In the classical limit, the theory would reduce to general relativity and conform to Newton's law of gravitation in the weak-field limit.

Thus, he challenged the arguments of clerical intellectuals who wanted to limit access to classical sources to prevent any moral harm to Christian readers.

The dissenters, who included Rabbi Joel Roth as well as a partial concurrence by Rabbi Daniel Nevins, argued for reaffirming the classical halakhic framework in which human decrees inform and often limit but never wholly abrogate law believed to be of Divine origin, stating that " we should acknowledge that God's law is beyond our authority to eliminate ", but should continue the traditional approach of applying strict evidentiary rules and presumptions that tend to render enforcement unlikely.

The correspondence principle states that the behavior of systems described by quantum theories reproduces classical physics in the limit of large quantum numbers.

For quantum mechanics, this translates into the need to study the so-called classical limit of quantum mechanics.

In particular, quantization, namely the construction of a quantum theory whose classical limit is a given and known classical theory, becomes an important area of quantum physics in itself.

A systematic understanding of its consequences has led to the phase space formulation of quantum mechanics, which works in full phase space instead of Hilbert space, so then with a more intuitive link to the classical limit thereof.

Such systems have ( in the classical limit ) an infinite number of normal modes and their oscillations occur in the form of waves that can characteristically propagate.

Much 19th century physics has been re-evaluated as the " classical limit " of quantum mechanics, and its more advanced developments in terms of quantum field theory, string theory, and speculative quantum gravity theories.

An important guide for making these choices is the correspondence principle, which states that the predictions of quantum mechanics reduce to those of classical mechanics when a system moves to higher energies or — equivalently — larger quantum numbers, i. e. whereas a single particle exhibits a degree of randomness, in systems incorporating millions of particles averaging takes over and, at the high energy limit, the statistical probability of random behaviour approaches zero.

This " high energy " limit is known as the classical or correspondence limit.

One can even start from an established classical model of a particular system, then attempt to guess the underlying quantum model that would give rise to the classical model in the correspondence limit.

correspondence limit was non-relativistic classical mechanics.

The laws of classical mechanics thus follow from the laws of quantum mechanics as a statistical average at the limit of large systems or large quantum numbers.

The gravitational field and the electromagnetic field are the only two fundamental fields in Nature that have infinite range and a corresponding classical low-energy limit, which greatly diminishes and hides their " particle-like " excitations.

In the " low-energy limit ", the quantum field-theoretic description of the electromagnetic field, quantum electrodynamics, does not exactly reduce to James Clerk Maxwell's 1864 theory of classical electrodynamics.

Small quantum corrections due to virtual electron-positron pairs give rise to small non-linear corrections to the Maxwell equations, although the " classical limit " of quantum electrodynamics has not been as widely explored as that of quantum mechanics.

This reproduces general relativity in the classical limit.

The classical central limit theorem describes the size and the distributional form of the stochastic fluctuations around the deterministic number µ during this convergence.

Random quantum events " average out " in the limit of large numbers of particles ( where the laws of quantum mechanics asymptotically approach the laws of classical mechanics ).

Andronicus or Andronikos is a classical Greek name ( Ανδρόνικος ), from the Gr. words " andras ", ( Gr. άνδρας ), i. e. man and " Nike " ( Gr. Νίκη ), i. e. victory.

In this noble prayer are evinced profound religious feeling and exalted thought, as well as ability to use the Hebrew language in a natural, expressive, and classical manner ( Jerusalem Talmud Rosh Hashanah i. 57a ).

Any two black holes that share the same values for these properties, or parameters, are indistinguishable according to classical ( i. e. non-quantum ) mechanics.

Events after World War I brought the more radical version of classical liberalism to a more conservative ( i. e. more moderate ) type of liberalism.

A nominal definition is the definition explaining what a word means, i. e. which says what the ' nominal essence ' is, and is definition in the classical sense as given above.

Euclid frequently used the method of proof by contradiction, and therefore the traditional presentation of Euclidean geometry assumes classical logic, in which every proposition is either true or false, i. e., for any proposition P, the proposition " P or not P " is automatically true.

The reliability of an expert system is the same as the reliability of a database, i. e. good, higher than that of a classical program.

* The four classical Sunni schools are, in chronological order: the Hanafi school, the Maliki school, the Shafi ' i school and the Hanbali school.

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.

The first is a typical classical orchestra ( i. e. Beethoven / Haydn ), the second is typical of an early / mid-romantic ( i. e. Brahms / Dvořák / Tchaikovsky ), late romantic / early 20th century ( i. e. Wagner / Mahler / Stravinsky ), to the common complement of a present day modern orchestras ( i. e. Adams / Barber / Copland / Glass ).

Classical economists on the contrary defined profit as what is left after subtracting costs except interest and risk coverage ; thus, if one leaves aside risk coverage for simplicity, the neoclassical zero-long-run-profit thesis would be re-expressed in classical parlance as profits coinciding with interest in the long period, i. e. the rate of profit tending to coincide with the rate of interest.

* ( i ) The older sense of classical Latin pāgānus is " of the country, rustic " ( also as noun ).

:" We were justified intuitionistically in using the classical 2-valued logic, when we were using the connectives in building primitive and general recursive predicates, since there is a decision procedure for each general recursive predicate ; i. e. the law of the excluded middle is proved intuitionistically to apply to general recursive predicates.

In classical randomized computation, the system evolves according to the application of stochastic matrices, which preserve that the probabilities add up to one ( i. e., preserve the L1 norm ).

The prerequisites for quantum teleportation are a qubit that is to be teleported, a conventional communication channel capable of transmitting two classical bits ( i. e., one of four states ), and means of generating an entangled EPR pair of qubits, performing a Bell measurement on the EPR pair, and manipulating the quantum state of one of the pair.

There is a lack of experimental evidence relating to quantum gravity, and classical physics adequately describes the observed effects of gravity over a range of 50 orders of magnitude of mass, i. e., for masses of objects from about 10 < sup >− 23 </ sup > to 10 < sup > 30 </ sup > kg.

Used singly and in combination these valves make the instrument fully chromatic, i. e., able to play all twelve pitches of classical music.

* Quantum tic tac toe allows players to place a quantum superposition of numbers on the board, i. e. the players ' moves are " superpositions " of plays in the original classical game.

Italian physicist Galileo Galilei ( 1564-1642 ), a champion of the Copernican model of the universe and an enormously influential figure in the history of kinematics and classical mechanicsThe foundation of modern dynamics was set out in Galileo's book Dialogo sopra i due massimi sistemi del mondo ( Dialogue on the two main world systems ) where the notion of inertia was implicit and used.

The classical lines of the church which Napoleon thought of as a Temple of Glory, dominated all the scene where we sat.

With classical art, all is settled.

In classical drama, such problems do not arise.

The breakdown of classical structures of meaning in all realms of western culture has given rise to several generations of artists who have documented the disintegrative processes.

The person of the artist becomes a final bastion of meaning in a world rendered meaningless by the march of events and the decay of classical religious and philosophical systems.

For better or worse we cannot regard `` imitation '' in the arts in the simple mode of classical rationalism or detached realism.

Experience is not seen, as it is in classical rationalism, as presenting us initially with clear and distinct objects simply located in space and registering their character, movements, and changes on the tabula rasa of an uninvolved intellect.

It was, of course, a little boy's fantasy of winning his mother to himself, and replacing the father who could not give her the things she wanted -- a classical oedipal fantasy if you like -- but if it were only this the story would be banal.

Hegel's profound admiration for the insights of the Greek tragedians indicates a broad channel of classical influence upon nineteenth-century philosophy.

Many students of literature know that classical defense.

It reminded me of my other professor, Edward Kennard Rand, of whom I had been so fond when I was at Harvard, the great mediaevalist and classical scholar who had asked me to call him `` Ken '', saying, `` Age counts for nothing among those who have learned to know life sub specie aeternitatis ''.

The recent history of the Dominican Republic is an almost classical study of the way in which even a professedly benevolent dictatorship tends to become oppressive.

Bible reading, even more so than good classical music, grows in depth and meaning upon repetition.

The portable record player with a pile of classical records beside it.

Since the Industrial Revolution, when factories emerged, this classical pattern has been followed.

In tularemia produced by aerosol exposure, one would not expect to find the classical ulcer of `` rabbit fever '' on a finger.

The open ceiling, with allegorical and classical figures thrown in masses against the sky: the closed frieze, formally divided into historical scenes and tightly tied to the stone walls, belong in their large ordering to the line of Correggio and his Baroque followers.

One had to manage the given subjects, three diverse recent events, so as to make them part of a classical frieze, -- that is, a pattern of large figures filling the space, with not much else, against a blank background.

The tonal novelties consist in the introduction of a few chords used in classical music for centuries.

-- On the basis of a differentiability assumption in function space, it is possible to prove that, for materials having the property that the stress is given by a functional of the history of the deformation gradients, the classical theory of infinitesimal viscoelasticity is valid when the deformation has been infinitesimal for all times in the past.

The study of Greek was the distinctive mark of boys destined to go to college, and Lucy Upton too expected to go to college and take the full classical course offered to men.

The attractive Greer Garson, who loves beautiful clothes and selects them as carefully as she does her professional roles, prefers timeless classical designs.

The Leningrad Kirov Ballet, which opened a series of performances Friday night at the Opera House, is, I think, the finest `` classical '' ballet company I have ever seen, and the production of the Petipa-Tschaikowsky `` Sleeping Beauty '' with which it began the series is incomparably the finest I have ever had the pleasure of witnessing.

If a man lived a classical life, he need not fear the spirits -- for only lack of virtue gave the spirits power over him.

Chabrier's delightful music stands just at the point where the classical, rationalist tradition, ( handed down to Chabrier largely in the form of operetta and salon music ) becomes virtually neo-classicism.