Many years ago, Ed Tryon suggested that our entire Universe might simply be a fluctuation of the vacuum. The paper appeared in Nature (volume 246, page 396), where he pointed out the curious fact that our Universe contains zero energy — provided it is “flat”, which observations confirm. The point Tryon jumped off from — the secret of making universes out of nothing at all, as vacuum fluctuations — is that the gravitational energy of the Universe is negative.
The way to understand this is that if you think of a collection of matter, such as the atoms that make up a star, or the bricks that make up a pile, the “zero of gravitational energy” associated with those objects is when they are far apart — as far apart as it is possible for them to be. The strange thing is, as the objects fall together under the influence of gravity they lose energy. They start with none, and end up with less. So gravitational energy is negative, from the perspective in which everyday energy (the mc^^2 in those atoms and bricks) is positive. Any object in the Universe, like a planet, or the Sun, which is not spread out as far as possible literally has a negative amount of gravitational energy. And if it shrinks, its gravitational energy becomes more negative.
The reason this was so interesting to Tryon is that the energy of all the matter in the Universe, all the mc^^2, is positive. What’s more, if you take a lump of matter and squeeze it into a singularity, then at the singularity the negative gravitational energy of the mass is exactly equal and opposite to its mass energy.
If this blows your mind, you are in good company. One of my favourite Albert Einstein anecdotes recounts a tale from more than half a century ago, during World War Two, when Einstein acted as a part-time consultant with the US Navy Department, assessing ideas for new weapons. Einstein didn’t actually work in Washington, but every couple of weeks George Gamow, another eminent physicist, would bring a briefcase full of ideas up to Princeton for Einstein to peruse. One day, as Gamow recalled in his book My World Line (Viking, New York, 1970), the two physicists were crossing the road together, on their way from Einstein’s home to the Institute for Advanced Study, when Gamow casually mentioned a new idea that he had heard from another physicist, Pascual Jordan. Jordan had mentioned, tongue in cheek, that a star could be made out of nothing at all, because at the point of zero volume its negative gravitational energy precisely cancels out its positive mass energy.
“Einstein stopped in his tracks,” Gamow tells us, “and, since we were crossing a street, several cars had to stop to avoid running us down.”
Jordan’s idea will not work for the formation of a star, because any star trying to form from a singularity in this way will be inside a black hole, invisible to the Universe at large. But it will work for the creation of an entire universe, within the black hole.
Provided that the Universe is indeed flat, the energy involved in making a universe from a singularity is indeed zero! It is, in the words of Alan Guth, “the ultimate free lunch”.
Adapted from In Search of the Big Bang.
My review of “The Theoretical Minimum”, by Leonard Susskind and George Hrabovsky (Basic Books), as published in the Wall Street Journal, 2-3 Februarty 2013. The “Mr” rather than “Dr” is their house style!
If you major in physics at university, it is pretty easy later in life to keep current with art, literature or music. But if you major in art, literature or music, no matter how interested you might be in science, it is hard to get to grips with the exciting new developments that make headlines without a basic understanding of physics. I know from experience how difficult it is to bridge this gap, and there is a natural tendency for popularizers of science (myself included) to focus on the popularizing more than on the scientific nitty-gritty.
There are a few notable exceptions. The selection of Richard Feynman’s lectures published posthumously as “Six Easy Pieces” heads the pack, which includes almost anything by the mathematician Jacob Bronowski, perhaps David Deutsch’s “The Fabric of Reality” and the archetypal example of real science laid out clearly for anyone to understand, Charles Darwin’s “On the Origin of Species.” But even these examples indicate that physics is intrinsically harder than biology, in the sense that you need more of the basics before you can comprehend the full story. That is why I can recommend Darwin’s writing but not Albert Einstein’s papers on relativity theory.
So what do you do if you enjoyed science at school or college but ended up with a different career and are still wondering what makes the universe tick? Maybe you subscribe to Scientific American, follow news stories about black holes and read reviews of science books without quite finding enough meat to satisfy you. If so, Leonard Susskind and George Hrabovsky’s “The Theoretical Minimum” is the book for you.
In this neat little book the authors aim to provide the minimum amount of knowledge you need about classical physics (that is, everything except quantum mechanics) to gain some real understanding of the world or to proceed to “the next level,” which would be freshman physics at university. They do so with great success, and in the process they pull the rug out from under the all too common attitude that, while a physicist who doesn’t appreciate art is a philistine, an artist who doesn’t appreciate physics is only doing what comes naturally.
Mr. Susskind is a professor of physics at Stanford University and more widely known as the author of “The Black Hole War” and “The Cosmic Landscape.” Mr. Hrabovsky got sidetracked from a possible career in science but even without a science degree ended up running a technological research center, Madison Area Science and Technology, in Wisconsin///NOTE: ///.
Their book grew out of a course taught by Mr. Susskind at Stanford for local people in what he calls “the nonacademic community.” He found that the students, eager to learn but with no need to worry about grades or exams, wanted “the real thing—with equations.” And he gave it to them. But don’t be scared by that word “equations.” If you understand stock-market derivatives or futures trading there is nothing here to worry about—provided you start at the beginning and follow the story methodically.
That is where Mr. Susskind, aided by Mr. Hrabovsky, is so good. Their relationship began when Mr. Hrabovsky viewed Mr. Susskind’s lectures online and sent him an email suggesting that the course be turned into a book. The resulting collaboration between master and pupil is perfect for getting the message across.
It begins disarmingly simply, with nothing so complicated as a coin toss but rather with a coin glued to the table so that it always shows the same side. What could be simpler? This clever reduction is how the authors introduce the idea in physics of a “system”—that is, a collection of objects that can change and interact over time. Every system has a set of possible states it can be in, snapshot-like specifications of the configuration of every component at a given moment. In the case of the glued-down coin, there is only one possible state: heads, say. The job of classical mechanics, the authors write, “is to predict the future” by working out (and then applying) the laws that determine what state a system will be in later based on what state it’s in now.
The law for the sticky coin is easy: The future state will always be the same as the current one. But from this trivial example the authors build gradually to systems with more states and more moving parts, including a six-sided die and, eventually, the universe. By the end of the book, the committed reader will be familiar with Maxwell’s equations, the late 19th-century breakthrough that unified electricity and magnetism in four simple equations, and will have a thorough understanding of the force of gravity and its influence on planetary orbits, the work for which Isaac Newton is justly famous.
Along the way you get beautifully clear explanations of famously “difficult” things like differential and integral calculus, what physicists mean by symmetries, and conservation laws. Despite the emphasis here on classical physics, “The Theoretical Minimum” actually takes the reader to the edge of an introduction to quantum mechanics; we can only hope that this will be the theme of the team’s next book.
The authors also spell out where scientists and philosophers from the past sometimes went wrong, and why. Aristotle, they explain, “lived in a world dominated by friction,” so to make things move you had to push them, and keep on pushing. But “one suspects that Aristotle never went ice skating, or he would have known that it is just as hard to stop a body as to get it moving.” The genius of Isaac Newton was that, although he too lived in a world dominated by friction, and as far as we know never went ice skating, he realized that every “body” keeps moving in a straight line at a constant speed unless it is acted on by a force.
So Messrs. Susskind and Hrabovsky give us the relevant equations, show how they work, lead us gently through some examples, and then offer basic exercises so that we can test our skill with the equations. Their explanations are clear but not wordy, as when they introduce momentum:
If you are struck by a moving object, the result depends not only on the velocity of the object but also on its mass. Obviously, a Ping-Pong ball at 30 miles per hour (about 13 meters per second) will have much less of a mechanical effect than a locomotive moving at about the same speed. In fact, the effect is proportional to the momentum of the object, which for now we shall define as the product of the velocity and the mass. Since the velocity is a vector, so is the momentum, denoted by the letter p. Thus pi = mivi.
It may sound like being back in school; but a better analogy would be with the way a personal trainer works, starting with easy exercises under supervision and building up to a more vigorous, unsupervised workout. And just like the pleasure of achieving a personal best in the gym, we have the pleasure of getting the right “answer” to a puzzle that would have baffled Aristotle but would have been as clear as day to Newton. It almost makes you think you could have been a Newton yourself, given the opportunity.
More subtly, along the way the authors expound what might be called the philosophy of science, making it clear why physics contains deep truths about the universe. Classical mechanics predicts the future, as the authors note, with far more success than alternatives such as astrology or the I Ching, but they are not afraid to spell out the limits of precision. Even if some of the equations do pass over the heads of some readers, Messrs. Susskind and Hrabovsky’s book is a powerful exposition of why science is “real” and a counter to the kind of wishful thinking employed by people who, for whatever reason, reject the scientific worldview.
This is the most important reason for recommending this book and books like it (few though they are). We live in a scientific world, where our everyday lives are dependent on the technology that science has provided for us. “Popular” accounts of things like black holes and quantum physics can make them seem like magic, which can lead some people to believe other seemingly magic worldviews are equally valid. They are not, and nowhere is the irony more apparent than when pseudoscientific ideas, such as claims that the world is about to end, are disseminated widely around the world using one of the ultimate achievements of real science, the Internet. Anyone who grasps the theoretical minimum outlined here will be well-placed to distinguish reality from wishful thinking.
And once you grasp this distinction, you are ready for a profound delight, the kind of thing that physicists (rightly) describe as “beautiful.” At the heart of this book, both physically and metaphorically, is the “principle of least action” (“action” being a technical term that refers, basically, to the overall energy in a system over time). The most important idea in physics, it can be summed up in the phrase “the universe is lazy.” Among many other things, the principle underpins why light moves in straight lines and how light “knows” which angle to turn through when it moves from one medium (such as air) to another (such as glass). The principle can be used to describe the parabola traced by a thrown baseball and, indeed, to derive Newton’s laws. If I had my way, all of physics would be taught starting with the principle of least action and working outward from there; “The Theoretical Minimum” comes close to realizing my dream. Armed with this insight, you’ll be able to appreciate beauty in an equation, as well as in a flower or a piece of music.
Which brings me to the audience for the book. The book most definitely hits the spot for the kind of mature, committed “nonacademic” that the authors have in mind. Equally, it is certainly not for the dilettante science-watcher happy with the kind of “pop science” accounts that deal as far as possible in words and images without worrying about the equations—not that I am knocking such books; I write them myself. But it is also just the right book for a much younger audience than the mature people with careers behind them who filled the classes at Stanford. It is spot-on for any young student of science to read before heading off to college to study physics seriously, and I shall certainly be recommending it in that connection. “The Theoretical Minimum” should also be required reading for our politicians and lawmakers—but that is probably hoping for too much.
Six Easy Pieces
by Richard Feynman (1963)
These transcripts of lectures given by Feynman at Caltech capture the informal flavor of the man talking to you, as well as conveying basic ideas in physics.
The Origins of Knowledge and Imagination
By Jacob Bronowski (1978)
Bronowski’s books were a profound influence on me in my youth. This one explores the nature of science and the differences between humans and other animals, covering everything from DNA to Turing Machines in erudite but accessible prose.
The Fabric of Reality
By David Deutsch (1997)
Subtitled ‘towards a theory of everything’ this book offers one physicist’s view of the state of human knowledge, presented in three strands: the many-worlds interpretation of quantum physics; the philosopher Karl Popper’s concept of how science works; and Charles Darwin and Alfred Wallace’s theory of evolution by natural selection.
The Origin of Species
By Charles Darwin (1859)
Darwin’s own account of natural selection is the clearest exposition of any major scientific theory by its discoverer. It requires no previous knowledge, is beautifully written, and has been continuously in print since 1859.
Mr. Tompkins in Paperback
By George Gamow (1965)
This is a bit of a wild card. Gamow was a pioneering quantum theorist who also dabbled in the study of DNA and cosmology. His “Mr. Tompkins” books are delightful, if slightly dated, accounts of the Big Ideas in 20th-century science seen through the eyes of his eponymous hero, a bank clerk. Whimsical, but strictly scientifically accurate.