Glossary of Important Terms

allowed state: One of a limited number of states in which an object may be measured in quantum mechanics. For example, a dog at rest can either be found on the floor, or on the sofa, but never halfway between the floor and the sofa.

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antimatter: Every particle in the universe has an antimatter equivalent, with the same mass and the opposite charge. When a particle of ordinary matter encounters its antiparticle, the two annihilate, converting their mass into energy.

Bell’s theorem: A mathematical theorem proved by John Bell, showing that entangled quantum particles have their states correlated in ways that no local hidden variable (LHV) theory can match.

classical physics: Physics theories developed before about 1900, describing the behavior of everyday objects. Core components are Newton’s laws of motion, Maxwell’s equations for electricity and magnetism, and the laws of thermodynamics.

coherence: A property of waves or wavefunctions, roughly defined as behaving as if the waves came from a single source.Adding together two coherent waves gives a clear interference pattern; adding together two incoherent waves gives a rapidly shifting pattern that smears out and becomes indistinct. The process of “decoherence” destroys the coherence between two waves from a single source through random and fluctuating interactions with a larger environment.

conservation of energy: The law of conservation of energy states that energy can be changed from one form to another, but the total energy of a given system is always the same. For example, a dog can convert the potential energy stored in food into kinetic energy as she chases a squirrel, but she cannot gain more kinetic energy than the total energy available in her food.

Copenhagen interpretation: The philosophical framework for quantum mechanics developed by Neils Bohr and colleagues at his institute in Denmark. The Copenhagen interpretation insists on an absolute split between microscopic systems, which are described by quantum mechanics, and macroscopic systems, which are described by classical physics. The interaction between a microscopic quantum system and a macroscopic measuring apparatus causes the wavefunction to “collapse” into one of the allowed states for that system.

decoherence: A process by which random, fluctuating interactions with the environment destroy our ability to see an interference pattern for a quantum particle. Decoherence is particularly important for the many-worlds interpretation, where it ensures that different branches of the wavefunction of the universe will not affect one another.

diffraction: A characteristic behavior of waves, in which waves passing through a narrow opening or around an obstacle spread out on the far side. A dog can hear a potato crisp hitting the kitchen floor from the living room because sound waves diffract through the kitchen door and around corners.

Einstein, Podolsky, and Rosen (EPR) paradox: A famous paper by Albert Einstein, Boris Podolsky, and Nathan Rosen that used entangled particles to argue that quantum mechanics was incomplete. Their argument has been proven wrong by experiments testing Bell’s theorem, but has led to the development of quantum teleportation and other quantum information technologies.

energy: A measure of an object’s ability to change its own motion or the motion of another object. Energy comes in many forms, such as kinetic energy, potential energy, and mass energy (Einstein’s E = mc 2). Energy may be converted from one form to another, but cannot be created or destroyed.

energy-time uncertainty: A variation of the Heisenberg uncertainty principle stating that it is impossible to know both the exact energy of some object and the exact time at which it was measured. This limits the lifetime of virtual particles in quantum electrodynamics.

entanglement: A quantum “connection” between two objects whose states are correlated in such a way that measuring one also determines the state of the other. A classical analogy is two dogs in the same room: either both will be awake, or both will be asleep. If you measure one dog to be awake, you immediately know that the other is also awake. Similar correlations exist for quantum particles, but their states are indeterminate until one of the two is measured, at which time the state of both is instantaneously determined, no matter how far apart they are.

Feynman diagram: A picture representing a possible sequence of events for a charged particle interacting with light. Each diagram stands for a calculation in QED, and the energy of the interacting particle is found by adding together all the possible diagrams for that particle. The diagrams are named after Richard Feynman, who invented them as a calculational shortcut.

gyromagnetic ratio/ “g-factor”: A number, given the symbol g, that determines how an electron interacts with a magnetic field. The simplest theory of quantum mechanics predicts that g = 2, but QED predicts a value that is very slightly larger. The experimentally measured value of g agrees with the QED prediction to fourteen decimal places.

Hawking radiation: A process by which “virtual particles” cause black holes to evaporate. When a particle-antiparticle pair appears near a black hole, one of the two can fall into the black hole, while the other escapes. In order to conserve energy, the black hole must lose a tiny bit of mass. Over time, the black hole is whittled down to nothing, one particle mass at a time.

interference: A phenomenon that occurs when two or more waves are added together. If the peaks of one wave line up with the peaks of the other (“in phase”), the result is a much larger wave. If the peaks of one wave line up with the valleys of the other (“out of phase”), the result is no wave at all. Interference patterns involving single particles are the clearest demonstration of quantum behavior.

kinetic energy: Energy associated with a moving object. For everyday objects, the kinetic energy is equal to half the mass times the speed squared (½ mv 2). A Great Dane has more kinetic energy than a Chihuahua moving at the same speed, while a hyperactive Siberian husky has more kinetic energy than a sleepy bloodhound of the same mass.

local hidden variable (LHV) theory: A theory of the sort preferred by Einstein, Podolsky, and Rosen. In an LHV theory, measurements made in one position are independent of measurements made at other positions (“local”), and particles are always in definite states, though the exact values are unknown (“hidden variables”). LHV theories cannot duplicate all the predictions of quantum mechanics (according to Bell’s theorem), and have been disproven in experiments by Alain Aspect, among others.

many-worlds interpretation: The philosophical frame-work for quantum mechanics developed by Hugh Everett III at Princeton in the 1950s. The many-worlds interpretation avoids the “wavefunction collapse” problem of the Copenhagen interpretation by saying that all possible measurement outcomes take place in different branches of the wavefunction—in some part of the wavefunction, every dog eats steak. Sadly, we only perceive a single branch. The other branches of the wavefunction are effectively separate universes, due to decoherence, which prevents the different branches from having a measurable effect on one another.

measurement: In quantum mechanics, an active process that changes the state of the system being measured. Before a measurement is made, a quantum object will be in a superposition of all the allowed states; after the measurement, the object will be in one and only one state. The Copenhagen interpretation and the many-worlds interpretation offer two different ways of describing what happens during a measurement.

modern physics: Physics theories developed after about 1900, consisting principally of relativity and quantum mechanics.

momentum: A quantity associated with motion that determines what will happen to an object during a collision. In classical physics, momentum is mass times velocity (p = mv); a small Chihuahua must be moving much faster than a Great Dane to have the same momentum. In quantum mechanics, the momentum of a particle determines its wavelength, through the de Broglie relation λ = h/p.

no-cloning theorem: A mathematical theorem showing that it is impossible to make a perfect copy of a quantum object without knowing its state in advance.

particle-wave duality: A feature of quantum mechanics, in which objects have both particle and wave properties. Classical physics says that light is a wave, but quantum physics says that a beam of light is also a stream of photons. Classical physics says that an electron is a particle, but quantum physics says that an electron also has a wavelength that depends on its momentum. Electrons and photons are each “quantum particles,” a third class of object that is neither particle nor wave, but has properties of each.

photoelectric effect: An effect discovered in the late 1800s, where light falling on metal knocks out electrons. Einstein explained the photoelectric effect in 1905 by applying Planck’s quantum hypothesis to light directly, describing a beam of light as a stream of photons.

photon: A “particle” of light. A beam of light may be thought of as a stream of particles, like kibble being poured into a dog’s bowl. Each photon has an energy given by Planck’s constant multiplied by the frequency associated with that color of light (E = hf).

Planck’s Constant (h): The constant that relates energy to frequency or momentum to wavelength in quantum physics.The measured value is h=6.6261×10-34 J-s, or 0.0000000 000000000000000000000000006261 J-s, which is a very small number indeed.

polarization: A property of light, corresponding to the direction of oscillation of the light wave in classical physics. Any polarization can be described as a combination of vertical and horizontal polarizations, and will determine the probability of that light passing through a vertical or horizontal polarizer.

polarizer/ polarizing filter: A material that allows through light polarized at some angle, and blocks light polarized 90° away from that angle. Light polarized at some intermediate angle has a probability of passing through that depends on the angle.

potential energy: Energy associated with an object that is not currently moving, but has the potential to start moving. A dog always has potential energy, even when sleeping: at the slightest sound, she can leap up and start barking at nothing.

probability: The wavefunction for a quantum object describes the probability of finding the object in any of its allowed states when a measurement is made. For example, there is a high probability of finding the dog in the kitchen, a high probability of finding the dog in the living room, and a very low probability of finding the dog on the sofa, if she knows what’s good for her.

quantum computer: A computer made up of “qubits” that not only can take values of “0” and “1” like the bits in a classical computer, but also superpositions of “0” and “1.” Such a computer could solve certain types of problems, such as the factoring of large numbers, much faster than a classical computer. The difficulty of factoring large numbers is the basis for modern cryptography, so a quantum computer would let an evil squirrel decipher your credit card transactions, and clean out your bank account to buy birdseed.

quantum electrodynamics: “QED” for short. The theory describing the interactions between charged particles and light, developed by Richard Feynman, Julian Schwinger, and Shin-Ichiro Tomonaga around 1950. Feynman’s formulation is the best known version, which describes interactions in terms of the exchange of “virtual particles.”

quantum eraser: A demonstration of quantum measurement in which an interference pattern is destroyed by making it possible to measure the exact path taken by a particle, but recovered by doing something to confuse that measurement.

quantum field theory: A theory that combines quantum mechanics with Einstein’s relativity, to cover particles moving at speeds close to the speed of light, and the interactions between such particles. The simplest quantum field theory is quantum electrodynamics.

quantum interrogation: A technique using the quantum Zeno effect to detect the presence of an object without letting it absorb even a single photon. Its applications to rabbit stalking should be obvious to any dog.

quantum mechanics/ quantum physics/ quantum theory: The subject of this book, quantum mechanics was developed in the first half of the twentieth century, and describes the behavior of and interactions among atoms, molecules, subatomic particles, and light.

quantum teleportation: A procedure for transferring the exact state of a quantum particle from one place to another without measuring it or moving it, using entangled particles as a resource. Sadly, it does not allow dogs to beam themselves into places where they can easily catch squirrels.

quantum Zeno effect: A demonstration of quantum measurement in which an object can be prevented from changing states by repeatedly measuring its state. The classical equivalent is a dog who prevents her owner from napping by constantly asking “Are you asleep?”

relativity: The theory developed by Albert Einstein to describe gravity and the behavior of objects moving at speeds close to the speed of light.

Schrödinger equation: The mathematical formula that physicists use to find the wavefunction for a particular quantum system, and predict how it changes in time.

Schrödinger’s cat: A thought experiment proposed by Erwin Schrödinger, intended to show the absurdity of quantum superpositions. He imagined a cat enclosed in a box with a device that had a 50% chance of killing the cat within one hour; quantum physics says that at the end of the hour the cat is equal parts alive and dead, until its state is measured. This experiment has made him a hero to canine physicists.

semiclassical argument: A description of a physical system that is mostly based on classical physics, with a few modern ideas added in an ad hoc manner. Examples of semiclassical models include the “Heisenberg microscope” (page 38) and the Bohr model of hydrogen (page 49).

state/ quantum state: A particular collection of properties (position, momentum, energy, etc.) describing an object. For example, “sleeping in the living room,” “sleeping in the kitchen,” and “running around the house” are three different possible states for a dog.

superposition state: In quantum mechanics, an object can exist in a superposition of two or more allowed states at the same time, until a measurement is made. Such superposition states give rise to interference patterns, which can be detected experimentally, even though the system can only be measured in one allowed state.

thermal radiation: Also called “black-body radiation,” the light that is emitted by a hot object, such as the characteristic red glow of a hot burner on a stove. The spectrum of this light depends only on the temperature of the object. Explaining this spectrum led Max Planck to introduce quantum mechanics.

tunneling: A quantum phenomenon in which a particle that does not have enough energy to pass over a barrier passes through the barrier anyway, appearing on the other side, like a bad dog digging a hole under a fence.

uncertainty principle/ Heisenberg uncertainty principle: One of a set of mathematical relationships limiting the precision with which complementary properties can be measured. The best known uncertainty principle is between momentum and position, and says that it is impossible to know both exactly where a rabbit is, and exactly how fast it is moving. Any attempt to specify the position more precisely will lead to increased momentum uncertainty, and vice versa. The energy-time uncertainty relationship is also important, as it determines the length of time that virtual particles can exist in QED.

virtual particle: A particle in a Feynman diagram that appears and disappears too quickly to be measured directly. These usually appear as pairs of one normal particle and one antimatter particle, most often one electron and one positron. In principle, anything can show up as a virtual particle, even a rabbit made of cheese.

wavefunction: A mathematical function whose square gives the probability of finding an object in any of its allowed states.In quantum mechanics, all objects are described by wave-functions.

zero-point energy: The tiny amount of energy that is always present in a quantum object, thanks to the wave nature of matter. Confined quantum particles are never perfectly at rest—they’re like puppies in a basket, always squirming and wriggling and shifting around, even when they’re asleep.