Hiding in the Mirror: The Quest for Alternate Realities, From Plato to String Theory (By Way of Alicein Wonderland, Einstein, and the Twilight Zone)

by Lawrence M. Krauss

  G L O S S A RY

  Alpha rays: Rays made up of the nuclei of helium, containing two neutrons and two protons, which are produced in the radioactive decays of various heavy nuclei.

  Angular momentum: A twisting force imparts angular momentum to objects, causing them to spin. Angular momentum is calculated as the product of the mass of an object times its rotational speed.

  Anomaly: Due to quantum mechanical effects, a symmetry of nature that appears in a classical theory (such as electromagnetism) can be violated at the quantum level. When this happens the symmetry is said to be anomalous, and the quantum mechanical contribution that violates the symmetry is said to be an anomaly. Several “anomalous symmetries” are known to exist in nature. However, it is very important that quantum mechanical effects do not spoil the gauge and general covariance symmetries that are at the heart of the four known forces in nature. Making sure this does not happen has played a key role in efforts to develop string theories as candidate theories for the natural world. Antiparticles: The laws of quantum mechanics and special relativity together imply that every elementary particle in nature must have an antiparticle, with equal mass and opposite electric charge. Many antiparticles have been created in the laboratory, and are used regularly in high-energy particle accelerators that explore the nature of matter and energy at fundamental scales. When particles and antiparticles collide, they can annihilate, producing pure radiation. Some neutral particles can be their own antiparticles. Asymptotic freedom: The remarkable property of the strong interaction, discovered in 1974, that the force between quarks becomes stronger as you pull the quarks apart. This is the opposite behavior from electromagnetism, which gets weaker as elementary charges are moved far apart from each other. Asymptotic freedom is presumably related to the fact that no observable isolated quarks exist in nature (a phenomenon called confinement). Beta rays: Rays made up of electrons, which are produced in the radioactive decays of various elementary particles and nuclei.

  Black body radiation: When a perfectly black solid, like the heating element on a stove, is heated up, it emits a continuous set of colors of radiation, changing from red hot to blue hot to white hot, for example. This distribution of radiation uniquely determines the temperature of the object, and was explained using the laws of quantum mechanics early in the twentieth century.

  Bootstrap model: An idea that achieved prominence in the 1960s in response to the growing number of strongly interacting elementary particles, which suggested that no elementary particles were truly fundamental, but rather that all particles could be made up of other elementary particles. It proposed instead that what was fundamental was the mathematical relationship between particles that governed their interactions with each other. Bootstrap models eventually led to the development of string theories that attempted to describe the interactions of strongly interacting elementary particles.

  Bosons: Elementary particles in which the spin angular momentum is quantized, having a value equal to an integer multiple of some fundamental quantum of angular momentum.

  Chirality: Certain objects, like our two hands, or the spiral structures that make up DNA can be said to be left handed or right handed, i.e., mirror images of each other. This property is called chirality. Elementary particles with spin angular momentum can be chiral, in that they can appear to be spinning in either a clockwise or a counterclockwise direction about their spin axis. One type of particle is called left handed, and the other right handed. Theories that distinguish between left-and right-handed particles are called chiral theories. The weak interaction is one such example as, for example, only left-handed neutrinos appear to sense the weak interaction. (As a result we do not even know if right-handed neutrinos exist in nature.)

  Cloud chamber: A device developed in the early part of the twentieth century that produces observable tracks when charged elementary particles, such as the particles in cosmic rays, traverse the chamber. When these particles more through the chamber the gas vapor surrounding the particles with which they collide condenses, producing a visible vapor trail. Different particles produce qualitatively different tracks.

  Compactification: In theories with extra dimensions beyond the three space and one time dimension of our experience, one has to explain why the other dimensions are not observed. One solution involves compactification, in which the extra dimensions are curled up into “balls” that are so small that no experiment yet performed could detect their existence. The process by which one goes from a higher-dimensional theory to an effective four-dimensional theory is called compactification, and trying to understand how this might occur is one of the major challenges of string theory, and other higher-dimensional theories.

  Conformal invariance: A mathematical symmetry that encompasses not only the general covariance that is at the basis of general relativity but extends it to include so-called scale transformations. If the world were conformally invariant, then the world would appear unchanged if I doubled the size of all objects, their masses, etc. This is clearly not the case, so conformal invariance is not a property of the real world as we measure it. However, it is an underlying property of string theories, and clearly one of the challengesof having string theory touch base with the world that we observe is to find mechanisms by which this symmetry is broken in our world. Connection tensor: A mathematical quantity that encodes the geometric nature of space. The connection tensor in particular explains how the length and orientation of a standard ruler might be measured to change as it moved between nearby points in a curved space. The connection tensor therefore encodes information about the curvature of space. Cosmic microwave background: The afterglow of the big bang, this radiation is a remnant from the earliest era of the expansion, when the temperature was so high that matter and radiation were in thermal equilibrium. Once the temperature had cooled sufficiently (to about three thousand degrees above absolute zero), protons and electrons began to be able to combine to form neutral atoms, which decoupled from the radiation so that the universe became transparent. The remnant radiation cooled as the universe expanded, and is now at a temperature of about three degrees above absolute zero. Cosmic rays: Energetic elementary particles of many different types that bombard the earth regularly from space. They originate from locations as close as our own sun, and as far away as the centers of distant galaxies. Dark Energy: When we add up the total amount of mass in the visible universe, and compare it to the total energy needed to result in the flat universe (see Flat universe) that we appear to live in, there is a factor of three too little mass to account for the flatness of space on large scales. At the same time, the observed expansion of the universe appears to be accelerating, which could only be the case if empty space possessed energy (see Vac- uum energy). The amount of energy needed to result in the observed acceleration turns out to be precisely that required to also account for a flat universe. We currently understand very little about this “dark energy,” which resides in empty space, and do not know if it is vacuum energy, or some other kind of yet more exotic form of energy.

  D-branes: Multidimensional surfaces (generalizations of two-dimensional membranes—hence the name) on which “open strings” that is, strings that are not closed loops, and that propagate in higher dimensions, can end. The “D” in D-branes does not refer to the dimensionality of the brane, but rather to the specific boundary conditions that are imposed at the end of the string as it merges with the brane. D-branes are now understood to be very important objects within string theory, though they were not known in the earliest formulations of the theory.

  Density fluctuations: Observed stars, galaxies, planets (and ultimately people) initially arose as very small inhomogeneities in the distribution of matter and radiation in the early universe, which collapsed due to their internal gravitational attraction. Regions where there was a very small excess of matter, for example, compared to the background value, would expand slightly more slowly than the background, eventually becoming so much more dense than the bac
kground that they decoupled from the expansion of the universe, and started to collapse. We believe this is how all large-scale structures now observable in the universe first formed. The question then becomes, what caused these initial density fluctuations in the early universe? We currently have reason to believe that they formed due to the quantum mechanical effects at very early times, as a result of inflation.

  Electron: An elementary particle with negative electric charge that comprises the outer parts of all atoms. Neutral atoms contain an equal number of electrons and protons, with the latter existing within a dense nucleus at the center of the atoms. As far as we know, the electron is absolutely stable.

  Equivalence principle: The principle that all objects fall at the same rate in a gravitational field. Einstein argued that this is equivalent to the notion that in a local free-falling frame, the effects of gravity will be unobservable. This principle formed a fundamental pillar of his general theory of relativity, because it allowed him to present a completely geometric description of gravity in which its effects could be ascribed to the curvature of space.

  Ether (also Aether) : The hypothetical substance that was believed for centuries to fill space and in which it was believed that light waves propagated. In 1887 the physicist Albert A. Michelson and his colleague, chemist Edward Morley, demonstrated experimentally that the ether, as a medium in which light traveled, did not exist. Later, in 1905, Einstein demonstrated that the existence of such an ether was in fact inconsistent with the laws of physics.

  Event horizon: A region surrounding a black hole, from which classically nothing, even light, can escape. As a result, once objects cross the event horizon observers outside of the black hole lose all information as to their future behavior.

  False vacuum: If we describe the vacuum state as the lowest energy state in which a system can exist (such as a region of empty space devoid of matter or energy), a false vacuum occurs when the lowest energy state in certain circumstances turns out not to remain the lowest energy state as those circumstance change. Possible examples include when the value of some external field, or the temperature of the system, changes. The system may exist in this false vacuum state for a long time, but it will eventually decay, by the rules of quantum mechanics, into the new lower energy state, releasing energy in the process. Fermions: Elementary particles in which the spin angular momentum is quantized, having a value equal to a half-integer multiple of some fundamental quantum of angular momentum. Flat universe: General relativity implies that space can curve in the presence of mass and energy. On the largest scales, if light travels in straight lines, this implies that the universe is spatially flat. A spatially flat universe is infinite in extent, and, if dominated by matter, will continue to expand forever, with the expansion rate slowing asymptotically, but never quite falling to zero. We appear to live in a flat universe, as far as we can tell, although not one dominated by matter.

  Gamma rays: The most energetic electromagnetic rays. The photons making up gamma rays can have energies as great as or greater than the energy associated with the rest mass of elementary particles such as electrons and protons.

  General covariance: A mathematical notion at the heart of Einstein’s general relativity theory that implies that the laws of physics are independent of any specific coordinate frame in which we choose to measure them. One of the implications of this is that for an observer in free fall in a gravitational field, the effects of gravity will appear to disappear. Another is that an observer accelerating upward in an elevator in empty space will experience a force pushing him toward the floor that will be completely indistinguishable from the force of gravity that he would experience if he was at rest in a gravitational field.

  Grand unification: The theoretical notion that the three nongravitational forces in nature—the weak, electromagnetic, and strong forces—can actually be unified in a single framework, and moreover, that at a very small scale, perhaps fifteen orders of magnitude smaller than we can measure today, all of these forces will appear to have the same strength.

  Grassmann variable: A mathematical quantity that has some properties of a normal number, but nevertheless has some vastly different properties. For example, when a Grassman number is multiplied by itself, it produces zero. Two different Grassman variables, A and B, when multiplied together in one order, say AB, equal the negative value when multiplied in the other order, so that AB = − BA. It turns out that these properties mimic the quantum mechanical properties that govern the behavior of fermions. Graviton: When one combines quantum mechanics and relativity, all forces are conveyed by the exchange of elementary particles, like the photon, the fundamental quantum of electromagnetism. We call the hypothetical particle that conveys gravitation the graviton. Individual gravitons have not yet been measured because of the weakness of gravity, although we have no reason not to believe they exist.

  GSO construction: A particular construction in string theory in ten dimensions, associated with the names Gliozzi, Scherk, and Olive, which removed the unwanted tachyon modes by introducing supersymmetry on the strings. Hadrons: Elementary particles that have strong interactions with other particles.

  Heterotic string: A string theory involving closed string loops in ten dimensions in which the different excitations of the string, moving in different directions along the string, behave quite differently. In fact, the left movers appear to live in a different number of dimensions than the right movers. In this way, it turns out that one can have consistent string theories in ten dimensions instead of twenty-six dimensions. Moreover the gauge symmetries that one hopes might be associated with the observed gauge symmetries in our world arise naturally as a part of this construction. Hierarchy problem: Gravity is much weaker than all of the other forces in nature. This extreme hierarchy of forces is currently not understood, and is one form of what is often called the hierarchy problem. Another example is that the length scale at which the strength of all the nongravitational forces appears to become the same—the length scale at which grand unification is thought to occur—appears to be very much smaller than the scale associated with the size of particles such as protons and neutrons, and nuclei. It turns out to be very difficult mathematically to devise theories in which this is the case, and trying to resolve this difficulty is the hierarchy problem.

  Hubble constant: In a uniformly expanding universe the recession velocity of distant objects away from us is proportional to their distance from us. The quantity determining the precise numerical relationship between velocity and distance is named the Hubble constant, in honor of Edwin Hubble, who first discovered this relation. Note that this quantity is not in fact a constant over cosmological times for most cosmological models. Hypercube: Another name for a four-dimensional cube (tesseract). Inflation: The idea, based on notions coming from the physics of elementary particles, that at very early times the universe underwent a brief period of extremely rapid expansion, during which distances increased by a factor greater than a billion, billion, billion, billion, in a fraction of a second. Such an expansion can naturally occur as the universe expanded and cooled at early times if there was a phase transition associated with a grand unified theory (see Grand unification), and can moreover explain all of the observed features of the universe today on the largest scales we can measure.

  Large hadron collider (LHC): The new large proton-proton collider being built at the European Center for Nuclear Research (CERN) in Geneva. Planned to come online by 2007–2008, it will achieve energies large enough to explore for the mechanism underlying the origin of mass of elementary particles, and may reveal other new phenomena such as supersymmetry and possible large extra dimensions. Local supersymmetry: This involves the mathematical formalism in which gravity and supersymmetry are combined together in one framework. One consequence of this is that the graviton, the fundamental quantum thought to convey the gravitational force, must have a fermionic partner, called the gravitino.

  Matrices: Mathematical objects which take the fo
rm of tables of numbers with separate entries in the different rows and columns. Matrices can be multiplied together, added together, etc. and thus have their own kind of algebra that is more complex than the algebra of simple real numbers. One of the eleven-dimensional limits of string theories that form a part of M-theory involves a description of nature in which matrices form the fundamental quantities akin to the numbers that describe positions in our four-dimensional space.

  Metric: The mathematical quantity, called a tensor, that determines how physical lengths are measured in terms of the coordinates one uses to label the points in some space. For example, on a sphere, the physical distance between neighboring lines of longitude decreases as one moves to the poles. The metric tensor contains this information of how the distance between lines of longitude changes as you move around the surface of the sphere.

  Moduli fields: In extra-dimensional theories such as string theory there are usually dynamical “fields” observable in our three-dimensional world that are associated with the actual radius of the presumably compactified and unobservable extra dimensions. These fields are called moduli fields, and their dynamics can either cause interesting new effects that might be measurable in our space, or cause severe empirical problems for model builders.

  Momentum: A force acting on an object over some time imparts momentum to that object. For objects moving slowly compared to the speed of light, the momentum of the object is given by multiplying the mass of the object by its speed.

  M-theory: The eleven-dimensional theory that is thought to underlie all known ten-dimensional string theories. Its existence was suggested once it was recognized that D-branes must be included in string descriptions, and these clarified the relationship between formerly disparate string models, suggesting some evidence of a yet higher dimensional theory. To date, no one has a clear understanding of the precise nature of this theory, or even what its fundamental variables are.