The theory of special relativity predicts that any such device would allow communication from the future to the past, which raises problems of causality, unless the device used general relativistic curved spacetimes as an integral part.

* BCS theory predicts the dependence of the value of the energy gap E at temperature T on the critical temperature T < sub > c </ sub >.

* BCS theory correctly predicts the Meissner effect, i. e. the expulsion of a magnetic field from the superconductor and the variation of the penetration depth ( the extent of the screening currents flowing below the metal's surface ) with temperature.

The theory of general relativity predicts that a sufficiently compact mass will deform spacetime to form a black hole.

The analogy was completed when Hawking, in 1974, showed that quantum field theory predicts that black holes should radiate like a black body with a temperature proportional to the surface gravity of the black hole.

Quantum field theory predicts a cosmological constant much like dark energy, but 120 orders of magnitude larger than that observed.

In contrast simple molecular orbital theory predicts that the hydrogen molecule dissociates into a linear superposition of hydrogen atoms and positive and negative hydrogen ions, a completely unphysical result.

Similarly, demand-and-supply theory predicts a new price-quantity combination from a shift in demand ( as to the figure ), or in supply.

Elementary demand-and-supply theory predicts equilibrium but not the speed of adjustment for changes of equilibrium due to a shift in demand or supply.

EPR tried to set up a paradox to question the range of true application of Quantum Mechanics: Quantum theory predicts that both values cannot be known for a particle, and yet the EPR thought experiment purports to show that they must all have determinate values.

String theory predicts the existence of gravitons and their well-defined interactions.

For example, at very high temperature and high pressure, unless there are sufficiently many flavors of quarks, the theory of quantum chromodynamics ( QCD ) predicts that quarks and gluons will no longer be confined within hadrons < i > because the strength of the strong interaction diminishes with energy .</ i > This property, which is known as asymptotic freedom, has been experimentally confirmed in the energy range between 1 GeV ( gigaelectronvolt ) and 1 TeV ( teraelectronvolt ).

The labor theory of value predicts that profits will be higher in labor-intensive industries than in capital-intensive industries, and empirical data contradicts this.

This theory thus predicts that a solution of rod-shaped objects will undergo a phase transition, at sufficient concentration, into a nematic phase.

Solved self-consistently, this theory predicts thermotropic nematic-isotropic phase transitions, consistent with experiment.

Although the aether is almost stationary according to Fresnel, his theory predicts a positive outcome of aether drift experiments only to second order in, because Fresnel's dragging coefficient would cause a negative outcome of all optical experiments capable of measuring effects to first order in.

Paul Dirac observed in 1931 that, because electricity and magnetism show a certain symmetry, just as quantum theory predicts that individual positive or negative electric charges can be observed without the opposing charge, isolated South or North magnetic poles should be observable.

While the supergravity description assumes a continuous space-time, Matrix theory predicts that, at short distances, non-commutative geometry takes over, somewhat similar to the way the continuum of water breaks down at short distances in favor of the graininess of molecules.

Of course this theorem is considered irrelevant by economists who do not believe that general equilibrium theory correctly predicts the functioning of market economies ; but it is given great importance by neoclassical economists and it is the theoretical reason given by them for combating monopolies and for antitrust legislation.

Specifically, he demonstrated an upper limit, known as Bell's inequality, regarding the strength of correlations that can be produced in any theory obeying local realism, and he showed that quantum theory predicts violations of this limit for certain entangled systems.

In particular, Abrikosov showed that Ginzburg-Landau theory predicts the division of superconductors into the two categories now referred to as Type I and Type II.

A theory of everything ( ToE ) or final theory is a putative theory of theoretical physics that fully explains and links together all known physical phenomena, and predicts the outcome of any experiment that could be carried out in principle.

His key contributions include topological tensor products of topological vector spaces, the theory of nuclear spaces as foundational for Schwartz distributions, and the application of L < sup > p </ sup > spaces in studying linear maps between topological vector spaces.

Binary relations are used in many branches of mathematics to model concepts like " is greater than ", " is equal to ", and " divides " in arithmetic, " is congruent to " in geometry, " is adjacent to " in graph theory, " is orthogonal to " in linear algebra and many more.

When the Banach algebra A is the algebra L ( X ) of bounded linear operators on a complex Banach space X ( e. g., the algebra of square matrices ), the notion of the spectrum in A coincides with the usual one in the operator theory.

More sophisticated theories are valence bond theory which includes orbital hybridization and resonance, and the linear combination of atomic orbitals molecular orbital method which includes ligand field theory.

Students of control engineering may start with a linear control system course dealing with the time and complex-s domain, which requires a thorough background in elementary mathematics and Laplace transform ( called classical control theory ).

* Conjugation in group theory, related to matrix similarity in linear algebra

Heinrich Zimmer also notes Christianity's emphasis on linear time ; he attributes this emphasis specifically to the influence of Saint Augustine's theory of history.

Cartesian coordinates are the foundation of analytic geometry, and provide enlightening geometric interpretations for many other branches of mathematics, such as linear algebra, complex analysis, differential geometry, multivariate calculus, group theory, and more.

Hilbert spaces are an important class of objects in the area of functional analysis, particularly of the spectral theory of self-adjoint linear operators, that grew up around it during the 20th century.

* Diffraction approximations illustrated – MIT site that illustrates the various approximations in diffraction and intuitively explains the Fraunhofer regime from the perspective of linear system theory.

Developments of the theory of linear models have encompassed and surpassed the cases that concerned early writers.

Today, the theory rests on advanced topics in linear algebra, algebra and combinatorics.

Provided the theory is linear with respect to the wavefunction, the exact form of the quantum dynamics modelled, be it the non-relativistic Schrödinger equation, relativistic quantum field theory or some form of quantum gravity or string theory, does not alter the validity of MWI since MWI is a metatheory applicable to all linear quantum theories, and there is no experimental evidence for any non-linearity of the wavefunction in physics.

LTI system theory describes linear time-invariant ( LTI ) filters of all types.

In the mathematical field of representation theory, group representations describe abstract groups in terms of linear transformations of vector spaces ; in particular, they can be used to represent group elements as matrices so that the group operation can be represented by matrix multiplication.

The bulk of this article describes linear representation theory ; see the last section for generalizations.

In each case, the designation " linear " is used to identify a subclass of models for which substantial reduction in the complexity of the related statistical theory is possible.

In chaos theory, the butterfly effect is the sensitive dependence on initial conditions, where a small change at one place in a deterministic nonlinear system can result in large differences to a later state.

Chaos theory and the sensitive dependence on initial conditions was described in the literature in a particular case of the three-body problem by Henri Poincaré in 1890.

Critical social theory is, in contrast, a form of self-reflective knowledge involving both understanding and theoretical explanation to reduce entrapment in systems of domination or dependence, obeying the emancipatory interest in expanding the scope of autonomy and reducing the scope of domination.

The breaking of rotation and boost invariance causes direction dependence in the theory as well as unconventional energy dependence that introduces novel effects, including Lorentz-violating neutrino oscillations and modifications to the dispersion relations of different particle species, which naturally could make particles move faster than light.

The unification of forces is possible due to the energy scale dependence of parameters in quantum field theory called renormalization group running, which allows parameters with vastly different values at collider energies to converge at much higher energy scales.

* In homotopy theory, the fundamental group of a space at a point, though technically denoted to emphasize the dependence on the base point, is often written lazily as simply if is path connected.

Max Weber's article has been cited as a definitive refutation of the dependence of the economic theory of value on the laws of psychophysics by Lionel Robbins, George Stigler, and Friedrich Hayek, though the broader issue of the relation between economics and psychology has come back into the academic debate with the development of " behavioral economics.

In this sense, string perturbation theory exhibits exactly the features one would expect of a perturbation theory that may exhibit a strong dependence on asymptotics ( as seen, for example, in the AdS / CFT correspondence ) which is a weak form of background dependence.

With guidance by molecular theory, the dependence of viscoelastic properties on these variables can be simplified by introducing additional concepts such as the free volume, the monomeric friction coefficient, and the spacing between entanglement loci, to provide a qualitative understanding and in many cases a quantitative prediction of how to achieve desired physical and chemical properties and ultimate microstructure.

This theory of persistence in structural unemployment has been referred to as an example of path dependence or " hysteresis ".

Observing the circular dependence of theory and observation in science, and classifying the sciences in this way, Comte may be regarded as the first philosopher of science in the modern sense of the term.

" The only new emphasis was Mao ’ s concern with two types of subjectivist deviation: 1 ) Dogmatism, the excessive reliance upon abstract theory ; 2 ) Empiricism, excessive dependence on experience.

" However, if additional evidence is available, from theory and / or from experiment ( such as density dependence ), there is no obstacle to incisive tests of the Arrhenius law.

As Bohm and Hiley worded it, " the Schrodinger equation for the quantum field does not have sources, nor does it have any other way by which the field could be directly affected by the condition of the particles [...] the quantum theory can be understood completely in terms of the assumption that the quantum field has no sources or other forms of dependence on the particles ".

Linked in with Marxist theories is dependency theory and the Core-Periphery Model, which argue that developed countries, in their pursuit of power, appropriate developing states through international banking, security and trade agreements and unions on a formal level, and do so through the interaction of political & financial advisors, missionaries, relief aid workers, and multinational corporations on the informal level, in order to integrate them into the capitalist system, strategically appropriating under-valued natural resources and labor hours and fostering economic & political dependence.

In probability theory and statistics there is an unrelated measure of linear dependence between random variables.

* Freedom House likewise studies the more general political and economic environments of each nation in order to determine whether relationships of dependence exist that limit in practice the level of press freedom that might exist in theory.

Sedimentation velocity experiments can also be used to study reversible chemical equilibria between macromolecular species, by either monitoring the number and molar mass of macromolecular complexes, by gaining information about the complex composition from multi-signal analysis exploiting differences in each components spectroscopic signal, or by following the composition dependence of the sedimentation rates of the macromolecular system, as described in Gilbert-Jenkins theory.

Observing the circular dependence of theory and observation in science, and classifying the sciences in this way, Comte may be regarded as the first philosopher of science in the modern sense of the term.