A particle physicist's view of virtual particles (with which I agree) ------------------------------------------------ Hendrik van Hees http://theorie.physik.uni-giessen.de/~hees/ wrote in an article from March 24, 2010 in sci.physics.research: I think the trouble with "virtual particles" is again just a mystification of rather simple facts. The problem is to speak in plain (English) language about things one cannot express in plain language but has to use mathematics. Another complication is, that this mathematics is quite dirty, but we have nothing better in physics than quantum (gauge) field theory, and in fact it's the best kind of theories we have so far. The Stueckelberg-Feynman trick is in fact no trick but a necessary mathematical construction, given the fact that (by definition!) physics deals with causal descriptions of nature, i.e., for any observer an observable fact "now" can depend only on events in his "past". That's also inherent in the very definition of time. So it doesn't make sense to have "particles" running backwards in time. That's why I wrote "modes of negative frequency" and not "plane-wave functions of negative energy" as is sometimes done even in textbooks, adding to the confusion rather than helping with the understanding. This forces us to write these modes with a creation operator instead of an annihilation operator in the expansion of the field operator. Nothing could be simpler than this! However, it makes relativistic "vacuum QFT" manifestly different (and more complicated) than non-relativistic "vacuum QFT". Solving these difficulties in turn solves a nearly one century old obstacle of classical field theory (i.e., Maxwell-Lorentz electromagnetics), namely the question of the back reaction of a particle's own electromagnetic field on its (accelerated) motion (at least in a perturbation- theoretical sense, and I only talk about interacting field theories in the perturbative sense in this posting!). The particle simply gets a self energy with a diverging mass and a diverging renormalization factor of the corresponding single-particle state. That these infinities appear in perturbation theory is no big surprise anymore nowadays, but was a bit obstacle in the early 30ies when QFT has been invented by Pauli, Born, Jordan, and Dirac. The solution came in 1948 with the discovery of renormalization theory (which was developed in full glory only in the mid 60ies or so with the works of Bogoliubov+Parasiuk, Hepp, and Zimmermann with their famous BPHZ formalism). Although it's not a very easy task in the concrete calculations, the physical meaning is simple. In perturbation theory, everything is expanded in terms of free-particle states. In QED that means that at 0th order perturbation theory there are non-interacting electrons and non-interacting photons. This already shows that this is a men-made construct and not a description of what we observe in nature! Particularly the electron in this order has no electromagnetic field around it and in the same way the photon (i.e., the elementary electromagnetic excitations) have no electron-positron cloud around it. Thus, one speaks (in the usual funny slang of QFT physicists) about "bare particles" and/or "bare fields". Now, taking into account the electromagnetic interaction, we calculate things with a "point of view" (technically speaking we formulate the theory in a free-particle Fock basis) which handles fictitious objects, namely the bare particles and bare fields. In reality, these objects don't exist. Thus, order by order perturbation theory, we have to construct the Fock basis of the real-particle/fields states, and this is done by expressing everything in terms of physical parameters (like wave-function normalization factors, masses and coupling constants), approximated in the sense of perturbation theory (which is formally an expansion in the coupling constant and/or \hbar). These parameters are perfectly finite and can be adjusted by observable facts. Fortunately there's a class of QFTs, called Dyson-renormalizable, where there's a finite number coupling and mass parameters which is sufficient to absorb all infinities of perturbation theory, i.e., the model has only a finite number of parameters. I don't speak about the other case, namely "effective theories" that are not renormalizable in the Dyson sense but can be used in a certain (mostly low-) energy range and are expansions with respect to powers in energy/momentum rather than in terms of coupling constants/hbar (although both expansions are closely related, which makes these theories very useful, like in chiral perturbation theory to describe the low-energy behavior of strongly interacting particles in terms of the hadronic "relevant" degrees of freedom rather than with quarks and gluons, which makes the issue of hadron interactions a very complicated matter). Another fortunate property of the perturbative expansion of interacting QFTs is that everything can be expressed in a *formal* diagrammatical way, invented first by Feynman. He presented this diagram technique to his astonished theory colleagues at the famous Shelter-Island conference. Nowadays this technique is nearly an own special subject in theoretical physics and far developed, particularly it's also applied in a much wider range of applications, particularly in many-body QT (be it non-relativistic of relativistic) in and out off equilibrium. Here, I stick to the special case of the "vacuum theory", dealing with a small number of particles (usually two in the initial and a few in the final state of a collision process). The original Feynman diagrams stand for terms in the perturbative expansion of scattering-matrix elements. This said, it is clear that one should not put too much physical interpretation into them although they are very intuitive, if one keeps their abstract meaning in mind, and S- matrix elements are pretty abstract objects. They are the probability amplitudes for the transition of an asymptotically free initial state (usually two particles which are prepared far away from each other with well-adjusted momenta (and sometimes also spin/polarization)) to an asymptotically free final state (whatever one decides to detect after the collision about the then approximately freely streaming reaction products). These kind of Feynman diagrams lead indeed to observable quantitities, namely these transition-probability rates which are usually expressed in terms of a cross section. The Feynman diagrams themselves are built out of elementary Feynman diagrams which stand for the bare-particle propagators (lines connecting two points, where the particle or antiparticle is created and reabsorbed again) and the interaction points where three or more lines meet at a space-time point where "a perturbation" occurs in the sense of perturbation theory. This also shows that the number of vertices in a diagram counts the number of coupling constants in the mathematical expression of the corresponding contribution to the S-matrix element. Unfortunately the internal propagator lines are also called "virtual particles" in the funny jargon of QFT physicists, and this gives all the trouble we are discussing about, but the words "virtual particles" in fact have no other meaning than that given by the mathematical expressions. It stands for a propagator of bare particles no more no less. A bare-particle propagator is of course not observable in principle since we cannot do experiments with bare particles/fields, because these are fictitous inventions of the human mind to organize the perturbation series! What is observable in principle are the properties of single real particles, meaning in a more accurate language, single-particle states for real particles. The properties of the single-particle states can be reconstructed from the full two-point Green's function which can also be calculated with the Feynman-diagram technique. Again, each Feynman diagram stands for a certain correction term to the bare propagator no more no less, and one has to ask what is observable. A single-particle state is characterized by some set of compatible observables, e.g., momentum and spin states. If it comes to asymptotically free (stable or quasi-stable) particles, there's also a relation between energy and momentum, and this is observable in principle (in case of a stable particle, it's a strict relation omega=omeg(\vec{p}), in the case of an unstable but long-lived single- particle excitation it's the spectral function). The spectral function is given by the imaginary part of the full propagator. Approximately (for not too broad spectral functions) the spectral function is characterized by the possition of the mass peak and its width, which in turn are given by the poles of the propagators in the complex energy plane, and this is what is observable in principle (e.g., looking at elastic pion-nucleon scattering one observes a strong resonance, called Delta(1232) or lepton scattering giving the W- and Z-boson peaks from weak interaction etc.). The notion of virtual particles doesn't play a big role in the interpretation of QFTs, it's only part of a convenient jargon of experts. Unfortunately in many attempts to popularize this fascinating theory by crude simplifications about the meaning of Feynman diagrams "virtual particles" are made to something intuitively "real", and that's imho a big didactical mistake. One shouldn't speak about the theory in these terms. To popularize particle physics it's much wiser to concentrate on phenomenology, i.e., the observable facts about particles rather than to chat about highly specialized theories which are not suitable for popularization since the real meaning of the abstract objects (including Feynman diagrams, as I hope to have made clear above) is incomprehensible without the appropriate training in theoretical physics (that's why relativistic QFT is taught only in higher semesters for physics majors, and renormalization theory and all that perhaps even only at graduate-student level). What one can popularize, however, is the general world view which follows from the application of quantum theory to real phenomena, but for that one shouldn't (and doesn't need to) talk about "virtual particles"!