The Science of Battlestar Galactica
Page 8
During its heyday in the 1950s, nuclear weapons testing provided scientists with data not just on the nuclear explosive itself, but also on its effect on the surrounding environment. asFrom this data, scientists have built up a set of formulae that we can use to estimate the effect a tactical nuke might have on Galactica. From the damage estimates in this episode and in the episode “Water,” it seems that the nuke detonated at the forward end of the flight pod, near the water bulkheads in the ship’s “alligator head.” Since the flight pod is 600 meters long and the damage seems confined to the forward quarter, we can estimate that the area of destruction was caused by a 10-kiloton nuke, detonated 3 meters from the hull.
Hull material Crater depth (meters)
Aluminum 12.6
Carbon-titanium 11.9
Uranium 7.1
Titanium 8.3
Tungsten 4.7
Iron 14.9
A schematic diagram of Battlestar Galactica.
The figures are even worse for a nuclear detonation at zero meters from the hull. For those cases, the hull crater would be on the order of 100 meters deep and would essentially have cut Galactica in two. Bad enough as these figures are, even if Galactica were made of pure tungsten, it would need to have an outer hull approximately 5 meters thick throughout the ship. Let us also assume that decks and bulkheads fill 10 percent of the interior. They have to be strong, but not as tough as the exterior, so we assume that they are composed of structural steel, which also happens to be lighter than tungsten. We can now estimate the mass of Galactica under those circumstances:• Outer measurements: 1,371 by 156 by 400 meters = 85,550,400 m3
• Inner measurements: 1,366 by 151 by 395 meters = 81,475,070 m3
• Estimated volume of tungsten hull: 4,075,3300 m3
• Estimated mass of Galactica’s hull: 78,845,010,000 kilograms
• Minus 15 percent (because Galactica is not perfectly rectangular): 66,682,587,100 kg
• Estimated volume of decks and bulkheads : 6,925,400 m3
• Mass of decks and bulkheads: 54,433,494,300 kg
• Estimated mass of Galactica: 121,116,081,400 kg
One hundred and twenty-one billion kilograms? That’s the mass of a small asteroid! We haven’t even counted the additional mass of Galactica’s interdecks, bulkheads, engines, equipment, fuel, water, and people, but no matter; they’re dwarfed by the sheer mass of the tungsten hull and structural members. So let us assume we have a working mass for Galactica: 121 billion kg.‹
The variable E stands for energy. In the International System of Units, energy is measured in joules. A joule is the energy required to move a one-kilogram mass vertically one meter in a gravitational field of one meter per second. Gravity of that strength would be about one-tenth Earth gravity, or slightly less than lunar gravity. Another way to put it: it’s the energy required to lift an apple one meter straight up from Earth’s surface, or the energy realized when an apple drops one meter to Earth’s surface. Since Earth’s gravity is 9.81 meters per second per second at sea level, one kilogram at one meter above Earth’s surface has a potential energy of 9.81 joules.
The following table takes a look at various masses and the energy released when they are converted entirely to energy.
The speed of light is a very large number, and that number squared is a huge number. When these quantities are multiplied together, it’s easy to see that a conversion of even a tiny amount of matter will yield enormous amounts of energy.at
CHAPTER 11
Special Relativity
So the universe is not quite as you thought it was. You’d better rearrange your beliefs, then. Because you certainly can’t rearrange the universe.
—Isaac Asimov and Robert Silverberg, Nightfall
Great leaps in science are rarely, if ever, done by consensus or by large groups. While nearly every scientist, working alone or in a team, contributes to the sum total of human knowledge, and while there is the occasional researcher who simply happens to be in the right place at the right time, often quantum jumps in our understanding of nature are made by a lone researcher who simply understands an important aspect of nature far better than everybody else . . . and can prove it. Albert Einstein was one such visionary. In 1905 he published an article entitled “On the Electrodynamics of Moving Bodies”1 that turned the scientific world on its head. It was in that article that Einstein first published his Special Theory of Relativity.
It had only been about three hundred years since science—an organized methodology for understanding and describing nature—had clawed its way out of the superstition of the Middle Ages. Based upon observable phenomena, science relies on such concepts as measurement, objectivity, and reproducibility of results. Special Relativity challenged two of those very pillars of science: measurement and objectivity. In fact, one implication of Special Relativity (SR) is that measurement is inherently subjective.
There are two postulates of Special Relativity. The first one states that there is no such thing as an absolute definition of motion in the universe, meaning also that there is no absolute standard of rest, either. Motion (or rest) must, therefore, be specified relative to something.
Think of a Viper about to be launched at a basestar. Relative to Galactica, in its reference frame, the Viper is receding from the ship. To the Cylons, the Viper is inbound and CBDRau in their reference frame.
Although neither Galactica nor the Basestar was moving relative to each other, the Viper was moving relative to both of them. In the Viper’s reference frame, however, both Galactica and the Basestar were moving and the Viper was stationary. In Special Relativity, all three viewpoints are equally valid.
The second postulate of Special Relativity states that the speed of light in a vacuum is a universal invariantav and is, as far as we know, the speed limit in our universe. As we have seen, photons have zero mass and propagate through a vacuum at 299,792,458 meters per second, or 186,282 miles per second (the speed of light, a value for which we normally use the variable c aw)—though they travel more slowly through other transparent media like air, glass, and water.ax No object that has mass (even the tiniest subatomic particle) or carries information can travel faster than the speed of light—in fact, no object with mass can even travel at the speed of light. We’ll explore how this rule may be broken, or at least severely bent, in chapter 22.
Starbuck holding the Arrow of Apollo, with Six looking on.
Kara “Starbuck” Thrace.
The simple fact that light has a finite speed has profound implications. Most importantly, it implies that space and time are inexorably linked. One fascinating implication of this is that when you look out into space, you also look back into time: the farther out you look, the farther back you look.
For example, our nearest celestial neighbor is the Moon, which is roughly 384,000 kilometers away. It takes reflected sunlight about 1.3 seconds to reach us after bouncing off the Moon. This means that when you see the Moon, you aren’t seeing it as it is now, you are seeing it as it was 1.3 seconds ago. It takes sunlight nearly eight and a half minutes to reach us; therefore, when you look at the Sun ay you do not see it as it is at present, you see it as it was when photons first left its surface eight and a half minutes ago. The brightest star in Earth’s night sky is named Sirius,az which is in the constellation Canis Major. The light from Sirius takes 8.6 years to reach us, so you’re seeing it as it was almost a decade ago. That distance is so enormous that astronomers have had to come up with a new metric, called a light-year.
Contrary to common misunderstanding, a light-year is not a measure of time. It is a measure of distance—the distance that light travels in one Earth year, roughly 9.5 trillion kilometers. It’s kind of numbing to think that Sirius, one of the closer stars, is roughly 81,700,000,000,000 km away—we instead say it is 8.6 light-years away and go on to other things.
When we discuss travel over the vast distances between star systems, we think in terms of traveling through four-dimensional
spacetime: three dimensions of space and one dimension of time.ba
An observer with a keen eye would have noticed how this was used in the episode “Lay Down Your Burdens, Part II.” Newly elected president Baltar signed the executive order to settle on the planet New Caprica. Although New Caprica was something less than hospitable, because it orbited a star embedded within a nebula, many believed that it would be nearly impossible for the Cylons to detect. At around this time Gina Inviere—a Cylon Six—detonated a nuclear warhead aboard the luxury liner Cloud Nine, taking two other ships and 4,400 souls in the process.
Although life was hard for the following year, the humans were hanging onto the belief that they had gone unnoticed by the Cylons. One ordinary day, without warning, an entire Cylon armada jumped into orbit, beginning the occupation of New Caprica. When the Cylons arrived on Colonial One, President Baltar asked their welcoming committee the obvious question: “How did you find us?”
A Five responds: “Quite by accident, actually. We were over a light-year away from here when we detected the radiation signature of a nuclear detonation.”
It took the radiation from that explosion just over a year to reach them. As soon as the Cylons detected the gamma radiation pulse from the nuclear explosion, they determined the direction from which the pulse came, rapidly assembled a fleet, and immediately jumped to New Caprica. That part took only a few hours or days; it had already taken the light a year to reach them.
The second tenet of Special Relativity—the speed of light in a vacuum is invariant—means that it is a universal constant. Two observers will always measure the exact same value for c no matter what their relative motion. While this may not seem particularly counterintuitive initially, it has some mind-boggling implications. If the speed of light is constant, that means that some other values we think of as constants—an object’s physical length, its mass, even the rate at which time passes—are variable. This is best clarified by an example.
Suppose Centurions have boarded Galactica. There is a firefight in the hangar bay with the Colonial Marines at the front of the bay and the Cylons at the rear. Both sides fire bullets that travel at 1,000 meters per second. You watch the firefight from the comparative safety of Rising Star as Galactica drifts slowly past at a relative speed of 10 meters per second. If you could measure the speed of the bullets the Cylons were shooting at the Marines relative to you, you would measure the bullets’ muzzle velocity (1,000 meters per second) plus the forward motion of Galactica (10 meters per second) for a combined velocity of 1,010 meters per second. If you could measure the speed of the bullets that the Marines fire at the Cylons—from the front of the hangar bay to the rear—you would measure their muzzle velocity minus Galactica’s forward velocity, or 990 meters per second. Nothing unexpected so far . . .
Now switch reference frames. Specifically, go back to the 1978 Battlestar Galactica, when both sides had guns that shot beams of light and went “Pew! Pew!” In this world, suppose Centurions have boarded Galactica. There is a firefight in the hangar bay with the Colonial Warriors at the front of the bay and the Cylons at the rear. You watch the firefight from the comparative safety of the Rising Star as Galactica drifts slowly past at a relative speed of 10 meters per second. Recall that in the original series, both the Colonials and the Cylons had projected energy weapons. Since the energy that comes from these types of weapons is a form of electromagnetic radiation, it naturally travels at the speed of light. If you were to measure the speed of the LASER pulses the Colonial Warriors were firing at the Cylons, you would measure c.bb If you measured the speed of the pulses the Cylons shot at the Warriors, you would also measure c. No matter how fast you were traveling—even if you were Apollo in his Viper zooming past the firefight—the speed of the laser blasts would be constant.
However, if the speed of light is a constant, irrespective of the relative motion of the source of the light and the receiver, then something else has to be flexible in order to make that so.
Time Dilation
Over the years many a controversialbc scientist, attempting to have his or her views embraced by mainstream science, has fallen back on the apocryphal argument “They laughed at Einstein at first, too!” But there’s no historical reference of anybody laughing at Einstein.bd While the implications arising from much of Einstein’s work were ground-breaking, counterintuitive, and changed the way we look at the very fabric of our existence, they were mathematically sound—and to a scientist, a mathematically rigorous argument is a convincing one. Einstein’s work spoke for itself.
If the mere mathematics of Einstein’s formulation of Special Relativity failed to prove compelling, several of the implications—like relativistic time dilation—have been verified experimentally. One outcome of SR is that time moves more slowly for you if you are moving relative to a reference that you have defined as “stationary”: a clock in motion moves more slowly than a clock standing still. As your speed increases to a large fraction of the speed of light, you are said to be traveling relativistically. When the passage of time is slower for a high-speed object, this is called relativistic time dilation. Experimental validation of time dilation was provided by rain: a rain of muons.
Muons are subatomic particles that have a negative charge and are like short-lived “cousins” of electrons: on average they decay into less massive subatomic particles in slightly over 2.2 microseconds. They are created when high-energy cosmic radiation from space interacts with Earth’s upper atmosphere. With such a short life span, even traveling at 0.99c most muons would travel an average distance of 650 meters before decaying. Few, if any, would ever reach the ground. Yet experiments have found that numerous muons, in fact, impact the surface of Earth because they travel at nearly the speed of light. Their lifetimes are extended due to time dilation.
Starbuck in her Viper.
Suppose Starbuck and Apollo rocket out of the launch tubes in their Vipers, bank in opposite directions, put a fair distance between them, then turn to face each other and come to a relative stop. Starbuck fires her engines to get up to her Viper’s top speed and coasts past Apollo. Once Starbuck is coasting—once her Viper has attained a state of uniform, nonaccelerated motion—we can ask ourselves, “Who is moving?” In Apollo’s frame, Starbuck is moving toward him. In Starbuck’s reference frame, it is Apollo who is approaching. Because of time dilation, as they pass by each other, they will disagree about the rate at which time passes. The “other” observer’s clock will seem to be slower: If Starbuck could see the clock on Apollo’s Viper, she would see that it was moving slower than hers. If Apollo could observe Starbuck’s clock, he would see her clock running slower than his! Seems impossible? Welcome to the wonderful world of Special Relativity.
This effect is more pronounced the faster the relative motion. Given two observers, like Apollo and Starbuck in our example, the equation for time dilation is:
This equation shows that the effect of time dilation gets markedly more pronounced as the relative motion of the two objects, in our example Vipers, approaches the speed of light. We see this also in the table to the right. If, for example, Kara’s Viper shot past Lee’s at 75 percent of the speed of light, and if she could view the clock on his Viper, she would perceive his clock moving at 66 percent of its normal speed. Lee, looking at Kara’s ship, would observe the samething—Kara’s clock is running at 66 percent of its normal speed.
Sam Anders referred to time dilation explicitly in the episode “No Exit” when discussing how the Final Five could travel from Earth to the Twelve Colonies while aging minimally: “Time dilation. We hadn’t developed Jump drives, so we traveled at relativistic, but subluminal, speed.”
We now understand how the Final Five can be over three thousand years old, but even the oldest of them doesn’t look a day over sixty-five!
Another allusion to time dilation appeared in an early draft of the episode “He That Believeth in Me.” When Kara returns from the dead, she has some obvious explaining to do in
order to convince Admiral Adama, among others, that she is not a Cylon—particularly when her Viper appeared “as if it were off the showroom floor.” Although two months had elapsed for the crew of Galactica, only six hours had elapsed on her Viper’s onboard clock. Kara’s explanation: “Look, I flunked the temporal relativity quiz in space-flight physics. I don’t understand the time disparity either.”
Time dilation as a function of relative speed
Velocity as a fraction of c Δtrest Δtmoving
0.1 10 sec 10.1 sec
0.5 10 sec 11.5 sec
0.75 10 sec 15.1 sec
0.9 10 sec 22.9 sec
0.99 10 sec 70.9 sec
0.999 10 sec 223.7 sec
Although this was a fun bit of exposition, it was also unnecessary to move the plot forward, so it was deleted in later drafts. Still, Kara’s line, as well as Anders’s line earlier, clearly shows that Battlestar Galactica was one of the rare science fiction TV series to make dramatic use of the bizarre implications of Special Relativity.
Lorentz Contraction
Measure the length of an object, like a spacecraft, at rest and you’ll come up with its rest length. Measure the length of an object, like a spacecraft, at relativistic speeds and you would measure a shorter length. The faster the object moved past you, the shorter its length would be. This effect is called the Lorentz Contraction or, more correctly, the Lorentz-Fitzgerald Contraction. If it seems unusual that time can travel at different rates for two objects with a high relative motion, it probably seems even more bizarre that spatial extent—an object’s length—is similarly variable. Then, again, given that space and time are intimately linked, perhaps this shouldn’t be surprising.