The Dirac sea is a theoretical model of the vacuum as an infinite sea of particles possessing negative energy. It was invented by the British physicist Paul Dirac in 1930 to explain the anomalous negative-energy quantum states predicted by the Dirac equation for relativistic electrons. The positron, the antimatter counterpart of the electron, was originally conceived of as a hole in the Dirac sea, well before its experimental discovery in 1932. Dirac, Einstein and others recognised that it is related to the 'metaphysical' aether [1]: Look up Vacuum in Wiktionary, the free dictionary. ... Negative energy can refer to several concepts: Energy in any system below an arbitrarily defined level (called reference level, ground state, or zero level). ... Articles with similar titles include physician, a person who practices medicine. ... Paul Adrien Maurice Dirac, OM, FRS (IPA: [dɪræk]) (August 8, 1902 – October 20, 1984) was a British theoretical physicist and a founder of the field of quantum physics. ... A quantum state is any possible state in which a quantum mechanical system can be. ... In physics, the Dirac equation is a relativistic quantum mechanical wave equation formulated by British physicist Paul Dirac in 1928 and provides a description of elementary spin-½ particles, such as electrons, consistent with both the principles of quantum mechanics and the theory of special relativity. ... Two-dimensional analogy of space-time curvature described in General Relativity. ... e- redirects here. ... The first detection of the positron in 1932 by Carl D. Anderson The positron is the antiparticle or the antimatter counterpart of the electron. ... In particle physics, antimatter extends the concept of the antiparticle to matter, whereby antimatter is composed of antiparticles in the same way that normal matter is composed of particles. ... For the following two reasons the electron hole was introduced into calculations: If an electron is excited into higher state it leaves a hole in its old state. ... Look up aether, ether in Wiktionary, the free dictionary. ...

... with the new theory of electrodynamics we are rather forced to have an aether. – P.A.M. Dirac, ‘Is There An Aether?,’ Nature, v.168, 1951, p.906.

The equation relating energy, mass and momentum in special relativity is:

E² = p²c² + m²c⁴,

In the special case of a particle at rest (ie p = 0, ) the above equation reduces to E² = m²c⁴, which is usually quoted as the familiar E = mc². However, this is a simplification because, while x•x = x², we can also see that (-x)•(-x)= x². Therefore, the correct equation to use to relate energy and mass in the Hamiltonian of the Dirac equation is:

E = ± mc².

Here the negative solution is antimatter, discovered by Carl Anderson as the positron. The interpretation of this result requires a Dirac sea, showing that the Dirac equation is not merely a combination of special relativity and quantum field theory, but it also implies that the number of particles cannot be conserved [2]. In particle physics, antimatter extends the concept of the antiparticle to matter, whereby antimatter is composed of antiparticles in the same way that normal matter is composed of particles. ... The first detection of the positron in 1932 by Carl D. Anderson The positron is the antiparticle or the antimatter counterpart of the electron. ...

Origins

The origins of the Dirac sea lie in the energy spectrum of the Dirac equation, an extension of the Schrödinger equation that is consistent with special relativity, that Dirac had formulated in 1928. Although the equation was extremely successful in describing electron dynamics, it possesses a rather peculiar feature: for each quantum state possessing a positive energy E, there is a corresponding state with energy -E. This is not a big difficulty when we are looking at an isolated electron, because its energy is conserved and we can simply choose not to introduce any negative-energy electrons. However, it becomes serious when we start to think about how to include the effects of the electromagnetic field, because a positive-energy electron would be able to shed energy by continuously emitting photons, a process that could continue without limit as the electron descends into lower and lower energy states. Real electrons clearly do not behave in this way. The quantum Hamiltonian is the physical state of a system, which may be characterized as a ray in an abstract Hilbert space (or, in the case of ensembles, as a trace class operator with trace 1). ... In physics, the Schrödinger equation, proposed by the Austrian physicist Erwin Schrödinger in 1925, describes the space- and time-dependence of quantum mechanical systems. ... Conservation of energy states that the total amount of energy in an isolated system remains constant, although it may change forms (for instance, friction turns kinetic energy into thermal energy). ... The electromagnetic field is a physical field that is produced by electrically charged objects and which affects the behaviour of charged objects in the vicinity of the field. ... The word light is defined here as electromagnetic radiation of any wavelength; thus, X-rays, gamma rays, ultraviolet light, infrared radiation, microwaves, radio waves, and visible light are all forms of light. ...

Dirac's solution to this was to turn to the Pauli exclusion principle. Electrons are fermions, and obey the exclusion principle, which means that no two electrons can share a single energy state within an atom. Dirac hypothesized that what we think of as the "vacuum" is actually the state in which all the negative-energy states are filled, and none of the positive-energy states. Therefore, if we want to introduce a single electron we would have to put it in a positive-energy state, as all the negative-energy states are occupied. Furthermore, even if the electron loses energy by emitting photons it would be forbidden from dropping below zero energy. The Pauli exclusion principle is a quantum mechanical principle formulated by Wolfgang Pauli in 1925. ... In particle physics, fermions are particles with half-integer spin, such as protons and electrons. ...

Dirac also pointed out that a situation might exist in which all the negative-energy states are occupied except one. This "hole" in the sea of negative-energy electrons would respond to electric fields as though it were a positively-charged particle. Initially, Dirac identified this hole as a proton. However, Robert Oppenheimer pointed out that an electron and its hole would be able to annihilate each other, releasing energy on the order of the electron's rest energy in the form of energetic photons; if holes were protons, stable atoms would not exist. Hermann Weyl also noted that a hole should act as though it has the same mass as an electron, whereas the proton is about two thousand times heavier. The issue was finally resolved in 1932 when the positron was discovered by Carl Anderson, with all the physical properties predicted for the Dirac hole. In physics, the proton (Greek proton = first) is a subatomic particle with an electric charge of one positive fundamental unit (1. ... J. Robert Oppenheimer[1] (April 22, 1904 – February 18, 1967) was an American theoretical physicist, best known for his role as the director of the Manhattan Project, the World War II effort to develop the first nuclear weapons, at the secret Los Alamos laboratory in New Mexico. ... Annihilation is defined as total destruction or complete obliteration of an object;[1] having its root in the Latin nihil (nothing). ... Properties In chemistry and physics, an atom (Greek ἄτομος or átomos meaning indivisible) is the smallest particle still characterizing a chemical element. ... Hermann Klaus Hugo Weyl (November 9, 1885 – December 9, 1955) was a German mathematician. ... Unsolved problems in physics: What causes anything to have mass? The U.S. National Prototype Kilogram, which currently serves as the primary standard for measuring mass in the U.S. Mass is the property of a physical object that quantifies the amount of matter and energy it is equivalent to. ... The first detection of the positron in 1932 by Carl D. Anderson The positron is the antiparticle or the antimatter counterpart of the electron. ... Carl Anderson at LBNL 1937 Carl David Anderson (3 September 1905 – 11 January 1991) was a U.S. experimental physicist. ...

Inelegance of Dirac sea

Despite its success, the idea of the Dirac sea tends not to strike people as very elegant. The existence of the sea implies an infinite negative electric charge filling all of space. In order to make any sense out of this, one must assume that the "bare vacuum" must have an infinite positive charge density which is exactly cancelled by the Dirac sea. Since the absolute energy density is unobservable — the cosmological constant aside — the infinite energy density of the vacuum does not represent a problem. Only changes in the energy density are observable. Landis also notes that Pauli exclusion does not definitively mean that a filled Dirac sea cannot accept more electrons, since, as Hilbert elucidated, a sea of infinite extent can accept new particles even if it is filled. This happens when we have a chiral anomaly and a gauge instanton. The cosmological constant (usually denoted by the Greek capital letter lambda: Λ) was proposed by Albert Einstein as a modification of his original theory of general relativity to achieve a stationary universe. ... Hilberts paradox of the Grand Hotel was a mathematical paradox about infinity presented by German mathematician David Hilbert (1862 – 1943): In a hotel with a finite number of rooms, it is clear that once it is full, no more guests can be accommodated. ...

The development of quantum field theory in the 1930s made it possible to reformulate the Dirac equation in a way that treats the positron as a "real" particle rather than the absence of a particle, and makes the vacuum the state in which no particles exist instead of an infinite sea of particles. This picture is much more convincing, especially since it recaptures all the valid predictions of the Dirac sea, such as electron-positron annihilation. On the other hand, the field formulation does not eliminate all the difficulties raised by the Dirac sea; in particular the problem of the vacuum possessing infinite energy. Quantum field theory (QFT) is the quantum theory of fields. ... Vacuum energy is an underlying background energy that exists in space even when devoid of matter (known as free space). ...

Modern applications

The Dirac sea interpretation and the "modern" QFT interpretation are related by a Bogoliubov transformation. In theoretical physics, the Bogoliubov transformation, named after Nikolay Bogolyubov, is a unitary transformation from a unitary representation of some canonical commutation relation algebra or canonical anticommutation relation algebra into another unitary representation, induced by an isomorphism of the CCR/CAR algebra. ...

Dirac's idea is quite correct in the context of solid state physics, where the valence band in a solid can be regarded as a "sea" of electrons. Holes in this sea indeed occur, and are extremely important for understanding the effects of semiconductors, though they are never referred to as "positrons". Unlike in particle physics, there is an underlying positive charge — the charge of the ionic lattice — that cancels out the electric charge of the sea. Solid-state physics, the largest branch of condensed matter physics, is the study of rigid matter, or solids. ... In solids, the valence band is the highest range of electron energies where electrons are normally present at zero temperature. ... For other uses, see Solid (disambiguation). ... A semiconductor is a solid whose electrical conductivity is in between that of a metal and that of an insulator, and can be controlled over a wide range, either permanently or dynamically. ...

In fiction

• The Dirac sea provides a mechanism for time-travel in Geoffrey A. Landis' Nebula Award-winning short story "Ripples in the Dirac Sea".

• The Dirac sea is also used as an energy source for A-POT weapons in The Fleet series of novels by Bill Fawcett and David Drake.

• While Dirac's name is never used, it is obvious that the description of E. E. Smith's negasphere in Gray Lensman is a fictional interpretation of the Dirac sea.

• The term Dirac sea also appears in the anime series Neon Genesis Evangelion twice. The twelfth Angel Leliel, which absorbs the Eva Unit 01, is believed to be comprised of a Dirac sea. Also, after Unit 04 self-destructs, it completely obliterates everything within an 89km radius, including the Second Branch of NERV in Nevada. Ritsuko Akagi speculates that the missing landmass had entered a Dirac sea.

Geoffrey A. Landis emerged in the late 1980s as one of the foremost scientist-writers in the science fiction genre. ... The Nebula is an award given each year by the Science Fiction and Fantasy Writers of America (SFWA), for the best science fiction/fantasy fiction published in the United States during the two previous years (see rolling eligibility below). ... Chesil Beach from Fortuneswell Chesil Beach (sometimes called Chesil Bank) is a 18 mile (29km) long, 200 metre wide and 18 metre high shingle tombolo in Dorset, southern England. ... Quinn Fawcett is the penname of a pair of authors, Chelsea Quinn Yarbro and Bill Fawcett, who also write separately. ... David Drake (born September 24, 1945) is a successful author of science fiction and fantasy literature. ... Gray Lensman in Astounding Oct. ... The Lensman series is a serial science fiction space opera by E. E. Smith. ... The main cast of the anime Cowboy Bebop (1998) (L to R: Spike Spiegel, Jet Black, Ed Tivrusky, Faye Valentine, and Ein the dog) For the oleo-resin, see Animé (oleo-resin). ... Original run October 4, 1995 – March 27, 1996 No. ... This article or section does not cite any references or sources. ... Unit 01 runs through Tokyo-3; the buildings in the background give a frame of reference for the size of the Eva. ... Unit 01 runs through Tokyo-3; the buildings in the background give a frame of reference for the size of the Eva. ... This is a glossary of terms from the anime and manga series Neon Genesis Evangelion. ... This article needs additional references or sources to facilitate its verification. ... In the fictional anime series Neon Genesis Evangelion, Ritsuko Akagi (赤木リツコ Akagi Ritsuko) is NERVs head scientist. ...

See also

• Fermi sea
• Positronium
• Vacuum energy
• Vacuum polarization
• Virtual particle