If the huge-density example looks a bit extreme, rest assured that it is not. There are three basic types of universes: closed, open, and flat. A typical closed universe created in the hot Big Bang would collapse in about 10-43 seconds into a state with the Planck density, unless it had a huge size to start with. A typical open universe created in the Big Bang would grow so fast that formation of galaxies would be impossible, and our bodies (if we were lucky enough to be born) would be instantly torn apart. Nobody could live in, let alone comprehend, the universe in either of these two cases. We can enjoy life in a flat, or nearly flat, universe (which is what we do now), but unless something special (inflation, see below) happens, this requires fine-tuning of initial conditions at the moment of the Big Bang with an incredible accuracy of about 10-60.
Recent developments in string theory, the most popular candidate for the role of the Theory of Everything, reveal an even broader spectrum of possible but incomprehensible universes. If we assume that our universe is described by string theory, does it mean that we know everything about the world around us? Consider a much simpler example: Recall that water can be liquid, frozen, or gaseous. Chemically it’s the same substance, but dolphins can live and comprehend the universe in their own way only if they are surrounded by liquid water. In this example, we have only three choices: liquid, ice, or vapor.
With string theory, according to its latest developments, we may have about 10500 (or more) choices of the possible state of the world surrounding us. All of these choices follow from the same basic theory. However, the universes corresponding to each of these choices would look as if they were governed by different laws of physics; their common roots would be well hidden. Since there are so many different choices, some of them, one hopes, can describe the universe we live in. But most of them would lead to a universe in which we could not live, build measuring devices, record events, or efficiently use mathematics and physics to predict the future.
When Einstein and Wigner were trying to understand why our universe is comprehensible and why mathematics is so efficient, everybody assumed that the universe was unique and uniform, and that the laws of physics were the same everywhere. This assumption was called the cosmological principle. We did not know why the universe was the same everywhere, we just took it for granted. Thus the problem described by Einstein and Wigner was supposed to apply to the whole universe. In this context, recent developments would only sharpen the formulation of the problem: If a typical universe is hostile to life as we know it, then we must be incredibly lucky to, by chance, live in the universe where life is possible and the universe comprehensible. This would indeed look like a miracle, like a “gift which we neither understand nor deserve.” Can we do better than rely on the miraculous?
In the last thirty years, the way we think about the origin and the global structure of our world has changed profoundly. First of all, we found that inflation, the exponentially rapid expansion of the early universe, makes the universe flat and thus potentially suitable for life. Moreover, the rapid stretching of the universe makes the part where we live extremely homogeneous. Thus we have found an explanation for the observed uniformity of the universe. However, we have also found that on a very, very large scale (well beyond the present observable horizon of about 1010 light-years), the universe becomes 100 percent nonuniform, because of quantum effects amplified by the explosive expansion of space.
In the context of string theory in combination with inflationary cosmology, this means that instead of looking like an expanding symmetric sphere, our world looks more like a multiverse—an incredibly large collection of exponentially large bubbles. Each one of these bubbles looks like a universe, and now we use the word “universe” to describe enormous, locally uniform parts of the world. One of the 10500 different laws of the low-energy physics originating from string theory operates inside each of these universes.
In some of these universes, quantum fluctuations are so large that any computations are impossible; mathematics there is inefficient, because predictions cannot be memorized and used. The lifetimes of some universes are too short. Other universes are long-lived but empty; their laws of physics do not allow the existence of any entities who could survive long enough to learn physics and mathematics.
Fortunately, among all possible parts of the multiverse, there should be some universes where life as we know it is possible. But our life is possible only if the laws of physics operating in our part of the multiverse allow formation of stable, long-lived structures capable of making computations. This implies existence of mathematical relations that can be used for the long-term predictions. The rapid development of the human race was possible only because we live in the part of the multiverse where the long-term predictions are so useful and efficient that they allow us to survive in the hostile environment and win in the competition with other species.
To summarize (and generalize), the inflationary multiverse consists of myriads of “universes” with all possible laws of physics and mathematics operating in each. We can live only in those universes where the laws of physics allow our existence, which requires making reliable predictions. In other words, mathematicians and physicists can live only in those universes that are comprehensible and where the laws of mathematics are efficient.
You can dismiss everything I just wrote as wild speculation. It’s interesting, however, that in the context of the new cosmological paradigm developed in the last thirty years we might be able, for the first time, to approach one of the most complicated and mysterious questions that bothered two of the greatest scientists of the 20th century.
ALFVÉN’S COSMOS
GEORGE DYSON
Science historian; author, Turing’s Cathedral: The Origins of the Digital Universe
A hierarchical universe can have an average density of zero, while containing infinite mass.
Hannes Alfvén (1908–1995), who pioneered the field of magnetohydrodynamics, against initial skepticism, to give us a universe permeated by what are now called Alfvén waves, never relinquished his own skepticism concerning the Big Bang. “They fight against popular creationism, but at the same time they fight fanatically for their own creationism,” he argued in 1984,* advocating, instead, for a hierarchical cosmology, whose mathematical characterization he credited to Edmund Edward Fournier d’Albe (1868–1933) and Carl Vilhelm Ludvig Charlier (1861–1934). Hierarchical does not mean isotropic, and observed anisotropy does not rule it out.
Gottfried Wilhelm Leibniz (1646–1716), a lawyer as well as a scientist, believed that our universe was selected, out of an infinity of possible universes, to produce maximum diversity from a minimal set of natural laws. It’s hard to imagine a more beautiful set of boundary conditions than zero density and infinite mass. But this same principle of maximum diversity warns us that it may take all the time in the universe to work the details out.
OUR UNIVERSE GREW LIKE A BABY
MAX TEGMARK
Cosmologist; associate professor of physics, MIT; scientific director, Foundational Questions Institute
What caused our Big Bang? My favorite deep explanation is that our baby universe grew like a baby human—literally. Right after your conception, each of your cells doubled roughly daily, causing your total number of cells to increase day by day as 1, 2, 4, 8, 16, etc. Repeated doubling is a powerful process, so your mom would have been in trouble if you’d kept doubling your weight every day until you were born: After nine months (about 274 doublings), you would have weighed more than all the matter in our observable universe combined.
Crazy as it sounds, this is exactly what our baby universe did, according to the inflation theory pioneered by Alan Guth and others. Starting out with a speck much smaller and lighter than an atom, it repeatedly doubled its size until it was more massive than our entire observable universe, expanding at dizzying speed. And it doubled not daily but almost instantly. In other words, inflation created our mighty Big Bang out of almost nothing, in a tiny fraction of a s
econd. By the time you reached about 10 centimeters in size, your expansion had transitioned from accelerating to decelerating. In the simplest inflation models, our baby universe did the same when it was about 10 centimeters in size, its exponential growth spurt slowing to a more leisurely expansion wherein hot plasma diluted and cooled and its constituent particles gradually coalesced into nuclei, atoms, molecules, stars, and galaxies.
Inflation is like a great magic show. My gut reaction is “This can’t possibly obey the laws of physics.” Yet under close enough scrutiny, it does. For example, how can one gram of inflating matter turn into two grams when it expands? Surely, mass can’t just be created from nothing? Interestingly, Einstein offered us a loophole via his special relativity theory, which says that energy e and mass m are related according to the famous formula e = mc2, where c is the speed of light. This means you can increase the mass of something by adding energy to it. For example, you can make a rubber band slightly heavier by stretching it: You need to apply energy to stretch it, and this energy goes into the rubber band and increases its mass. A rubber band has negative pressure, because you need to do work to expand it. Similarly, the inflating substance has to have negative pressure in order to obey the laws of physics, and this negative pressure has to be so huge that the energy required to expand it to twice its volume is exactly enough to double its mass. Remarkably, Einstein’s general theory of relativity says that this negative pressure causes a negative gravitational force. This in turn causes the repeated doubling, ultimately creating everything we can observe from almost nothing.
To me, the hallmark of a deep explanation is that it answers more than you ask. And inflation has proven to be the gift that keeps on giving, churning out answer after answer. It explained why space is so flat, which we’ve measured to about 1 percent accuracy. It explained why, on average, our distant universe looks the same in all directions, with only 0.002 percent fluctuations from place to place. It explained the origins of these 0.002 percent fluctuations as quantum fluctuations stretched by inflation from microscopic to macroscopic scales, then amplified by gravity into today’s galaxies and cosmic large-scale structure. It even explained the cosmic acceleration that nabbed the 2011 physics Nobel Prize as inflation, restarting in slow motion, doubling the size of our universe not every split second but every 8 billion years—which has transformed the debate from whether inflation happened or not to whether it happened once or twice.
It’s now becoming clear that inflation is an explanation that doesn’t stop—inflating or explaining.
Just as cell division didn’t make just one baby and stop, but a huge and diverse population of humans, it looks as though inflation didn’t make just one universe and stop, but a huge and diverse population of parallel universes, perhaps realizing all possible options for what we used to think of as physical constants. Which would explain yet another mystery: the fact that many constants in our universe are so fine-tuned for life that if they changed by small amounts, life as we know it would be impossible—there would be no galaxies, or no atoms, say. Even though most of the parallel universes created by inflation are stillborn, there will be some where conditions are just right for life, and it’s not surprising that this is where we find ourselves.
Inflation has given us an embarrassment of riches—and embarrassing it is. Because this infinity of universes has brought about the so-called measurement problem, which I view as the greatest crisis facing modern physics. Physics is all about predicting the future from the past, but inflation seems to sabotage this. Our physical world is clearly teeming with patterns and regularities, yet when we try quantifying them to predict the probability that something particular will happen, inflation always gives the same useless answer: infinity divided by infinity.
The problem is that whatever experiment you make, inflation predicts that there will be infinite copies of you obtaining each physically possible outcome in an infinite number of parallel universes, and despite years of teeth-grinding in the cosmology community, no consensus has emerged on how to extract sensible answers from these infinities. So, strictly speaking, we physicists are no longer able to predict anything at all. Our baby universe has grown into an unpredictable teenager.
This is so bad that I think a radical new idea is needed. Perhaps we need to somehow get rid of the infinite. Perhaps, like a rubber band, space can’t be expanded ad infinitum without undergoing a big snap? Perhaps those infinite parallel universes get destroyed by some yet undiscovered process, or perchance they’re, for some reason, mere mirages? The very deepest explanations provide not just answers but questions as well. I think inflation still has some explaining left to do.
KEPLER ET AL. AND THE NONEXISTENT PROBLEM
GINO SEGRÈ
Physicist, University of Pennsylvania; author, Ordinary Geniuses: Max Delbruck, George Gamow, and the Origins of Genomics and Big Bang Cosmology
In 1595, Johannes Kepler proposed a deep, elegant, and beautiful solution to the problem of determining the distance from the sun of the six then-known planets. Nesting (like Russian dolls) each of the five Platonic solids within a sphere, arranged in the proper order—octahedron, icosahedron, dodecahedron, tetrahedron, cube—he proposed that the succession of spherical radii would have the same relative ratios as the planetary distances. Of course the deep, elegant, and beautiful solution was also wrong, but then, as Joe E. Brown famously said at the conclusion of Some Like It Hot, “Nobody’s perfect.”
Two thousand years earlier, in a notion that would come to be described as the Harmony of the Spheres, Pythagoras had already sought a solution by relating those distances to the sites on a string where it needed to be plucked in order to produce notes pleasing to the ear. And almost 200 years after Kepler’s suggestion, Johann Bode and Johann Titius offered, with no underlying explanation, a simple numerical formula that supposedly fit the distances in question. So we see that Kepler’s explanation was neither the first nor the last attempt to explain the ratios of planetary-orbit radii, but in its linking of dynamics to geometry it remains, for me, the deepest, as well as being the simplest and most elegant.
In a strict sense, none of the three proposals is strictly wrong. They are instead solutions to a problem that doesn’t exist, for we now understand that the location of planets is purely accidental, a by-product of how the swirling disk of dust that circled our early sun evolved, under the force of gravity, into its present configuration. The realization that there was no problem came as our view expanded from one in which our planetary system was central to a far greater vision, in which it is one of an almost limitless number of such systems scattered throughout the vast numbers of galaxies comprising our universe.
I have been thinking about this because, together with many of my fellow theoretical physicists, I have spent a good part of my career searching for an explanation of the masses of the so-called elementary particles. But perhaps the reason it has eluded us is a proposal that is increasingly gaining credence—namely, that our visible universe is only a random example of an essentially infinite number of universes, all of which contain quarks and leptons with masses taking different values. It just happens that in at least one of those universes, the values allow for there being at least one star and one planet where creatures that worry about such problems live.
In other words, a problem we thought was central may once again have ceased to exist, as our conception of the universe has grown—in this case, been extended to one of many universes. If this is true, what grand vistas may lie before us in the future? I only hope that our descendants may have a much deeper understanding of these problems than we do and that they will smile at our feeble attempts to provide a deep, elegant, and beautiful solution to what they have recognized as a nonexistent problem.
HOW INCOMPATIBLE WORLDVIEWS CAN COEXIST
FREEMAN DYSON
Theoretical physicist, Institute for Advanced Study; author, A Many-Colored Glass: Reflections on the Place of Life in the Universe
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br /> The situation I am trying to explain is the existence side by side of two apparently incompatible pictures of the universe. One is the classical picture of our world as a collection of things and facts that we can see and feel, dominated by universal gravitation. The other is the quantum picture of atoms and radiation that behave in an unpredictable fashion, dominated by probabilities and uncertainties. Both pictures appear to be true, but the relationship between them is a mystery.
The orthodox view among physicists is that we must find a unified theory that includes both pictures as special cases. The unified theory must include a quantum theory of gravitation, so that particles called gravitons must exist, combining the properties of gravitation with quantum uncertainties.
I am looking for a different explanation of the mystery. I ask whether a graviton, if it exists, could conceivably be observed.
I do not know the answer to this question, but I have one piece of evidence that the answer may be no. The evidence is the behavior of one piece of apparatus—the gravitational-wave detector called LIGO (Laser Interferometer Gravitational-Wave Observatory) now operating in Louisiana and Washington State. The way LIGO works is to measure very accurately the distance between two mirrors by bouncing light from one to the other. When a gravitational wave comes by, the distance between the two mirrors will change very slightly. Because of ambient and instrumental noise, the actual LIGO detectors can only detect waves far stronger than a single graviton. But even in a totally quiet universe, I can answer the question of whether an ideal LIGO detector could detect a single graviton. The answer is no. In a quiet universe, the limit to the accuracy of measurement of distance is set by the quantum uncertainties in the positions of the mirrors. To make the quantum uncertainties small, the mirrors must be heavy. A simple calculation, based on the known laws of gravitation and quantum mechanics, leads to a striking result. To detect a single graviton with a LIGO apparatus, the mirrors must be exactly so heavy that they will attract each other with irresistible force and collapse into a black hole. In other words, Nature herself forbids us to observe a single graviton with this kind of apparatus.
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