Yet another particle physicist's view and my comments
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The particle physicist Michael Peskin, coauthor of a well-known 
text book on quantum field theory, apparently sends a canned answer 
to everyone asking by email about virtual particles; see, e.g., 
#55 of
   http://www.physicsforums.com/showthread.php?t=75307&page=10 

Let me just comment what he says; Peskin's parts are indicated by a 
leading >.


> I am not sure what you mean by "fictitous".

This seems to refer to the question being answered; he says that the 
question was vague because the word ''ficticious'' has no definite 
meaning; so he cannot be sure what is meant. Therefore he now explains
what the meaning of real could be, so that you can make your choice
about what you should believe.

> Light gives a good example.  Light is part of electromagnetism.  
> It is carried by photons, individual particles that move from place 
> to place at the speed of light.  Photons can be created and detected 
> individually, so I assume that you consider them "real".

They are commonly regarded as real, detectable by a click of 
photodetectors. So he asks for agreement on this concept of reality.


> Another part of electromagnetism is the Coulomb potential. 
> A negative charge is attracted to a positive charge at a distance.  
> In elementary physics, we say that the positive charge sets up an 
> electric field, and the negative charge experiences a force when it 
> interacts with this electric field.  The positive charge receives an 
> equal and opposite reaction force. In quantum theory, the interaction 
> of a quantum particle (e.g. an electron) with the Coulomb field 
> extracts a definite quantum of momentum from the positive charge and 
> transfers it to the negative charge.  To describe this transfer of 
> momentum, we say that a "virtual photon" passes between the positive 
> charge and the electron.

Here he gives his definition of how he uses the term virtual particle.

Note that he assumes that the speaker is a layman, since the picture he 
gives is valid only in a certain simplified view (the tree approximation
of scattering theory). There are ways to set up the theory that the 
Coulomb potential appears as part of the Hamiltonian; then it is _not_ 
mediated by virtual photons. This is the reason why the meaning of 
virtual photons depends on the approach taken to analyze the problem, 
and why it doesn't make much sense to ascribe these virtual photons a 
reality comparable to the reality of ordinary photons. This is also 
reflected in the name ''virtual''.


> The virtual photon carries
> 
>          Energy  <   (momentum) x c
> 
> so formally it has negative mass. 

Here Peskin makes an unintended mistake; formally it has imaginary mass,
since the formula he has in mind is
    Energy^2 = (mass x c^2)^2 + (momentum x c)^2
(Usually, one uses units where c=1; then this equation reads 
E^2=n^2+p^2, which you can find in many textbooks.)

The mistake shows that he is talking lightly, to someone whom he doesn't
expect to follow formal arguments closely - so that the formal 
difference between negative mass and imaginary mass doesn't count.
In any case, he tells that these virtual photons have strange 
properties that ordinarily would disqualify them from being real.


> There is even a sense in which it is transferred instantaneously or 
> even goes backward in time, although other electrodynamic effects 
> add to this one so that there is no violation of causality.

Here he gives more of these strange properties.


> The virtual photon is not a real particle, but it is certainly real, 
> in the sense that the electron really does change its momentum in 
> the encounter.

This sentence sounds like a contradiction in itself, but actually he is 
here using 'real' in three different meanings. In more explicit words, 
he says that ''The virtual photon is not a real particle'' in the sense 
of real he had defined before (the measurable photon traveling with the 
speed of light c) ''but it is certainly real'' in a different sense, 
namely ''in the sense that the electron really'' (i.e., in an observable
sense, i.e., analogous to the measurable photon) ''does change its 
momentum in the encounter''.

In other words, while the virtual photon is not ''real'' in the agreed 
sense of measurability, its effect on the electron is ''real''.


> I hope that this makes the nature of a "virtual particle" clearer.  

Namely that whether it is real depends on which sort of definition of
the concept of real you have. If 'real'' means measurable, a virtual 
particle is not real; but if ''real'' only means that it is used 
figuratively to illustrate a different, measurable effect then a 
virtual particle is real.


> To learn more, I recommend the beautiful book by Richard Feynman: 
> QED, the Strange Theory of Light and Matter (Princeton U. Press, 
> 1988).

Here he refers the person asking to a source where one can learn more
(still on laymen's level, but leading to a deeper understanding of what 
goes on). He completely avoided to address the deeper (but abstract) 
level on which quantum theory makes sense without all the strangeness 
that accompanies the attempts to make the quantum world visually 
accessible to laymen.