— String Theory and the Illusion of Intelligent Design
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“Your Highness, I have no need of this hypothesis.”—Pierre-Simon de Laplace (1749-1827), reply made to Napoléon when asked why his celestial mechanics had no mention of God
Preface
Evidence has been accumulating for an explanation of the “illusion of intelligent design” that depends only on the principles of physics, mathematics, and the laws of large numbers. This is what The Cosmic Landscape is about: the scientific explanation of the apparent miracles of physics and cosmology and its philosophical implications.
Introduction
more common binary star system,*
All it takes is a small change in Newton’s laws, or the rules of atomic physics, and poof—life would either be instantly extinguished or would never have formed.
Life as we know it
The miracle of the eye is only an apparent miracle. I think the design enthusiasts are on better ground when it comes to physics and cosmology. Biology is only part of the story of creation. The Laws of Physics and the origin of the universe are the other part, and here again, incredible miracles appear to abound. It seems hopelessly improbable that any particular rules accidentally led to the miracle of intelligent life.
Failed to consider the number of lifeless planets
There are many ways it could go bad—so bad that life as we know it would be totally impossible.
Chemistry is really a branch of physics: the physics of the valence electrons, i.e., those that orbit the nucleus at the outer edges of the atom.
But are the Laws of Physics elegant in the physicist’s sense? If the only criterion for how the universe works is that it should support life, it may well be that the whole structure is a clumsy, ungainly “Rube Goldberg machine.”
Chapter One: The World According To Feynman
I’m not a historian, but I’ll venture an opinion: modern cosmology really began with Darwin and Wallace. Unlike anyone before them, they provided explanations of our existence that completely rejected supernatural agents.
Once the magic was removed from the origin of living creatures, the way lay open to a purely scientific explanation of creation.
“Why is a certain constant of nature one number, instead of another?” will have answers that are entirely different from what physicists had hoped. No unique value will be picked out by mathematical consistency, since the Landscape permits an enormous variety of possible values. Instead, the answer will be, “Somewhere in the megaverse, the constant equals this number; somewhere else it is that number. We live in one tiny pocket where the value of the constant is consistent with our kind of life. That’s it! That’s all! There is no other answer to the question.”
But why is it so unpredictable? It’s because each collision magnifies minute differences in the starting positions and velocities of the balls, so that even the tiniest deviation eventually leads to an entirely different outcome. [This kind of ultra-sensitivity to initial conditions is called chaos, and it is a ubiquitous feature of nature.] Trying to reproduce a pool game is not like reproducing a chess game.
No amount of precision would allow anything more than statistical predictions of outcomes. The classical billiard player might resort to statistics just because the initial data were imperfectly known or because solving the equations of motion might be too hard. But the quantum player has no choice.
These quanta are packets of energy that cannot be subdivided, and that fact creates certain limitations when one attempts to form accurate images of small objects.
Even if we removed as much kinetic energy as possible, this residual fluctuation motion could not be eliminated. Brian Greene has used the term quantum jitters to describe this motion, and I will follow his lead. The kinetic energy associated with the quantum jitters is called zero-point energy, and it cannot be eliminated.
In a real material subject to the laws of quantum mechanics, the molecular kinetic energy can never be totally removed, even at absolute zero!
Position and velocity are by no means unique in having an Uncertainty Principle. There are many pairs of so-called conjugate quantities that cannot be determined simultaneously: the better one is fixed, the more the other fluctuates. A very important example is energy-time uncertainty principle: it is impossible to determine both the exact time that an event takes place and the exact energy of the objects that are involved.
For this reason the fields are in a constant state of jittering fluctuation that cannot be eliminated. And, as you might expect, this leads to a certain amount of energy, even in absolutely empty space.
When both slits are opened, not a single particle arrives at the locations where the destructive interference took place. This is despite the fact that photons do arrive at these places when only one slit is open.
“If you come to a fork in the road, take it.”—YOGI BERRA
When the motion of an electron is suddenly disturbed, it may respond by shaking off a photon. The process, called photon emission, is the basic event of Quantum Electrodynamics. Just as all matter is built of particles, all processes are built from the elementary events of emission and absorption.
When matter meets antimatter, look out! The particles and antiparticles will combine and disappear (annihilate), but not without leaving over their energy in the form of photons. The antiparticle twin of the electron is called the positron. It appears to be a new addition to the list of particles, but according to Feynman, the positron is not really a new object: he thought of it as an electron going backward in time!
He pictured the incoming electron as “turning around in time” and temporarily moving toward the past, then turning around again toward the future. The two ways of thinking—either in terms of positrons and electrons or in terms of electrons moving backward in time—are completely equivalent.
The photon jumping across the gap between the electrons is the origin of the electric and magnetic forces between them.
The continual exchange of photons between the nucleus and the atomic electrons provides the force that holds the atom together.
But if nature is not deterministic, neither is it completely chaotic.
In other words, only one lucky electron out of 137 emits a photon. That is the meaning of α: it is the probability that an electron, as it moves along its trajectory, will capriciously emit a photon.
The fine structure constant also controls the strength of the exchange diagrams, which in turn, determine the strength of electric forces among charged particles. It controls how tightly the atomic nucleus pulls the electrons toward it. As a consequence it determines how big the atom is, how fast the electrons move in their orbits, and ultimately controls the forces between different atoms that allow them to form molecules.
But there are two big differences between QED and QCD. The first is a quantitative difference: the numerical constant governing the emission of gluons is not as small as the fine structure constant. It is called αQCD (alpha-QCD) and is about one hundred times larger than the fine structure constant.
The whole thing would be a very unappealing concoction if it were not for one thing: it describes the properties of elementary particles, nuclei, atoms, and molecules with incredible precision. But there is a cost. It can be accomplished only by introducing about thirty “constants of nature”—masses and coupling constants—whose values have no other justification than that they “work.”
Astronomers routinely study the light from far-off sources and disentangle the spectral lines that were emitted or absorbed by distant atoms. The relations between individual spectral lines are intricate, but they are always the same, no matter where and when the light originated. Just about any change in the local Laws of Physics would change the details, so we have excellent evidence that the laws are the same in all parts of the observed universe.
Chapter Two: The Mother Of All Physics Problems
Blackboards meant physicists.
Quantum fluctuations can create particles for a short period of time, as in the following figures.
These short-lived quantum particles that fill the vacuum are called virtual particles, but their effects can be quite real. In particular, they cause the vacuum to have energy. The vacuum is not the state of zero energy. It is merely a state of minimum energy.
But if energy and mass are the same thing, then this sentence could also be read: “Energy is the source of the gravitational field.” In other words, all forms of energy affect the gravitational field and, therefore, also influence the motion of nearby masses. The vacuum energy of quantum field theory is no exception. Even empty space will have a gravitational field if the energy density of the vacuum is not zero. Objects will move through empty space as if there were a force on them. The interesting thing is that if the vacuum energy is a positive number, then its effect is a universal repulsion, a kind of antigravity that would tend to drive galaxies apart.
At the earliest times that we can see, slight variations in the density and pressure amounted to a few parts in 100,000. In other words, the variations in density were 100,000 times smaller than the density itself. The tendency for gravity to cause clumping is not measured by the overall density of matter but by these small variations. Even those infinitesimal irregularities were enough to get the process of galaxy formation started.
According to the principles of quantum mechanics, everything that can fluctuate does fluctuate. If space is deformable, then even it has the “quantum jitters.”
The world at the Planck scale is a very unfamiliar place, where geometry is constantly changing, space and time are barely recognizable, and high-energy virtual particles are perpetually colliding and forming tiny black holes that last no longer than a single Planck time.
When we combine the theory of elementary particles with the theory of gravity, we discover the horror of a cosmological constant big enough to not only destroy galaxies, stars, and planets but also atoms, and even protons and neutrons—unless. Unless what? Unless the various bosons, fermions, masses, and coupling constants that go into calculating the vacuum energy conspire to cancel the first 119 decimal places.
Chapter Three: The Lay Of The Land
The Landscape has hundreds, maybe thousands, of dimensions. Almost all of the Landscape describes environments that are lethal to life, but a few of the low-lying valleys are habitable. The Landscape is not a real place. It doesn’t exist as a real location on the earth or anywhere else. It doesn’t exist in space and time at all. It’s a mathematical construct, each of whose points represents a possible environment or, as a physicist would say, a possible vacuum.
Einstein claimed that the electromagnetic field was really composed of a very large number of indivisible particles that he called photons. In small numbers, photons, or what are the same thing, light quanta behave like particles, but when many of them move in a coordinated way, the whole collection behaves like a field—a quantum field. This relation between particles and fields is very general. For each type of particle in nature, there is a field, and for each type of field there is a particle. Thus, fields and particles often go by the same name. The electromagnetic field (the collective name for electric and magnetic fields) could be called the photon field. The electron has a field.
Particles that move with the speed of light cannot have any mass,
The Landscape of this book also has its highlands, lowlands, mountains, and valleys. It’s not little balls that roll around on it: whole pocket universes occupy locations on the Landscape! What do I mean when I say that a pocket universe occupies a place in the Landscape? It’s more or less the same as reporting the winter weather in Denver by saying that “the city occupies the point twenty-five on the thermometer scale.”
Mass is inertia; the more massive a body is, the harder it is to get it moving or to stop it. To determine the mass of an object, you subject it to a known force and measure its acceleration: the ratio of force to acceleration is its mass.
The electron would be so light that it could not be contained within the atom.
Chapter Four: The Myth Of Uniqueness And Elegance
Uniqueness is another property that is especially highly valued by theoretical physicists. The best theories are ones that are unique in two senses. First of all, there should be no uncertainty about their consequences. The theory should predict all that is possible to predict and no more. But there is also a second kind of uniqueness that would be especially treasured in what Steven Weinberg calls a final theory. It is a kind of inevitability—a sense that the theory could not be any other way. The best theory would be not only a theory of everything, but it would be the only possible theory of everything.
Four elements and one dynamical principle: you would be surprised at how much they could explain. The only thing missing was uniqueness. I don’t see why there can’t be additional elements: earth, air, fire, water, red wine, cheese, and garlic.
For most purposes gravity is completely unimportant for elementary-particle physics. As we will see in later chapters, the gravitational force between particles—for example, quarks in a proton—is many orders of magnitude weaker than the other forces of nature. Gravity is far too feeble to play a role in any experiment involving elementary particles, at least for the foreseeable future. For this reason traditional elementary-particle physicists have been content to completely ignore the effects of gravity. But there are two practical reasons for wanting a deeper understanding of the connections between gravity and the microscopic quantum world. The first has to do with the structure of elementary particles. Although the gravitational force is negligible for electrons in an atom (or quarks in a proton), as the distance between particles gets smaller, gravity begins to assert itself. All forces become stronger as the separation decreases, but the gravitational force increases more rapidly than any other. In fact by the time two particles get within a Planck distance of each other, the force of gravity is a good deal stronger than electric forces or even the forces that bind quarks together. If the “Russian nesting doll” paradigm (things made of ever smaller things) continues to hold sway, the ordinary elementary particles may turn out to be made of even tinier objects that are in some sense held together by gravity. The second practical reason for understanding the links between gravity and quantum theory involves cosmology. In the next chapter we will see that gravity is the force that governs the growth of the universe. When the universe was very young and expanding at a stupendous rate, gravity and quantum mechanics were important in equal measure. A lack of understanding of the connection between these two great theories will ultimately frustrate our efforts to get to the bottom of the Big Bang. But there is a third reason that physicists are driven to combine quantum theory with general relativity: an esthetic reason. For a physicist, unlike a poet, the biggest crime against esthetics is the crime of inconsistency. Even worse than an ugly theory, incompatible principles are an attack on the basic values we hold dear. And for most of the twentieth century, gravity and quantum mechanics have been incompatible.
Perhaps part of the reason that the enemies of String Theory haven’t pounced is that string theorists have kept their Achilles heel under wraps until fairly recently. I suspect that now that it is becoming more public, partly through my own writings and lectures, the kibitzers on the sidelines will be grinning and loudly announcing, “Ha ha, we knew it all along. String Theory is dead.” My own guess is that the inelegance and lack of uniqueness will eventually be seen as strengths of the theory. A good, honest look at the real world does not suggest a pattern of mathematical minimality.
The consensus among particle physicists, especially those who expect supersymmetry to be a feature of nature, is that well over one hundred separate constants of nature are in no known way related. Far from being the simple, elegant structure sometimes suggested by physicists, the current most fundamental description of nature seems like something Rube Goldberg himself might have designed. A Rube Goldberg theory, then, may be fitting. While the Standard Model is a huge advance in describing elementary particles, it doesn’t explain itself. It is rather complicated, far from unique, and certainly incomplete. What, then, is special about our beloved Standard Model? Absolutely nothing—there are 10500 others, just as consistent. Nothing, that is, except that it permits—maybe even encourages—the existence of life.
What some of them see is a bunch of remarkable coincidences: The universe is a fine-tuned thing. It grew big by expanding at an ideal rate. If the expansion had been too rapid, all of the material in the universe would have spread out and separated before it ever had a chance to condense into galaxies, stars, and planets. On the other hand, if the initial expansion had not had a sufficient initial thrust, the universe would have turned right around and collapsed in a big crunch much like a punctured balloon. The early universe was not too lumpy and not too smooth. Like the baby bear’s porridge, it was just right. If the universe had started out much lumpier than it did, instead of the hydrogen and helium condensing into galaxies, it would have clumped into black holes. All matter would have fallen into these black holes and been crushed under the tremendously powerful forces deep in the black hole interiors. On the other hand, if the early universe had been too smooth, it wouldn’t have clumped at all. A world of galaxies, stars, and planets is not the generic product of the physical processes in the early universe; it is the rare and, for us, very fortunate, exception. Gravity is strong enough to hold us down to the earth’s surface, yet not so strong that the extra pressure in the interior of stars would have caused them to burn out in a few million years instead of the billions of years needed for Darwinian evolution to create intelligent life. The microscopic Laws of Physics just happen to allow the existence of nuclei and atoms that eventually assemble themselves into the large “Tinkertoy” molecules of life. Moreover, the laws are just right, so that the carbon, oxygen, and other necessary elements can be “cooked” in first-generation stars and dispersed in supernovae.
Chapter Five: Thunderbolt From Heaven
One galaxy, twice as far as another, appeared to recede twice as fast. This was a new, totally unexpected, regularity in the universe: a new cosmological law, Hubble’s Law. Galaxies are receding away from us with velocity proportional to their distance.
Cosmologists and astronomers almost always assume that the universe is homogeneous and isotropic; no matter where you are in the universe and which direction you are facing, you see the same thing. I don’t mean the nearby details but the overall, large-scale features of the universe. Cosmologists call this assumption the cosmological principle.
The reason is the simple fact that the universe is only about fourteen billion years old. In that time light could not have traveled more than fourteen billion light-years; light from more distant places just hasn’t reached us yet.
In a similar fashion, by measuring the velocity of stars in the outermost parts of a rotating galaxy, astronomers can measure the galaxy’s mass. And what do they find? The galaxies are all heavier than the astronomers had thought. Roughly speaking, every galaxy is about ten times more massive than all the visible stars and interstellar gas that it contains. The remaining nine-tenths of the mass is a mystery. It is almost certainly not made of the things that comprise ordinary matter: protons, neutrons, and electrons. Cosmologists call it dark matter: dark because it gives off no light.
The amount of mass in the universe appears to be five times too small to either close the universe or even to make it flat. But surveying cosmic triangles seems to leave little doubt that the geometry of the universe is flat.
The ordinary and dark matter together add up to about 30 percent of the mass needed to flatten or close the universe. The obvious way out of the dilemma is to make up the missing 70 percent in the form of a cosmological constant.
These conclusions concerning the existence of a cosmological constant are so important that I want to repeat them. The existence of a small cosmological constant, representing 70 percent of the energy in the universe, solves the two biggest puzzles of cosmology. First, the additional energy is just enough to make the universe flat. This fact removes the awkward discrepancy between the observed flatness of space and the fact that the mass in the universe was insufficient to render it flat. The second paradox that is eliminated by the cosmological constant is the equally awkward discrepancy that the oldest stars appear older than the universe. In fact, the same vacuum energy—70 percent of the total—remarkably, is exactly what is needed to make the universe a little older than these ancient stars.
Because of the Hubble expansion, the plasma that originally emitted the primordial light is receding away from us with a large velocity. In fact, using the Hubble Law, we can calculate the velocity of this recession, and the result is only slightly less than the speed of light.
Some small, primordial lumpiness had to be there to seed the formation of galaxies. If the seeds were too weak, galaxies would not have formed; if too strong, the lumps would have grown too rapidly and collapsed to black holes. Cosmologists strongly suspected that under this boring homogeneous background, the seeds of future galaxies were there to see. Even better, theoretical cosmologists had a pretty good idea how strong the density contrasts had to be in order to create the galaxies as we see them now. The difference between the microwave intensity in different directions would have to be about 100,000 times smaller than the average intensity.
cosmic microwave data directly show that the universe was extremely homogeneous in early times. Moreover, it is also very large, large enough to appear flat to cosmic surveyors. The bottom line is that the universe is many times bigger than the portion that we can see,
If the universe doubled one hundred times or more during this period, it would have grown to such large proportions that it would be as flat and homogeneous as the CMB requires.
But it now appears all but certain that galaxies and other large-scale structures are remnants of original minute quantum fluctuations that were expanded and enhanced by the unrelenting effect of gravity. The idea that the universe is at an exact point in the Landscape is a little too simple. Like everything else, quantum fields such as the Higgs field have the jitters. Quantum mechanics is enough to ensure that the fields do fluctuate from point to point in space. No amount of Inflation can iron out the random quantum fluctuations that every field must have.
By the time Inflation ended and the universe tipped over the edge of the ledge, the accumulated quantum wrinkles had built up and formed the minute density contrasts that eventually grew to become galaxies.
It is all but certain that the entire universe is many, many orders of magnitude bigger than the part we can see.
Chapter Six: On Frozen Fish And Boiled Fish
One of the great scientific events of the twentieth century occurred when the cosmologist Fred Hoyle was able to predict one of these nuclear details just from the fact that we are here.
Just a small increase or decrease in the energy of the excited carbon nucleus, and all the work of making galaxies and stars would have been in vain; but as it is, carbon atoms—and thus, life—can exist.
If the lumpiness had been much less, let’s say, 10–6, in the early universe, galaxies would be small and the stars, very sparse. They would not have had sufficient gravity to hang on to the complex atoms that were spewed out by supernovae; these atoms would have been unavailable for the next generation of stars. Make the density contrast a little less than that, and no galaxies or stars would form at all. What would happen if the lumpiness were larger than 10–5? A factor of one hundred larger, and the universe would be full of violent, ravenous monsters that would swallow and digest galaxies before they were even finished forming.
One hundred million antiprotons found 100,000,000 partners and, together, they committed suicide, leaving 200,000,000 photons and just 1 leftover proton. These leftovers are the stuff we are made of.
The known universe has 1011 galaxies, each with 1011 planets, for a grand total of 1022 opportunities to satisfy the special requirement for liquid water. With that many planets there is near certainty that many will be habitable.
One-percent coincidences happen about 1 percent of the time.
Anthropically, the lifetime of the proton may have to be a good deal longer than the age of the universe. To see why, let’s suppose that the proton lifetime were twenty billion years. The decay of an unstable particle is an unpredictable event that can happen any time. When we say that the proton lifetime is twenty billion years, we mean that, statistically, the average proton will last that long. Some will decay in one year, and some in forty billion years. Your body has about 1028 protons. If the proton lifetime were twenty billion years, about 1018 of those protons would decay every year. 9 This is a negligible fraction of your protons, so you don’t have to worry about disappearing. But each proton that decays in your body shoots out energetic particles: photons and positrons and pions. These particles moving through your body have the same effects as exposure to radioactivity: cell damage and cancer. If 1018 protons decay in your body, they will kill you. So the anthropic constraints on proton decay may be stronger than what you naively think. As far as we know, a lifetime of a million times the age of the universe—1016 years—is long enough not to jeopardize life. On anthropic grounds we can rule out all valleys of the Landscape where the average proton lifetime is less than this. But we know that the proton lives vastly longer than 1016 years. In a tank of water with roughly 1033 protons, we would expect to see one proton decay each year if the lifetime were 1033 years. Physicists, hoping to witness a few protons decaying, have constructed huge underground chambers filled with water and photoelectric detectors. Sophisticated modern detectors can detect the light from just a single decay. But so far, no cigar; not a single proton has ever been seen to disintegrate. Evidently the lifetime of the proton is even longer than 1033 years, but the reason is unknown.
The simplest generalization of the Standard Model to a GUT brings the proton lifetime to just around 1033 or 1034 years.
Richard Feynman once remarked, “Philosophers say a great deal about what is absolutely necessary for science, and it is always, so far as one can see, rather naive, and probably wrong.”
Good scientific methodology is not an abstract set of rules dictated by philosophers. It is conditioned by, and determined by, the science itself and the scientists who create the science. What may have constituted scientific proof for a particle physicist of the 1960’ s—namely the detection of an isolated particle—is inappropriate for a modern quark physicist who can never hope to remove and isolate a quark. Let’s not put the cart before the horse. Science is the horse that pulls the cart of philosophy.
In each case that I described—quarks, inflation, Darwinian evolution—the accusers were making the mistake of underestimating human ingenuity.
Falsification, in my opinion, is a red herring, but confirmation is another story. (Perhaps this is what Smolin really meant.) By confirmation I mean direct positive evidence for a hypothesis rather than absence of negative evidence.
Just as generals are always fighting the last war, philosophers are always parsing the last scientific revolution.
But so what? The principle says nothing beyond the fact that life formed. This is a kind of willful missing of the point. As usual I find it helpful to rely on an analogy. I call it the Cerebrothropic Principle. The Cerebrothropic Principle is intended to answer the question, “How did it happen that we developed such a big, powerful brain?”
Chapter Seven: A Rubber Band-Powered World
The S-matrix is basically a table of quantum-mechanical probabilities. You plug in the input, and the S-matrix tells you the probability for a given output. The table of probabilities depends on the direction and energy of both the incoming and outgoing particles, and according to the prevailing ideology of the mid-1960s, the theory of elementary particles should be confined to studying the way the S-matrix depends on these variables.
During that period I spent long hours by myself, working in the attic of my house. I hardly came out, and when I did I was irritable. I barked at my wife and ignored my kids. I couldn’t put the formula out of my mind, even long enough to eat dinner. But then for no good reason, one evening in the attic I suddenly had a “eureka moment.” I don’t know what provoked the thought. One minute I saw a spring, and the next I could visualize an elastic string, stretched between two quarks and vibrating in many different patterns of oscillation.
The ordinary proton and neutron are the lowest energy configurations of the bola, with the quarks at rest at the ends of very short, unstretched strings. The quarks at the ends of the strings can be set into motion in a number of ways. The bola can be spun around its center, the centrifugal force stretching the strings and pushing the quarks out from the center. This spinning motion requires energy (remember E = mc2), and that makes spinning hadrons heavier. As noted earlier, the jargon for a particle with extra energy is that it is excited. The quarks can also be excited without rotating. One way is through oscillating motions, moving toward and away from the center, in and out, in and out. In addition the strings themselves can be bent into curved, vibrating patterns almost as if they were plucked with a guitar pick.
The more massive ones had odd names that would mean absolutely nothing to most young physicists today.
To represent the history of the string, we need to fill in the spaces between the flashes. The result is a tube through space: a two-dimensional cylinder.
He suggested that the smooth, continuous world sheet is really a network or mesh of closely spaced lines and vertices. In other words it is a very complicated, but otherwise ordinary, Feynman diagram composed of a great many propagators and vertices.
Edwin Abbott’s famous nineteenth-century book Flatland describes life in a world of only two dimensions of space.
One of my biggest frustrations is that I have never succeeded in finding an elementary explanation of why String Theory is happy only if the number of dimensions is 9 + 1. Nor has anyone else. What I will tell you is that it has to do with the violent jittery quantum motion of a string. These quantum fluctuations can pile up and get completely out of control unless some very delicate conditions are met. And those conditions are met only in 9 + 1 dimensions.
All forces in nature—be they gravitational, electric, or nuclear—have the same origin.
The determining factor for the range of a particular force is the mass of the messenger: the lighter the messenger, the longer the range. The reason that gravity and electric forces are long range is that the graviton and photon are massless.
The very high-frequency quantum fluctuations are so wild and out of control that the quark ends are most likely found far away at the very edges of the universe. It sounds crazy but the bits of string jitter and jiggle so violently that if you looked very quickly, you would discover that they are infinitely far away!
Chapter Eight: Reincarnation
The key to the unexplained diversity of elementary particles—their electric charge, color, strangeness, isospin, and more—is very likely the extra six dimensions that previously dogged our efforts to explain hadrons!
If one additional direction of space were added to the usual 3 + 1 dimensions, the geometry of space would encompass not only Einstein’s gravitational field but also Maxwell’s electromagnetic field. Gravity and electricity and magnetism would be unified under a single all-encompassing theory.
The astonishing thing was that the extra force was identical to the electric force between charged particles. Moreover, the electric charge of each particle was nothing but the component of momentum in the extra dimension. If the two particles cycled in the same direction around the compact space, they repelled each other. If they moved in opposite directions, they attracted. But if either of them did not cycle in the compact direction, then only the ordinary gravitational attraction affected them.
supersymmetry is most definitely not an exact symmetry of nature. At best it is a fairly badly broken symmetry—the kind of distorted symmetry that a badly warped funhouse mirror would imply. In fact no superpartner has ever been discovered for any of the known elementary particles.
supersymmetry so simplifies the mathematics of quantum field theory and String Theory that it allows theorists to know things that would otherwise be far beyond calculation.
In a supersymmetric world the violent effects due to quantum fluctuations would be tamed, leaving the particle masses undisturbed. Moreover, even a distorted supersymmetry would alleviate the problem a great deal if the distortion were not too severe.
Although a particular symmetry may be broken to a greater or lesser degree in our little home valley, that doesn’t mean that the symmetry is broken in all corners of the Landscape. Indeed, the portion of the String Theory Landscape that we know most about is the region where supersymmetry is exact and unbroken. Called the supersymmetric moduli space (or supermoduli space), it is the portion of the Landscape where every fermion has its boson and every boson has its fermion. As a consequence, the vacuum energy is exactly zero everywhere on the supermoduli space.
Of course this also implies that some pockets of the megaverse will be supersymmetric. But there are no superstring theorists to enjoy it.
Ordinary theories are consistent only if gravity is left out. String Theory is consistent only if it includes gravity.
He had discovered that all five versions of String Theory were really solutions to a single theory: not many theories, but many solutions. In fact they all belonged to a family that includes one more member, a theory that Witten called M-theory. Moreover, the six theories each correspond to some extreme value of the moduli: some distant limiting corner of the Landscape. As in the example of the magnetic field, the moduli could be continuously varied so that one theory morphed into any of the others!
Chapter Nine: On Our Own?
Is the human race anywhere near being smart enough? I mean collectively, not individually. Are the combined talents of humanity sufficient to solve the great riddle of existence? Is the human mind even wired in the right way to be able to understand the universe? What are the chances that the combined and diverse intellects of the world’s greatest physicists and mathematicians will be able to divine the final theory with only the absurdly limited experiments that will be possible?
In an ordinary atom an electron can absorb the energy of nearby photons and be “kicked up” into a more energetic configuration. 4 Dirac now showed his real brilliance. He reasoned that the same thing could happen to the negative-energy electrons that fill the vacuum; photons could kick negative-energy electrons up to positive-energy states. What would be left over would be one electron with positive energy and a missing negative-energy electron—a hole in the Dirac Sea. Being a missing electron, the hole would seem to have the opposite electric charge from the electron and would look just like a particle of positive charge. This, then, was Dirac’s prediction: particles should exist identical to electrons, except with the opposite electric charge. These positrons, which Feynman would later interpret as electrons going backward in time, Dirac pictured as holes in the vacuum.
Chapter Ten: The Branes Behind Rube Goldberg’S Greatest Machine
It has much more to do with the fact that it was constructed for the particular purpose of describing some limited facts about our own world. They were built piecemeal, from experimental data, with the particular goal of describing (not explaining) our own vacuum. These theories admirably do the job that they were designed to do but no more.
Overfitting, worse prediction
You might think the creatures on the membrane would have no way of telling that more dimensions exist, but that would not be quite right. The giveaway would be the properties of the gravitational force. Remember that gravity is caused by gravitons jumping between objects. But gravitons are closed strings without ends. They have no reason to stick to the brane. Instead, they freely travel through all of space. They can still be exchanged between objects on the brane but only by traveling out into the extra dimensions, then back to the brane.
Most string theorists think we really do live on a brane-world, floating in a space with six extra dimensions. And perhaps there are other branes floating nearby, microscopically separated from us but invisible (to us) because our photons stick to our own brane, and theirs stick to their brane. Though invisible, these other branes would not be impossible to detect: gravity, formed of closed strings, would bridge the gap. But isn’t that exactly what dark matter is: invisible matter whose gravitational pull is felt by our own stars and galaxies?
In fact with five carpets, stuck together in a stack of two and a stack of three, he can make a world with Laws of Physics that have many similarities to the Standard Model!
Even if you spaced the points a Planck length apart and made the sheet as big as the known universe, you would get only a measly 1060 points. The number 10500 is so staggeringly large that I can’t think of any way of graphically representing that many points.
But the real point is that with that many randomly chosen values for the cosmological constant, there will be a huge number in the tiny “window of life” that Weinberg calculated. No fine-tuning is needed to make sure of that. Of course it will be only a minute fraction of the valleys that are in the anthropic window of opportunity—roughly one out of 10120.
Chapter Eleven: A Bubble Bath Universe
What is the alternative? The answer is that nature somehow makes use of all the possibilities. Is there a natural mechanism that would have populated a megaverse with all possible environments, turning them from mathematical possibilities to physical realities? This is what an increasing number of theoretical physicists believe—myself included. I call this view the populated Landscape.
Some systems have the remarkable property that they appear stable for long periods of time but eventually undergo very sudden and unforeseen catastrophic changes. These systems are called metastable.
A vacuum with a positive cosmological constant is a lot like a supercooled or superheated liquid. It is metastable and can decay by nucleating bubbles. Every vacuum corresponds to a valley in the Landscape with a particular altitude or energy density. However, although the vacuum may seem quiet and featureless to our coarse senses, quantum fluctuations continually create tiny bubbles of space whose properties correspond to neighboring valleys. Usually the bubbles quickly shrink and disappear. But if the neighboring valley has lower altitude, then every so often a bubble will appear that is large enough to start growing.
When an object crosses the horizon, it says good-bye forever. Some objects may even have initially formed beyond the horizon. The observer can never have any knowledge of them. But if such objects are permanently beyond the limits of our knowledge, do they matter at all? Is there any reason to include the regions outside the horizon in a scientific theory? Some philosophers would argue that they are metaphysical constructions that have no more business in a scientific theory than the concepts of heaven, hell, and purgatory.
I believe this whole discussion is based on a fallacy. In a universe governed by quantum mechanics, the apparent ultimate barriers are not so ultimate. In principle, objects behind horizons are quite within our grasp, but only in principle.
At some time in the past, the universe existed in a state of very large energy density, probably trapped in an inflationary expansion. Almost all cosmologists will agree that a history of rapid exponential inflation is very likely the explanation of many puzzles of cosmology. In chapter 5 we learned about the observational basis for this belief. It seems all but certain that the observable history of our universe began about fourteen billion years ago at a point in the Landscape with enough energy density to inflate our patch of space by at least 1020 times. That is probably an enormous underestimate. The energy density during this period was very large—how large we don’t know for sure but vastly larger than anything we can make in the laboratory, even during the most violent collisions of elementary particles in the largest accelerators. It appears that at that time, the universe was not quite trapped in a valley of the Landscape but was resting on a slightly tilted plateau. As it inflated, our pocket of space (the observable universe) slowly rolled down the shallow tilt, toward a sudden, steep ledge, and when it got to the edge of the ledge, it quickly descended, converting potential energy to heat and particles. This event, which created the material of the universe, is called reheating. Finally, the universe rolled down to our present valley, with its tiny anthropic cosmological constant. That’s it: cosmology as we know it was a brief roll from one value of the vacuum energy to another.
Unfortunately, as I explained in chapter 7, even life forms as alien as superstring theorists probably cannot survive in a supersymmetric world.
From the perspective of the entire megaverse, the history is not a sequence or series of events. The megaverse description is a more parallel view of things—many pocket universes, evolving in parallel.
quantum mechanics is not a theory that predicts the future from the past, but rather it determines the probabilities for the possible alternate outcomes of an observation.
What is evident is that the only way to avoid wave-function collapse is to include the entire observable universe as well as all the branches of the wave function in the quantum description. That is the alternative to Bohr’s pragmatic rule of terminating the story by collapsing the wave function.
Collapsing the wave function is a useful device to cut away all the unneeded baggage, but to many physicists this rule seems to be an arbitrary external intervention by the observer—a procedure not in any way based on the mathematics of quantum mechanics. Why should the mathematics give rise to all the other branches if their only role is to be thrown away?
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To understand the puzzlement that attends quantum mechanics, it is helpful to ask why, in a Newtonian world of absolute certainty, one would ever discuss probability at all. The answer is simple: probabilities enter Newtonian physics for the simple reason that one is almost always ignorant of the exact initial conditions of an experiment. In the coin flipping experiment, if one knew the exact details of the hand that threw the coin, the air currents in the room, and all the other relevant details, there would be no need for probabilities. Each throw would lead to a definite outcome. Probability is a convenient trick to compensate for our practical inability to know the details. It has no fundamental place in the Newtonian laws.
Chapter Twelve: The Black Hole War
The energy of the courageous star traveler who braved the horizon crossing eventually reappears as “pure light and radiance.”
One should not get the idea that information comes out of the black hole in an easily accessible form. It comes out in a form that is so scrambled that in practical terms it would be impossible to unscramble. But the debate was not about practicalities. It was about laws of nature and principles of physics. What, exactly, constitutes information, especially if it is scrambled beyond recognition?
What does the lieutenant make of it? If he doesn’t know the shuffling rule, he has nothing but a random, meaningless sequence of letters that conveys no information. But the information is there, nevertheless.
One of the strangest discoveries of modern physics is that the world is a kind of holographic image. But even more surprising, the number of pixels the hologram comprises is proportional only to the area of the region being described, not the volume.
Chapter Thirteen: Summing Up
The existence of other pocket universes remains, and will remain, a conjecture, but a conjecture with explanatory power.
Linde has expressed his opinion: “Those who dislike anthropic principle are simply in denial. This principle is not a universal weapon, but a useful tool, which allows us to concentrate on the fundamental problems of physics by separating them from the purely environmental problems, which may have an anthropic solution. One may hate the Anthropic Principle or love it, but I bet that eventually everyone is going to use it.”
there is a hidden assumption that is an integral part of the Anthropic Principle, namely: the existence of life is extremely delicate and requires very exceptional conditions.
As much as I would very much like to balance things by explaining the opposing side, I simply can’t find that other side.
A new baby universe is born inside the black hole. In other words universes are replicators that reproduce in the interior of black holes. If this is so, Smolin argues, then by a process of repeated replication—black holes forming inside universes, which are inside black holes, which are inside universes, and so on—an evolution will take place toward maximally fit universes. By fit Smolin means having the ability to produce a large number of black holes and, therefore, a large number of offspring.
With its ultrasmall cosmological constant and its paucity of black holes, our universe is particularly unfit to replicate.
But much of the controversy over the Anthropic Principle has to do with a more ambitious agenda, the hope that it can substitute for the silver bullet in predicting all of nature. This is an unreasonable expectation. There is no reason why every feature of nature should be determined by the existence of life. Some features will be determined by mathematical reasoning of the traditional kind, some by anthropic consideration, and some features may just be accidental environmental facts.
“Why is the orbital distance of our planet from the source of heat so finely tuned?” But the answer of the codmologists is the same. The universe is big. It has many stars and planets, and some small fraction are just the right distance for liquid water and for fish.
degrees of freedom
It is a long shot, but those large-scale density contrasts could have information about the formation of our bubble from a previous epoch with a larger cosmological constant.
the vacuum energy didn’t depart without leaving something behind. It was converted into more ordinary forms of energy, namely, heat and particles, the stuff of the current universe.
But giving up on the possibility of more direct tests is certainly premature. It is true that theory and experiment usually proceed “hand in hand,” but it’s not always the case. It took more than two decades for Alan Guth’s inflationary universe to be tested by observation. In the early days almost everyone thought the idea was interesting but could never be tested. I think even Alan himself was skeptical of ever confirming its truth. Even more extreme was Darwin’s theory. It was based on general observations about the world and a very clever hunch. But a direct, controlled, experimental test must have seemed completely impossible—you would need a time machine to take you back millions, if not billions, of years. In fact it took about one hundred years for ingenious biologists and chemists to figure out how to subject the theory to rigorous laboratory tests. Sometimes theory has to forge ahead to light the way.
Epilogue
For my own tastes, elegance and simplicity can sometimes be found in principles that don’t at all lend themselves to equations. I know of no equations that are more elegant than the two principles that underpin Darwin’s theory: random mutation and competition. This book is about an organizing principle that is also powerful and simple. I think it deserves to be called elegant, but again, I don’t know an equation to describe it, only a slogan: “A Landscape of possibilities populated by a megaverse of actualities.”
The ultimate existential question, “Why is there Something rather than Nothing?” has no more or less of an answer than before anyone had ever heard of String Theory. If there was a moment of creation, it is obscured from our eyes and our telescopes by the veil of explosive Inflation that took place during the prehistory of the Big Bang. If there is a God, she has taken great pains to make herself irrelevant. Let me then close this book with the words of Pierre-Simon de Laplace that opened it: “I have no need of this hypothesis.”
About The Author
Plasma is just another word for gas that has had its atoms ionized. In other words, some of the electrons have been torn free of the nucleus and are free to wander through the gas, unattached to atoms.