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Duality of Light and Matter
Published in Zbigniew Ficek, Quantum Physics for Beginners, 2017
An aside: The Heisenberg uncertainty principle has created a long debate on the validity of quantum physics. Most scientists interpret physical phenomena as events taking place “out there,” independent of any measurement or observation. At the same time, quantum theory stands in conflict with such naive notions of reality. As we have already learned, the Heisenberg uncertainty principle sets a limit on the precision with which two complementary observables can be measured. For example, a measurement of momentum of a particle disturbs the position of the particle. To many people, this is an unsatisfactory feature of quantum physics. The most notable objector, of course, was Einstein, whose concern about the uncertainty principle is expressed in his famous statement: Is the state of the Universe disturbed if a mouse looks at it?.
The Different Thermodynamics: What Ought to Be the Proper Mathematical Instrument?
Published in Evgeni B. Starikov, A Different Thermodynamics and Its True Heroes, 2019
The degree of this uncertainty was related directly to Planck’s constant—the same value that Max Planck had calculated in 1900 in his original quantum calculations of thermal energy. Heisenberg found that certain complementary quantities in quantum physics ought to be linked by this sort of uncertainty:Position and momentum (momentum is mass times velocity);Energy and time;
Symbols, Terminology, and Nomenclature
Published in W. M. Haynes, David R. Lide, Thomas J. Bruno, CRC Handbook of Chemistry and Physics, 2016
W. M. Haynes, David R. Lide, Thomas J. Bruno
tential from all the other electrons. The new potential that results is used to repeat the calculation and the procedure continued until convergence is reached. Also called self-consistent field (SCF) method. Heat capacity* - Defined in general as dQ/dT, where dQ is the amount of heat that must be added to a system to increase its temperature by a small amount dT. The heat capacity at constant pressure is Cp = (H/T)p; that at constant volume is CV = (E/T)V , where H is enthalpy, E is internal energy, p is pressure, V is volume, and T is temperature. An upper case C normally indicates the molar heat capacity, while a lower case c is used for the specific (per unit mass) heat capacity. [1] Heat of formation, vaporization, etc. - See corresponding terms under Enthalpy. Hectare (ha) - A unit of area equal to 104 m2. [1] Heisenberg uncertainty principle - The statement that two observable properties of a system that are complementary, in the sense that their quantum-mechanical operators do not commute, cannot be specified simultaneously with absolute precision. An example is the position and momentum of a particle; according to this principle, the uncertainties in position q and momentum p must satisfy the relation pq h/4, where h is Planck's constant. Heitler-London model - An early quantum-mechanical model of the hydrogen atom which introduced the concept of the exchange interaction between electrons as the primary reason for stability of the chemical bond. Helicon - A low-frequency wave generated when a metal at low temperature is exposed to a uniform magnetic field and a circularly polarized electric field. Helmholz energy (A) - A thermodynamic function defined by A = E-TS, where E is the energy, S the entropy, and T the thermodynamic temperature. [2] Hemiacetals - Compounds having the general formula R2C(OH)OR' (R' not equal to H). [5] Henry (H)* - The SI unit of inductance, equal to Wb/A. [1] Henry's law * - An expression which applies to an ideal dilute solution in which one or more gasses are dissolved, viz., pi = Hixi, where pi is the partial pressure of component i above the solution, xi is its mole fraction in the solution, and Hi is the Henry's law constant (a characteristic of the given gas and solvent, as well as the temperature). Hermitian operator - An operator A that satisfies the relation um*Aundx = ( un*Aum dx)*, where * indicates the complex conjugate. The eigenvalues of Hermitian operators are real, and eigenfunctions belonging to different eigenvalues are orthogonal. Hertz (Hz) - The SI unit of frequency, equal to s-1. [1] Heterocyclic compounds - Cyclic compounds having as ring members atoms of at least two different elements, e.g., quinoline, 1,2-thiazole, bicyclo[3.3.1]tetrasiloxane. [5] Heusler alloys - Alloys of manganese, copper, aluminum, nickel, and sometimes other metals which find important uses as permanent magnets. Holography - A technique for creating a three-dimensional image of a object by recording the interference pattern between a light beam diffracted from the object and a reference beam. The image can be reconstructed from this pattern by a suitable optical system.
Quantum models of cognition and decision
Published in International Journal of Parallel, Emergent and Distributed Systems, 2018
If P1P2 − P2P1 = 0, then operators commute (they are commutative). Then, order of events does not matter: P1P2 = P2P1. Such operators has common basis, and questions they represent are compatible. If P1P2 − P2P1 ≠ 0 then such operators do not commute (they are not commutative – they do not have a common basis). Then, P1P2 ≠ P2P1 and result of action on any state vector depends on order of events. It is reflected in quantum mechanics as the Heisenberg’s uncertainty principle: there are certain pairs of physical properties of a particle, known as complementary variables (e.g. momentum of a particle and its corresponding position) that cannot be simultaneously measured, because the more precisely the position of some particle is determined, the less precisely its momentum can be known, and vice versa. If this is the case, order of measurements is crucial.
Information flow in context-dependent hierarchical Bayesian inference
Published in Journal of Experimental & Theoretical Artificial Intelligence, 2022
Chris Fields, James F. Glazebrook
Within this Bayesian picture, mutually-incoherent cocones lead to incoherent object identification, incoherent categorisation and/or mereological assembly, and incoherent inferences about appropriate action. Intrinsic contextuality, in other words, provokes inferential incoherence, as Examples 7.1, 7.2 and 7.3 illustrate. How can a hierarchical Bayesian classifier cope with intrinsic contextuality? Here the definition of a context as what is observed shows both its strength and its weaknesses. The effects of a context can be better understood, and hence predicted, by expanding it: embedding it in a larger context by observing more. In the limit, direct influences become predictable, so no longer surprising. A context can, however, only be expanded by deploying additional co-deployable observables. If not all available observables are co-deployable, mutually-incoherent contexts and hence intrinsic contextuality will remain. The challenge for a Bayesian classifier is, then, to be able to recognise when observables are not co-deployable, or equivalently, when concepts like ‘beautiful’ in the ‘Snow Queen’ experiment (Example 7.3) switch between mutually-incoherent meanings. Quantum theory formalises the needed knowledge in Bohr’s notion of complementarity: observables are complementary whenever their operators do not commute (Bohr, 1928). Moving beyond a formalised theory, however, is challenging. Observers cannot, in general, determine by observation what observables they are deploying (Fields and Marcianò, 2019b). ‘Learning the hard way’ by working backwards from outcomes that reveal the effects of incoherent inferences is the fallback option (again cf. the discussion in 4.2); indeed this is how complementarity was discovered by physics. Working backwards requires memory, time, and other resources that can be in short supply in a dynamic environment.