I tested out a lot of the ideas in this book in the class “The Science of Science Fiction” offered at St. Mary’s College in the spring semester of 2009. I thank the students in the class, Roger Ding, Adam Hammett, Galen Hench, Devon Jerrard, Malory Knott, James Moderski, David Panks, Abby Taylor, and David Tondorf-Dick, for beta testing much of the material in the second and fourth sections of the book. I’m sorry there wasn’t enough room in the book to include their great class projects. I also ran a much earlier version of this class at Cleveland State University in 1996. I thank the students who took that course, although I no longer have their names.
My mother, Louise Adler, read one of the earlier drafts of the book and gave me a lot of support and several practical suggestions about organizing the work. Finally, and most important, I thank my wife, Karen, and our daughters, Alexandra and Cassandra, for their love and support at all times, especially while I was writing the book. Scio quid sit amor.
APPENDIX: NEWTON’S THREE LAWS OF MOTION
I’ve chosen to concentrate on known laws of science in this book. This is unlike many books on science fiction, which concentrate on the unknown, or on more speculative laws. Because I’m a physicist, most of the book is devoted to the physics in science fiction. However, to understand this, it is essential to know the basics. In this case, that means understanding the laws of motion as set forth by Sir Isaac Newton 300 years ago. This appendix offers a very short introduction to the laws of motion and to two special cases of accelerated motion: constant acceleration and motion around a circle at constant speed. I am assuming that my readers have some concepts of what force, velocity, and mass are, even if they are not exactly what physicists mean by those terms.
There are three important concepts that need to be discussed before we can introduce the laws: displacement, velocity, and acceleration. Displacement of something means moving it from one place to another. It includes both the distance moved and the direction it moved in, specified in relation to some coordinate system. Velocity is how fast an object is moving, plus some indication of the direction in which the object is moving. It is the time derivative of displacement:
where r is displacement and v is velocity. Boldface indicates that we need to include the direction the object is moving in as well as the distance it moved when specifying both velocity and displacement. There are a number of ways to do this. Readers who are interested in a deeper understanding should consult an introductory physics textbook such as Fundamentals of Physics [246].
Acceleration is the rate at which velocity changes. From calculus, we specify this as:
where a is acceleration. Because the definition includes direction, if an object changes either its direction of motion or its speed, it is undergoing acceleration.
A.1 NEWTON’S LAWS OF MOTION
Newton’s first law: No experiment can be used to distinguish between moving at constant velocity or standing still. This is not the normal way in which Newton’s first law is usually written, but it is the most accurate. All motions are relative motions. Because forces produce accelerations, we can only measure changes in velocity, not absolute velocities themselves.
Before discussing Newton’s second law, we need to define force. A force is a push or a pull.
Newton’s second law: Forces produce acceleration. In mathematical terms,
Here, m is the mass of the object. Pushes or pulls produce changes in the speed or direction of an object but don’t produce velocity directly. This is one of the subtlest aspects of Newton’s second law.
Newton’s third law: If object A exerts a force on object B, B exerts an equal but oppositely directed force on A. If I push on the wall with a force of 100 N (about equivalent to a weight of 20 pounds), the wall pushes back on me with an equal force in the opposite direction. The third law leads to the conservation of momentum discussed in chapters 2, 6, and 15.
Special cases: There are only two cases of accelerated motion considered at any length in this book—constant acceleration and circular motion at constant speed.
Constant acceleration: If a force of size F acts on an object and the force is constant in time and always pointing in the same direction, the object will have a constant acceleration:
I am using plain text to specify the size of the force and acceleration without reference to direction. The object will move in a straight line. If the object starts with zero speed, it will have a speed over time given by the formula:
and displacement
It’s traditional to use x or y to indicate displacement when the object moves in a straight line. The symbol x is usually used to indicate horizontal motion and y vertical motion such as free fall under the influence of gravity.
Circular motion at constant speed: Motion in a circle is accelerated even though the speed is constant because the direction is continually changing. The force needed is directed toward the center of the circle. This type of motion is often called centripetal (“center-pointing”) motion because of this. The magnitude of the acceleration is given by
where v is the speed and R the radius of the circle. The true force producing the motion (the centripetal force) is directed inward, but someone traveling on the object in motion will seem to experience an outward-pointing centrifugal force of the same size. This centrifugal force is an illusion due to Newton’s first law, but it is often useful.
A.2 FUNDAMENTAL FORCES
There are only four fundamental forces, and we experience only two of them (gravitational and electromagnetic) in ordinary life. Equations describing them are used as needed in the text. The forces are the following:
Gravity: We are all most familiar with this force. Surprisingly, it is the weakest of the four fundamental forces by a very large factor. It acts between two bodies which have mass and is always attractive (that is, always pulls objects together).
Electromagnetic force: This force exists between charged objects. There are two types of charges, called + (the sign of the proton charge) and − (the sign of the electron charge.) Like charges repel, unlike attract. There are two odd things about this force: first, charges are quantized. Measurable charges come in integer multiples of the electron charge. No one really knows why. Second, the electromagnetic force is stronger than the gravitational force by a factor of 1040. Again, there’s no really good explanation why the strengths of the two forces are so unbalanced.
If charges are in motion, they create a magnetic field. If they oscillate back and forth, they create light. These are part of the electromagnetic force as well, but their properties aren’t as simple as the force between nonmoving charges. I discuss some of these things in chapter 3, but if you want a more complete explanation, see any first-year physics textbook.
Strong force: The nucleus of the atom is composed of protons and neutrons. Therefore, it is composed of a lot of positive charges pushing against each other. The nucleus doesn’t explode: some force must hold it together. This is the strong force. It is a force exerted between nucleons; it doesn’t extend to very far distances as the electromagnetic or gravitational forces do. It essentially dies off at distances much larger than about 10−15 m. The force is really between the quarks inside each of the nucleons. The force between neutrons and protons is just that which “leaks out.”
Weak force: This is a force responsible for certain types of decays such as the neutron into the proton, electron, and electron-antineutrino. It is very interesting: unlike the other forces, it can distinguish between right and left, and between antimatter and matter. It is very short range, but may be responsible for the existence of matter in the universe. Because of the asymmetry between matter and antimatter, during the Big Bang a very small (about one in a billion) preponderance of matter over antimatter arose. Most of the matter and all of the antimatter annihilated; the small remnant left over is the matter we see in the universe today.
Derived forces: All other forces are derived from the fundamental ones. Chemical bonds are electromagnetic in origin. Th
ey are due to the attractions and repulsions of the charges in the atoms making up the molecules. Friction is also electromagnetic in origin, as is almost every force we see acting on the large scale. Tension? Due to chemical bonding. Drag force? Due to impacts of molecules on bodies moving through a fluid. Again, chemical, meaning electromagnetic.
Physicists would like to show somehow that all four fundamental forces are merely manifestations of one even more fundamental. So far, our best efforts haven’t worked. In the 1970s, Glashow, Weinberg, and Salaam were able to show a fundamental link between the electromagnetic and weak force, but that’s about it so far.
BIBLIOGRAPHY
[1] BBC News. Kepler 22-b: Earth-like planet confirmed. http://www.bbc.co.uk/news/science-environment-16040655.
[2] CERN. Antimatter FAQs. http://livefromcern.web.cern.ch/livefromcern/antimatter/faq.html.
[3] Crank Dot Net. Einstein was wrong. http://www.crank.net/einstein.html.
[4] The Extrasolar Planets Encyclopedia. Catalog, s.v. “Imaging.” http://exoplanet.eu/catalog-imaging.php.
[5] The Extrasolar Planets Encyclopedia. Catalog, s.v. “Fomalhaut.” http://exoplanet.eu/star.php?st=Fomalhaut.
[6] NASA. NASA discovers first earth-size planets beyond our solar system. News release. http://www.jpl.nasa.gov/news/news.cfm?release=2011-390.
[7] NASA. Hubble Space Telescope FAQs. http://www.spacetelescope.org/about/faq/.
[8] NASA. Kennedy Space Center FAQs. http://science.ksc.nasa.gov/pao/faq/faqanswers.htm.
[9] NASA. Nuclear Pulse Space Vehicle Survey. vol. I, Summary. Technical report. National Aeronautics and Space Administration, Huntsville, AL, September 1964.
[10] NASA. Space Settlements: A Design Study. Edited by Richard D. Johnson and Charles Holbrow. Technical Report NASA SP-413. National Aeronautics and Space Administration, Ames Research Center, 1975.
[11] National Space Society. Space settlement design contest 2009 results. http://www.nss.org/settlement/nasa/Contest/Results/2009/ASTEN.pdf.
[12] Space Exploration Technologies Corporation. Dragon. http://www.spacex.com/dragon.php/.
[13] Space Exploration Technologies Corporation. Falcon 1e pricing and performance. http://www.spacex.com/falcon1.php/#pricing and performance.
[14] Space.Com. Endeavor’s shuttle launch delay comes with a large price tag. http://www.space.com/11525-space-shuttle-endeavour-launch-delay-cost.html.
[15] Television Tropes & Idioms. Recycled IN SPACE! http://tvtropes.org/pmwiki/pmwiki.php/Main/RecycledINSPACE.
[16] U.S. Census Bureau. Census death rate statistics. http://www.census.gov/compendia/statab/cats/transportation/motor vehicle accidents and fatalities.html.
[17] J. Ackeret. Zur Theorie der Raketen. Helvetica Physica Acta, 19:103–112, 1946.
[18] Douglas Adams. The Hitchhiker’s Guide to the Galaxy. Harmony Books, New York, 1979.
[19] Douglas Adams. The Restaurant at the End of the Universe. Ballantine Books, New York, 2005.
[20] Fred C. Adams and Gregory Laughlin. A dying universe: The long-term fate and evolution of astrophysical objects. Reviews of Modern Physics, 69(2):337–372, 1997.
[21] Poul Anderson. The Avatar. Putnam, New York, 1978.
[22] Poul Anderson. Tau Zero. Doubleday, Garden City, NY, 1970.
[23] Poul Anderson. The Earth Book of Stormgate. Berkley, New York, 1978.
[24] P. K. Aravind. The physics of the space elevator. American Journal of Physics, 75(2):125–130, 2007.
[25] Svante Arrhenius and Joens Elias Fries. The Destinies of the Stars. G. P. Putnam’s Sons, New York, 1918.
[26] Yuri P. Artutsanov. Skyhook: Old idea. Science, 158(3803):946–947, 1967.
[27] Yuri P. Artutsanov. Into space without rockets: A new idea for space launch. Znaniye-Sila, 7:25, 1969.
[28] Henri Arzeliès. Relativistic Kinematics. Pergamon Press, Oxford, 1966.
[29] W. L. Bade. Relativistic rocket theory. American Journal of Physics, 21:310–312, 1953.
[30] Arnold Barnett and Mary K. Higgins. Airline safety: The last decade. Management Science, 35(1):1–21, 1989.
[31] Roger R. Bate, Donald D. Mueller, and Jerry E. White. Fundamentals of Astrodynamics. Dover Publications, New York, 1971.
[32] Greg Bear. The Forge of God. Tor, New York, 1987.
[33] Greg Bear. Moving Mars. Tor, New York, 1993.
[34] Greg Bear. Anvil of Stars. Warner Books, New York, 1992.
[35] Edward Belbruno. Fly Me to the Moon. Princeton University Press, Princeton, NJ, 2007.
[36] John S. Bell. On the Einstein-Podolsky-Roden paradox. Physics, I, pp. 195–200, 1964.
[37] Gregory Benford and Larry Niven. Bowl of Heaven. Tom Doherty Associates, New York, 2012.
[38] Alfred Bester. The Stars My Destination. New American Library, New York, 1956.
[39] William J. Borucki et al. Kepler22b: A 2.4 Earth radius planet in the habitable zone of life of a sun-like star (preprint). http://arxiv.org/pdf/1112.1640v1, December 2011.
[40] Ray Bradbury. The Martian Chronicles. Doubleday, Garden City, NY, 1950.
[41] Kenneth Brower. The Starship and the Canoe. Holt, Rinehart & Winston, New York, 1978.
[42] Todd A. Brun. Computers with closed timelike curves can solve hard problems efficiently. Foundations of Physics Letters, 16(3):245–253, 2003.
[43] Edgar Rice Burroughs. A Princess of Mars. Doubleday, Garden City, NY, 1912.
[44] R. W. Bussard. Galactic matter and interstellar flight. Astronomica Acta, 6:97–111, 1960.
[45] Jim Butcher. Proven Guilty. Roc, New York, 2007.
[46] A. G. W. Cameron, ed. Interstellar Communication: A Collection of Reprints and Original Contributions. W. A. Benjamin, New York, 1963.
[47] Bradley W. Carroll and Dale A. Ostlie. An Introduction to Modern Astrophysics, 2nd ed. Addison-Wesley, San Francisco, CA, 2007.
[48] Hendrik G. B. Casimir. On the attraction between two perfectly conducting plates. Proceedings of the Koninklijke Nederlandse Akademic van Wetenschappen, 51:793–795, 1948.
[49] David Charbonneau, Timothy M. Brown, Robert W. Nayes, and Ronald L. Gilliland. Detection of an extrasolar planet atmosphere. Astrophysical Journal, 568:377–384, 2002.
[50] G. K. Chesterton. The Napoleon of Notting Hill. Dover Publications, New York, 1991.
[51] C. B. Clark. Experience in a non-inertial lab. Physics Teacher, 17:526, 1979.
[52] Arthur C. Clarke. Childhood’s End. Harcourt, Brace & World, New York, 1953.
[53] Arthur C. Clarke. The City and the Stars. Harcourt, Brace, New York, 1956.
[54] Arthur C. Clarke. Profiles of the Future, rev. ed. Harper and Row, New York, 1973.
[55] Arthur C. Clarke. The Promise of Space. Harper & Row, New York, 1968.
[56] Arthur C. Clarke. The Fountains of Paradise. Harcourt Brace Jovanovich, New York, 1979.
[57] Arthur C. Clarke. 2010: Odyssey Two. Ballantine Books, New York, 1982.
[58] Arthur C. Clarke and Stanley Kubrick. 2001: A Space Odyssey. Hutchinson, London, 1968.
[59] Hal Clement. Mission of Gravity. Doubleday, Garden City, NY, 1954.
[60] Giuseppe Cocconi and Philip Morrison. Search for interstellar communications. Nature, 184:844–846, 1959.
[61] Paul J. Crutzen and Eugene F. Stoermer. The “anthropocene.” Global Change Newsletter, 41:17–18, May 2000.
[62] Ingri D’Aulaire and Edgar Parin D’Aulaire. D’Aulaire’s Book of Norse Mythology. New York Review of Books, New York, 1967.
[63] J. Dennis and L. Choate. Some problems with artificial gravity. Physics Teacher, 8:441, 1970.
[64] Jared Diamond. The Third Chimpanzee: The Evolution and Future of the Human Animal. HarperCollins, New York, 1992.
[65] Jared Diamond. Guns, Germs, and Steel: The Fates of Human Societies. W. W. Norton, New York, 1999.
[66] Jared M. Diamond. Collapse: How Societies Choose to Fail or Succeed. Viking, New York, 2005.
[67] Philip K. Dick. Ubik. Doubleday, Garden City, NY, 1969.
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[68] Philip K. Dick. Galactic Pot-Healer. Vintage Books, New York, 1994.
[69] John D. Durand. Historical estimates of world population: An evaluation. Population and Development Review, 3(3):253–296, 1977.
[70] Damien Duvivier and Michel Wautelet. From the microworld to King Kong. Physics Education, 41:386–390, 2006.
[71] Freeman Dyson. Search for artificial stellar sources of infrared radiation. Science, 131(1341):1667–1668, 1960.
[72] Freeman Dyson. Interstellar transport. Physics Today, pp. 41–45, October 1968.
[73] Freeman Dyson. Time without end: Physics and biology in an open universe. Reviews of Modern Physics, 51(3):447–460, 1979.
[74] Freeman Dyson. The search for extraterrestrial technology. In Selected Papers of Freeman Dyson, 557–571. American Mathematical Society, 1996.
[75] George Dyson. Project Orion: The True Story of the Atomic Spaceship. Henry Holt, New York, 2002.
[76] Bradley C. Edwards. The Space Elevator: Niac Phase 1 Report. Technical report. NASA Institute for Advanced Concepts, Atlanta, GA, 2001.
[77] Bradley C. Edwards. The Space Elevator: Niac Phase 2 Report. Technical report. NASA Institute for Advanced Concepts, Atlanta, GA, 2003.
[78] A. Einstein, B. Podolsky, and N. Rosen. Can quantum-mechanical description of reality be considered complete? Physical Review, 47:777–780, 1935.
[79] Robert Erlich. Faster-than-light speeds, tachyons, and the possibility of tachyonic neutrinos. American Journal of Physics, 71(11):1109–1114, 2003.
[80] Gerald Feinberg. Possibility of faster-than-light particles. Physical Review, 159(5):1089–1105, 1967.
[81] Richard P. Feynman. The Character of Physical Law. MIT Press, Cambridge, MA, 1967.
[82] Richard P. Feynman, Anthony J. G. Hey, and Robin W. Allen. The Feynman Lectures on Computation. Addison-Wesley, New York, 1996.
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