by Peter Byrne
Glossary
ABM Acronym for anti-ballistic missile systems, which are expensive to build and cheap to fool.
Alcoholism, drug addiction Substance abuse is a mental illness with definable symptoms.
Altruism Evolutionary biologists now regard group altruism as a significant force behind evolutionary success.
Anthropic principle The idea that whatever explanation one has of the structure of the universe, it must be compatible with the fact that we exist as observers.
Amplitude, wave function The wave-like attributes of a quantum system expressed as a complex number, i.e. a number that uses “i,” the “imaginary” number that is the square root of minus 1. An amplitude (or wave function) is constructed from a series of measurement experiments, although, arguably, it exists regardless of human agency.
Born rule The postulate that squaring the value of an amplitude obtained from a measurement interaction gives the classical probability that the same amplitude will result from a repetition of the measurement experiment. This predictive rule is the fundamental tool of quantum mechanics.
Bell’s theorem John S. Bell’s mathematical proof that local hidden variable theories and the predictions of quantum mechanics are incompatible. The theorem does not rule out the existence of non-local hidden variables as theorized by David Bohm.
DeBroglie-Bohm hidden variables interpretation A non-relativistic, non-linear quantum theory with a universal wave function and no requirement for the presence of an observer. It treats particles as guided on classical trajectories by probability or “pilot” waves.
Classical physics The mechanistic physics of Newton and Maxwell in which a theoretical knowledge of all initial conditions of a system allows for the determination of subsequent conditions along a continuum of cause and effect.
Collapse postulate John von Neumann’s axiom that a measurement of a superposed quantum system causes the system to “jump” into but one element of the superposition.
Commutation relation In the quantum formalism, when two matrices of complex numbers (A & B) are multiplied together, they do not necessarily commute. There are cases in which A × B ≠ B × A. The difference is a tiny number based upon Planck’s constant. This phenomenon reflects fundamental features of quantum mechanics (see: Heisenberg uncertainty principle).
Complementarity Niels Bohr’s philosophy that reality is composed of mutually exclusive phenomena—such as waves and particles. Arbitrarily partitioning the universe between classical and quantum realms, it declares that the microscopic world must be interpreted solely in terms of classical physics.
Correspondence principle Bohr’s method of analogizing events in the indeterministic quantum world to events described by the laws of classical physics.
Consistent histories interpretation This approach treats the universe quantum mechanically and assigns probabilities to both microscopic and macroscopic states before measurement-type interactions take place. It considers classical physics to be an approximate representation of quantum reality.
Containment The geopolitical strategy articulated after the Second World War by George F. Kennan that called for controlled isolation of the socialist states, short of threatening war.
Copenhagen interpretation An amalgam of various philosophical approaches popularly attributed to Bohr, von Neumann, Werner von Heisenberg, and others. It posits that we can only speak about quantum mechanics experimentally and by reducing it to classical concepts through wave function collapse. Because this approach allowed physicists to “shut up and calculate,” it was the prevailing interpretation in the West during the much of the 20th century. Socialist physicists, however, tended to consider it a positivistic and non-materialist explanation.
Cosmology The study of the origin and evolution of the universe.
Cybernetics As coined by the polymath, Norbert Wiener, cybernetics treats information as a physical quantity subject to the laws of entropy and probability. It recognized the role of “feedback loops,” i.e. random output that becomes corrective input.
Decision theory Similar to game theory, it parameterizes the branching process of decision-making in terms of utilities, probabilities, and considerations of “rationality.”
Decoherence In practice, the irreversible entanglement of a quantum system with its environment.
Degrees of freedom The number of variables in an equation. The more opportunities an object has to change, the more variables are required to reflect this freedom.
Deterrence In the context of the Cold War: threatening perceived enemies with destruction if they attack while trying to moderate the threat enough so that they do not attack preemptively, as both sides are mirroring each other.
Dualism Involves a metaphysical commitment to two distinct, but often causally related phenomena. In quantum physics, the idea that a quantum object behaves like a wave and, also, a particle. In philosophy, the separation of mind and body, spirit and matter.
Entanglement, correlation When two or more quantum systems interact their properties may become correlated, linked, entangled. This relation may persist for objects that become superluminally separated. In terms of observation: if you know something about one of the systems, you also know something about its partner. Entangled systems can be viewed as a single system with its own wave function.
Entropy A measure of disorder.
Fallout Pulverized material stirred up and irradiated by thermonuclear explosions and distributed by the prevailing winds.
Fourier analysis A mathematical method that works in classical mechanics to break down complex oscillations into simpler parts. In quantum mechanics, the method decomposes a wave function into its constituent wave functions.
Game theory A mathematical method of modeling complex systems (economics, evolution, warfare) in which choices are assigned probabilities and utility values.
Generalized Lagrange Multiplier Method An improvement upon Lagrange’s optimization method that brought cost-benefit analysis into the computer age. Everett’s GLM algorithm assigns “prices” to the use of specific resources while weighing the constraints inhibiting the utilization of those resources and delineating optimal performance paths in complex situations affected by hundreds of variables.
General relativity Einstein’s theory that gravity is embedded in a geometrized space-time.
Heisenberg uncertainty principle Some properties of quantum objects (e.g. time and energy, position and momentum) cannot be simultaneously measured to a degree of accuracy greater than Planck’s constant.
Hidden variables interpretation The idea that quantum mechanics is an incomplete description of the world.
Hilbert space The complex number-valued space used to represent quantum mechanical states. States are treated as vectors in this mathematical system, which describes superposition, interference, and entanglement with a precision that classical language cannot touch.
Idealism The idea that reality is an idea.
Information Everett viewed information as a measure of the spread of a probability distribution.
Interference A property of waves in which the positive and negative values represented by crests and troughs add when combined. In quantum mechanics, the values are complex numbers.
Irreversibility The Schrödinger equation is reversible, i.e. the evolution of quantum states works forwards and backwards in time. There are, however, some physical processes that do not appear to be reversible—the thermodynamical “arrow of time,” for example. Or, in practice, quantum entanglement.
Landscape The equations of the string theory Landscape require 10500 universes to encompass a full range of solutions.
Lebesque measure A measure of length, area, or volume. It can be applied to Hilbert space as well as classical (phase) space.
Linearity The Schrödinger equation evolves each element of a superposed wave function deterministically.
Locality, non-locality One notion of locality is the relativistic rule that information cannot be transfer
red between any two points in space faster than the speed of light. Non-locality is the apparent failure of that rule, as evidenced by the experimental verification of quantum entanglement in which information appears to be instantly communicated between separated but entangled objects. Copenhagen-type quantum mechanics cannot explain non-locality, but the MWI deals with it easily by asserting that as all outcomes occur, there is no need for non-locality, or “action at a distance.”
Matrix mechanics Heisenberg conceived the use of matrices (arrays) of complex numbers to depict static relationships between quantum states. The method is basically equivalent to Schrödinger’s wave mechanics, but particularly suited to treating such continuously valued properties as the position of a particle.
Measurement problem The paradox that the Schrödinger equation evolves quantum superpositions through time with each element of the superposition intact, and yet we experience only one element of a superposition in our classical space.
Momentum Velocity times mass.
Mutual assured destruction The game-Theoretic doctrine of war preparation that underlay the expansion of nuclear weapons systems during the Cold War by both superpowers. Its premise was that superiority in first strike capabilities would deter an opponent from attacking, except out of fear of attack by an opponent fearing attack from an opponent fearing …
Multiverse The collection of all universes. In the Everettian model, it is described as a universal wave function.
Negentropy The opposite of entropy or disorder. A state with high negentropy has low probability, i.e. it contains more information relative to a state of higher probability or lower negentropy.
Ontological argument A supposedly logical construct proving the existence of a god.
Path integrals, sum over histories A method invented by Richard Feynman for calculating the motion of particles in which entire trajectories (histories) have amplitudes.
Planck’s constant: h Also called the quantum of action, it is a fundamental constant of nature. It is the ratio of the energy of a quantum of energy to its frequency. Very tiny (at 6.626 × 10-34 Joules), it governs the exchange of quanta, i.e. the minimum amount of energy by which an electromagnetic (or gravitational) system can change.
Positivism The philosophy of science that reality can only be described as a record of experimental results. We cannot talk meaningfully about anything that cannot be empirically validated.
Probability calculus A set of rules that define the properties of probability. It allows us to make predictions based upon the relative frequency of past events.
Probability distribution In quantum mechanics: as constructed from a series of experimental observations on a microscopic system, the distribution contains the results of such measurements, translated as a range of classical probabilities that add to unity (100 percent).
Psycho-physical parallelism Articulated by von Neumann as the requirement that a scientific theory should correspond to our experience of physical reality.
Quantum state A collection of data sufficient to allow us to make predictions about transformations of the data; represented as a vector in Hilbert space.
Rationality The definition appears to be fluid. According to von Neumann-Morgenstern’s Theory of Games and Economic Behavior, “It may safely be stated that there exists, at present, no satisfactory treatment of the question of rational behavior…. The chief reason for this lies, no doubt, in the failure to develop and apply suitable mathematical methods to the problem; this would have revealed that the maximum problem which is supposed to correspond to the notion of rationality is not at all formulated in an unambiguous way. …. [It] is much more complicated than the popular and the ‘philosophical’ use of the word ‘rational’ indicates.” [von Neumann, J. and Morgenstern, O. (2004). 9.] von Neumann and Morgenstern went on to suggest that maximization of personal (not social) utility was rational behavior, but Rapoport critiqued their argument as circular and tautological (see Chapter 6). It currently appears that acting altruistically at the group level is far more rational (as shown by evolutionary biology) than the utilitarian pursuit of narrowly perceived self-interests as iconized by game theory and capitalist economics.
Realism In the philosophy of science: that an objective reality exists independent of human or divine agency or perception.
Recursion A feedback loop. A simple computer program instruction, “add 1 to the result just obtained,” is recursive, for instance. It allows a series of operations to advance and conclude without having to write a new instruction at every step. But the recursive method can bog down in paradox. It is not possible to resolve the truth of the recursive statement, “All reporters are liars. I am a reporter.”
Schrödinger equation The time-dependent partial differential equation invented by Erwin Schrödinger in 1926. It is the standard tool for calculating changes in quantum states viewed as wave-like entities.
Single Integrated Operating Plan (SIOP) The United States’ targeting plan for nuclear war. As late as 1998, the SIOP targeted the former Soviet Union. It is extraordinarily complex and ultra-secret and is seemingly unaffected by disarmament talks.
Solipsism My idea that reality is my idea.
Special relativity A theory based upon the assumption that the speed of light is constant and that the laws of physics are the same for all observers. Features of Einstein’s theory are that there is no privileged frame of reference in four-dimensional space-time; that energy and mass are equivalent; and that objects become infinitely massive and time-dilated when moving at the speed of light (photons do not have mass).
Spin The intrinsic (non-orbital) angular momentum of an electron, nucleus, or elementary particle at rest. It comes in discreet quantities and is affected by magnetic fields.
Superposition principle For any two or more possible quantum mechanical states, the superposition of these states is also possible. The wave function of an object contains data that, in sum, list all of the configurations of all of the possible properties of the quantum object. Each datum or configuration or element of a wave function is also a wave function and, therefore, the seed of a probability value. The Schrödinger equation deterministically evolves each element in a wave function through time linearly as if each element is equally and potentially real without singling out any element as more probable or more real than any other. A coherent superposition allows for these elements to interfere with each other, i.e. to continuously evolve as combined wave functions. But interference effects are absent in an incoherent superposition of quantum states (or wave functions or state vectors) and each element in an incoherent superposition has statistical properties, meaning that predictions regarding its future coordinates in classical reality (phase space) can be made (using the Born rule). The phenomenon of superposition applies, in theory, to macroscopic objects as well as microscopic, but due to decoherence effects we do not normally see such items as cannonballs or the Eiffel Tower in superpositions. As a metaphor: consider a double- or triple- or infinitely exposed photograph: a superimposition of images representing real things.
Tautology In logic, a proposition that is true by virtue of its abstract form—its conclusion is identical to its premise. In philosophy, a tautological statement conflates cause and effect. In language, a tautological statement is self-referential—it lacks meaningful content or useful definition, i.e. “If A is true, then not-A is false.” Or: “A dog is a canine.” Or: “There is no god but God.”
Unitary As it evolves elements of a superposition through time, the Schrödinger equation preserves these amplitudes so that, when squared, their sum will always equal 1 (100 percent).
Variable A quantity or force that changes in value.
Vector A mathematical object that represents both magnitude and direction. For example: an arrow in flight.
Wargasm Cold War operations researchers often used sexualized language to describe the doctrine of launching the entire arsenal of nuclear weapons in a first or second strike.
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br /> Wave function A complex number representing data gathered by observing and recording such properties as position and momentum of quantum objects. It can be described as a vector in an infinite-dimensional mathematical space (Hilbert space) that obeys certain laws. Squaring a wave function (or amplitude) gives the classical probability that the same wave function will reoccur under identical circumstances.
Wigner’s friend A famous thought experiment that asks what happens when an observer of a quantum measurement is part of the system observed.
Acknowledgments
Special thanks:
Mark Everett for trusting me with his father’s papers and his family archive; and for commenting on draft chapters.
Stacey L. Evans for reading raw drafts and making many helpful suggestions and for her’s and our son Miles’ good will in the face of late nights and lost weekends and minor car accidents caused by day dreaming about probabilities.
Simon Saunders, H. Dieter Zeh, and Jeffery A. Barrett for many stimulating conversations about Everett, probability, decoherence, and the philosophy of quantum mechanics. David Deutsch for several talks.