Hiding in the Mirror: The Quest for Alternate Realities, From Plato to String Theory (By Way of Alicein Wonderland, Einstein, and the Twilight Zone)
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Muon: An unstable elementary particle, with a lifetime of one millionth of a second, that appears to be identical to the electron, except that its mass is about two hundred times greater. When it was first observed, the physicist I. I. Rabi uttered, “Who ordered that?”
Naturalness: In physics formulas one often finds numbers comparable to unity, such as 2 or pi. However, physicists call it “unnatural” when one finds in a formula a very large or very small dimensionless number, like 0.00000000000000000000000001 or 35,000,000,000,000,000,000,000, 000,000. The ratio between the strength of gravity and electromagnetism is one such very small number, for example, which is why the hierarchy problem is one form of a naturalness problem.
Neutrino: A light neutral particle produced in the radioactive decay of a neutron (and various other particles). The neutrino has no electromagnetic or strong interactions, and thus interacts so weakly with matter that neutrinos produced in the decay of a neutron can, on average, travel right through the Earth without a single collision or interaction.
Neutron: A neutral elementary particle with a mass comparable to that of the proton, and comprising, along with the proton, all atomic nuclei. Free neutrons are unstable, decaying into protons, electrons, and neutrinos with an average lifetime of about ten minutes.
Nonabelian gauge theory: A different name for Yang-Mills theories that reflects the mathematical symmetry, called gauge invariance, that underlies them. Non-Euclidean geometry: The specific application of Riemannian geometry to spaces that are not flat.
Parallax: The amount by which nearby objects, when viewed from different vantage points, will shift in comparison to distant background objects. The magnitude of this shift can be used to determine the distance of the nearby objects.
Parity: A parity transformation interchanges left and right. Certain interactions, like the electromagnetic interaction, do not distinguish between left and right. However, the weak interaction remarkably does distinguish between left and right, so that neutrons rotating around a certain axis will produce electrons that preferentially head off in one hemisphere, as opposed to the other hemisphere. Photon: The elementary “quantum” of the electromagnetic field, a.k.a. light. Because of quantum mechanics, light has both wavelike and particlelike properties. In particular light of a given frequency is transmitted via many individual photons, so that for light of a low enough intensity, a detector will be able to detect the individual packets of energy carried by these particles, and never any smaller amounts.
Pions: Elementary particles produced in the collisions of energetic protons with matter. These particles, about ten times lighter than the proton, are made up of a quark and an antiquark, and are unstable with a lifetime of less than a millionth of a billionth of a second.
Planck scale: This is the length scale (or equivalently the energy scale) at which quantum mechanical effects relevant to gravity cannot be ignored. Because gravity is so weak at normal scales, it turns out that one must go to incredibly small scales before quantum effects become important. The Planck length scale is about 10–33cm.
Precession: If a rotating or orbiting object returns to its initial position, and repeats precisely the same motion again, there is no precession. However, if upon returning to the same position, the next orbit, or rotation, is shifted compared to the first, so that the motion does not exactly repeat after one such cycle, one says that the orbit or rotation is precessing. Proton: An elementary particle with positive electric charge equal and opposite to that found on the electron. The proton, which weighs almost two thousand times as much as the electron, is located, along with neutral particles called neutrons, within the dense nucleus at the center of atoms. As far as we can measure, the proton is absolutely stable, but most grand unified theories predict the proton can decay with a lifetime too long to have yet been measured.
Quantum electrodynamics (QED): The theory that successfully combines quantum mechanics, relativity, and electromagnetism to correctly predict all phenomena that have been observed associated with the interactions of matter and electromagnetic radiation.
Quark confinement: The property that is associated with the fact that isolated quarks are not observed in nature. While this property of the strong interaction has not been mathematically proved yet, it appears to arise naturally as a corollary to the fact that the force between quarks gets weaker as they get closer together, and stronger as you pull them apart. If this behavior continues indefinitely as you try and pull them apart, it would take an infinite amount of energy to produce a single quark, isolated from all its neighbors.
Riemannian geometry: A generalization of the flat two-dimensional geometric relations of Euclid, applied instead to spaces that can also be curved and that can also involve more than two dimensions.
Scattering: When two elementary particles collide together many different things can happen, from a simple grazing collision in which the particles are each deflected, to collisions in which the particles change their identities, and in which new elementary particles are created. All of these processes are called scattering processes.
Singularity: Generally describes the mathematical characteristic of any quantity that can grow infinitely large. When referred to points in space, a singularity refers to a region of space where the density of matter and energy grows infinitely large, and where the classical laws of general relativity appear to break down. Spacetime supersymmetry: A mathematical symmetry that incorporates supersymmetry with the other known symmetries of space and time, including the fact that the laws of physics are unchanged from place to place, and from time to time.
Spacetime: The four-dimensional universe made up of three dimensions of space and one dimension of time, unified together by Einstein in his special theory of relativity, and first described by Hermann Minkowski. Spectra: The set of colors of electromagnetic radiation emitted by different gases when you heat them up. Each element has a unique set of such colors that identifies it. The laws of quantum mechanics allow us to calculate the spectrum of light emitted by atoms, in agreement with observations. Spontaneous symmetry breaking: This occurs when some symmetry of nature, such as left-right symmetry, is violated by the particular circumstances in which we find ourselves, but not by the underlying laws of physics that govern that situation. So, for example, while electromagnetism does not distinguish left from right, and electromagnetic interactions are those that are chiefly responsible for the makeup of material objects, I can nevertheless find myself standing next to a mountain on one side of me and an ocean on another side of me. In this case, I can clearly distinguish my left side from my right side. Such an accident of my particular circumstances represents an example of spontaneous symmetry breaking. Here is another one: Say you are having dinner at a large round table. After everyone sits down, every place-setting looks identical, and glasses are located both to the left and right of each person. Nothing distinguishes which glass is associated with which person until the first person picks up a glass. After that, the original symmetry is broken, and every glass is associated with a unique person.
Supergravity: Another name for local supersymmetry. Supersymmetry: A mathematical symmetry that relates elementary particles having different spin angular momentum. Specifically, supersymmetry implies that for all particles having integer spin (bosons) there should exist particles of equal mass having half-integer spin (fermions). Tachyon: A hypothetical elementary particle which travels faster than the speed of light, and which can never be slowed down to below the speed of light. Such a particle could appear to an outside observer to be traveling backward in time. Generally, if a theory appears to predict tachyonic states, it is a sign that there is something unstable in the theory. Often such a prediction is associated with a violation of unitarity in the theory. Tensor algebra: Mathematical relations that involve objects with multiple separate components, each of which can have a different dependence on both space and time.
Tesseract: A four-dimensional version of a three-dimensional cub
e. The “faces” of this hypercube comprise eight different three-dimensional cubes. Torus: A donut-shaped object, with a hole in the center. One can produce such an object by taking a flat piece of paper and pasting together two opposite edges, and then the other two opposite edges. Alternatively, one can simply lay the paper flat and merely “identify” the two edges, so that for example, whenever an object heads off the right edge of the paper it would appear coming in from the left edge. In the language of topology, a torus therefore is topologically distinct from a flat piece of paper, in that it has a hole, but geometrically it can still be considered flat. Uncertainty principle: One of the fundamental principles of quantum mechanics that implies there are certain combinations of quantities associated with any object that can never be measured exactly. For example, both the position and the momentum (see momentum) of an object cannot be known together with absolute accuracy. As one measures the position of an object more and more accurately, the uncertainty in knowledge about its momentum will increase. Since this minimum combined uncertainty in position and momentum is, however, very small, the effect of the uncertainty principle is not usually directly observed on scales much larger than the size of atoms.
Unitarity: A fundamental mathematical property of nature that essentially says that probabilities do not change over time. Simply put, it implies that when one considers all of the different possibilities that may arise when one particle interacts with another, and sums up the different probabilities, they will add up to unity.
Vacuum energy: The energy associated with empty space, containing no matter or radiation. While common sense says that this energy should be zero, the laws of quantum mechanics and relativity together imply that empty space is full of a swarm of “virtual particles” that pop in and out of existence on a timescale so short we cannot observe them directly. When we try to calculate what the contribution of these particles might be to the energy of empty space, we come up with a very large number—indeed, far larger than anything we measure today. We currently do not understand why this prediction is incorrect. At the same time, any such energy, if it exists, is gravitationally repulsive, and could cause the observed expansion of the universe to accelerate. This is what we observe today in the universe on large scales.
Virtual particles: The laws of quantum mechanics and special relativity together imply that elementary particles and their antiparticles can spontaneously appear together out of empty space, exist for a short time, and then annihilate again, leaving nothing but empty space. As long as they do so for periods so short that we cannot measure them directly, their existence is ensured by the uncertainty principle. While virtual particles cannot be directly observed, their indirect effects can be observed, and predictions agree well with observations.
Vortex rings: A ring, like a smoke ring, that is stable and can move about, maintaining its form even as it moves through some background medium like air.
Warped space: This has, alas, nothing to do with Star Trek. Rather, it is a term that has been used to describe certain extra-dimensional theories with possibly large extra dimensions. In these theories the geometry (and hence the strength of gravity) in the three spatial dimensions we experience is not separated from the existence of the higher dimension(s), but is rather a function of where you are located in the higher dimension(s). In this case, it is possible not only for all familiar particles and nongravitational forces to be confined on our three-dimensional space, but also for gravity to be effectively restricted to lie in our space, leaving the higher dimensions thus far undetected, but in fact allowing the possibility of their detection in new high energy accelerators such as the large hadron collider, and also allowing a possible new approach to the hierarchy problem. Wavelength: For any periodic wave, with peaks and crests, the distance between successive peaks is called the wavelength of the wave. Weak scale: This is the energy (or length) scale at which the weak interaction, responsible for the nuclear reactions inside the sun, for example, becomes of roughly comparable order in strength as the electromagnetic interaction, and which the mathematical symmetry between these two forces of nature, which is spontaneously broken at large scales, becomes manifest.
Yang-Mills theory: This represents a wide class of physical theories that are generalizations of electromagnetism, in which the particles that play the role of photons in electromagnetism, which are neutral, are instead charged, and also can have a mass, and therefore have more complicated interactions with one another and with other particles than photons do. Both the weak force and the strong force are described by Yang-Mills theories.
Table of Contents
HIDING IN THE MIRROR
A L S O B Y L A W R E N C E M . K R A U S S
HIDING IN THE MIRROR
V I K I N G
For my mother . . . at last!
There is a dimension, beyond that which is known to man. It is a dimension as vast as space and as timeless as infinity.
R E M I N I S C E N C E
C H A P T E R 1
C H A P T E R 2
C H A P T E R 3
C H A P T E R 4
C H A P T E R 5
C H A P T E R 6
C H A P T E R 7
C H A P T E R 8
C H A P T E R 9
C H A P T E R 1 0
C H A P T E R 1 1
C H A P T E R 1 2
C H A P T E R 1 3
C H A P T E R 1 4
C H A P T E R 1 5
C H A P T E R 1 6
C H A P T E R 1 7
E P I L O G U E
A C K N O W L E D G M E N T S
G L O S S A RY