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dark matter modified gravity

. Quantum Physics: virtual particles

Empty Space is not so Empty: restrictions by uncertainty principle

Have you ever wonder about the empty space in which our earth is revolving around the Sun? What is this emptyness? Is it really empty, devoid of any matter and energy? I have always thought about this emptyness.

In physics, a virtual particle is a particle that exists for a limited time and space, introducing uncertainty in their energy and momentum due to the Heisenberg Uncertainty Principle. (Indeed, because energy and momentum in quantum mechanics are time and space derivative operators, then due to Fourier transforms their spans are inversely proportional to time duration and position spans, respectively). Virtual particles exhibit some of the phenomena that real particles do, such as obedience to the conservation laws. If a single particle is detected, then the consequences of its existence are prolonged to such a degree that it cannot be virtual. Virtual particles are viewed as the quanta that describe fields of the basic force interactions, which cannot be described in terms of real particles. Examples of these are static force fields, such as a simple electric or magnetic field, or any field that exists without excitations that result in its carrying information from place to place.

Virtual particles should not be confused with antiparticles or virtual antiparticles. The concept of virtual particles necessarily arises in the perturbation theory of quantum field theory, where interactions (essentially forces) between real particles are described in terms of exchanges of virtual particles. Any process involving virtual particles admits a schematic representation known as a Feynman diagram which facilitates the understanding of calculations.

A virtual particle is one that does not precisely obey the m2c4 = E2 − p2c2 relationship for a short time. In other words, their kinetic energy may not have the usual relationship to velocity — indeed, it can be negative. The probability amplitude for them to exist tends to be canceled out by destructive interference over longer distances and times. They can be considered a manifestation of quantum tunnelling. The range of forces carried by virtual particles is limited by the uncertainty principle, which regards energy and time as conjugate variables; thus virtual particles of larger mass have more limited range.
There is not a definite line differentiating virtual particles from real particles — the equations of physics just describe particles (which includes both equally). The amplitude that a virtual particle exists interferes with the amplitude for its non-existence; whereas for a real particle the cases of existence and non-existence cease to be coherent with each other and do not interfere any more. In the quantum field theory view, "real particles" are viewed as being detectable excitations of underlying quantum fields. As such, virtual particles are also excitations of the underlying fields, but are detectable only as forces but not particles. They are "temporary" in the sense that they appear in calculations, but are not detected as single particles. Thus, in mathematical terms, they never appear as indices to the scattering matrix, which is to say, they never appear as the observable inputs and outputs of the physical process being modelled. In this sense, virtual particles are an artifact of perturbation theory, and do not appear in a non-perturbative treatment. As such, their objective existence as "particles" is questionable; however, the term is useful in informal, casual conversation, or in rendering concepts into layman's terms. There are two principal ways in which the notion of virtual particles appears in modern physics. They appear as intermediate terms in Feynman diagrams; that is, as terms in a perturbative calculation. They also appear as an infinite set of states to be summed or integrated over in the calculation of a semi-non-perturbative effect. In the latter case, it is sometimes said that virtual particles cause the effect, or that the effect occurs because of the existence of virtual particles.

There are many observable physical phenomena resulting from interactions involving virtual particles. All tend to be characterized by the relatively short range of the force interaction producing them. Some of them are:
•The Coulomb force (static electric force) between electric charges. It is caused by the exchange of virtual photons. In symmetric 3-dimensional space this exchange results in the inverse square law for electric force. Since the photon has no mass, the coulomb potential has an infinite range.
•The Magnetic field between magnetic dipoles. It is caused by the exchange of virtual photons. In symmetric 3-dimensional space this exchange results in the inverse square law for magnetic force. Since the photon has no mass, the coulomb potential has an infinite range.
•The so-called near field of radio antennas, where the magnetic effects of the current in the antenna wire and the charge effects of the wire's capacitive charge are detectable, but both of which effects disappear with increasing distance from the antenna much more quickly than do the influence of conventional electromagnetic waves, for which E is always equal to cB, and which are composed of real photons.
•The strong nuclear force between quarks is the result of interaction of virtual gluons. The residual of this force outside of quark triplets (neutron and proton) holds neutrons and protons together in nuclei, and is due to virtual mesons such as the pi meson and rho meson.
•The weak nuclear force - it is the result of exchange by virtual W bosons.
•The spontaneous emission of a photon during the decay of an excited atom or excited nucleus; such a decay is prohibited by ordinary quantum mechanics and requires the quantization of the electromagnetic field for its explanation.
•The Casimir effect, where the ground state of the quantized electromagnetic field causes attraction between a pair of electrically neutral metal plates.
•The van der Waals force, which is partly due to the Casimir effect between two atoms,
•Vacuum polarization, which involves pair production or the decay of the vacuum, which is the spontaneous production of particle-antiparticle pairs (such as electron-positron).
•Lamb shift of positions of atomic levels.
•Hawking radiation, where the gravitational field is so strong that it causes the spontaneous production of photon pairs (with black body energy distribution) and even of particle pairs.
Most of these have analogous effects in solid-state physics; indeed, one can often gain a better intuitive understanding by examining these cases. In semiconductors, the roles of electrons, positrons and photons in field theory are replaced by electrons in the conduction band, holes in the valence band, and phonons or vibrations of the crystal lattice. A virtual particle is in a virtual state where the probability amplitude is not conserved.
Paul Dirac was the first to propose that empty space (a vacuum) can be visualized as consisting of a sea of virtual electron-positron pairs, known as the Dirac sea. The Dirac sea has a direct analog to the electronic band structure in crystalline solids as described in solid state physics. Here, particles correspond to conduction electrons, and antiparticles to holes. A variety of interesting phenomena can be attributed to this structure.
Virtual particles in Feynman diagrams
The calculation of scattering amplitudes in theoretical particle physics requires the use of some rather large and complicated integrals over a large number of variables. These integrals do, however, have a regular structure, and may be represented as Feynman diagrams. The appeal of the Feynman diagrams is strong, as it allows for a simple visual presentation of what would otherwise be a rather arcane and abstract formula. In particular, part of the appeal is that the outgoing legs of a Feynman diagram can be associated with real, on-shell particles. Thus, it is natural to associate the other lines in the diagram with particles as well, called the "virtual particles". Mathematically, they correspond to the propagators appearing in the diagram.
In the image above and to the right, the solid lines correspond to real particles (of momentum p1 and so on), while the dotted line corresponds to a virtual particle carrying momentum k. For example, if the solid lines were to correspond to electrons interacting by means of the electromagnetic interaction, the dotted line would correspond to the exchange of a virtual photon. In the case of interacting nucleons, the dotted line would be a virtual pion. In the case of quarks interacting by means of the strong force, the dotted line would be a virtual gluon, and so on.

One-loop diagram with fermion propagator

It is sometimes said that all photons are virtual photons.[1][2] This is because the world-lines of photons always resemble the dotted line in the above Feynman diagram: the photon was emitted somewhere (say, a distant star), and then is absorbed somewhere else (say a photoreceptor cell in the eyeball). Furthermore, in a vacuum, a photon experiences no passage of (proper) time between emission and absorption. This statement illustrates the difficulty of trying to distinguish between "real" and "virtual" particles as mathematically they are the same objects and it is only our definition of "reality" which is weak here. In practice, a clear distinction can be made: real photons are detected as individual particles in particle detectors, whereas virtual photons are not directly detected; only their average or side-effects may be noticed, in the form of forces or (in modern language) interactions between particles.
Virtual particles need not be mesons or bosons, as in the example above; they may also be fermions. However, in order to preserve quantum numbers, most simple diagrams involving fermion exchange are prohibited. The image to the right shows an allowed diagram, a one-loop diagram. The solid lines correspond to a fermion propagator, the wavy lines to bosons.
Virtual particles in vacuo.
Formally, a particle is considered to be an eigenstate of the particle number operator where is the particle annihilation operator and the particle creation operator (sometimes collectively called ladder operators). In many cases, the particle number operator does not commute with the Hamiltonian for the system. This implies the number of particles in an area of space is not a well-defined quantity but like other quantum observables is represented by a probability distribution. Since these particles do not have a permanent existence, they are called virtual particles or vacuum fluctuations of vacuum energy. In a certain sense, they can be understood to be a manifestation of the time-energy uncertainty principle in a vacuum, which bears some similarity to Aether theories.
An important example of the "presence" of virtual particles in a vacuum ...
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