dear Kish see this link

http://en.wikipedia.org/wiki/Virtual_particle

In a way the concept of virtual particles appears to be clear. These entities are represented by the inner lines of Feynman diagrams and they do not obey the relativistic energy-momentum relation. That is a clear definition.

A relation to the matter/antimatter distinction does not exist.

However, it appears to be a very good question whether virtual particles actually "exist" i.e. if they play a causal role. There is the common talk about virtual particles beeing exchanged and thus mediating interactions. This view was critizied e.g. by Mario Bunge (1970) in his „Virtual Processes and Virtual Particles: Real or Fictitious?”, International Journal for Theoretical Physics, Vol. 3, No. 6, 507-508. A rather forceful argument to the same effect was given by Weingard  in his „Virtual Particles and the Interpretation of Quantum Field Theory“, in: H. R. Brown und R. Harré (Hrsg.) „Philosophical Foundations of Quantum Field Theory” 1988, Oxford: OUP. Weingards bottom line is, that virtual particles are an artifact of perturbation theory only.

There exist two views:

I thought virtual particles were characterized by not   necessarily obeying Heisenberg's uncertainty relation?

It is supposed that we cannot see them, because the needed time is infinitesimal Δt->dt and we have not the tools for it... (It is not my opinion)

Dear Oliver, if virtual particles did not exist, a new concept would be required to explain effects based on the virtual particle existence, such as Casimir effect, Lamb shift, Hawking radiation, interaction between particles, etc.

As far as I know, each of these effects can be explained without reference to virtual particles, even though the virtual particles approach certainly has a big appeal, as it unifies all these phenomena, whereas the other approaches might look unrelated.

The Casimir effect is essentially the same as the van der Waals force. It vanishes in the limit of vanishing fine structure constant, whereas the virtual particles of the vacuum would continue to "exist". Hence the Casimir effect can be explained independently of vacuum fluctuations. I have also seen explanations of the Hawking radiation that do not refer to virtual particles. About the Lamb shift I am unsure, but I believe it is explicable without virtual particles within stochastic electrodynamics. As to the interaction between particles, the virtual particles are just a way to visualize it, based on perturbation theory -- the interaction could be thought of as entirely due to a field (without invoking any particles directly).

Dear Zoltan,

my point is actually more modest (Iet's say: I try to be no crackpot). I am happy with QED explaining Lamb-shift, Casimireffect and so on. However, the (agreed fuzzy) notion of existence is a different business.

In fact we are talking here about terms in a superposition. Recall that the observable xsection is essentially the square of the scattering matrix element, which (the matrix element) might be calculated as a perturbative series. A similar situation occurs in QM when you describe the infamous two-slit experiment. Let's psi_1 and psi_2 be the contributions of the electron beam passing through slit 1 and 2. The oberservable pattern is given by |psi_1+psi_s|**2. Can you interpret the single terms in this superposition "realistically"? Certainly not -- the electron did not pass through one of the slits following a trajectory (leaving QM debates aside). The same argument applies in the virtual paricle argument. In fact: you do not even need to invoke QM. A decomposition of an oszilation into harmonics is a similar example. 

You see the point: terms in a superposition might be pure calculation devices for a description of the entity which is composed out of them.  This is how I understand Weingard. By the way: if somebody guesses matrix elements from symmetry-arguments alone she never deals with virtual particles. Perturbation theory is a special tool only.

The difference is rather formal. Real particles are situated on the mass shell, i.e. their 4-vector of momentum satisfies the rule p^2=-m^2 where m is the rest mass. For virtual particles this equality is not true. 

Yes, the only difference is that for a real, and free let me add, particle the difference between the squares of the energy and of the momentum is equal to the square of the mass (in natural units) (why "rest" mass, mass is an invariant does not depend on speed). E^2–p^2=m^2. This is not true for virtual particles. As observed by Peter

Let me just recall that there are cases in which it is even meaningless to distinguish the two cases. Consider for example the reaction e+ e– -> mu+ mu– in a collider like LEP. At the first order  two Feynman diagrams contribute. 1. the electron and the positron annihilate in a photon that soon origins the mu+ mu– pair in the final state. 2. same with a Z in place of the photon. For the largest fraction of energies both are virtual. But we can tune the machine with its centre of mass energy equal to the mass of the zed. The intermediate zed is then on the mass shell, hence it is real. However, the mass of the zed is not a unique value, but rather its values are distributed on a probability curve that has a definite width (the inverse of the lifetime). So that by varying the machine energy one can change smoothly from "very virtual" to "quasi real" to "real" to "virtual again", you name them. There is no sharp difference.

On the other hand, I assume that the photon would be “real” if its state satisfied on the mass shell equation E^2=|p|^2, because the photon “rest” mass is zero.

Yes, Zoltan, correct, a part the world "rest". "It implies that mas depends on velocity (which is never zero for a photon btw. When a photon can be at rest?). That is the wrong concept of "relativistic mass", namely m gamma c^2, where gamma is the Lorentz factor. The relativistic mass is not else than the energy (m gamma) multiplied by c^2. It is the fourth component of a four vector in space-time. The mass is instead a scalar in space time, namely invariant under Lorentz transformation, independent on velocity

For Real particles: E^2 - (pc)^2 > 0  

For photon particles: E^2 - (pc)^2 = 0 

For Vertual particles: E^2 - (pc)^2  < 0  

Ramanand

 not correct

For Real particles: E^2 - (pc)^2 =(mc^2)^2 >0. Each particle has a definite value of the mass m

For real photon particles: E^2 - (pc)^2 = 0

For Virtual particles: E^2 - (pc)^2 ≠ (mc^2)^2 , can be >0 =0 or

According to the quadratic E^2 - (pc)^2 =(mc^2)^2 and E^2 - (pc)^2 = 0 equations, the energy (E) can have positive and negative values for particles and photons. However, the negative energy value was not detected for real particles, but the same time, it is assumed that one component of virtual particle pair has negative energy value to explain the Hawking radiation. In this case, virtual photons and real particles could have negative energy value.

Dirac-Equation (the relativistic generalization of Schrodinger's equation) Interprets Positron as a hole in negative energy state; which is observable.

Dear Ramanand, as I know, the positron, as a “real” particle, does not have negative energy value. It is the antimatter counterpart of the electron. Antimatter (“real”) carries positive energy and mass, just like regular matter. The positron differs from the electron by their electric charge. The positron has an opposite electric charge (+1e) than an electron (-1e).

Dear Zoltan, ‘virtual particles’ refer to internal lines in Feynman diagrams, which stand for certain transition amplitudes within an S matrix formalism. Mathematically, ‘virtual particles’ result from interchanging annihilation and creation operators during the evaluation of products of field operators. These commutators are essentially delta functions of a momentum difference and delta functions are certainly not particles. Therefore, the notion ‘virtual particle’ is grossly misleading, but we have to live with it: It is the suggestive power of the Feynman diagrams that causes the association of the internal lines with some kind of ‘intermediate particles’.

Unfortunately, a lot of nonsense can be found in the literature about ‘virtual particles’ in useless attempts to give a mathematically well-defined notion a ‘physical meaning’. This has led to senseless ideas of virtual particles that pop in and out of existence, to ‘off-shell’ particles and to a ‘physical vacuum' that is full of virtual particle-antiparticle pairs.

In Feynman’s seminal papers of 1949/50 on quantum electrodynamics you can find the details of the S matrix formalism, especially of the role of ‘virtual photons’. In short, in Feynman’s formulation ‘real photons’ are ‘virtual quanta’ that are ‘exchanged’ over a large distance, so that they can be observed as individual quanta in a detector. The answer to the question whether photons are ‘real’ or ‘virtual’ depends on how you define ‘real’.

Thank you for provided answers.

In conclusion, I assume that the virtual particle concept is used as a mathematical expression for the mathematical modeling of interactions between particles. The virtual particles do not have physical meaning and, therefore, do not exist.

People are free to believe the quantum theory they want to believe in. But most of the answers here are narrow. If you learn quantum theory by way of mathematical formalisms, it's easy to imagine that's all they are. However the quantum field is a physical spacetime extension. At each spacetime point the field's amplitude varies, according to Schrodinger's wavefunction. A point amplitude denotes virtual particle existence, while the field is composed of virtual particle superpositions. Because we don't understand how this works doesn't make it less real.

Brian:

"If you learn quantum theory by way of mathematical formalisms, it's easy to imagine that's all they are."

Zoltan's question was about the meaning of 'virtual particles'. This is a notion used within a pertubation algorithm. It is therefore part of a 'mathematical formalism' and has a well-defined mathematical meaning there. It is not something that we ever observed or will observe in a physical experiment. We use the algorithm to describe 'real' experiments, but this does not make the algorithm or parts of it 'real', unless you have some uncommon definition for the word 'real'. 

Dear Zoltan

This an excellent question. In quantum field theory, forces are transmitted by particles, and fields are associated with particles which transmit the forces. The particles of the electromagnetic field are the photons. In quantum electrodynamics all electromagnetic fields are associated with photons, and the interaction between the charged particles occurs when one charged particle emits a virtual photon that is then absorbed by another charged particle. The photon has to be a virtual photon, because emission of a real photon would violate energy and momentum conservation. If, for example, an electron initially at rest emitted a photon, the final state would consist of an electron and a photon moving off in opposite directions, a configuration which necessarily has more energy than the initial at-rest electron. But the uncertainty principle prevents a contradiction.

http://electron6.phys.utk.edu/phys250/modules/module%206/standard_model.htm

Zero-point energy, also called quantum vacuum zero-point energy, is the lowest possible energy that a quantum mechanical physical system may have; it is the energy of its ground state. All quantum mechanical systems undergo fluctuations even in their ground state and have associated zero-point energy, a consequence of their wave-like nature. The uncertainty principle requires every physical system to have a zero-point energy greater than the minimum of its classical potential as well. This results in motion even at absolute zero. If the zero point energy in space (vacuum) exists, how can we explain the zero-point energy without using the uncertainty principle?

If we carefully review a pair production and decay and the results of high energy particle collisions, from the relation E= mc2 this question will be raised whether in addition to being convertible of energy into mass and vice versa, the other concepts can be derived as well. Are there common rules in the energy structure and elementary particles? If we continue to believe that in the Standard Model, elementary particles are point particles and unstructured, we cannot resolve ambiguities in modern physics. This is our attempt to answer these questions. See following articles:

https://www.researchgate.net/publication/279288309_Graviton_and_virtual_photons?ev=prf_pub

https://www.researchgate.net/publication/308890409_Photon-Graviton_Interaction_and_CPH_Theory?ev=prf_pub

Article Graviton and virtual photons

Article Photon-Graviton Interaction and CPH Theory

Real particles = measurable particles in LAB.

Virtual particles = particles which can not be measured directly in LAB and which are used to explain the internal interaction mechanism according to a physical theory.

 Dear Edwin

Sure, but this question arises, how we can describe virtual particles (in a special case virtual photon) indirectly?

Virtual particles in a pair do not separate from each other by more than one wave length. Then the virtual pair quickly recombines into equivalent vacuum energy, but reoccurs just as quickly as the same or different type of virtual pair. A Planck frequency is associated with the virtual pair, and Planck units together with the uncertainty principle govern the occurrences. On average a percentage ( at present about 100%*(14.67 /16) )  of the virtual pairs will have virtual electrical charges and virtual magnetic fields from the oscillating charges, related to the fine structure constant. In other threads I have suggested the virtual energy potentials of mass, gravity, and electromagnetic LC oscillators all are equal in flat space,  It leads to an argument about FLRW metric, in which I suggested the EM component should be changed to weaken gravity as it does in other metrics. Many people disagree. If my version prevails then QFT is reconciled with GR requirement of small net curvature, and dark energy might become unnecessary. Also in QFT the infinities of vacuum energy become finite, but very large, and fully committed to enforcing the physical laws and constants which reside in space.

Real particles separate by more than one wave length, and make real gamma rays when they recombine. The energy has to come from somewhere other than the vacuum, at least in part. Any energy taken from the vacuum is reclaimed by the vacuum in the time allowed by Heisenberg Uncertainty.

Virtual photons are just instances in the vacuum oscillators where no virtual mass potential is instantiated for one or more cycles of the local oscillators. As with virtual particles the virtual photons do not separate by more than one wave length, and quickly recombine with no net change in the local curvature.

Real photons have identical antiphotons and recombine as a scattering of photons in which the directions of spins account for the concept of antiphotons. 

Vacuum oscillators resonate when energy is being conserved and nothing is propagating through them. Any propagation introduces a stress energy component. Like classical oscillators the quantum oscillators change amplitude (or wave length) and frequency under stress, causing departure from resonance, meaning energy is momentarily not conserved, providing a microscopic mechanism for propagation. Each type of propagation introduces a different type of polarization in the vacuum. In the time allowed by Heisenberg uncertainty, the vacuum returns to resonance when the propagating stress energy has departed some distance.

A better understanding of the microscopic vacuum is the key to advancement of space science and transport in deep space at high speed. This is why I ask so many question about the fundamental principles of space.  

As Walter already explained, virtual particles have a well defined meaning as parts of the mathematical expressions appearing in the scattering or decay amplitudes in perturbation theory. In particular, in the Feynman diagrams virtual particles appear as internal lines, real particles as external lines. A factor in the overall mathematical expression corresponds to each line. The complete expression corresponds to a measurable quantity, but this is not the case for each factor separately.

Both virtual and real particles have energy (E), momentum (p) and mass (m). The mass m of a "real" particle is  given by E^2–(pc)^2=(mc^2)^2 [note that E=mc^2 is true ONLY if the particle is at rest; hence it is never true for a photon]. The mass is a fundamental property (like the charge) of a particle type (electron, proton, photon,...). Like the charge it is an invariant, independent of the velocity of the particle. The masses of the (real) particles are non negative quantities (Photon mass is zero).

Virtual particles differ from the real ones because their energy and their momentum do not obey the relation E^2–(pc)^2=(mc^2)^2. In jargon we say that virtual particles are not on the mass-shell.

In quantum electrodynamics (QED), all interactions between charged particles is described with respect to exchange of photons. The photon has to be a virtual photon, because emission of a real photon would violate energy and momentum conservation.

http://electron6.phys.utk.edu/phys250/modules/module%206/standard_model.htm

It should be noted that there is no consensus about virtual particles, some physicists agreed virtual particle exist, and others are believed that they are merely a mathematical bookkeeping device for QED.

http://www.scientificamerican.com/article/are-virtual-particles-rea/

https://plus.maths.org/content/quantum-pictures

In quantum electrodynamics (QED), a charged particle consequently propagates exchange particles containing electromagnetic force. This process does not have any effect on properties of a charged particle like mass and electric charge. How can be justified this phenomena? If a charged particle as a producer (generator) has an output that is known as a virtual photon, then what is its input?

Virtual photons in CPH Theory: there are two types of virtual photons, positive virtual photon (y+) and negative virtual photon (y-) that each of them is formed of number same-sign sub quantum energies.

A real photon is formed of a positive virtual photon and a negative virtual photon:

y=(y+)+(y-)

https://www.researchgate.net/publication/303988070_Generalization_of_the_Dirac%27s_Equation_and_Sea?ev=prf_pub

https://www.researchgate.net/publication/302313653_Adaptive_Review_of_Three_Fundamental_Questions_in_Physics?ev=prf_pub

Article Generalization of the Dirac's Equation and Sea

Article Adaptive Review of Three Fundamental Questions in Physics