## Monday, 28 April 2014

### Do Virtual particles exist

Well been having a ding dong with my bete noir on the physics forums about whether or not virtual particles exist. In my opinion they don't but unfortunately the popular physics literature abounds with such ideas and so the myth is generated that they actually do exist.

A really good overview of why they can't really be said to exist is given here

http://www.mat.univie.ac.at/~neum/physfaq/topics/virtual

I'll just summarise the salient points

What do we mean by a virtual particle ? Let's start by describing what they are not they are not tempory resonances detected at places like CERN those are real particles.

A virtual particle is one which is said to be exchanged during a particle interaction, the story goes because of the Uncertainty principle applied to energy and time.

$$dE dT >= \frac{h}{2\pi}$$

In a particle interaction there is the possibility of a temporal violation of the conservation of energy and so a particle can be formed which then gets immediately absorbed by the other particle.

The classic example is QED where electrons are said to exchange a virtual photon between them when they scatter off each other. And because of the uncertainty principle a positron can be seen equivalent to an electron moving backwards in time. Those phrases should be enough to raise the suspicions of any one who seeks a rational basis for physics. It's all a bit of fudge really.

The whole idea of virtual particle exchange particles is an artefact of the use of Feynman diagrams. A Feynman diagram is a term in a perturbation series expansion because we have no other tool to calculate
with. Essentially in quantum field theory one has a set of propagaters (Green Functions) representing the free particles and  a set of vertices to represent the interaction between them..  A Feynaman diagram is essentially a graphical representation of a complicated mathematical expression representing the interaction.

The simplest are the Tree diagrams essentially an H combined by putting two vertices together. This gives a second order contribution to the scattering process the external legs of the H represent the electron or other particle and the internal line represents the 'exchanged photon' But the internal line can also split to give more complicated diagrams involving loops such as ----O--- or even ----O-----O---- that would be the virtual photon dissociating into an electron and a positron and recombining to form a photon and so forth.

The total contribution to a Feynman diagram expansion is a sum over all possible diagrams the contribution to which decreases as the number of loops increases. Whilst the Feynman diagram expansion is intuitive it should be stressed we are not talking about actual processes. If we were then the infinite series would have to be summed up. As a literal interpretation that would mean that in each particle interaction there would be an infinite number of processes that occur and so the interaction could just not happen.

So a virtual particle is simply an internal line in a Feynman diagram nothing more, it is an artefact of the need to use perturbation theory and so cannot be real. Yes electrons and photons interact with each other and yes the use of Feynman diagrams gives rise to some of the most accurate results in physics for at least QED anyway. But I do find it worrying that what is essentially a metaphor is taken literally, a bit like fundamentalist religion I guess. Hopefully sooner rather than later someone will find a way to solve Quantum Field theory non-perturbatively and the Feynman picture will vanish until that day however we are stuck with it.