# Virtual Particles

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## Virtual Particles

particles existing in intermediate states of short duration, for which the usual relation between energy, momentum, and mass is not fulfilled. Other characteristics of virtual particles are electric charge, spin, baryon charge, and others, such as those of the corresponding real particles.

The concept of virtual particles and virtual processes occupies a central place in modern quantum field theory. In this theory, the interaction of particles and their mutual transformations are considered as the creation or absorption by one free particle of other (virtual) particles. Any particle continuously emits and absorbs virtual particles of different types. For example, a proton emits and absorbs virtual pi-mesons (in addition to other virtual particles) and, owing to this finds itself surrounded by a cloud of virtual particles whose number (generally speaking) is indefinite.

From the viewpoint of classical physics, a free particle (a particle that has no external forces acting on it—that is, a particle at rest or moving uniformly and rectilinearly) can neither create nor absorb another particle (for example, a free electron cannot emit or absorb a photon), because such processes violate either the law of the conservation of energy or the law of the conservation of momentum. In fact, an electron at rest has the minimal possible energy (the rest energy, equal, according to the theory of relativity, to *m∞ ^{2}*, where

*m*is the electron’s rest mass and

_{0}*c*is the velocity of light). Consequently, such an electron cannot emit a photon, which always has energy, since, in this situation, the law of the conservation of energy would be violated. If the electron moves with constant velocity, it likewise cannot always (at the expense of its kinetic energy) create a photon, because in such a process the law of the conservation of momentum would be violated; the momentum loss by the electron associated with the energy loss in the photon formation would be larger than the momentum of the photon of corresponding energy (on account of the mass difference between these particles). The same argument is valid in the process of photon absorption by a free electron.

The situation in quantum mechanics is different. According to the fundamental principle of quantum mechanics, the uncertainty principle, any particle that “lives” for a short time interval *Δt* has an energy that is not exactly fixed. The spread of possible energy values *ΔE* satisfies the inequality *ΔE ≥h/Δ _{t}*, where

*h*is Planck’s constant. Analogously, a particle that exists only in a region of dimension

*Δ*has a momentum spread of

_{x}*Δp*on the order of

_{x}*Δp*. The energy and momentum continuously fluctuate and during small time intervals can “temporarily violate” (in the classical sense) the law of the conservation of energy; the processes that take place within small volumes can be accompanied by “local violations” of the law of the conservation of momentum.

_{x}≥h/Δ_{x}It is only owing to the uncertainty principle that the emission and absorption of a virtual photon by a free electron and other analogous processes are possible. It is only necessary that the total process of emission and absorption take place in a sufficiently short time, so that the “violation” of the law of the conservation of energy connected with it is encompassed by the uncertainty relation. The laws of the conservation of electric charge and certain other characteristics of microparticles (baryon charge, lepton charge) for such virtual processes are rigidly satisfied.

These facts can also be interpreted in a different way. Namely, we can assume that energy is conserved even in processes that take place in times as short as desired, but the usual relation of a particle’s kinetic energy to its momentum and mass, *E = p ^{2}/2m_{0}*, is violated; at high velocities, the corresponding relativistic relation

*E*is violated. Both points of view are essentially equivalent. How-ever, in the development of the mathematical apparatus of quantum field theory, the second point of view is preferable.

^{2}= c^{2}p^{2}+c^{4}m^{2}_{0}The interaction of ordinary, real particles in the overwhelming majority of cases takes place by means of the emission and absorption (exchange) of virtual particles. The energy and momentum of real particles before and after the reaction remain invariable, and, during the reaction, the laws of the conservation of these quantities are not satisfied. The entire theory is so constructed that any reaction can be rep-resented as the result of different virtual processes that proceed during the short reaction time.

Besides the exchange of virtual particles, a large role in the theory is played by the formation of virtual particles upon absorption of a single real particle by another real particle. For example, the Compton effect, that is, the process of the scattering of a photon by an electron, proceeds mainly owing to the following mechanism: first, the photon is absorbed by the electron forming a virtual electron, and then this virtual electron again breaks down into a real electron and real photon, which have other directions of motion and energy, that is, are scattered.

Although virtual particles differ from real particles in the fact that they do not satisfy the ordinary relation between energy and momentum (because of which they cannot be detected separately by an elementary-particle counter or other similar devices, which are always classical instruments), there is no sufficient grounds to consider them nonexistent. Physicists have renounced the classical continuous Faraday-Maxwell field as not corresponding to reality. Consequently, if it is assumed that the appearance of virtual particles in theory is only a consequence of approxi-mate computational methods (there is also such a point of view), then we inevitably return to the theory of the particle interaction at a distance without any intermediary. However, science rejected a similar formulation of a long-range theory a long time ago.

G. IA. MIAKISHEV