Virtual Particles what are they ,Can our universe exist without them and is it just possible that they have much deeper similarities with real particles .

 

What are Virtual Particles?.

A virtual particle is a theoretical transient particle that exhibits some of the characteristics of an ordinary particle, while having its existence limited by the uncertainty principle. The concept of virtual particles arises in the perturbation theory of quantum field theory where interactions between ordinary particles are described in terms of exchanges of virtual particles. A process involving virtual particles can be described by a schematic representation known as a Feynman diagram, in which virtual particles are represented by internal lines.

Virtual particles do not necessarily carry the same mass as the corresponding real particle, although they always conserve energy and momentum. The closer its characteristics come to those of ordinary particles, the longer the virtual particle exists. They are important in the physics of many processes, including particle scattering and Casimir forces. In quantum field theory, forces—such as the electromagnetic repulsion or attraction between two charges—can be thought of as due to the exchange of virtual photons between the charges. Virtual photons are the exchange particle for the electromagnetic interaction.

The term is somewhat loose and vaguely defined, in that it refers to the view that the world is made up of "real particles". "Real particles" are better understood to be excitations of the underlying quantum fields. Virtual particles are also excitations of the underlying fields, but are "temporary" in the sense that they appear in calculations of interactions, but never as asymptotic states or indices to the matrix. Thats until perhaps you look at more closely at some of the particles and their behavior examples include neutrinos and the varying mass of protons . The accuracy and use of virtual particles in calculations is firmly established, but as they cannot be detected in experiments, deciding how to precisely describe them is a topic of debate.Although widely used, they are by no means a necessary feature of QFT, but rather are mathematical conveniences - as demonstrated by lattice field theory, which avoids using the concept altogether.

Properties of virtual particles

A virtual particle does not precisely obey the energy–momentum relation m²c⁴ = E² − p²c². Its kinetic energy may not have the usual relationship to velocity. It can be negative  This is expressed by the phrase off mass shell. The probability amplitude for a virtual particle to exist tends to be canceled out by destructive interference over longer distances and times. As a consequence, a real photon is massless and thus has only two polarization states, whereas a virtual one, being effectively massive, has three polarization states. Something that is in a way similar to what a neutrino would exhibit

Quantum tunnelling may be considered a manifestation of virtual particle exchanges. 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.

Written in the usual mathematical notations, in the equations of physics, there is no mark of the distinction between virtual and actual particles. The amplitudes of processes with a virtual particle interfere with the amplitudes of processes without it, whereas for an actual 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, actual particles are viewed as being detectable excitations of underlying quantum fields. Virtual particles are also viewed as excitations of the underlying fields, but appear only as forces, not as detectable particles. They are "temporary" in the sense that they appear in some 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.

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 contribute to a mechanism that mediates the effect, or that the effect occurs through the virtual particles.

Virtual Particles and their role in the real universe: 

There are many observable physical phenomena that arise in interactions involving virtual particles. For bosonic particles that exhibit rest mass when they are free and actual, virtual interactions are characterized by the relatively short range of the force interaction produced by particle exchange. Confinement can lead to a short range, too. Examples of such short-range interactions are the strong and weak forces, and their associated field bosons.

For the gravitational and electromagnetic forces, the zero rest-mass of the associated boson particle permits long-range forces to be mediated by virtual particles. However, in the case of photons, power and information transfer by virtual particles is a relatively short-range phenomenon (existing only within a few wavelengths of the field-disturbance, which carries information or transferred power), as for example seen in the characteristically short range of inductive and capacitative effects in the near field zone of coils and antennas.

some field interactions which may be seen in terms of virtual particles 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 cube law for magnetic force. Since the photon has no mass, the magnetic potential has an infinite range.
• Electromagnetic induction. This phenomenon transfers energy to and from a magnetic coil via a changing electro magnetic field.
• 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 is the result of exchange by virtual W and Z 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.
• The Impedance of free space, which defines the ratio between the electric field strength |E| and the magnetic field strength |H |: Z₀ = | E|⁄|H|.^[8]
• Much of the so-called near-field of radio antennas, where the magnetic and electric effects of the changing current in the antenna wire and the charge effects of the wire's capacitive charge may be (and usually are) important contributors to the total EM field close to the source, but both of which effects are dipole effects that decay with increasing distance from the antenna much more quickly than do the influence of "conventional" electromagnetic waves that are "far" from the source^[.]These far-field waves, for which E is (in the limit of long distance) equal to cB, are composed of actual photons. Actual and virtual photons are mixed near an antenna, with the virtual photons responsible only for the "extra" magnetic-inductive and transient electric-dipole effects, which cause any imbalance between E and cB. As distance from the antenna grows, the near-field effects (as dipole fields) die out more quickly, and only the "radiative" effects that are due to actual photons remain as important effects. Although virtual effects extend to infinity, they drop off in field strength as 1⁄r² rather than the field of EM waves composed of actual photons, which drop 1⁄r

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. Examples of macroscopic virtual phonons, photons, and electrons in the case of the tunneling process were presented by Günter Nimtz and Alfons A. Stahlhofen

Feymann 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 actual, on-shell particles. Thus, it is natural to associate the other lines in the diagram with particles as well, called the "virtual particles". In mathematical terms, they correspond to the propagators appearing in the diagram.

In the adjacent image below, the solid lines correspond to actual 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

Virtual particles may be mesons or vector 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.

Pair Production:

Virtual particles are often popularly described as coming in pairs, a particle and antiparticle which can be of any kind. These pairs exist for an extremely short time, and then mutually annihilate, or in some cases, the pair may be boosted apart using external energy so that they avoid annihilation and become actual particles, as described below. The implication of a mirror universe in close interaction with our universe is tempting at this point to think about .

This may occur in one of two ways.

 In an accelerating frame of reference, the virtual particles may appear to be actual to the accelerating observer; this is known as the Unruh effect. In short, the vacuum of a stationary frame appears, to the accelerated observer, to be a warm gas of actual particles in thermodynamic equilibrium.

Another example is pair production in very strong electric fields, sometimes called vacuum decay. If, for example, a pair of atomic nuclei are merged to very briefly form a nucleus with a charge greater than about 140, (that is, larger than about the inverse of the fine-structure constant, which is a dimensionless quantity), the strength of the electric field will be such that it will be energetically favorable to create positron–electron pairs out of the vacuum or Dirac sea, with the electron attracted to the positron to annihilate the positive charge. This pair-creation amplitude was first calculated by Julian Schwinger in 1951.

Mathematically:

The mathematical equations that describe virtual particles are part of the mathematical framework of quantum field theory. In this framework, the behavior of particles and fields is described by a set of equations known as the "Lagrangian," which is a mathematical function that specifies how the particles and fields interact with one another.

The equations that describe virtual particles are derived from the Lagrangian using a mathematical technique called "perturbation theory." Perturbation theory is a method of approximating the behavior of a complex system by breaking it down into simpler parts and then analyzing the effects of small perturbations.

In quantum field theory, the formation of an electron as a virtual particle can be described by a process known as electron-positron annihilation. This process involves the collision of a particle and its corresponding antiparticle, resulting in the conversion of their mass into energy and the creation of a pair of virtual particles that quickly annihilate each other.

The mathematical equation that describes the annihilation of an electron and a positron and the creation of a pair of virtual particles is:

e- + e+ → γ* → e- + e+

In this equation, "e-" represents an electron, "e+" represents a positron, and "γ*" represents a virtual photon. The arrow indicates the direction of the reaction, and the double arrow indicates that the photon is a virtual particle that is created and destroyed during the reaction.

The formation of a positron as a virtual particle can be described by the inverse process of electron-positron annihilation. In this case, a pair of virtual particles are created, which then interact to form a positron and an electron.

The mathematical equation that describes the creation of a positron as a virtual particle is:

γ* → e- + e+ → e+

In this equation, "γ*" represents a virtual photon that is created from the interaction of two particles, and "e-" and "e+" represent an electron and a positron, respectively. The arrow indicates the direction of the reaction, and the double arrow indicates that the photon is a virtual particle that is created and destroyed during the reaction.

The main difference between real particles and virtual particles is that real particles are particles that can be directly observed or detected, while virtual particles are not directly observable or detectable in the same way.

Real particles are particles that have a well-defined mass, charge, and spin, and they can be detected through their interactions with other particles or through their effects on detectors. Examples of real particles include electrons, protons, and photons.

Virtual particles, on the other hand, are particles that exist only as disturbances in the underlying fields of quantum mechanics. They do not have a well-defined mass, charge, or spin, and they cannot be directly detected or observed. Instead, their existence is inferred from the effects they have on other particles and fields. Virtual particles can arise due to the fluctuations in the underlying fields or due to the interactions between particles and fields.

Another key difference between real particles and virtual particles is that real particles are stable and can exist indefinitely, while virtual particles are typically unstable and exist only for very short periods of time before they decay or annihilate with other particles. This is because virtual particles are not bound by the usual conservation laws that apply to real particles.

Despite these differences, real particles and virtual particles are both important components of the quantum mechanical description of the behavior of subatomic particles, and both play a crucial role in determining the properties and behavior of matter and energy in the universe.

Real particles, such as real electrons and real positrons, differ from virtual particles in that they are stable and have well-defined properties such as mass, charge, and spin. Real particles can exist independently and can be detected through their interactions with other particles or their effects on detectors. In contrast, virtual particles are not stable and have uncertain properties, and their existence is inferred from the effects they have on other particles and fields.

While it is true that all particles, including real particles, are subject to energy fluctuations in the quantum vacuum, this does not mean that real particles "borrow" energy for their existence. Instead, the energy fluctuations in the vacuum affect all particles equally, and they do not have a net effect on the properties or stability of real particles.

In the case of the nucleus, the behavior of particles is described by the strong force, which is mediated by gluons rather than photons. While gluons can exchange energy between particles, this does not involve borrowing or lending energy, but rather the transfer of energy through the exchange of particles.

In summary, while real particles and virtual particles may both be subject to energy fluctuations in the quantum vacuum, real particles differ from virtual particles in that they are stable and have well-defined properties. The behavior of particles in complex environments, such as the nucleus, is governed by the laws of quantum mechanics and the interactions between particles and fields, but this does not involve borrowing or lending energy for the existence of real particles.

It is true that particles such as electrons, positrons, muons, and neutrinos can exist as part of more complex structures, such as atoms and molecules. In these cases, the energy of the individual particles is conserved as part of the larger system. However, it is important to note that the individual particles themselves still have well-defined properties, including mass, charge, and spin, and their energy is still conserved in interactions with other particles.

Additionally, even when particles are part of a larger system, the energy conservation still applies to each individual particle, as well as to the system as a whole. This is because energy conservation is a fundamental law of nature that applies at all scales, from individual particles to entire galaxies.

In summary, while particles can exist as part of more complex structures, their individual properties and energy conservation still apply, both within the larger system and in interactions with other particles.

Here are the mathematical equations describing an electron, a positron, and a muon, respectively:

Electron: The Dirac equation describes the behavior of a free electron in relativistic quantum mechanics:

(iγ^μ∂_μ - m)ψ = 0

where ψ is the electron wave function, γ^μ are the Dirac gamma matrices, ∂_μ is the partial derivative with respect to the four spacetime coordinates, and m is the mass of the electron.

Positron: The behavior of a real positron can be described by the Dirac equation as well, but with a positive sign in front of the mass term:

(iγ^μ∂_μ + m)ψ = 0

where ψ is the positron wave function, γ^μ are the Dirac gamma matrices, ∂_μ is the partial derivative with respect to the four spacetime coordinates, and m is the mass of the positron.

Muon: The behavior of a muon can be described by a similar equation, called the Dirac-Pauli equation, which takes into account the muon's spin:

(iγ^μ(D_μ - ieA_μ) - m)ψ = 0

where ψ is the muon wave function, γ^μ are the Dirac gamma matrices, D_μ is the covariant derivative, A_μ is the electromagnetic potential, e is the elementary charge, and m is the mass of the muon.

Particles in quantum mechanics are often described by wavefunctions that exhibit wave-like properties, such as interference and diffraction, as well as particle-like properties, such as definite positions and momenta when measured. This is known as wave-particle duality, and it arises due to the probabilistic nature of quantum mechanics, where the wavefunction gives the probability amplitude of finding the particle at a particular location or with a particular momentum.

It is important to note that the wave-like behavior of particles is not just a phenomenon that arises due to the interaction with an observer or measurement apparatus, but is an inherent property of the particle itself. This is supported by a wide range of experimental evidence, including interference experiments with electrons and other particles.

if particles  existed due to the fact that real particles as well as virtual particle were borrowing energy and paying it back via photons and gluons and w and z bosons resulting in the wave particle duality we would then describe  them mathematically as follows for real particles.

The wave-particle duality of particles can be mathematically described by their wavefunctions, which obey the Schrödinger equation or the Dirac equation, depending on whether the particle is non-relativistic or relativistic, respectively. These equations describe how the wavefunction of a particle evolves over time, and how it interacts with other particles and fields.

For example, the Schrödinger equation for a non-relativistic particle of mass m in a potential V(x) is given by:

iℏ ∂ψ/∂t = (-ℏ^2/2m) ∇^2ψ + V(x)ψ

where ψ(x,t) is the wavefunction of the particle at position x and time t, ∇^2 is the Laplacian operator, and ℏ is the reduced Planck constant. This equation describes how the wavefunction of the particle evolves over time, and how it interacts with the potential V(x).

Similarly, the Dirac equation for a relativistic particle, such as an electron or a positron, is given by:

(iγ^μ∂_μ - m)ψ = 0

where γ^μ are the Dirac gamma matrices, ∂_μ is the partial derivative with respect to the four spacetime coordinates, and m is the mass of the particle. This equation describes the behavior of the particle's wavefunction in a relativistic framework, and how it interacts with other particles and fields.

In both cases, the wave function describes the probability amplitude of finding the particle at a particular location or with a particular momentum, and the wave-particle duality arises due to the probabilistic nature of quantum mechanics.

The borrowing of energy via photons, gluons, and other bosons is a feature of the quantum vacuum and the fundamental interactions between particles, which can be described by the laws of quantum field theory.

But when we consider unruh effect the possibility that virtual particles are actually real particles in a mirror universe comes to mind this is especially a tight fit for a massless photon with two polarizations states and becomes a neutrino with mass and three polarization states ,But perhaps the reader might see other implications or possibilities and is free to comment below

                                                                     Image of Neutrino and fine structure below