Local quantum field theories were the basis of high-energy physics in the XX century. Any such theory postulated some symmetric and covariant expression, which, according to the principle of minimal action, would describe all the variety of physical effects allowed by the model. In earlier days, this model action was used to derive the equations of motion, and a number of exact solutions have been obtained for simple cases. However, many-body equations could never be solved exactly, and approximations were necessary to obtain practically usable results. Many approximate theories have been build in various areas of quantum theory, from atomic physics, to quantum gravity. Those of them that did not introduce any phenomenological elements exploited the same fundamental method, perturbation theory. The perturbational approach splits the full action into two parts, one of them describing a simpler system, with already known physical properties, and the other part being treated as a small correction to "zero-order" behavior, so that the motion of the "perturbed" system could be expanded in a series by the powers of perturbation: in the first order, perturbation couples the elements of the simplified system just once, the second order terms account for the possible double couplings, and so on. When diagrams have been invented as a convenient technique for constructing perturbation series, equations of motion came to almost perfect neglect, as the perturbation series could be reconstructed directly from the action, rather than from any equations. Physicists went in for computing higher-order diagrams, and nobody put much thought to the original strongly coupled theory before distinction between zero-order action and perturbation.

There was a price to pay.

First of all, the perturbation series did not seem to converge in many physically important cases. Infrared and ultraviolet divergences haunted quantum field theory from the very beginning, and many ingenious tricks were invented to overcome this difficulty and obtain final solutions. For most interactions the perturbation part of the action was not small, and the series could only be considered as asymptotic. Physicists learned to "renormalize" the theory up to any given order, removing all the divergences. Perturbation theory has been complemented with renormalization theory, and some expressions for model action have been proven to lead to theories renormalizable to any order—a new criterion of physical sense!

Second, physicists got accustomed to treating approximate solutions as the only true physics, they began to think in perturbational terms and interpret natural phenomena from that only viewpoint. Mathematical tricks were often reformulated in a quasi-physical manner, and artificial constructions seemed a true picture of what really happens. Thus the idea of virtual particles was born.

In any order of perturbation, the expression for the transition amplitude (or any other appropriate quantity, like S-matrix, K-matrix, propagators, evolution operators, density matrix etc.) takes the form that can be formally interpreted as a superposition of all possible transitions from the initial to final state via a sequence of intermediate states, coupled to each other by perturbation. The intermediate states do not need to have the same energy (or any other parameters) as the initial and final states. Therefore, it is only the initial and final states that are considered as physical, in the sense that they have proper symmetry and obey conservation laws; intermediate states may violate physical symmetries and hence they are not observable—that is, virtual. For instance, in atomic scattering, an unbound state of the system target+projectile may have complex resonance structure due to formation of virtual bound states "embedded in continuum". From the perturbational viewpoint, this is interpreted as temporary formation of a single particle from two particles (target and projectile), with subsequent dissociation into the original (or some other) set of particles. That is, the number of particles in the system may change from physical to virtual states and between virtual states. In quantum field theory, the same technique applied to gauge fields (electromagnetic fields first of all, in quantum electrodynamics) lead to the picturesque idea of massive particles born by fields and annihilating back into vacuum. This picture of particles popping out "from nothing" and disappearing "into nothing" is obviously appealing to idealistic philosophers and theologians, since it gives enough room for spiritualism in-between the virtual particle births. The apparent violation of causality in the virtual states is easy to attribute to the will of some deity, or some existential abstraction of consciousness.

But virtual particles are not real. They are nothing but an artifact of a particular computation technique. Yes, they help to solve complex physical problems and obtain practically acceptable results. However, the same results can be obtained differently. For instance, perturbation theory involves summation (integration) over all the intermediate states; it is assumed that they form a complete set. It is well known, that one can always choose a different basis set for such a summation, which won't influence any physical results. For instance, there are mathematical tricks that allow to replace a continuous specter of intermediate states with a discrete set (Sturmian expansions); such intermediate states can hardly be interpreted in terms of any physical fields or particles. This illustrates the absurdity of putting too much confidence in the vulgar descriptions of physical models. Such figurative descriptions are necessary to visualize abstract mathematical procedures, thus making them more tractable; however, they do not necessarily correspond to any physical reality—no more than the complex conglomeration of rods and wheels invented by Maxwell to visualize his theory of electromagnetism.

Using non-perturbative techniques for solving the equations of motion, we can obtain the same complex structure as in perturbation theory, but with no need for intermediate states or particles. This approach is physically attractive, and it is indeed employed in atomic and chemical physics ("close coupling" schemes). Unfortunately, we cannot even derive the equations of motion in some cases, and it would be almost impossible to directly solve them for many-body systems with variable number of particles. That is why we need perturbational methods, but as a computation tool rather than the language of explanation.

While the picture of virtual particles as independent entities is basically unphysical, there is a more adequate idea applicable to description of complex structure formation in physical systems—collective effects. It is well known that the motion of nonlinear media can exhibit various structures existing for a long time, and finally dissipating (like phonons, solitons etc.). In this view, resonance structures observed in quantum physics can be explained as quasi-stable collective modes of motion in many-body systems. The system moves as if there were virtual particles or states, though this resemblance can never be complete. Quantum states are determined for the whole system, and they evolve according to the system's equations of motion; however, for some time, the structure of the state can resemble a collection of distinct particles coupled by relatively weak interactions. When the lifetime of such dynamic formations is much less than the characteristic time of system evolution, we speak about virtual particles. While external fields are weak compared to the system's inner interactions, they do not resolve individual "virtual" structures, and all we see is their combined effect (resonances). However, a strong external field can penetrate a virtual structure, transforming it into an observable entity. For instance, a drop-like bulge can be formed at the mouth of a water tube; it may vibrate, or change its size and shape for some time, still joined to the rest of the water in the tube—then gravity or mechanical shock will complete the formation of a falling drop. In this sense, one can say that virtual structures are incomplete structures, or quasi-structures. Obviously, their incompleteness is in their relation to the whole: virtual structures are always substructures of something more complete. In physics, we usually deal with well-defined systems, which can be deemed to be structurally complete; their substructures will, in general, be virtual. However, in a wider scope, any existing structure can only exist within the same and only world, and every thing can be considered as virtual in certain respects, unless one can forget, for some time, about its being linked to the rest of the world.