In following this general principle, Mason provides the observer with a natural eye progression from foreground to background, and the illusion of depth is instantly created.

Therefore the second principle of the plan must be that, while providing for all-out hostilities, its effectiveness is not dependent on general war.

By applying this general principle, a great number of complex compounds of osmium, ruthenium, iridium, and rhenium, with triphenylphosphine, triphenylarsine, and triphenylstibine have been obtained in this laboratory during the past few years.

An alphabet is a standard set of letters ( basic written symbols or graphemes ) which is used to write one or more languages based on the general principle that the letters represent phonemes ( basic significant sounds ) of the spoken language.

While administrative decision-making bodies are often controlled by larger governmental units, their decisions could be reviewed by a court of general jurisdiction under some principle of judicial review based upon due process ( United States ) or fundamental justice ( Canada ).

This incident, coupled with Stalin's demands for the restitution of the Turkish provinces of Kars, Artvin and Ardahan to the Soviet Union ( which were lost by Turkey with the Russo – Turkish War of 1877 – 1878, but were regained with the Treaty of Kars in 1921 ) was one of the main reasons why Turkey decided to give up its general principle of neutrality in foreign affairs.

As a general principle, Fe < sup > 3 +</ sup > ions are used to oxidize the ore.

In almost all areas of the law ( even those where there is a statutory framework, such as contracts for the sale of goods, or the criminal law ), legislature-enacted statutes generally give only terse statements of general principle, and the fine boundaries and definitions exist only in the common law ( connotation 1 ).

As a general principle, the person who broke a rule should not benefit by it, and the other players should not lose by it.

It was later realized that Einstein's model was just one of a larger set of possibilities, all of which were consistent with general relativity and the cosmological principle.

* 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.

As a basic starting point it is normally assumed that, for the purposes of analysis, the general algorithm is known ; this is Shannon's Maxim " the enemy knows the system " -- in its turn, equivalent to Kerckhoffs ' principle.

" Naturality " is a principle, like general covariance in physics, that cuts deeper than is initially apparent.

In turn, when B is replaced with a list of attached atoms, A itself is excluded in accordance with the general principle of not doubling back along a bond that has just been followed, but a ghost atom for A is included so that the double bond is properly represented from both ends.

Later on, during the nineteenth and early twentieth centuries, this French revolutionary principle – though not of course its specific way to identify the “ general will ” – percolated into first Socialist and then Fascist political thinking.

Dialectical materialism is essentially characterized by the thesis that history is the product of class struggles and follows the general Hegelian principle of philosophy of history, that is the development of the thesis into its antithesis which is sublated by the Aufhebung (" synthesis "), although this three-part process was not explicitly characterized in terms of a thesis, antithesis, and synthesis in Hegel's writings.

One of the few general approaches is through the Hasse principle.

Then he announced to the world: " The independence of Austria, for which he has fallen, is a principle that has been defended and will be defended by Italy even more strenuously ", and then replaced in the main square of Bolzano the statue of Walther von der Vogelweide, a Germanic troubadour, with that of Drusus, a Roman general who conquered part of Germany.

However, quantum field theories that are " local " in this sense appear to violate the principle of locality as defined by EPR, but they nevertheless do not violate locality in a more general sense.

Such cases led to a general mistrust of food additives, and an application of the precautionary principle led to the conclusion that only additives that are known to be safe should be used in foods.

Fichte's account proceeds from the general principle that the I must set itself up as an individual in order to set itself up at all, and that in order to set itself up as an individual it must recognize itself as it were to a calling or summons ( Aufforderung ) by other free individual ( s ) — called, moreover, to limit its own freedom out of respect for the freedom of the other.

It thus satisfies a more stringent general principle of relativity, namely that the laws of physics are the same for all observers.

However, at the current level of accuracy, these observations cannot distinguish between general relativity and other theories in which the equivalence principle is valid.

The general principle of producing a GMO is to add new genetic material into an organism's genome.

Its central principle is that vanguardism by cadres of small, fast-moving paramilitary groups can provide a focus for popular discontent against a sitting regime, and thereby lead a general insurrection.

In general, a quantum computer with qubits can be in an arbitrary superposition of up to different states simultaneously ( this compares to a normal computer that can only be in one of these states at any one time ).

In particular, many media are linear, or nearly so, so the calculation of arbitrary wave behavior can be found by adding up responses to individual sinusoidal waves using the superposition principle to find the solution for a general waveform.

In the general case, if a complete basis set of solutions is chosen, any real laser beam can be described as a superposition of solutions from this set.

In general physical situations are not purely described by plane waves, so for generality the superposition principle is required ; any wave can be made by superposition of sinusoidal plane waves.

The most general state is a superposition of the possibilities:

In linear problems, for example, a family of linearly independent solutions can be used to construct general solutions through the superposition principle.

Decoherence shows how a macroscopic system interacting with a lot of microscopic systems ( e. g. collisions with air molecules or photons ) moves from being in a pure quantum state — which in general will be a coherent superposition ( see Schrödinger's cat )— to being in an incoherent mixture of these states.

In general, the superposition is written with undetermined coefficients, which are then variationally optimized to find the lowest possible energy for the given set of basis wavefunctions.

A general solution to the homogeneous electromagnetic wave equation in rectangular coordinates may be formed as a weighted superposition of all possible elementary plane wave solutions as:

For states with a definite energy, this is a statement of the De Broglie relation between frequency and energy, and the general relation is consistent with that plus the superposition principle.

The most general motion of a system is a superposition of its normal modes.

The general solution is a superposition of the normal modes where c < sub > 1 </ sub >, c < sub > 2 </ sub >, φ < sub > 1 </ sub >, and φ < sub > 2 </ sub >, are determined by the initial conditions of the problem.

By writing a very general stimulus ( in a linear system ) as the superposition of stimuli of a specific, simple form, often the response becomes easier to compute,

Due to the Law of superposition ( the empirical rule stating that, in general, the older things are lower down ), this implies, according to Eilat Mazar, that the foundation-and hence the building-was constructed somewhere between Iron Age I and Iron Age II ( roughly between the 11th and 10th centuries BC ).

Bootstrapping is using very general consistency criteria to determine the form of a quantum theory from some assumptions on the spectrum of particles.

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

" The general consensus is that these public key algorithms are insecure at any key size if sufficiently large quantum computers capable of running Shor's algorithm become available.

Due to the smallness of Planck's constant it is practically impossible to realize experiments that directly reveal the wave nature of any system bigger than a few atoms but, in general, quantum mechanics considers all matter as possessing both particle and wave behaviors.

The general concept of a chemical reaction has been extended to non-chemical reactions between entities smaller than atoms, including nuclear reactions, radioactive decays, and reactions between elementary particles as described by quantum field 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.

Between 1919 and 1923, Fermi studied general relativity, quantum mechanics, and atomic physics.

These are based on classical mechanics and are modified in quantum mechanics and general relativity.

In string theory, Eric G. Gimon and Petr Hořava have argued that in a supersymmetric five-dimensional Gödel universe, quantum corrections to general relativity effectively cut off regions of spacetime with causality-violating closed timelike curves.

However, unanswered questions remain, the most fundamental being how general relativity can be reconciled with the laws of quantum physics to produce a complete and self-consistent theory of quantum gravity.

When describing graviton interactions, the classical theory ( i. e., the tree diagrams ) and semiclassical corrections ( one-loop diagrams ) behave normally, but Feynman diagrams with two ( or more ) loops lead to ultraviolet divergences ; that is, infinite results that cannot be removed because the quantized general relativity is not renormalizable, unlike quantum electrodynamics.

Since classical general relativity and quantum mechanics seem to be incompatible at such energies, from a theoretical point of view this situation is not tenable.

String theories are quantum theories of gravity in the sense that they reduce to classical general relativity plus field theory at low energies, but are fully quantum mechanical, contain a graviton, and are believed to be mathematically consistent.

Analogous to the quantum versus classical reformation, Einstein's general and special theories of relativity have expanded the scope of mechanics beyond the mechanics of Newton and Galileo, and made fundamental corrections to them, that become significant and even dominant as speeds of material objects approach the speed of light, which cannot be exceeded.

Relativistic corrections are also needed for quantum mechanics, although general relativity has not been integrated.

Two main modern developments in mechanics are general relativity of Einstein, and quantum mechanics, both developed in the 20th century based in part on earlier 19th century ideas.

While Maxwell's equations are consistent within special and general relativity, there are some quantum mechanical situations in which Maxwell's equations are significantly inaccurate: including extremely strong fields ( see Euler – Heisenberg Lagrangian ) and extremely short distances ( see vacuum polarization ).

These and other differences hindered the development of the string theory as being the theory that united quantum mechanics and general relativity successfully.

Although originally expressed in Newton's third law, the conservation of linear momentum also holds in special relativity ( with a modified formula ) and, with appropriate definitions, a ( generalized ) linear momentum conservation law holds in electrodynamics, quantum mechanics, quantum field theory, and general relativity.

fit the requirement that, this result does not hold for more general quantum states.