• RSS
  • Facebook
  • Twitter
Showing posts with label Quantum Mechanics. Show all posts
Showing posts with label Quantum Mechanics. Show all posts
Abhijeet
Comments


In particle physics and quantum chemistry, antimatter is the extension of the concept of the antiparticle to matter, where antimatter is composed of antiparticles in the same way that normal matter is composed of particles. For example, an antielectron (a positron, an electron with a positive charge) and an antiproton (a proton with a negative charge) could form an antihydrogen atom in the same way that an electron and a proton form a normal matter hydrogen atom. Furthermore, mixing matter and antimatter would lead to the annihilation of both in the same way that mixing antiparticles and particles does, thus giving rise to high-energy photons (gamma rays) or other particle–antiparticle pairs.

There is considerable speculation both in science and science fiction as to why the observable universe is apparently almost entirely matter, whether other places are almost entirely antimatter instead, and what might be possible if antimatter could be harnessed, but at this time the apparent asymmetry of matter and antimatter in the visible universe is one of the greatest unsolved problems in physics. The process of developing particles and antiparticles is called baryogenesis.


Notation

One way to denote an antiparticle is by adding a bar (or macron) over the particle's symbol. For example, the proton and antiproton are denoted as p and p, respectively. The same rule applies if you were to address a particle by its constituent components. A proton is made up of u u d quarks, so an antiproton must therefore be formed from uud antiquarks. Another convention is to distinguish particles by their electric charge. Thus, the electron and positron are denoted simply as e and e+ respectively.

Origin (naturally occurring production)

Asymmetry

Most objects observable from the Earth seem to be built of matter rather than antimatter. There is no current reasoning over why matter prevailed over antimatter, but many believe it was the result of asymmetry, and some scientists believe that the ratio of this asymmetry was roughly a billion antimatter particles to a billion and one matter particles. Antiparticles are created everywhere in the universe where high-energy particle collisions take place. High-energy cosmic rays impacting Earth's atmosphere (or any other matter in the solar system) produce minute quantities of antimatter in the resulting particle jets, which are immediately annihilated by contact with nearby matter. It may similarly be produced in regions like the center of the Milky Way Galaxy and other galaxies, where very energetic celestial events occur (principally the interaction of relativistic jets with the interstellar medium). The presence of the resulting antimatter is detectable by the gamma rays produced when positrons annihilate with nearby matter. The gamma rays' frequency and wavelength indicate that each carries 511 keV of energy (i.e. the rest mass of an electron or positron multiplied by c2). Recent observations by the European Space Agency’s INTEGRAL (International Gamma-Ray Astrophysics Laboratory) satellite may explain the origin of a giant cloud of antimatter surrounding the galactic center. The observations show that the cloud is asymmetrical and matches the pattern of X-ray binaries, binary star systems containing black holes or neutron stars, mostly on one side of the galactic center. While the mechanism is not fully understood, it is likely to involve the production of electron-positron pairs, as ordinary matter gains tremendous energy while falling into a stellar remnant.

Artificial production

Antiparticles are also produced in any environment with a sufficiently high temperature (mean particle energy greater than the pair production threshold). During the period of baryogenesis, when the universe was extremely hot and dense, matter and antimatter were continually produced and annihilated. The presence of remaining matter, and absence of detectable remaining antimatter, also called baryon asymmetry, is attributed to violation of the CP-symmetry relating matter and antimatter. The exact mechanism of this violation during baryogenesis remains a mystery.

Positrons are also produced via the radioactive beta+ decay, but this mechanism can be considered as "natural" as well as "artificial".

Antihydrogen

In 1995 CERN announced that it had successfully created nine antihydrogen atoms by implementing the SLAC/Fermilab concept during the PS210 experiment. The experiment was performed using the Low Energy Antiproton Ring (LEAR), and was led by Walter Oelert and Mario Macri. Fermilab soon confirmed the CERN findings by producing approximately 100 antihydrogen atoms at their facilities.

The antihydrogen atoms created during PS210, and subsequent experiments (at both CERN and Fermilab) were extremely energetic ("hot") and were not well suited to study. To resolve this hurdle, and to gain a better understanding of antihydrogen, two collaborations were formed in the late 1990s — ATHENA and ATRAP. In 2005, ATHENA disbanded and some of the former members (along with others) formed the ALPHA Collaboration, which is also situated at CERN. The primary goal of these collaborations is the creation of less energetic ("cold") antihydrogen, better suited to study.

In 1999 CERN activated the Antiproton Decelerator, a device capable of decelerating antiprotons from 3.5 GeV to 5.3 MeV — still too "hot" to produce study-effective antihydrogen, but a huge leap forward. In late 2002 the ATHENA project announced that they had created the world's first "cold" antihydrogen. The antiprotons used in the experiment were cooled sufficiently by decelerating them (using the Antiproton Decelerator), passing them through a thin sheet of foil, and finally capturing them in a Penning trap. The antiprotons also underwent stochastic cooling at several stages during the process.

The ATHENA team's antiproton cooling process is effective, but highly inefficient. Approximately 25 million antiprotons leave the Antiproton Decelerator; roughly 10 thousand make it to the Penning trap. In early 2004 ATHENA researchers released data on a new method of creating low-energy antihydrogen. The technique involves slowing antiprotons using the Antiproton Decelerator, and injecting them into a Penning trap (specifically a Penning-Malmberg trap). Once trapped the antiprotons are mixed with electrons that have been cooled to an energy potential significantly less than the antiprotons; the resulting Coulomb collisions cool the antiprotons while warming the electrons until the particles reach an equilibrium of approximately 4 K.

While the antiprotons are being cooled in the first trap, a small cloud of positron plasma is injected into a second trap (the mixing trap). Exciting the resonance of the mixing trap’s confinement fields can control the temperature of the positron plasma; but the procedure is more effective when the plasma is in thermal equilibrium with the trap’s environment. The positron plasma cloud is generated in a positron accumulator prior to injection; the source of the positrons is usually radioactive sodium.

Once the antiprotons are sufficiently cooled, the antiproton-electron mixture is transferred into the mixing trap (containing the positrons). The electrons are subsequently removed by a series of fast pulses in the mixing trap's electrical field. When the antiprotons reach the positron plasma further Coulomb collisions occur, resulting in further cooling of the antiprotons. When the positrons and antiprotons approach thermal equilibrium antihydrogen atoms begin to form. Being electrically neutral the antihydrogen atoms are not affected by the trap and can leave the confinement fields.

Using this method ATHENA researchers predict they will be able to create up to 100 antihydrogen atoms per operational second. ATHENA and ATRAP are now seeking to further cool the antihydrogen atoms by subjecting them to an inhomogeneous field. While antihydrogen atoms are electrically neutral, their spin produces magnetic moments. These magnetic moments vary depending on the spin direction of the atom, and can be deflected by inhomogeneous fields regardless of electrical charge.

The biggest limiting factor in the production of antimatter is the availability of antiprotons. Recent data released by CERN states that when fully operational their facilities are capable of producing 107 antiprotons per second. Assuming an optimal conversion of antiprotons to antihydrogen, it would take two billion years to produce 1 gram of antihydrogen (approximately 6.02×1023 atoms of antihydrogen.) Another limiting factor to antimatter production is storage. As stated above there is no known way to effectively store antihydrogen. The ATHENA project has managed to keep antihydrogen atoms from annihilation for tens of seconds — just enough time to briefly study their behaviour.

Hydrogen atoms are simplest objects, that can be considered as "matter" rather than as just particles. Simultaneous trapping of antiprotons and antielectrons was reported and the cooling is achieved; there are patents on the way of production of antihydrogen.

Antihelium

A small number of nuclei of the antihelium isotope, \overline{\mathrm{^3He}} have been created in collision experiments.

Preservation

Antimatter cannot be stored in a container made of ordinary matter because antimatter reacts with any matter it touches, annihilating itself and the container. Antimatter that is composed of charged particles can be contained by a combination of an electric field and a magnetic field in a device known as a Penning trap. This device cannot, however, contain antimatter that consists of uncharged particles, and atomic traps are used. In particular, such a trap may use the dipole moment (electrical or magnetic) of the trapped particles; at high vacuum, the matter or anti-matter particles can be trapped (suspended) and cooled with slightly off-resonant laser radiation (see, for, example, magneto-optical trap and Magnetic trap). Small particles can be also suspended by just intensive optical beam in the optical tweezers.

Cost

Antimatter is said to be the most expensive substance in existence, with an estimated cost of $300 billion per milligram. This is because production is difficult (only a few atoms are produced in reactions in particle accelerators), and because there is higher demand for the other uses of particle accelerators. According to CERN, it has cost a few hundred million Swiss Francs to produce about 1 billionth of a gram.

Several NASA Institute for Advanced Concepts-funded studies are exploring whether it might be possible to use magnetic scoops to collect the antimatter that occurs naturally in the Van Allen belts of Earth, and ultimately, the belts of gas giants like Jupiter, hopefully at a lower cost per gram.

Uses

Medical

Antimatter-matter reactions have practical applications in medical imaging, such as positron emission tomography (PET). In positive beta decay, a nuclide loses surplus positive charge by emitting a positron (in the same event, a proton becomes a neutron, and neutrinos are also given off). Nuclides with surplus positive charge are easily made in a cyclotron and are widely generated for medical use.

Fuel

In antimatter-matter collisions resulting in photon emission, the entire rest mass of the particles is converted to kinetic energy. The energy per unit mass (9×1016 J/kg) is about 10 orders of magnitude greater than chemical energy (compared to TNT at 4.2×106 J/kg, and formation of water at 1.56×107 J/kg), about 4 orders of magnitude greater than nuclear energy that can be liberated today using nuclear fission (about 40 MeV per 238U nucleus transmuted to Lead, or 1.5×1013 J/kg), and about 2 orders of magnitude greater than the best possible from fusion (about 6.3×1014 J/kg for the proton-proton chain). The reaction of 1 kg of antimatter with 1 kg of matter would produce 1.8×1017 J (180 petajoules) of energy (by the mass-energy equivalence formula E = mc²), or the rough equivalent of 47 megatons of TNT. For comparison, Tsar Bomba, the largest nuclear weapon ever detonated, reacted an estimated yield of 57 Megatons, which required the use of hundreds of kilograms of fissile material (Uranium/Plutonium).

Not all of that energy can be utilized by any realistic technology, because as much as 50% of energy produced in reactions between nucleons and antinucleons is carried away by neutrinos, so, for all intents and purposes, it can be considered lost.

The scarcity of antimatter means that it is not readily available to be used as fuel, although it could be used in antimatter catalyzed nuclear pulse propulsion. Generating a single antiproton is immensely difficult and requires particle accelerators and vast amounts of energy—millions of times more than is released after it is annihilated with ordinary matter due to inefficiencies in the process. Known methods of producing antimatter from energy also produce an equal amount of normal matter, so the theoretical limit is that half of the input energy is converted to antimatter. Counterbalancing this, when antimatter annihilates with ordinary matter, energy equal to twice the mass of the antimatter is liberated—so energy storage in the form of antimatter could (in theory) be 100% efficient.

Antimatter production is currently very limited, but has been growing at a nearly geometric rate since the discovery of the first antiproton in 1955 by Segrè and Chamberlain. The current antimatter production rate is between 1 and 10 nanograms per year, and this is expected to increase to between 3 and 30 nanograms per year by 2015 or 2020 with new superconducting linear accelerator facilities at CERN and Fermilab. Some researchers claim that with current technology, it is possible to obtain antimatter for US$25 million per gram by optimizing the collision and collection parameters (given current electricity generation costs). Antimatter production costs, in mass production, are almost linearly tied in with electricity costs, so economical pure-antimatter thrust applications are unlikely to come online without the advent of such technologies as deuterium-tritium fusion power (assuming that such a power source actually would prove to be cheap). Many experts, however, dispute these claims as being far too optimistic by many orders of magnitude. They point out that in 2004; the annual production of antiprotons at CERN was several picograms at a cost of $20 million. This means to produce 1 gram of antimatter, CERN would need to spend 100 quadrillion dollars and run the antimatter factory for 100 billion years. Storage is another problem, as antiprotons are negatively charged and repel against each other, so that they cannot be concentrated in a small volume. Plasma oscillations in the charged cloud of antiprotons can cause instabilities that drive antiprotons out of the storage trap. For these reasons, to date only a few million antiprotons have been stored simultaneously in a magnetic trap, which corresponds to much less than a femtogram. Antihydrogen atoms or molecules are neutral so in principle they do not suffer the plasma problems of antiprotons described above. But cold antihydrogen is far more difficult to produce than antiprotons, and so far not a single antihydrogen atom has been trapped in a magnetic field.

Since the energy density is vastly higher than these other forms, the thrust to weight equation used in antimatter rocketry and spacecraft would be very different. In fact, the energy in a few grams of antimatter is enough to transport an unmanned spacecraft to Mars in a few minutes. In comparison, the Mars Global Surveyor took eleven months to reach Mars using conventional means. It is hoped that antimatter could be used as fuel for interplanetary travel or possibly interstellar travel, but it is also feared that, as a side-effect of antimatter propulsion, the design of antimatter weapons might become an equal reality.

One researcher of the CERN laboratories, which produces antimatter on a regular basis, said:

If we could assemble all of the antimatter we've ever made at CERN and annihilate it with matter, we would have enough energy to light a single electric light bulb for a few minutes.

Antimatter in fiction

Existence of anti-particles is more "sci-" than "fiction" . However, until now, the anti-world, or even macroscopic amounts of antimatter exist rather in jokes and sci-fi novels, than in laboratories. One of these novels is Dan Brown's "Angels and Demons" in which the whole story centers around production of antimatter at the CERN facility and its possible use in terrorism because of the awesome power of an annihilation.

Pop culture

The 1960s hit television show The Man from U.N.C.L.E. dealt with the potential of antimatter in an episode called The Suburbia Affair. Pianist and comedian Victor Borge played a pianist and scientist who had come up with a formula for antimatter and, fearing its destructive potential, hid in a bizarre suburban development populated by single adults and couples who hate children. Borge's character, Dr. Rutter, disguised his formula in a dissonant piece of music until forced to reveal it to the evil organization, THRUSH (Technological Hierarchy for the Removal of Undesirables and Subjugation of Humanity). The good guys, Illya Kuryakin and Napoleon Solo, arrive to save the day and, after a plea from the wounded Rutter, destroy the computer where the antimatter formula has been stored. In another 20 years, Rutter warns, someone else will come up with the formula.

In the television series Star Trek, the Enterprise (starship) was equipped with a faster-than-light drive called a "Warp Drive", which harnessed the energy released by matter-antimatter annihilation to propel the vessel at superluminary velocity, as well as weapons called "Photon Torpedoes", which contained a charge of antimatter contained in an unspecified manner, and could be fired at enemy vessels much like missiles from a present day fighter plane.

Military

Because of its potential to release immense amounts of energy in contact with normal matter, there has been interest in various weapon uses, potentially enabling miniature warheads of pinhead-size to be more destructive than modern-day nuclear weapons. An antimatter particle colliding with a matter particle releases 100% of the energy contained within the particles, while a hydrogen bomb only releases about 0.7% of this energy. This gives a clue to how effective and powerful this force is. However, this development is still in early planning stages, though antimatter weapons are popular in science fiction such as in Peter F. Hamilton's Night's Dawn Trilogy , Sega and Petroglyph's RTS game Universe at War, Dan Brown's Angels and Demons and Star Trek where the production of antimatter leads to the possibility of use as both a fuel and highly effective weapon. At the moment, the traps are not very efficient, and it is more constructive to just create all the antimatter at the moment it would be used.

Cartoons

In the Dilbert cartoon strip from June 30, 2008, Dilbert creates an "anti-Dilbert" using a particle accelerator.

Stanisław Lem

In the novel The Cyberiad, Stanisław Lem describes the building up the antimatter in the following way:

  • The machine, however, had already begun. First it manufactured antiprotons, then antielectrons, antineutrons, antineutrinos, and labored on, until from out of all this antimatter an antiworld took shape, ..

In another novel, The Invincible , the researchers fail to fight the self-organizing microrobots, even though they use antimatter as a weapon.
In the novel Eden , humans use antimatter as a weapon, but it does not help them to understand anything about the civilization they met.

[...]

Categories: ,
Abhijeet
Comments


Corresponding to most kinds of particles, there is an associated antiparticle with the same mass and opposite electric charge. For example, the antiparticle of the electron is the positively charged antielectron, or positron, which is produced naturally in certain types of radioactive decay.

The laws of nature are very nearly symmetrical with respect to particles and antiparticles. For example, an antiproton and an antielectron can form an antihydrogen atom, which has almost exactly the same properties as a hydrogen atom. A physicist whose body was made of antimatter, doing experiments in a laboratory also made of antimatter, would find almost exactly the same results in all experiments. This leads to the question of why the formation of matter after the Big Bang resulted in a universe consisting almost entirely of matter, rather than being a half-and-half mixture of matter and antimatter. The discovery of CP violation helped to shed light on this problem by showing that this symmetry, originally thought to be perfect, was only approximate.

Particle-antiparticle pairs can annihilate each other, producing photons; since the charges of the particle and antiparticle are opposite, charge is conserved. For example, the antielectrons produced in natural radioactive decay quickly annihilate themselves with electrons, producing pairs of gamma rays.

Antiparticles are produced naturally in beta decay, and in the interaction of cosmic rays in the Earth's atmosphere. Because charge is conserved, it is not possible to create an antiparticle without either destroying a particle of the same charge (as in beta decay), or creating a particle of the opposite charge. The latter is seen in many processes in which both a particle and its antiparticle are created simultaneously, as in particle accelerators. This is the inverse of the particle-antiparticle annihilation process.

Although particles and their antiparticles have opposite charges, electrically neutral particles need not be identical to their antiparticles. The neutron, for example, is made out of quarks, the antineutron from antiquarks, and they are distinguishable from one another because an antineutron, unlike a neutron, will rapidly annihilate itself by colliding with neutrons in ordinary matter. However, it is speculated that some neutral particles (such as some proposed types of WIMPs) are their own antiparticles, and can therefore annihilate with themselves. Some particles have no antiparticles; these include the photon, the hypothetical graviton, and any other hypothetical massless gauge bosons.


History

Experiment

In 1932, soon after the prediction of positrons by Paul Dirac, Carl D. Anderson found that cosmic-ray collisions produced these particles in a cloud chamber— a particle detector in which moving electrons (or positrons) leave behind trails as they move through the gas. The electric charge-to-mass ratio of a particle can be measured by observing the curling of its cloud-chamber track in a magnetic field. Originally, positrons, because of the direction that their paths curled, were mistaken for electrons travelling in the opposite direction.

The antiproton and antineutron were found by Emilio Segrè and Owen Chamberlain in 1955 at the University of California, Berkeley. Since then the antiparticles of many other subatomic particles have been created in particle accelerator experiments. In recent years, complete atoms of antimatter have been assembled out of antiprotons and positrons, collected in electromagnetic traps[citation needed].

Hole theory

... the development of quantum field theory made the interpretation of antiparticles as holes unnecessary, even though it lingers on in many textbooks. — Steven Weinberg in The quantum theory of fields, Vol I, p 14, ISBN 0-521-55001-7

Solutions of the Dirac equation contained negative energy quantum states. As a result, an electron could always radiate energy and fall into a negative energy state. Even worse, it could keep radiating infinite amount of energy because there were infinitely many negative energy states available. To prevent this unphysical situation from happening, Dirac proposed that a "sea" of negative-energy electrons fills the universe, already occupying all of the lower energy states so that, due to the Pauli exclusion principle no other electron could fall into them. Sometimes, however, one of these negative energy particles could be lifted out of this Dirac sea to become a positive energy particle. But when lifted out, it would leave behind a hole in the sea which would act exactly like a positive energy electron with a reversed charge. These he interpreted as the proton, and called his paper of 1930 A theory of electrons and protons.

Dirac was aware of the problem that his picture implied an infinite negative charge for the universe. Dirac tried to argue that we would perceive this as the normal state of zero charge. Another difficulty was the difference in masses of the electron and the proton. Dirac tried to argue that this was due to the electromagnetic interactions with the sea, until Hermann Weyl proved that hole theory was completely symmetric between negative and positive charges. Dirac also predicted a reaction e+p+γ+γ, where an electron and a proton annihilate to give two photons. Robert Oppenheimer and Igor Tamm proved that this would cause ordinary matter to disappear too fast. A year later, in 1931, Dirac modified his theory and postulated the positron, a new particle of the same mass as the electron. The discovery of this particle the next year removed the last two objections to his theory.

However, the problem of infinite charge of the universe remains. Also, as we now know, bosons also have antiparticles, but since they do not obey the Pauli exclusion principle, hole theory doesn't work for them. A unified interpretation of antiparticles is now available in quantum field theory, which solves both these problems.

Particle-antiparticle annihilation

Main article: Annihilation
An example of a virtual pion pair which influences the propagation of a kaon causing a neutral kaon to mix with the antikaon. This is an example of renormalization in quantum field theory— the field theory being necessary because the number of particles changes from one to two and back again.
An example of a virtual pion pair which influences the propagation of a kaon causing a neutral kaon to mix with the antikaon. This is an example of renormalization in quantum field theory— the field theory being necessary because the number of particles changes from one to two and back again.

If a particle and antiparticle are in the appropriate quantum states, then they can annihilate each other and produce other particles. Reactions such as e + e+γ + γ (the two-photon annihilation of an electron-positron pair) is an example. The single-photon annihilation of an electron-positron pair, e + e+γ cannot occur because it is impossible to conserve energy and momentum together in this process. The reverse reaction is also impossible for this reason. However, in quantum field theory this process is allowed as an intermediate quantum state for times short enough that the violation of energy conservation can be accommodated by the uncertainty principle. This opens the way for virtual pair production or annihilation in which a one particle quantum state may fluctuate into a two particle state and back. These processes are important in the vacuum state and renormalization of a quantum field theory. It also opens the way for neutral particle mixing through processes such as the one pictured here: which is a complicated example of mass renormalization.

Properties of antiparticles

Quantum states of a particle and an antiparticle can be interchanged by applying the charge conjugation (C), parity (P), and time reversal (T) operators. If |p,σ,n> denotes the quantum state of a particle (n) with momentum p, spin J whose component in the z-direction is σ, then one has

\ =\ (-1)^{J-\sigma}\ |p,-\sigma,n^c>," src="http://upload.wikimedia.org/math/f/9/3/f939715c2fcc4903a97ab75f6f464cef.png">

where nc denotes the charge conjugate state, i.e., the antiparticle. This behaviour under CPT is the same as the statement that the particle and its antiparticle lie in the same irreducible representation of the Poincare group. Properties of antiparticles can be related to those of particles through this. If T is a good symmetry of the dynamics, then


\ \alpha \ |-p,-\sigma,n>," src="http://upload.wikimedia.org/math/f/8/d/f8d3799d13242a913eb5ceaa416684e1.png">
\ \alpha \ |-p,\sigma,n^c>," src="http://upload.wikimedia.org/math/f/9/c/f9c86089f2ecd6c51afb77ac2c80f0cd.png">
\ \alpha \ |p,\sigma,n^c>," src="http://upload.wikimedia.org/math/0/2/d/02d15a211d56cd786c40c7579502032b.png">

where the proportionality sign indicates that there might be a phase on the right hand side. In other words, particle and antiparticle must have

Quantum field theory

This section draws upon the ideas, language and notation of canonical quantization of a quantum field theory.

One may try to quantize an electron field without mixing the annihilation and creation operators by writing

\psi (x)=\sum_{k}u_k (x)a_k e^{-iE(k)t},\,

where we use the symbol k to denote the quantum numbers p and σ of the previous section and the sign of the energy, E(k), and ak denotes the corresponding annihilation operators. Of course, since we are dealing with fermions, we have to have the operators satisfy canonical anti-commutation relations. However, if one now writes down the Hamiltonian

H=\sum_{k} E(k) a^\dagger_k a_k,\,

then one sees immediately that the expectation value of H need not be positive. This is because E(k) can have any sign whatsoever, and the combination of creation and annihilation operators has expectation value 1 or 0.

So one has to introduce the charge conjugate antiparticle field, with its own creation and annihilation operators satisfying the relations

b_{k\prime} = a^\dagger_k\ \mathrm{and}\ b^\dagger_{k\prime}=a_k,\,

where k has the same p, and opposite σ and sign of the energy. Then one can rewrite the field in the form

\psi(x)=\sum_{k_+} u_k (x)a_k e^{-iE(k)t}+\sum_{k_-} u_k (x)b^\dagger _k e^{-iE(k)t},\,

where the first sum is over positive energy states and the second over those of negative energy. The energy becomes

H=\sum_{k_+} E_k a^\dagger _k a_k + \sum_{k_-} |E(k)|b^\dagger_k b_k + E_0,\,

where E0 is an infinite negative constant. The vacuum state is defined as the state with no particle or antiparticle, i.e., a_k |0\rangle=0 and b_k |0\rangle=0. Then the energy of the vacuum is exactly E0. Since all energies are measured relative to the vacuum, H is positive definite. Analysis of the properties of ak and bk shows that one is the annihilation operator for particles and the other for antiparticles. This is the case of a fermion.

This approach is due to Vladimir Fock, Wendell Furry and Robert Oppenheimer. If one quantizes a real scalar field, then one finds that there is only one kind of annihilation operator; therefore real scalar fields describe neutral bosons. Since complex scalar fields admit two different kinds of annihilation operators, which are related by conjugation, such fields describe charged bosons.

The Feynman-Stueckelberg interpretation

By considering the propagation of the negative energy modes of the electron field backward in time, Richard Feynman reached a pictorial understanding of the fact that the particle and antiparticle have equal mass m and spin J but opposite charges q. This allowed him to rewrite perturbation theory precisely in the form of diagrams, called Feynman diagrams, of particles propagating back and forth in time. This technique now is the most widespread method of computing amplitudes in quantum field theory.

This picture was independently developed by Ernst Stueckelberg, and has been called the Feynman-Stueckelberg interpretation of antiparticles.

[...]

Categories: ,
Abhijeet
Comments


This figure compares conventional facsimile transmission with quantum teleportation (see above). In conventional facsimile transmission the original is scanned, extracting partial information about it, but remains more or less intact after the scanning process. The scanned information is sent to the receiving station, where it is imprinted on some raw material (eg paper) to produce an approximate copy of the original. By contrast, in quantum teleportation, two objects B and C are first brought into contact and then separated. Object B is taken to the sending station, while object C is taken to the receiving station. At the sending station object B is scanned together with the original object A which one wishes to teleport, yielding some information and totally disrupting the state of A and B. The scanned information is sent to the receiving station, where it is used to select one of several treatments to be applied to object C, thereby putting C into an exact replica of the former state of A.
[...]

Categories: ,
Abhijeet
Comments



Quantum TeleportationTeleportation is the name given by science fiction writers to the feat of making an object or person disintegrate in one place while a perfect replica appears somewhere else. How this is accomplished is usually not explained in detail, but the general idea seems to be that the original object is scanned in such a way as to extract all the information from it, then this information is transmitted to the receiving location and used to construct the replica, not necessarily from the actual material of the original, but perhaps from atoms of the same kinds, arranged in exactly the same pattern as the original. A teleportation machine would be like a fax machine, except that it would work on 3-dimensional objects as well as documents, it would produce an exact copy rather than an approximate facsimile, and it would destroy the original in the process of scanning it. A few science fiction writers consider teleporters that preserve the original, and the plot gets complicated when the original and teleported versions of the same person meet; but the more common kind of teleporter destroys the original, functioning as a super transportation device, not as a perfect replicator of souls and bodies.


In 1993 an international group of six scientists, including IBM Fellow Charles H. Bennett, confirmed the intuitions of the majority of science fiction writers by showing that perfect teleportation is indeed possible in principle, but only if the original is destroyed. In subsequent years, other scientists have demonstrated teleportation experimentally in a variety of systems, including single photons, coherent light fields, nuclear spins, and trapped ions. Teleportation promises to be quite useful as an information processing primitive, facilitating long range quantum communication (perhaps unltimately leading to a "quantum internet"), and making it much easier to build a working quantum computer. But science fiction fans will be disappointed to learn that no one expects to be able to teleport people or other macroscopic objects in the foreseeable future, for a variety of engineering reasons, even though it would not violate any fundamental law to do so.
In the past, the idea of teleportation was not taken very seriously by scientists, because it was thought to violate the uncertainty principle of quantum mechanics, which forbids any measuring or scanning process from extracting all the information in an atom or other object. According to the uncertainty principle, the more accurately an object is scanned, the more it is disturbed by the scanning process, until one reaches a point where the object's original state has been completely disrupted, still without having extracted enough information to make a perfect replica. This sounds like a solid argument against teleportation: if one cannot extract enough information from an object to make a perfect copy, it would seem that a perfect copy cannot be made. But the six scientists found a way to make an end run around this logic, using a celebrated and paradoxical feature of quantum mechanics known as the Einstein-Podolsky-Rosen effect. In brief, they found a way to scan out part of the information from an object A, which one wishes to teleport, while causing the remaining, unscanned, part of the information to pass, via the Einstein-Podolsky-Rosen effect, into another object C which has never been in contact with A. Later, by applying to C a treatment depending on the scanned-out information, it is possible to maneuver C into exactly the same state as A was in before it was scanned. A itself is no longer in that state, having been thoroughly disrupted by the scanning, so what has been achieved is teleportation, not replication. As the figure to the left suggests, the unscanned part of the information is conveyed from A to C by an intermediary object B, which interacts first with C and then with A. What? Can it really be correct to say "first with C and then with A"? Surely, in order to convey something from A to C, the delivery vehicle must visit A before C, not the other way around. But there is a subtle, unscannable kind of information that, unlike any material cargo, and even unlike ordinary information, can indeed be delivered in such a backward fashion. This subtle kind of information, also called "Einstein-Podolsky-Rosen (EPR) correlation" or "entanglement", has been at least partly understood since the 1930s when it was discussed in a famous paper by Albert Einstein, Boris Podolsky, and Nathan Rosen. In the 1960s John Bell showed that a pair of entangled particles, which were once in contact but later move too far apart to interact directly, can exhibit individually random behavior that is too strongly correlated to be explained by classical statistics. Experiments on photons and other particles have repeatedly confirmed these correlations, thereby providing strong evidence for the validity of quantum mechanics, which neatly explains them. Another well-known fact about EPR correlations is that they cannot by themselves deliver a meaningful and controllable message. It was thought that their only usefulness was in proving the validity of quantum mechanics. But now it is known that, through the phenomenon of quantum teleportation, they can deliver exactly that part of the information in an object which is too delicate to be scanned out and delivered by conventional methods.

[...]

Categories: ,