Although modern quantum optics tells us that there also is a semi-classical explanation of the photoelectric effect — the emission of electrons from metallic surfaces subjected to electromagnetic radiation — the photon was historically ( although not strictly necessarily ) used to explain certain observations.

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.

Although spin and the Pauli principle can only be derived from relativistic generalizations of quantum mechanics the properties mentioned in the last two paragraphs belong to the basic postulates already in the non-relativistic limit.

Although these semiclassical models contributed to the development of quantum mechanics, many further experiments starting with Compton scattering of single photons by electrons, first observed in 1923, validated Einstein's hypothesis that light itself is quantized.

Although the mathematical basis of quantum chemistry had been laid by Schrödinger in 1926, it is generally accepted that the first true calculation in quantum chemistry was that of the German physicists Walter Heitler and Fritz London on the hydrogen ( H < sub > 2 </ sub >) molecule in 1927.

Although quantum computing is still in its infancy, experiments have been carried out in which quantum computational operations were executed on a very small number of qubits ( quantum bits ).

Although it is often claimed that the photoelectric and Compton effects require a quantum description of the EM field, this is now understood to be untrue, and proper proof of the quantum nature of radiation is now taken up into modern quantum optics as in the antibunching effect.

Although some quantum gravity theories such as string theory and other unified field theories ( or ' theories of everything ') attempt to unify gravity with the other fundamental forces, others such as loop quantum gravity make no such attempt ; they simply quantize the gravitational field while keeping it separate from the other forces.

Although string theory had its origins in the study of quark confinement and not of quantum gravity, it was soon discovered that the string spectrum contains the graviton, and that " condensation " of certain vibration modes of strings is equivalent to a modification of the original background.

Although these first studies focused on the counterintuitive properties of entanglement, with the aim of criticizing quantum mechanics, eventually entanglement was verified experimentally, and recognized as a valid, fundamental feature of quantum mechanics.

Although such communication is prohibited in the thought experiment described above, some argue that superluminal communication could be achieved via quantum entanglement using other methods that don't rely on cloning a quantum system.

Although it is difficult to draw a line separating wave – particle duality from the rest of quantum mechanics, it is nevertheless possible to list some applications of this basic idea.

Although it was hoped recently that quantum effects could not violate an achronal version of the averaged null energy condition, violations have nevertheless been found, so it remains an open possibility that quantum effects might be used to support a wormhole.

Although Dirac did not at first fully appreciate what his own equation was telling him, his resolute faith in the logic of mathematics as a means to physical reasoning, his explanation of spin as a consequence of the union of quantum mechanics and relativity, and the eventual discovery of the positron, represents one of the great triumphs of theoretical physics, fully on a par with the work of Newton, Maxwell, and Einstein before him.

Although hydrogen-like orbitals are still used as pedagogical tools, the advent of computers has made STOs preferable for atoms and diatomic molecules since combinations of STOs can replace the nodes in hydrogen-like atomic orbital.

Although the Atari 5200's internal design was extensively based on that of the 400 / 800 home computers, the differences were sufficient that games designed for one would not run directly on the other.

Although high-end computers may be bought retail in the same manner as the common computer, they are frequently built by their owners.

Although any music which uses computers in its composition or realisation is computer-generated to some extent, the use of computers is now so widespread ( in the editing of pop songs, for instance ) that the phrase computer-generated music is generally used to mean a kind of music which could not have been created without the use of computers.

Although the term is most commonly used to describe computers and software, it may also be used to describe human behaviors, methods, and tools.

Although it still serves as an example for the new edition of Tanenbaum and Woodhull's textbook, it is comprehensively redesigned to be " usable as a serious system on resource-limited and embedded computers and for applications requiring high reliability.

Although about half of that money was spent on CPUs used in desktop or laptop personal computers, those count for only about 2 % of all CPUs sold.

Although some problems in statistical physics can be solved analytically using approximations and expansions, most current research utilizes the large processing power of modern computers to simulate or approximate solutions.

Although Watson is well known for his alleged 1943 statement, " I think there is a world market for maybe five computers ", there is scant evidence he made it.

Although some applications had counterparts using earlier technologies such as the spark gap transmitter or mechanical computers, it was the invention of the vacuum tube with three electrodes triode and its capability of electronic amplification that made these technologies widespread and practical.

Although most x86 processors used in new personal computers and servers have 64-bit capabilities, to avoid compatibility problems with older computers or systems, the term x86-64 ( or x64 ) is often used to denote 64-bit software, with the term x86 implying only 32-bit.

Although the 48K Spectrum's audio hardware was not as capable as chips in other popular 8-bit home computers of the era, computer musicians David Whittaker and Tim Follin produced notable multi-channel music for the machine.

Although there is a significant amount of human contact in this process, computers play an important role, especially for so-called " program trading ".

Although Macintosh-based systems would continue to dominate the market, in 1986, the GEM-based Ventura Publisher was introduced for MS-DOS computers.

Although there are other mainframe emulators which perform a similar function, Hercules is significant in that it enables private individuals to run mainframe computer software on their own personal computers.

Although integrated software existed for these computers, they usually lacked features compared to their standalone equivalents, largely due to memory limitations.

Although the output of modern computers is generally all in the form of dot matrices, computers may internally store data as either a dot matrix or as a vector pattern of lines and curves.

Although DCS is not a common event, its potential severity is such that much research has gone into preventing it, and underwater divers use dive tables or dive computers to set limits on their exposure to pressure and their ascent speed.

Although the site may not contain the features themselves, there are often opportunities to include them as additional interest to the site.

Although Andrena is gregarious, so that we may find hundreds and hundreds of burrows together, we must still call it a solitary bee.

Although it is in some ways comparable to a voluntary sale of assets for cash, to which section 203 quite clearly applies, the courts and Treasury have held that acquiring corporations in several types of non-taxable reorganizations may sue for refund of taxes paid by transferors.

Although a large number of coatings systems, particularly at low thicknesses fail cohesively by the cutting mechanism, frequently a second type of cohesive failure may also take place.

Although there are seven other types of annual awards presented by the Academy ( the Irving G. Thalberg Memorial Award, the Jean Hersholt Humanitarian Award, the Gordon E. Sawyer Award, the Scientific and Engineering Award, the Technical Achievement Award, the John A. Bonner Medal of Commendation, and the Student Academy Award ) plus two awards that are not presented annually ( the Special Achievement Award in the form of an Oscar statuette and the Honorary Award that may or may not be in the form of an Oscar statuette ), the best known one is the Academy Award of Merit more popularly known as the Oscar statuette.

Although this may seem extreme, the arguments.

Narayanan – AIR India Reporter 1988 Court Page No. 1381 ; 1988 Volume No. 3 SCC Court Cases Page No. 366 ; 1988 PLJR 78 – Although an affidavit may be taken as proof of the facts stated therein, the Courts have no jurisdiction to admit evidence by way of affidavit.

Although the terms adiabatic and isocaloric can often be interchanged, adiabatic processes may be considered a subset of isocaloric processes ; the remaining complement subset of isocaloric processes being processes where net heat transfer does not diverge regionally such as in an idealized case with mediums of infinite thermal conductivity or non-existent thermal capacity.

Although the range and precise application of defenses varies between jurisdictions, the following represents a list of the defenses that may apply to all levels of assault:

Although agates may be found in various kinds of rock, they are classically associated with volcanic rocks and can be common in certain metamorphic rocks.

Although details of the negotiations are lacking, Gruffydd ap Llywelyn swore loyalty to King Edward, but the oath may not have had any obligations on Gruffydd's part to Edward.

Although he was in charge of the project for the papal villa, the Villa Pamphili, now Villa Doria Pamphili, outside the Porta San Pancrazio in Rome, he may have had professional guidance on the design of the casino from the architect / engineer Girolamo Rainaldi and help with supervising its construction from his assistant Giovanni Francesco Grimaldi.

" Although a Greek, he may have been a soldier of the Persian army when Clazomenae was suppressed during the Ionian Revolt.

Although the term aeon may be used in reference to a period of a billion years ( especially in geology, cosmology or astronomy ), its more common usage is for any long, indefinite, period.

Although asado is eaten all over the country, its origin may be traced back to the Pampas.

Although these effects may be either beneficial or detrimental, the location of the area is crucial in determining the extent of the impact that abiotic stress will have.

Although most audio file formats support only one type of audio data ( created with an audio coder ), a multimedia container format ( as Matroska or AVI ) may support multiple types of audio and video data.

Although they may not recognize themselves as antiglobalists and are pro-capitalism, some economists who don't share the neoliberal approach of international economic institutions have strongly influenced the movement.

Although aluminium has a low gastrointestinal absorption, accumulation may occur mainly in the presence of renal insufficiency.

Although reactions to any drug may vary from person to person, generally those medications that contain aluminum or calcium are the likeliest to cause constipation, those that contain magnesium are the likeliest to cause diarrhea.

Although Anabaptists began with the Radical Reformers in the 16th century, certain people and groups may still legitimately be considered their forerunners due to a similar approach to the interpretation and application of the Bible.

Although Atlanta ’ s lack of bike lanes may deter many residents from cycling, the city ’ s transportation plan calls for the construction of 226 miles of bike lanes by 2020, with the BeltLine helping to achieve this goal.

Although Zermelo's fix allows a class to describe arbitrary ( possibly " large ") entities, these predicates of the meta-language may have no formal existence ( i. e., as a set ) within the theory.

Although initial studies suggested that antioxidant supplements might promote health, later large clinical trials with a limited number of antioxidants detected no benefit and even suggested that excess supplementation with certain putative antioxidants may be harmful.