The strongest appeal of the Copernican formulation consisted in just this: ideally, the justification for dealing with special problems in particular ways is completely set out in the basic ' rules ' of the theory.

According to the special theory of relativity, the aberration looks as a transform of the celestial sphere due to different frames of reference and is virtually a special case of velocity addition, namely one of the light beam and frames ' relative velocity v. The formula from relativistic aberration can be simplified to

Partition theory studies various enumeration and asymptotic problems related to integer partitions, and is closely related to q-series, special functions and orthogonal polynomials.

But, according to Einstein's theory of special relativity, no information-bearing signal or entity can travel at or faster than the speed of light, which is finite.

Because many outstanding problems in number theory, such as Goldbach's conjecture are equivalent to solving the halting problem for special programs ( which would basically search for counter-examples and halt if one is found ), knowing enough bits of Chaitin's constant would also imply knowing the answer to these problems.

These coordinates are a very special example of a more general concept of local coordinates from the theory of differential forms.

A special case of this is a Lorentzian manifold, which is the mathematical basis of Einstein's general relativity theory of gravity.

This theory has the advantage of avoiding the infinite regress without claiming special, possibly arbitrary status for some particular class of beliefs.

( This observation led to Albert Einstein's development of the theory of special relativity.

After important contributions of Hendrik Lorentz and Henri Poincaré, in 1905, Albert Einstein solved the problem with the introduction of special relativity, which replaces classical kinematics with a new theory of kinematics that is compatible with classical electromagnetism.

* Emission theory, a competing theory for the special theory of relativity, explaining the results of the Michelson-Morley experiment

He considered an accelerating box, and noted that according to the special theory of relativity, the clock rate at the bottom of the box was slower than the clock rate at the top.

In category theory, a branch of mathematics, a functor is a special type of mapping between categories.

Under the special theory of relativity, a particle ( that has rest mass ) with subluminal velocity needs infinite energy to accelerate to the speed of light, although special relativity does not forbid the existence of particles that travel faster than light at all times ( tachyons ).

If confirmed, this would imply special relativity is an approximation to a more general theory, but since the relevant comparison would ( by definition ) be outside the observable universe, it is difficult to imagine ( much less construct ) experiments to test this hypothesis.

Although the theory of special relativity forbids objects to have a relative velocity greater than light speed, and general relativity reduces to special relativity in a local sense ( in small regions of spacetime where curvature is negligible ), general relativity does allow the space between distant objects to expand in such a way that they have a " recession velocity " which exceeds the speed of light, and it is thought that galaxies which are at a distance of more than about 14 billion light-years from us today have a recession velocity which is faster than light.

In 1843 Kummer introduced the concept of ideal number, which was developed further by Dedekind ( 1876 ) into the modern theory of ideals, special subsets of rings.

Soon after publishing the special theory of relativity in 1905, Einstein started thinking about how to incorporate gravity into his new relativistic framework.

It was clearly superior to Newtonian gravity, being consistent with special relativity and accounting for several effects unexplained by the Newtonian theory.

Dr. Bonnor begins with a discussion of the relativistic theories of the universe, based on the general theory of relativity.

*: The article on Whorf states " Drawing on Nietzsche's ideas of perspectivism Alfred Korzybski developed the theory of general semantics which has been compared to Whorf's notions of linguistic relativity.

Also, general relativity has passed stringent tests on the scale of the Solar System and binary stars while extrapolation to cosmological scales has been validated by the empirical successes of various aspects of the Big Bang theory.

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

In 1915, Albert Einstein developed his theory of general relativity, having earlier shown that gravity does influence light's motion.

Physical cosmology, as it is now understood, began with the twentieth century development of Albert Einstein's general theory of relativity and better astronomical observations of extremely distant objects.

Areas relevant to cosmology include particle physics experiments and theory, including astrophysics, general relativity, and plasma physics.

In 1916, Albert Einstein published his theory of general relativity, which provided a unified description of gravity as a geometric property of space and time.

There is no definite or clear way to define the total energy of the universe due to the most widely accepted theory of gravity, general relativity.

* the equivalence principle, whether or not Einstein's general theory of relativity is the correct theory of gravitation, and if the fundamental laws of physics are the same everywhere in the universe.

* An introduction including more on general relativity and quantum field theory than most.

This theory extends general relativity by removing a constraint of the symmetry of the affine connection and regarding its antisymmetric part, the torsion tensor, as a dynamical variable.

Research on these geometries led to, among other things, Einstein's theory of general relativity, which describes the universe as non-Euclidean.

* The strong cosmic censorship hypothesis asserts that, generically, general relativity is a deterministic theory, in the same sense that classical mechanics is a deterministic theory.

For example, in the 19th century, the Sun appeared to be no more than 20 million years old, but the Earth appeared to be no less than 300 million years ( resolved by the discovery of nuclear fusion and radioactivity, and the theory of quantum mechanics ); or current attempts to resolve theoretical differences between quantum mechanics and general relativity.

An implication of Einstein's theory of general relativity is that Euclidean space is a good approximation to the properties of physical space only where the gravitational field is weak.

As discussed in more detail below, Einstein's theory of relativity significantly modifies this view.

In a 1919 test of the general theory of relativity, stars ( marked with short horizontal lines ) were photographed during a solar eclipse.

Einstein's theory of general relativity shows that the true geometry of spacetime is not Euclidean geometry.

The theory predicts a linear dependence of Af on Af, where J is the experimentally determined Curie-Weiss constant.

* 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 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.