Quote: waves in a confined space exist only at definite frequencies, e.g. sound in an organ pipe [»feynRP_1965]

Quote: the probability amplitudes of electrons in an atom are constrained, they exist at definite energies

Quote: if a particle is to be bound in a potential well, it can do so only if it has a very definite energy; otherwise get exponential growth of the amplitude to be outside of the potential well [»feynRP_1965]

Quote: the first indication that classical physics was wrong was Maxwell's work on specific heats; molecules have discrete energy levels [»feynRP_1963]

Quote: perhaps quantum phenomena and relativity theory can not be unified: different mathematical domains, even false theories can be amazingly accurate [»wignEP2_1960]

Quote: geometry and dynamics are linked together; motion is not curves (world-lines) in space-time

Quote: the things that really are in the world without us, are those motions by which these seemings are caused

Quote: in the classical limit, the quantum mechanics of a system will agree with Newtonian mechanics [»feynRP_1965]

Quote: Newton's laws approximate the actual quantum-mechanical laws of motion on a fine scale; Newton's laws fortunately become more accurate as the scale increases indefinitely [»feynRP_1963]

Quote: the laws of conservation of momentum and energy hold exactly in quantum mechanics [»heisW_1927]

Quote: symmetries are the basis of all conservation laws of quantum mechanics; e.g., conservation of energy, momentum, angular momentum, parity

Quote: "When we know the present precisely, we can predict the future" is not the conclusion but the assumption; observation is a selection that limits what is possible; quantum mechanics establishes the final failure of causality

Quote: only the theory itself can decide what is and is not observable [»heisW_1927]

Quote: observation breaks the connection between the past and future course of phenomena [»bohrN_1934]

Quote: quantum effects blur the distinction between phenomenon and observation; the basis for classical ideas of motion

Quote: we are both onlookers and actors in the great drama of existence

Quote: can not separate atomic operations from their measuring instruments; all description is inherently classical

Quote: the product of location precision and momentum precision is proportional to Plank's constant [»heisW_1927]

Quote: uncertainty principle: any apparatus that can detect the path of an electron will disturb it sufficiently to destroy any interference patterns

Quote: the uncertainty principle is a side effect of quantum mechanics; the true view is the addition of probability amplitudes for all the ways an event can happen [»feynRP_1985]

Quote: the idea of a particle is limited; if we know the wavelength exactly, the location is unknown; if we know the location exactly, the momentum is unknown [»feynRP_1965]

Quote: uncertainty principle of Heisenberg: the product of the uncertainties in the position and momentum of a particle is greater than Planck's constant [»feynRP_1965]

Quote: uncertainty principle, general form: one can not build equipment to distinguish two alternatives without at the same time destroying the pattern of interference

Quote: the quantum of action makes it impossible to consider a system's configuration and state of motion independently; Heisenberg's uncertainty principle [»debrL_1937]

Quote: any ordering in space-time requires an exchange of energy and momentum between the observed and observer; thus breaking the measurement [»bohrN_1934]

Quote: our most precise description of nature must be in terms of probabilities; the uncertainty principle [»feynRP_1963]

Quote: in a hydrogen atom, the uncertainty of the electron's position is as large as the atom itself; an electron is like a cloud representing its probability density

Quote: quantum mechanics has indeterminacy relations where mechanical variables are associated in conjugate pairs [»heisW_1927]

Quote: momentum-energy indeterminacy refers to particles while space-time indeterminacy refers to waves

Quote: the statistical relations of quantum mechanics are due to the indeterminacy of conjugate quantities such as momentum and energy [»heisW_1927]

Quote: processes are discontinuous in small regions and short times; it is clearly meaningless to speak about one velocity at one position [»heisW_1927]

Quote: concepts of classical, physical theory have an exact analog for atomic processes; but, conjugate quantities suffer an indeterminacy purely by the observational procedures [»heisW_1927]

Quote: the word "simultaneous" requires the speed of light; sharper definitions are not possible; a constant speed of light does not contradict concepts of position, velocity, and time [»heisW_1927]

Quote: quantum-theoretical quantity is a matrix whose diagonal is the classical value with nondiagonal terms as the uncertainty [»heisW_1927]

Quote: with quantum mechanics the only thing that can be predicted is the probability of different events; the events themselves can not be predicted [»feynRP_1965]

Quote: can only employ probability for the occurrence of individual processes; free choice between stationary states; like radioactive decay [»bohrN_1934]

Quote: the statistical relations of quantum mechanics are due to the indeterminacy of conjugate quantities such as momentum and energy [»heisW_1927]

Quote: the quantum wave is not a physical phenomenon; given an initial observation, its intensity is the probability of the corpuscle and its spectral structure the probabilities of its states of motion [»debrL_1937]

Quote: under quantum mechanics, all measurement irreversibly changes a process, and the only stability is statistical [»thomR_1975]

Quote: matter in quantum mechanics is an active agent making choices between alternative possibilities according to probabilistic laws

Quote: Nature herself does not even known which way the electron is going to go; intrinsically probabilistic [»feynR_1965]

Quote: Euripides--does random careless chance and change, alone control the world? [»euri_425]

Quote: cannot abandon, actually and forever, the idea of direct representation of physical reality; nor believe that events in nature behave as a game of chance [»einsA5_1940]

Quote: probabilitistic laws of radiation fundamentally different than statistical analysis of complex system; with radiation, there is no individuality or elementary process [»bohrN_1949]

Quote: avoid ascribing attributes to God in everyday language; e.g., Does God play dice? [»bohrN_1949]

Quote: any atomic system can theoretically be separated by filters into a set of base states where the future behavior depends only on the base state [»feynRP_1965]

Quote: with a base state of a quantum-mechanical system, the future is independent of the past [»feynRP_1965]

Quote: all base states of a quantum-mechanical system are completely different

Quote: a filter for a different set of quantum-mechanical base states removes the history about previous filters [»feynRP_1965]

Quote: a quantum mechanical state is described by the amplitudes to be in each of some selected set of base states [»feynRP_1965]

Quote: an apparatus is described by the amplitudes to go from one base state to another; from these numbers anything can be calculated

Quote: the base states of a quantum mechanical system are generally infinite

Quote: quantum mechanics uses the amplitude of the probability of finding a system of electrons in a given configuration; since the function is linear it can be represented as the superposition of states of definite energy [»feynRP_1963]

Quote: barrier penetration by a quantum mechanical amplitude to cross a narrow region where kinetic energy is negative; e.g., alpha-particle decay of uranium [»feynRP_1965]

Quote: the amplitude to go from one quantum-mechanical state to another is the complex conjugate of the amplitude to go in the opposite direction

Quote: the vector potential of quantum mechanics is a bookkeeping device to evaluate the effect of all currents on a point [»meadCA6_1997]

Quote: quantum mechanics: determine the probability of an event by squaring the sum of the arrows for each way an event could happen

Quote: if you could in principle distinguish the alternative final states, their probabilities sum; if you can not, their probability amplitudes sum [»feynRP_1965]

Quote: a magnetic or electrical field changes the phase of the probability amplitude to arrive via any trajectory by the space or time integrals respectively [»feynRP_1964]

Quote: the probability of an event in an ideal experiment is the square of the probability amplitude of the event

Quote: if there are alternative events, the probability amplitudes sum and there is interference; if can detect which alternative, the probabilities sum and there is no interference

Quote: the amplitude to get between quantum-mechanical states is the sum of the amplitudes to go between their base states

Quote: complementarity is particle-wave duality applied to indeterminacy relations; indeterminacy ensures the internal consistency of each extreme view [»heisW_1927]

Quote: evidence from different experiments is complementary; can not be comprehended within a single picture; measurement and experiment are intertwined [»bohrN_1949]

Quote: need both corpuscles and waves to explain matter and radiation; complementary aspects of reality [»debrL_1937]

Quote: can only study different complementary types of atomic phenomena [»bohrN_1949]

Quote: quantum mechanics describes discontinuous change by the continuous change of the probabilities of possible states [»einsA_1949]

Quote: compare quantum behavior to bullets without interference and to waves with interference; if no detection, electrons are like waves but with detection, electrons are like bullets [»feynRP_1965]

Quote: the "particle waves" of quantum mechanics are unlike anything else

Quote: bullets behave as waves but the wavelengths are so tiny that detectors can not detect them; instead see their average behavior [»feynRP_1965]

Quote: personal identity and thinking is like particle and wave descriptions; in both cases, observation has an effect [»bohrN_1934]

Quote: in quantum mechanics the force concept is replaced by the concepts of energy and momentum, frequencies and wavelengths [»feynRP_1964]

Quote: matter is nothing but force; matter does not itself exist; we experience matter as force [»wallAR_1870, OK]

Quote: in mechanics one can not reason from the small to the large; even though geometry is independent of scale [»galiG_1638]

Quote: quantum mechanics is about matter and light on an atomic scale [»feynRP_1965]

Quote: atomistic phenomena occurs in discrete states and discontinuous transitions; like stationary waves in an organ pipe or vibrating string (de Broglie) [»einsA5_1940]

Quote: the resistance of atoms to compression is a quantum-mechanical effect [»feynRP_1965]

Quote: for identical particles, the order of arrival can not be distinguished and the alternatives will interfere with each other [»feynRP_1965]

Quote: the quantum conditions of stability in atoms is a resonance phenomena; integers are as natural as they are for vibrating cords [»debrL_1937]

Quote: matter and light behaves the same; matter can display interference and defraction in a crystal or grating [»debrL_1937]

Quote: superconductors provide direct access to the quantum nature of matter [»meadCA6_1997]

Quote: quantization occurs because the phase must match at both ends of a closed, superconducting loop [»meadCA6_1997]

Quote: with superconductors, understand quantum effects via waves

Quote: use a loop for superconductor model of quantum effects; ends are either shorted or insolated; persistent current if shorted [»meadCA6_1997]

Quote: the arrival order of Bose particles interfere with a positive sign while Fermi particles interfere with a negative sign; e.g., photons and electrons respectively

Quote: identical particles interfere only if they have identical spin states

Quote: for composite objects, half-integral spin imitates a Fermi particle while integral spin imitates a Bose particle

Quote: when there are n identical Bose particles present, the probability of adding another particle is enhanced by n+1 [»feynRP_1965]

Quote: the condition of n, non-interacting, identical Bose particles acts the same as a harmonic oscillator [»feynRP_1965]

Quote: two Fermi particles, e.g., electrons, can not be in the same state; much of the material world hinges on this fact [»feynRP_1965]

Quote: in helium the electrons can have opposite spins; in lithium, one electron must be at a lower energy level with different chemical properties [»feynRP_1965]

Quote: the three electrons in lithium are identical; so the picture of electron shells is only an approximate one

Quote: the protons of multiple hydrogen atoms can not approach each other because their electrons must be in different states [»feynRP_1965]

Quote: reality should have a purely algebraic theory since quantum phenomena are completely described by a finite set of numbers; not a continuous field [»einsA_1956, OK]

Quote: introduction to quantum computing and error correction; exponential speedup but difficult to access the results [»riefE9_2000]

Quote: at some stage, the quantum linear superposition becomes actual alternatives one of which is observed; may happen at the one-graviton level [»penrR_1989]

Quote: perhaps we can write an equation for life; perhaps it is quantum mechanics; God may not be needed to explain the complexities of the world

Quote: perhaps mind is quantum gravity selecting one of many superpositioned alternatives [»penrR_1989]

Quote: if atoms do not swerve a little, where does freewill come from? these motions have their beginning in the whim of each atom [»lucr_55]

Quote: atoms have to swerve a little, by the smallest possible degree; otherwise they would fall like rain and never collide [»lucr_55]

Quote: freewill is due to the slight swerve of atoms, at a random time and place

Quote: Petri assumed that metrics do not exist for space, time, or any physical magnitude [»petrCA1_1966]

Quote: an actor is either active (receiving messages) or idle; can only learn about an undisturbed state by acting on it, active state is inaccessible [»mantMJ2_1983]