by Michio Kaku
Thus, the multiverse idea allows one to combine both the creation mythology of Christianity with the Nirvana of Buddhism into a single theory that is compatible with known physical laws.
Meaning in a Finite Universe
In the end, I believe that we create our own meaning in the universe.
It is too simple and easy to have some guru come down from the mountaintop, bearing the meaning of the universe. The meaning of life is something that we have to struggle to understand and appreciate. Having it given to us defeats the whole purpose of meaning. If the meaning of life were available for free, then it would lose its meaning. Everything that has meaning is the result of struggle and sacrifice, and is worth fighting for.
But it is hard to argue that the universe has a meaning if the universe itself will eventually die. Physics, in some sense, has a death warrant for the universe.
Despite all learned discussions about meaning and purpose in the universe, perhaps it is all for naught, because the universe is doomed to die in a Big Freeze. According to the second law of thermodynamics, everything in a closed system must eventually decay, rust, or fall apart. The natural order of things is to decline and eventually cease to exist. It seems inescapable that all things must die when the universe itself dies. So whatever meaning we may ascribe to the universe will eventually be wiped away when the universe itself dies.
But once again, perhaps the merger of the quantum theory with relativity provides an escape clause. We said that the second law of thermodynamics eventually dooms the universe in a closed system. The key word is closed. In an open universe, where energy can enter from the outside, it is possible to reverse the second law.
For example, an air conditioner seems to violate the second law because it takes in chaotic hot air and cools it down. But an air conditioner gets energy from the outside, from a pump, and hence is not a closed system. Likewise, even life on Earth seems to violate the second law, because it takes just nine months to convert hamburgers and french fries into a baby, which truly is a miracle.
So why is life possible on the Earth? Because we have an external source of energy, the sun. The Earth is not a closed system, so sunlight allows us to extract energy from the sun to create the food necessary to feed a baby. So the second law of thermodynamics has an escape clause. Sunlight makes evolution to higher forms possible.
In the same way, it is possible to use wormholes to open a gateway to another universe. Our universe appears to be closed. But one day, perhaps facing the death of the universe, our descendants may be able to use their formidable scientific know-how to channel enough positive energy to open a tunnel through space and time, and then use negative energy (from the quantum Casimir effect) to stabilize the gateway. One day, our descendants will master the Planck energy, the energy at which space and time become unstable, and use their powerful technology to escape our dying universe.
In this way, quantum gravity, instead of being an exercise in the mathematics of eleven-dimensional space-time, becomes a cosmic interdimensional lifeboat allowing intelligent life to evade the second law of thermodynamics and escape to a much warmer universe.
So the theory of everything is more than just a beautiful mathematical theory. Ultimately, it could be our only salvation.
Conclusion
The search for the theory of everything has led us into a quest to find the ultimate unifying symmetry of the universe. From the warmth of a summer breeze to the glory of a blazing sunset, the symmetry we see all around us is a fragment of the original symmetry found at the beginning of time. That original symmetry of the superforce was broken at the instant of the Big Bang, and we see remnants of that original symmetry wherever we admire the beauty of nature.
I like to think that perhaps we are like two-dimensional Flatlanders living in some mythical flat plane, unable to visualize the third dimension, which is considered just a superstition. In the beginning of time in Flatland, there was once a beautiful three-dimensional crystal that, for some reason, was unstable and shattered into a million pieces that rained down on Flatland. For centuries, the Flatlanders have tried to reassemble these pieces like a jigsaw puzzle. Over time, they were able to assemble them into two gigantic pieces. One piece was called gravity, the other piece was called the quantum theory. Try as they might, the Flatlanders could never fit these two pieces together. Then one day, an enterprising Flatlander made an outrageous conjecture that set everyone laughing. Why not, he said, using mathematics, lift one of the pieces into an imaginary third dimension so they can fit together, one on top of the other? When this was done, the Flatlanders were amazed and astonished at the dazzling, shimmering jewel that suddenly emerged before them, with its perfect, glorious symmetry.
Or, as Stephen Hawking wrote,
If we do discover a complete theory, it should in time be understandable in broad principle by everyone, not just a few scientists. Then we shall all, philosophers, scientists, and just ordinary people, be able to take part in the discussion of the question of why it is that we and the universe exist. If we find the answer to that, it would be the ultimate triumph of human reason—for then we would know the mind of God.
ACKNOWLEDGMENTS
In writing this book, I am deeply in debt to my agent, Stuart Krichevsky, who has been faithfully at my side for all these decades, giving me sound and wise advice. I always trust his judgment and his intimate understanding of both literary and scientific matters.
I also would like to thank my editor, Edward Kastenmeier, who has guided several of my books with his firm hand and sharp insight. He was the one who suggested that I write this book, and has shepherded the book through all its various stages. This book would have been impossible without his thoughtful and honest advice.
I would also like to thank my colleagues, associates, and friends in the scientific field. In particular, I would like to thank the following Nobel laureates for generously giving me their time and deep insights into physics and the sciences: Murray Gell-Mann, David Gross, Frank Wilczek, Steve Weinberg, Yoichio Nambu, Leon Lederman, Walter Gilbert, Henry Kendall, T. D. Lee, Gerald Edelman, Joseph Rotblat, Henry Pollack, Peter Doherty, and Eric Chivian. Lastly, I would like to thank the more than four hundred physicists and scientists with whom I have had the pleasure of interacting with, both as collaborators in string research, as well as through my weekly science radio programs, the various TV programs that I have hosted for BBC-TV and the Discovery and Science Channels, and my work as the science correspondent for CBS-TV.
For a more complete list of the scientists whom I have had the pleasure of interviewing, please see my book The Physics of the Future. For a more complete list of prominent string theorists whose work I reference in this book, see my Ph.D.-level textbook Introduction to String Theory and M-Theory.
NOTES
Introduction to the Final Theory
But many others have also tried: In the past, many of the giants of physics have tried to create their own unified field theory and failed. In retrospect, we see that a unified field theory must satisfy three criteria:
It must include all of Einstein’s theory of general relativity.
It must include the Standard Model of subatomic particles.
It must yield finite results.
Erwin Schrödinger, one of the founders of the quantum theory, had a proposal for the unified field theory that was actually studied earlier by Einstein. It failed because it did not reduce to Einstein’s theory correctly and could not explain Maxwell’s equations. (It also lacked any description of electrons or atoms.)
Wolfgang Pauli and Werner Heisenberg also proposed a unified field theory that included fermion matter fields, but it was not renormalizable and did not incorporate the quark model, which would come decades later.
Einstein himself investigated a series of theories that ultim
ately failed. Basically, he tried to generalize the metric tensor for gravity and the Christoffel symbols to include antisymmetric tensors, in an attempt to include Maxwell’s theory in his own theory. This ultimately failed. Simply expanding the number of fields in Einstein’s original theory was not enough to explain Maxwell’s equations. This approach also made no mention of matter.
Over the years, there have been a number of attempts to simply add matter fields to Einstein’s equations, but they have been shown to diverge at the one-loop quantum level. In fact, computers have been used to calculate the scattering of gravitons at the one-loop quantum level, and it has been shown to be conclusively infinite. So far, the only known way to eliminate these infinities at the lowest one-loop level is to incorporate supersymmetry.
A more radical idea was proposed as early as 1919 by Theodor Kaluza, who expressed Einstein’s equations in five dimensions. Remarkably, when one curls one dimension into a tiny circle, one finds the Maxwell field coupled to Einstein’s gravity field as a result. This approach was studied by Einstein but was eventually abandoned because no one understood how to collapse one dimension. More recently, this approach has been incorporated into string theory, which collapses ten dimensions to four dimensions and in the process generates the Yang-Mills field. So of the many approaches made for a unified field theory, the only path that survives today is the Kaluza higher-dimensional approach, but generalized to include supersymmetry, superstrings, and supermembranes.
More recently, there is a theory called loop quantum gravity. It investigates Einstein’s original four-dimensional theory in a new way. However, it is a theory of pure gravity, without any electrons or subatomic particles, and hence cannot qualify as a unified field theory. It makes no mention of the Standard Model, because it lacks matter fields. Also, it is not clear if the scattering of multiloops in this formalism is truly finite. There is speculation that the collision between two loops yields divergent results.
Chapter 1: Unification—The Ancient Dream
“It is with Isaac Newton”: Steven Weinberg, Dreams of a Final Theory (New York: Pantheon, 1992), 11.
So the equations of Newton: Because Newton’s Principia was written in a purely geometric fashion, it is clear that Newton was aware of the power of symmetry. It is also clear that he exploited the power of symmetry intuitively to calculate the motion of the planets. However, because he did not use the analytic form of calculus, which would involve symbols like X2 + Y2, his manuscript does not represent symmetry analytically in terms of coordinates X and Y.
“We can scarcely avoid”: Quotefancy.com, https://quotefancy.com/quote/1572216/James-Clerk-Maxwell-We-can-scarcely-avoid-the-inference-that-light-consists-in-the-transverse-undelations-of-the-same-medium-which-is-the-cause-of-electric-and-magnetic-phenomena.
“So the symmetry”: Technically speaking, Maxwell’s equations are not perfectly symmetrical between electric and magnetic fields. For example, electrons are the sources of electric fields, but Maxwell’s equations predict the presence of sources for the magnetic field as well, called monopoles (i.e., isolated north and south poles of magnetism), which have never been seen. Therefore, some physicists have conjectured that these monopoles may eventually be discovered.
Chapter 2: Einstein’s Quest for Unification
“I am nothing but”: Abraham Pais, Subtle Is the Lord (New York: Oxford University Press, 1982), 41.
“A storm broke loose”: Quotation.io, https://quotation.io/page/quote/storm-broke-loose-mind.
“I owe more to Maxwell”: Albrecht Fölsing, Albert Einstein, trans. and abridged Ewald Osers (New York: Penguin Books, 1997), 152.
“mathematician’s patterns”: Wikiquotes.com, https://en.wikiquote.org/wiki/G._H._Hardy.
This means that the three: So although special relativity has a four-dimensional symmetry, as seen by the simple four-dimensional Pythagorean theorem X2 + Y2 + Z2 − T2 (in certain units), time enters with an extra minus sign compared to the other spatial dimensions. This means that time is indeed the fourth dimension, but of a special type. In particular, it means you cannot easily go back and forth in time (otherwise time travel would be commonplace). One easily goes back and forth in space, but not easily in time, because of this extra minus sign. (Also, notice that we have set the speed of light to be 1, in certain units, to make it clear that time enters into special relativity as the fourth dimension.)
“As an older friend”: Brandon R. Brown, “Max Planck: Einstein’s Supportive Skeptic in 1915,” OUPblog, Nov. 15, 2015, https://blog.oup.com/2015/11/einstein-planck-general-relativity.
“For some days”: Fölsing, Albert Einstein, 374.
“as if I had been wandering”: Denis Brian, Einstein (New York: Wiley, 1996), 102.
“A new scientific truth does not”: Johann Ambrosius and Barth Verlag (Leipzig, 1948), p. 22, in Scientific Autobiography and other papers.
“Everyone who had any substantial contact”: Jeremy Bernstein, “Secrets of the Old One—II,” New Yorker, March 17, 1973, 60.
Chapter 3: Rise of the Quantum
“I think I can safely say”: https://en.wikiquote.org/wiki/Talk:Richard_Feynman.
“I will never forget the sight”: quoted in Albrecht Fölsing, Albert Einstein, trans. and abridged Ewald Osers (New York: Penguin Books, 1997), 516.
“It was the greatest debate”: quoted in Denis Brian, Einstein (New York: Wiley, 1996), 306.
With the success of quantum theory: Even today, there is no universally accepted solution to the cat problem. Most physicists simply use quantum mechanics as a cookbook that always yields the proper answer and ignore the subtle, deep philosophical implications. Most graduate courses on quantum mechanics (including the one that I teach) simply mention the cat problem but offer no definitive solution. Several solutions have been proposed, which are usually variations of two popular approaches. One is to acknowledge that the consciousness of the observer has to be part of the measuring process. There are variations to this approach, depending on how you define “consciousness.” Another approach, which is gaining popularity among physicists, is the multiverse theory, where the universe splits in half, with one universe containing the live cat, and another containing a dead cat. It is, however, nearly impossible to go back and forth between these two universes, because they have “decohered” from each other—that is, they no longer vibrate in unison, so they can no longer communicate with each other. In the same way that two radio stations cannot interact with each other, we have decohered from all the other parallel universes. So bizarre quantum universes might coexist with ours, but communicating with them is almost impossible. We might have to wait longer than the lifetime of the universe to pass into these parallel universes.
Chapter 4: Theory of Almost Everything
“You are on a lion hunt”: Denis Brian, Einstein (New York: Wiley, 1996), 359.
“I believe I am right”: quoted in Walter Moore, A Life of Erwin Schrödinger (Cambridge: Cambridge University Press, 1994), 308.
“We in the back”: Nigel Calder, The Key to the Universe (New York: Viking, 1977), 15.
“It was an uncanny encounter”: quoted in William H. Cropper, Great Physicists (Oxford: Oxford University Press, 2001), 252.
“The numerical agreement”: Steven Weinberg, Dreams of a Final Theory (New York: Pantheon, 1992; New York: Vintage, 1994), 115.
“This is just not sensible mathematics”: John Gribbin, In Search of Schrödinger’s Cat (New York: Bantam Books, 1984), 259.
“if I had known”: quoted in Dan Hooper, Dark Cosmos (New York: HarperCollins, 2006), 59.
“I have committed”: Frank Wilczek and Betsy Devine, Longing for Harmonies (New York: Norton, 1988), 64.
Physicist Sheldon Glashow would exclaim: Robert P. Crease and Charles C. Mann, The Second Creation (New York: Macmill
an, 1986), 326.
They realized that by cobbling together three theories: The mathematical symmetry that mixes three quarks is called SU(3), the special unitary Lie group of degree 3. So by rearranging the three quarks according to the symmetry SU(3), the final equation for the strong nuclear force must remain the same. The symmetry that mixes the electron and neutrino in the weak nuclear force is called SU(2), the Lie group in degree 2. (In general, if we start with n fermions, then it is straightforward to write down a theory with SU(n) symmetry.) The symmetry coming from Maxwell’s theory is called U(1). Therefore, by gluing these three theories together, we find that the Standard Model has symmetry SU(3) × SU(2) × U(1).
Although the Standard Model fits all the experimental data on subatomic physics, the theory seems contrived, because it is based on mechanically patching three forces together.
Second, the Standard Model: To compare the simplicity of Einstein’s equations to the complexity of the Standard, we note that Einstein’s theory can be summarized in just a short equation:
while the Standard Model’s equations (in highly abbreviated form) require most of the page to write, detailing the various quarks, electrons, neutrinos, gluons, Yang-Mills particles, and Higgs particles.
Remarkably, we know that all physical laws of the universe can, in principle, be derived from this one page of equations. The problem is that the two theories—Einstein’s relativity theory and the Standard Model—are based on different mathematics, different assumptions, and different fields. The ultimate goal is to merge these two sets of equations into a single, finite unified fashion. The key observation is that any theory claiming to be the theory of everything must contain both sets of equations, yet remain finite. So far, of all the various theories that have been proposed, the only theory that can do this is string theory.
