Probable impossibilities, p.2
Probable Impossibilities, page 2
Now, the infinity of the small. Like the cosmos at large, atoms are mostly empty space. In each atom, a tiny nugget at the center, called the nucleus, is surrounded by electrons, almost weightless by comparison and orbiting at a distance a hundred thousand times the size of the nucleus. Let us travel to smaller sizes. The atomic nucleus is divisible, composed of smaller particles called protons and neutrons. And each of those is made of even smaller particles, called quarks, whose sizes were first measured with giant particle accelerators in 1969. A quark is about one hundred million times smaller than an atom.
Are quarks the end of the line, the smallest objects in nature? If he were alive today, Pascal would say no. He would simply imagine cutting a quark into two, then cutting each of those pieces in two, and so on, ad infinitum. If we follow through with this Pascalian prescription, however, we eventually hit another limit. We reach a point where gravitational physics and quantum physics come together in an unholy marriage. Gravitational physics, described by Einstein’s theory of general relativity, tells us that the geometries of space and time are affected by mass and energy. That is, a mass like the Sun bends space the same way that a bowling ball on a trampoline sinks and flexes the mat beneath it. Masses also make time flow more slowly the closer you are to the mass.
The other partner in the marriage is quantum physics. Quantum physics, also developed in the 1920s, shows that in the subatomic realm, particles take on a hazy, nondefinite character, behaving as if they existed in several places at once. Although we don’t yet have a theory of “quantum gravity,” we can still estimate the size of the region in which quantum physics and gravitational physics would merge. This ultra-tiny scale is called the “Planck length,” named after the physicist Max Planck, a pioneer in quantum physics. The Planck length is 10-33 centimeters, a hundred million billion times smaller than a quark. Another way to visualize the infinitesimal size we are talking about: the Planck length is smaller than the nucleus of an atom by about the same ratio as the nucleus is smaller than the state of Rhode Island. It staggers the mind that we have anything at all to say about such infinitesimal elements of reality.
Because of the hazy, nondefinite character of quantum physics (called the Heisenberg uncertainty principle), at the dimensions of the Planck length, space and time churn and seethe, with the distance between any two points wildly fluctuating from moment to moment, and time randomly speeding and slowing, perhaps even going backward and forward. In such a situation, time and space no longer exist in a way that has meaning to us. The sensation of smooth time and space that we experience in our large world of houses and trees results only from averaging out this extreme lumpiness and chaos at the Planck length, in the same way that the graininess of a beach disappears when looked at from a thousand feet up.
Thus, if we relentlessly halve space again and again, paying homage to Pascal, searching for the infinity of the small, once we arrive at the phantasmagoric world of Planck, space no longer has meaning. Instead of probing the nature of the infinity of the small, we have invalidated the words used to ask the question. Space has been blown thin by an ancient glassblower, so thin that it dissolves into nothingness. The Planck world is a ghost world. It is a world without “time” and without “space.” Just as Pascal suggested, we find ourselves at the abyss between nothingness and infinity. And in doing so, we have found limits to the smallest and largest things observable, limits imposed by the science of two and a half centuries after Pascal.
Scientists today, especially physicists, have also reached a point where their imagination far exceeds the possibility of experimental testing. Physicists have hypothesized that the smallest elements of nature are not particles, like electrons, but extremely tiny one-dimensional “strings” of energy, the size of the Planck length—a size that would require particle accelerators larger than the Earth to explore. Physicists have also speculated about the existence of other universes, possibly infinite in extent, which will never be in contact with our universe and thus are impossible to confirm. Cosmologists have theorized about the origin of our universe. Did time and space begin with the Big Bang, or did they exist before, in some quantum haze? Although there are various theories to answer these questions, it is unlikely that we will ever know which, if any, is correct. In sum, we have added much detail to Pascal’s two infinities, we have embroidered his imagination with more advanced imagination, but we still find ourselves in the realm of the hypothetical as opposed to the definite, and we may remain there for a long time, perhaps an infinite time. A great philosopher of science, Karl Popper, once said that a proposition is not scientific unless it can be falsified—that is, unless one can perform an experiment that proves it wrong. At any given moment in history, the scientific theories and ideas we endorse are those that have not been falsified. If we can never test the infinities of the small and the infinities of the large, perhaps these notions are not scientific after all. But they are certainly vibrant in the realm of the imagination.
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Finally, I would like to return to the invocation of human beings in Pascal’s passage from the Pensées—the physical aspects, the philosophical, and the psychological. Pascal could simply have said that the universe extends to infinity, both in the large and the small. But he refers to cosmic scales in terms of human beings. First, compared to the infinitely large: “What is man in the infinite?” And then, compared to the infinitely small: “For who will not be astounded at the fact that our body, which a little while ago was imperceptible in the universe…is now a colossus, a world, or rather a whole in respect of the nothingness [smallness] which we cannot reach?” Man has a “body given him by nature between these two abysses of the Infinite and Nothing.”
Using our modern knowledge of the sizes of things, we can say very specifically where human beings fit in the hierarchy of the cosmos. How many times should the size of a human body be halved to reach the size of an atom (a size unknown until the twentieth century)? The answer is about 33. Going in the opposite direction, one can ask how many times the size of the human body should be doubled to reach the size of a typical star, like our Sun, the largest object known by Pascal. The answer is 30. Thus, counting in doublings, the size of a human being is nearly halfway between an atom and a star—certainly not two infinities, but a minuscule thing of the natural world at one end and a gargantuan at the other. So, although Pascal did not have the quantitative knowledge of the cosmos we have today, there is a sense in which we human beings, at least physically, are indeed between the large and the small.
More interesting, perhaps, are the psychological and even theological tones in the passage: “He who regards himself in this light will be afraid of himself…and will tremble at the sight of these marvels…[Man] is equally incapable of seeing the Nothing from which he was made, and the Infinite in which he is swallowed up.” As mentioned earlier, Pascal was extremely devout, even in the context of his time and place. Undoubtedly, in these sentences Pascal was referring to the insignificance and limitations of Man in the divine sensorium of God. The “Nothing” here probably refers to divine Creation—both the creation of human beings and the creation of the universe as a whole. Man’s incapability of fathoming nothingness and infinity, known only to God, reminds me of the passage in Milton’s Paradise Lost, published a mere five years after Pascal’s death, in which Adam questions the angel Raphael about celestial mechanics. Raphael offers some vague hints and then says that “the rest / From Man or Angel the great Architect / Did wisely to conceal, and not divulge / His secrets to be scann’d by them who ought / Rather admire.”
It is clear that there are boundaries to humankind’s knowledge. But I disagree with Pascal that we human beings should fear what we do not understand, the infinities on both sides of us. Certainly there are fundamental limits to exploring the large and the small, as discussed above. But are we to “tremble” at their contemplation? Are we to bemoan our inability to grasp such things? Einstein once wrote, “The most beautiful experience we can have is the mysterious. It is the fundamental emotion which stands at the cradle of true art and true science.” By the “mysterious,” I do not think Einstein was referring to something fearful or supernatural. I believe he was speaking about the boundary between the known and the unknown. Standing at that boundary is an exhilarating experience. And it is a deeply human experience—concerning what the human mind understands and what that mind does not yet understand. The boundary between the known and the unknown is not a static boundary. It moves as we acquire new knowledge and understanding. Five hundred years ago, we did not understand the nature of heat or electricity. A hundred years ago, we did not understand the mechanism by which living organisms provide instructions to create descendant living organisms. The boundary between the known and the unknown constantly shifts. The other side is the “mysterious.” That other side intrigues us, it stimulates us, it provokes us, it haunts us. And it produces new science, and new art.
NOTHINGNESS
What Came Before the Big Bang?
On Wednesday, February 11, 1931, Albert Einstein met for more than an hour with a small group of American scientists in the cozy library of the Mount Wilson Observatory, near Pasadena, California. The subject was cosmology, and Einstein was poised to make one of the more momentous statements in the history of science. With his theories of relativity and gravity long confirmed and his Nobel ten years old, he was at this time the most famous scientist in the world. (“Photographers lunged at me like hungry wolves,” he wrote in his diary when his ship landed in New York two months earlier.)
For years, Einstein had insisted, like Aristotle and Newton before him, that the universe was a magnificent and immortal cathedral, fixed for all of eternity. In this picture, time runs from the infinite past to the infinite future, but little changes over time. Einstein dismissed the evolving cosmology of a Russian physicist as formally correct but of no physical significance. When a prominent Belgian scientist proposed in 1927 that the universe was growing in size like an expanding balloon, Einstein pronounced the idea “abominable.”
Recently, however, the great physicist had been confronted with telescopic evidence that the distant galaxies were in flight. Perhaps even more convincing to him, his mathematical model for a static universe had been shown to be like a pencil balanced on its point: give it a tiny nudge and it starts to move. By the time he arrived in Pasadena, Einstein was ready to acknowledge a cosmos in flux. In his thick German accent, he told the surrounding men in their suits and ties that the observed motion of the galaxies “has smashed my old construction like a hammer blow.” Then he swung down his hand to emphasize the point. What rose in the shards of that hammer blow was the Big Bang cosmology: the universe is not static and everlasting; rather, it “began” some fourteen billion years ago and has been expanding ever since. According to current data, our universe will keep expanding forever.
Sean Carroll, a professor of physics at the California Institute of Technology, is a Big Bang cosmologist. But more than that, he is one of a small platoon of physicists who call themselves “quantum cosmologists.” He wants to know what happened at the very beginning, and maybe even before that. Carroll and other quantum cosmologists believe that not only the universe was created at the Big Bang, but perhaps time itself. With pencil and paper, these theoretical physicists are investigating what, if anything, existed before the Big Bang, whether time had a beginning, and why we can tell the future from the past. Such bedrock questions in physics, seriously posed only recently, might be likened to Descartes asking for proof of his existence. Such questions are also related to Pascal’s notion that we, and the universe, emerged from “nothingness.” According to modern cosmologists, the entire observable universe was once microscopic in size. Thus Pascal’s idea of the infinitely small, his “nothingness,” might be associated with the origin of our universe.
Quantum cosmology is speculative work. For one thing, the birth of our universe was a one-performance event, and we weren’t there in the audience. But more importantly, an understanding of the very beginning requires a knowledge of gravity at enormously high densities of matter and energy, so-called quantum gravity, discussed in the last chapter. Physicists believe that in this quantum era, the entire universe we see today was far smaller than a single atom—roughly a million billion billion times smaller (assuming the universe went through an inflationary epoch). The temperature was nearly a million billion billion billion degrees. And time and space churned like boiling water. Of course, such things are unimaginable. But theoretical physicists try to imagine them with pencil and paper and mathematics. Somehow, time as we know it emerged in that fantastically dense nugget. Or perhaps time already existed, but what appeared was the arrow of time, the direction toward the future.
Physicists hope that within the next fifty years or so, string theory or other new theoretical work will provide a good understanding of quantum gravity, including an explanation of how the universe began. Until then, some of the deepest minds in physics, including Stephen Hawking and Andrei Linde and Alexander Vilenkin, have debated different hypotheses, each backed up with pages of calculations. But it is a tiny field, not for the timid. Carroll explained to me its allure: “high risk, high gain.” And down the rabbit hole we go.
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When I reached Sean Carroll by Skype, he was wearing a hoodie and jeans in the comfortable study of his home in Los Angeles. I was stationed in an uninhabitable guest room of my home in Concord, Massachusetts—practically next door on the scale of a galaxy. Carroll was relaxed as he talked about his favorite subject. Forty-nine years old, barrel-chested with a full head of reddish hair, puffy cheeks and jowls, a mischievous schoolboy glint in his eye, Carroll is an articulate explicator of science as well as a well-regarded physicist. He’s written scientific papers with titles like “What If Time Really Exists?” and popular books such as From Eternity to Here: The Quest for the Ultimate Theory of Time. He quotes from people like Parmenides and Heraclitus.
Carroll is obsessed with the relative smoothness and order of the universe. Order in physics has a precise meaning. It can be quantified. Furthermore, conditions of disorder are more probable than conditions of order, just as a deck of cards, once shuffled, is more likely to be found with the cards jumbled up than with the cards arranged by number and suit. Applying those considerations to the cosmos at large, physicists expect that given the amount of matter in the observable universe, we would expect it to be far more disordered and lumpy than it actually is. To be more exact, our observable universe has something like a hundred billion galaxies in it, which, when viewed over sufficiently large expanses of space, look as smooth as a pebbly beach seen from afar. Any large volume of space looks about like any other large volume. But it would be far more probable, say the physicists, to see that same material concentrated in a much smaller number of ultra-large galaxies or large clusters of galaxies or perhaps even in a single massive black hole—analogous to all the sand on a beach concentrated in a few silicon boulders.
The improbable smoothness of the observable universe, in turn, points toward unusually tidy conditions near the Big Bang. We don’t understand why. But it’s a clue. Not a shrinking violet with his cosmological opinions, Carroll told me, “I strongly believe that the low entropy [i.e., high order and smoothness] of the early universe is a puzzle that the wider cosmology community doesn’t take nearly as seriously as they should. Misunderstandings like that offer opportunities for making new breakthroughs.” Carroll and other physicists believe that order is intimately connected to the “arrow” of time. In particular, the forward direction of time is determined by the movement of order to disorder. For example, a movie of a glass goblet falling off a table and shattering on the floor would look normal to us; if we saw a movie of scattered shards of glass jumping off the floor and gathering themselves into a goblet perched on the edge of the table, we would say that movie was being played backward in time. Likewise, clean rooms left unattended become dusty with time, not cleaner. What we call the “future” is the condition of increasing mess; what we call the “past” is increasing tidiness. Our ability to easily distinguish between the two shows that our world has a clear direction of time. (Only theoretical physicists worry about such things.) So too in the cosmos at large. Stars radiate heat and light, slowly extinguish their nuclear fuel, and finally turn into cold cinders drifting through space. Never does the reverse happen.
Which brings us back to the unusual orderliness of our universe. Working with Alan Guth, a pioneering cosmologist at the Massachusetts Institute of Technology, Carroll has developed a not-yet-published theory called “Two-Headed Time.” In this theory, time has existed forever. But unlike in the static models of Aristotle and Newton and Einstein, the universe changes as the eons go by. Furthermore, the evolution of the cosmos is symmetric in time, with the behavior of the universe before the Big Bang a nearly mirror image of its behavior after the Big Bang. Until fourteen billion years ago, the universe was contracting. It reached a minimum size at the Big Bang (which we call t = 0) and has been expanding ever since, like a Slinky that falls to the floor, reaches a maximum compression upon impact, and then bounces back to larger dimensions. A few other quantum cosmologists have proposed related models. Because of unavoidable random fluctuations required by quantum physics, the contracting universe would not be an exact mirror image of the expanding universe, so that a physicist named Alan Guth probably did not exist in the contracting phase of our universe. But the before and after would look extremely similar.
