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How real are 'virtual particles'?
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Virtual particles are used in perturbation theory with
Feynman diagrams. (See the FAQ entry ''Why Feynman diagrams''
for an explanation of their meaning. They do _not_ describe
processes in space and time, but certain multiple integrals...)
Feynman diagrams change their nature depending on the way
one does perturbation theory and what is resummed.
In their treatise on QED, Landau and Lifshitz discuss virtual particles
in Section 79. They start at the outset with the remark that things
depend on which kind of perturbation theory is used, and contrast
'virtual' explicitly with 'real'. Virtual particles are called that
in contrast to 'real particles' which are observable and hence real.
Unlike the latter, virtual particles occuring in computations _must_
have disappeared from the formulas by the time the calculations lead
to something that can be compared with experiment.
Whence their 'reality' if there is any is like the reality of
characters in a dream. For example, just as we can fly in a dream,
virtual particles can be faster than light (since they may have
imaginary mass)...
The issue is somewhat controversial since there is no unambiguous
understanding of what being real means. For some of this controversial
discussion, see the thread ''Are virtual particles really there?''
on the Physics Forum at
http://www.physicsforums.com/showthread.php?t=75307 (from 2010)
and a related thread at
http://www.physicsforums.com/showthread.php?t=44616 (from 2004)
The following is a more detailed discussion of the question how
meaningful it is to ascribe some sort of reality to virtual particles.
All language is only an approximation to reality, which simply is.
But to do science we need to classify the aspects of reality
that appear to have more permanence, and consider them as real.
Nevertheless, all concepts, including 'real' have a fuzziness
about them, unless they are phrased in terms of rigorous mathematical
models (in which case they don't apply to reality itself but only to
a model of reality).
In the informal way I use the notion, 'real' in theoretical physics
means a concept or object that
- is independent of the computational scheme used to extract information
from a theory,
- has a reasonably well-defined and consistent formal basis
- does not give rise to misleading intuition.
This does not give a clear definition of 'real', of course.
But it makes for example charge distributions, inputs and outputs of
(theoretical models of) scattering experiments, and quarks something
real, while making bare particles and virtual particles artifacts of
perturbation theory.
Quarks must be considered real because one cannot dispense with them
in any coherent explanation of high energy physics.
Virtual particles must not be considered real since they arise only in
a particular approach to high energy physics - perturbation theory
before renormalization - that does not even survive the modifications
needed to remove the infinities. Moreover, the virtual particle content
of a real state depends so much on the details of the computational
scheme (canonical or light front quantization, standard or
renormalization group enhances perturbation theory, etc.) that
calling virtual particles real would produce a very weird picture of
reality.
Whenever we observe a system we make a number of idealizations
that serve to identify the objects in reality with the
mathematical concepts we are using to describe them. Then we calculate
something, and at the end we retranslate it into reality. If our initial
initialization was good enough and our theory is good enough, the final
result will match reality well. Because of this idealization,
'real' real particles (moving in the universe) are slightly different
from 'mathematical' real particles (figuring in equations).
Modern quantum electrodynamics and other field theories are based on
the theory developed for modeling scattering events.
Scattering events take a very short time compared to the
lifetime of the objects involved before and after the event. Therefore,
we represent a prepared beam of particles hitting a target as a single
particle hitting another single particle, and whenever this in fact
happens, we observe end products, e.g. in a wire chamber.
Strictly speaking (i.e., in a fuller model of reality), we'd have to
use a multiparticle (statistical mechanics) setting, but this is never
done since it does not give better information and the added
complications are formidable.
As long as we prepare the particles long (compared to the scattering
time) before they scatter and observe them long enough afterwards,
they behave essentially as in and out states, respectively.
(They are not quite free, because of the electromagnetic self-field
they generate, this gives rise to the infrared problem in quantum
electrodynamics and can be corrected by using coherent states.)
The preparation and detection of the particles is outside this model,
since it would produce only minute corrections to the scattering event.
But to treat it would require to increase the system to include source
and detector, which makes the problem completely different.
Therefore at the level appropriate to a scattering event, the 'real'
real particles are modeled by 'mathematical' in/out states, which
therefore are also called 'real'. On the other hand, 'mathematical'
virtual particles have nothing to do with observations, hence have no
counterpart in reality; therefore they are called 'virtual'.
The figurative virtual objects in QFT are there only because of the
well-known limitations of the foundations of QFT. In a nonperturbative
setting they wouldn't occur at all. (Indeed, they do not exist in
lattice gauge theory, which is a nonperturbative approximation method.
They also do not exist in exactlty solvable 2-dimensional conformal
field theories, although their perturbation theory also produces the
same sort of feynman diagrams as QED in 4 dimensions.)
This can be seen most clearly by comparing with ordinary quantum
mechanics. One could also do nonrelativistic quantum mechanics with
virtual objects but no one does so (except sometimes in motivations
for QFT), because it does not add value to a well-understood theory.
Virtual particles are an artifact of perturbation theory that
give an intuitive (but if taken too far, misleading) interpretation
for Feynman diagrams. More precisely, a virtual photon, say,
is an internal photon line in one of the Feynman diagrams. But there
is nothing real associated with it. Detectable photons are never
virtual, but always real, 'dressed' photons.
Virtual particles, and the Feynman diagrams they appear in,
are just a visual tool of keeping track of the different terms
in a formal expansion of scattering amplitudes into multi-dimensional
integrals involving multiple propaators - the momenta of the virtual
particles represent the integration variables.
They have no meaning at all outside these integrals.
They get out of mathematical existence once one changes the
formula for computing a scattering amplitude.
Therefore virtual particles are essentially analogous to virtual
integers k obtained by computing
log(1-x) = sum_k x^k/k
by expansion into a Taylor series. Since we can compute the
logarithm in many other ways, it is ridiculous to attach to
k any intrinsic meaning. But ...
... in QFT, we have no good ways to compute scattering amplitudes
without at least some form of expansion (unless we only use the
lowest order of some approximation method), which makes
virtual particles look a little more real. But the analogy
to the Taylor series shows that it's best not to look at them
that way. (For a very informal view of quantum electrodynamics in
terms of clouds of virtual particles see
http://groups.google.com/groups?selm=3EBBE37C.4D771C4B%40univie.ac.at
and the later mails in this thread.)
A sign of the irreality of virtual particles is the fact that
when one does partial resummations of diagrams (which is essential for
renormalization), many of the virtual particles disappear.
A fully nonperturbative theory would sum everything, and no virtual
particles would be present anymore. Thus virtual particles are
entirely a consequence of looking at QFT in a perturbative way
rather than nonperturbatively.
In the standard covariant Feynman approach, energy (cp_0) and
momentum (\p; the backslash indicates 'boldface') is conserved,
and virtual particles are typically off-shell (i.e., they
do not satisfy the equation p^2 = p_0^2 - \p^2 = m^2 for physical
particles). To see this, try to model a vertex in which an electron
(mass m_e) absorbs a photon (mass 0). One cannot keep the incoming
electron and photon and the outgoing photon on-shell (satisfying
p^2 = m^2) without violating the energy-momentum balance.
However, many physicists work in light front quantization.
There one keeps all particles on-shell, and instead has energy and
momentum nonconservation (removed formally by adding an additional
'spurion').
The effect of this is that the virtual particle structure of the
theory is changed completely: For example, the physical vacuum and
the bare vacuum now agree, while in the standard approach,
the vacuum looks like a highly complicated
medium made up from infinitely many bare particles....
But bare particles must still be dressed to become physical,
though less heavily than in the traditional Feynman approach.
Another group of physicists calculate consequences of the standard
model using quantization on a lattice.
Here virtual particles are completely absent.
Clearly concepts such as virtual particles that depend so much
on the method of quantization cannot be regarded as being real.
Of course, physicists would not talk of virtual particles if the concept
had no relevance at all. One can argue with virtual particles to get an
intuitive idea of 'dressing', and to gain in this way some
understanding of phenomena such as the Casmir effect, Rabi
oscillations, the Lamb shift, anomalous magnetic moments, etc.
From a nonperturbative point of view, these effects all show up as
a consequence of renormalized, effective interactions between
physical (dressed, on-shell) particles.
However, these virtual particles do not live in space and time,
and are not created and annihilated somewhere or sometime.
They occur in the interpretation of expressions for scattering
amplitudes that have meaning only at infinitely long times,
and describe the cumulative long-time transition behavior of
_real_ particles (asymptotic states). A description in time would
require a time-resolved version of quantum field theory which hasn't
been developed so far.
See also earlier discussions on s.p.r. such as
http://www.lns.cornell.edu/spr/2003-06/msg0051674.html
also
http://www.lns.cornell.edu/spr/1999-02/msg0014762.html
and followups; maybe
http://www.lns.cornell.edu/spr/2003-05/msg0051023.html
is also of interest.
[For a longwinded alternative view of virtual particles
that I do _not_ share but rather find misleading, see
http://www.desy.de/user/projects/Physics/Quantum/virtual_particles.html]