He wrote, "It is more important to have beauty in one's equations than to have them fit experiments..." Cole, p. 225.
11: FASTER THAN LIGHT.
As physicist Matt Visser of Washington University says.... Cavelos, p. 137.
Sir Martin Rees, Royal Astronomer of Great Britain, even says... Kaku, Parallel Worlds, p. 307.
"I thought there should be a way of using these concepts..." Cavelos, p. 151.
"In back, they wouldn't see anything-just black-because the light of the stars..." Cavelos, p. 154.
"We would need a series of generators of exotic matter..." Cavelos, p. 154.
"Pa.s.s through this magic ring and-presto!..." Kaku, Parallel Worlds, p. 121.
He says, "You need about minus one Jupiter ma.s.s to do the job..." Cavelos, p. 145.
"But it will also turn out that the technology for making wormholes..." Hawking, p. 146.
12: TIME TRAVEL.
In the novel Ja.n.u.s Equation, writer G. Spruill explored one... Nahin, p. 322.
"As for the present, if it were always present and never moved..." Pickover, p. 10.
"Because we physicists have realized that the nature of time..." Nahin, p. ix.
As physicist Richard Gott has said, "I don't think there's any question..." Pickover, p. 130.
Gott says, "A collapsing loop of string large enough..." Kaku, Parallel Worlds, p. 142.
"If he marries in the past can he be tried for bigamy..." Nahin, p. 248.
13: PARALLEL UNIVERSES.
Henderson writes, "Like a Black Hole,..." Kaku, Hypers.p.a.ce, p. 22.
"At first glance, I like your idea enormously..." Pais, p. 330.
Enrico Fermi, horrified at the proliferation of subatomic particles... Kaku, Hypers.p.a.ce, p. 118.
Max Tegmark of MIT believes that in fifty years... Max Tegmark, New Scientist Magazine, November 18, 2006, p. 37.
Schrodinger railed against this interpretation of his theory... Cole, p. 222.
"So I hope you can accept nature as She is-absurd." Greene, p. 111.
Another viewpoint on the paradox is the "many worlds" idea... Yet another attractive feature of the "many worlds" interpretation is that no further a.s.sumptions other than the original wave equation are required. In this picture we never have to collapse wave functions or make observations. The wave function simply divides all by itself, automatically, without any intervention or a.s.sumptions from the outside. In this sense, the "many worlds" theory is simpler conceptually than all the other theories, which require outside observers, measurements, collapses of waves, and so forth. It is true that we are burdened with infinite numbers of universes, but the wave function keeps track of them, without any further a.s.sumptions from the outside.
One way to understand why our physical universe seems so stable and secure is to invoke decoherence, that is, that we have decohered from all these other parallel universes. But decoherence does not eliminate these other parallel universes. Decoherence only explains why our universe, among an infinite set of universes, seems so stable. Decoherence is based on the idea that universes can split into many universes, but that our universe, via interactions from the environment, becomes quite separated from these other universes.
n.o.bel laureate Frank Wilczek says, "We are haunted..." Kaku, Parallel Worlds, p. 169.
14: PERPETUAL MOTION MACHINES.
"It was Santa Claus and Aladdin's lamp of the whole world," Asimov, p. 12.
In theory, a perpetual motion machine of the second type... Some people have objected, declaring that the human brain, representing perhaps the most complex object ever created by mother nature in the solar system, violates the Second Law. The human brain, consisting of over 100 billion neurons, is unrivaled in complexity by anything out to 24 trillion miles of the Earth, to the nearest star. But how can this vast reduction in entropy be compatible with the Second Law, they ask? Evolution itself seems to violate the Second Law. The answer to this is that the decrease in entropy created by the rise of higher organisms, including humans, came at the expense of raising the total entropy elsewhere. The decrease in entropy created by evolution is more than balanced out by the increase in entropy in the surrounding environment, that is, the entropy of sunlight hitting the Earth. The creation of the human brain via evolution does lower entropy, but this is more than compensated for by the chaos that we create (e.g., pollution, waste heat, global warming, etc.).
One of the proponents of this idea... Tesla, however, was also a tragic figure, probably cheated out of the royalties of many of his patents and inventions that paved the way for the coming of radio, TV, and the telecommunications revolution. (We physicists, however, have guaranteed that the name of Tesla will not be forgotten. We have named the unit of magnetism after him. One tesla equals 10,000 gauss, or roughly twenty thousand times the magnetic field of the Earth.) Today he is largely forgotten, except that his more eccentric claims have become the stuff of conspiracy buffs and urban legend. Tesla believed that he could communicate with life on Mars, solve Einstein's unfinished unified field theory, split the Earth in half like an apple, and develop a death ray that could destroy ten thousand airplanes from a distance of 250 miles. (The FBI took his claim of a death ray so seriously that it seized much of his notes and laboratory equipment after his death, some of which are still kept in secret storage even today.) Tesla was at the height of his fame in 1931 when he made the front page of Time magazine. He regularly dazzled the public by unleashing huge bolts of lightning, containing millions of volts of electrical energy, to gasping audiences. Tesla's undoing, however, was that he was notoriously sloppy with his finances and his legal affairs. Pitted against the battery of lawyers representing the emerging electrical giants of today, Tesla lost control over his most important patents. He also began to show signs of what is today called OCD (obsessive-compulsive disorder), being obsessed with the number "three." He later became paranoid, living in dest.i.tution in the New Yorker Hotel, fearing being poisoned by his enemies, and was always one step ahead of his creditors. He died in total poverty at the age of eighty-six in 1943.
EPILOGUE: THE FUTURE OF THE IMPOSSIBLE.
Astronomer John Barrow notes, "Historians still debate..." Barrow, Impossibility, p. 47.
Mathematician David Hilbert, in rejecting Comte's claims... Barrow, Impossibility, p. 209.
"Two hundred years ago, you could ask anybody,..." Pickover, p. 192.
"All the great questions about the nature of the Universe-from its beginning to its end-turn out to be unanswerable." Barrow, Impossibility, p. 250.
"But gravitational waves from [the] inflation area are relics of the universe..." Rocky Kolb, New Scientist Magazine, November 18, 2006, p. 44.
"These efforts will reveal intimate details of the Big Bang singularity..." Hawking, p. 136.
"Do the laws of physics permit highly advanced civilizations..." Barrow, Impossibility, p. 143.
"In 2056, I think you'll be able to buy a T-shirt..." Max Tegmark, New Scientist Magazine, November 18, 2006, p. 37.
Today the leading (and only) candidate for a theory... The reason for this is that when we take Einstein's theory of gravity and add quantum corrections, these corrections instead of being small are infinite. Over the years physicists have devised a number of tricks to eliminate these infinite terms, but they all fail for a quantum theory of gravity. But in string theory these corrections vanish exactly for several reasons. First, string theory has a symmetry, called supersymmetry, which cancels many of these divergent terms. Also string theory has a cutoff, the length of string, which helps to control these infinities.
The origin of these infinities actually goes back to cla.s.sical theory. Newton's inverse-square law says that the force between two particles is infinite if the distance of separation goes to zero. This infinity, which is apparent even in Newton's theory, carries over to the quantum theory. But string theory has a cutoff, the length of the string, or the Planck length, which allows us to control these divergences.
"We would then be able to observe them in the sky..." Alexander Vilenkin, New Scientist Magazine, November 18, 2006, p. 51.
Astrophysicist John Barrow summarizes this logic this way... Barrow, Impossibility, p. 219.
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Kaku, Michio. Einstein's Cosmos. New York: Atlas Books, 2004.
---. Hypers.p.a.ce. New York: Anchor Books, 1994.
---. Parallel Worlds: A Journey Through Creation, Higher Dimensions, and the Future of the Cosmos. New York: Doubleday, 2005.
---. Visions: How Science Will Revolutionize the 21st Century. New York: Anchor Books, 1997.
Lemonick, Michael. The Echo of the Big Bang. Princeton, NJ: Princeton University Press, 2005.
Mallove, Eugene, and Gregory Matloff. The Starflight Handbook: A Pioneer's Guide to Interstellar Travel. New York: Wiley and Sons, 1989.
Nahin, Paul J. Time Machines. New York: Springer Verlag, 1999.
Pais, A. Subtle Is the Lord. New York: Oxford University Press, 1982.
Pickover, Clifford A. Time: A Traveler's Guide. New York: Oxford University Press, 1998.
Randi, James. An Encyclopedia of Claims, Frauds, and Hoaxes of the Occult and Supernatural. New York: St. Martin's Press, 1995.
Rees, Martin. Before the Beginning: Our Universe and Others. Reading, Ma.s.s.: Perseus Books, 1997.
Sagan, Carl. The Cosmic Connection: An Extraterrestrial Perspective. New York: Anchor Press, 1973.
Thorne, Kip S. Black Holes and Time Warps: Einstein's Outrageous Legacy. New York: W. W. Norton, 1994.
Ward, Peter D., and Donald Brownlee. Rare Earth: Why Complex Life Is Uncommon in the Universe. New York: Springer Science, 2000.
Weinberg, Steve. Dreams of a Final Theory: The Search for Fundamental Laws of Nature. New York: Pantheon Books, 1992.
Wells, H. G. The Time Machine: An Invention. London: McFarland and Co., 1996.
Other books by Michio Kaku.
EINSTEIN'S COSMOS VISIONS.
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