deflected more and more toward the object’s center as it gets closer to the object. If the Raptor is traveling relatively fast to start with, it is only slightly deflected from its path before the encounter. But if the Raptor travels along a slightly different trajectory, either with less velocity or angled more directly at the planet, it will simply be pulled directly toward the center of the planet and the pilot will earn an immortal place in the Colonial Navigation Hall of Shame.
Gravity warps spacetime like bowling balls (or marbles) on a trampoline.
Of course, gravity doesn’t only affect planets and spaceships. Once an astronaut’s body overcomes its initial confusion and gets adapted to weightlessness, the really bad stuff starts—and it’s all because the human body is a lazy sack of bones that won’t work at anything it doesn’t have to. Once you’re in microgravity, your muscles start to come to the realization, “Hey! I don’t have to stretch and pull to keep this body upright anymore. I don’t have to climb stairs, or perform the careful nonstop push-me-pull-you balancing act of sitting on a chair. I can just relax into a semi-fetal hunch and float. Cool!” More dangerously, your heart says pretty much the same thing: “Woohoo! No more fighting gravity to pump blood to the extremities! I can just take it easy and let the blood and other body fluids pool in the chest!”
Unfortunately, having evolved over billions of years in a gravitational field, the human body becomes confused by the sudden absence of the pull of gravity. Not being smart enough to have worked weightlessness into its repertoire of things that can possibly go wrong, the only thing your body knows when you’re floating in space is that there is too much blood, and other body fluids, in your chest. When the same thing happens on Earth, that signals that you are overhydrated. Therefore, when you’re in space, your body makes the mistake of treating a space symptom like an Earth symptom, and acts accordingly. You pee. A lot.
Your bones, having heard everything the muscles are saying about not straining, decide to take life easy as well. “The muscles aren’t pulling as strongly against us,” your bones say. “We don’t need all this calcium to keep this body upright. Let’s get rid of some. Hey urine, a little help here?” Since your body already has gotten the signal to urinate prodigiously, the bones take advantage of this and start to shed calcium and potassium. Your kidneys, not used to all these minerals flowing out in such concentrations, do their best to handle the flow, but they also start to protest. Meanwhile your heart says, “Hang on, I need that potassium to maintain my rhythm—oh no, wait! I’m carrying such a light load, I don’t need much potassium. Piss away!” The problem is that if you do suddenly need to exercise (in a space emergency, for example), your potassium-starved heart will have a tendency to become slightly arrhythmic.
So living in microgravity weakens your heart, overtaxes your kidneys, causes bone loss, and makes you pee a lot. You know what that sounds like? It sounds like being old. Space flight makes you feel old. So much for those doctors who said that life in microgravity could be a “fountain of youth.”
There are ways to cir
cumvent, or at least minimize, the bodily effects of microgravity. Sticking to a fanatical exercise schedule (exercising up to three hours a day!) can help to mitigate some of the health problems listed above, but not all. Even if you were to exercise for six hours a day, you are by definition not exercising for eighteen hours a day, and in weightlessness not exercising really means not exercising. The good stress that exercise puts on your heart can never match the weakening effect of near-zero G, and as a result even the most strenuous orbital exercisers (often astronauts who have served in the Marine Corps) still have health problems when they return to Earth.
This implies that in a spacefaring society like the Twelve Colonies, a complete zero-G environment could quickly result in the development of “microcultures”—different classes of personnel based upon gravity tolerance. In the military there would the spaceship grunts who would remain on board forever, never setting foot on a planetary surface again (and who could therefore afford to become zero-G acclimated). There would also be the elite fighter pilots who would spend their days training in their spacecraft, emphasizing cardio workouts. One interesting by-product of this, though, is that better cardiovascular fitness yields a lower blood pressure. That’s good, right? However, lower blood pressure makes it more difficult for a body to pump blood to the head during the high-G maneuvering of combat. The pilots would need G-suits similar to those worn by modern fighter pilots—clothing worn around the lower extremities that compresses the legs and rear end during high-G maneuvering, hence squeezing blood into the head. Another separate category would be the Colonial Marines, who would have to do both cardiovascular workouts and weightlifting on the chance that they would be needed to make planetfall somewhere. No organization, even one that places great emphasis on separation of rank, would find it easy to maintain efficiency with a crew divided into separate cultures as such. So it’s almost imperative to create artificial gravity if you’re going to create a civilization in space.
The Science of Battlestar Galactica Page 9