Editing Quantum electrodynamics (section)

===Basic constructions===
Suppose we start with one electron at a certain place and time (this place and time being given the arbitrary label ''A'') and a photon at another place and time (given the label ''B''). A typical question from a physical standpoint is: "What is the probability of finding an electron at ''C'' (another place and a later time) and a photon at ''D'' (yet another place and time)?". The simplest process to achieve this end is for the electron to move from ''A'' to ''C'' (an elementary action) and for the photon to move from ''B'' to ''D'' (another elementary action). From a knowledge of the probability amplitudes of each of these sub-processes – ''E''(''A'' to ''C'') and ''P''(''B'' to ''D'') – we would expect to calculate the probability amplitude of both happening together by multiplying them, using rule b) above. This gives a simple estimated overall probability amplitude, which is squared to give an estimated probability.{{Citation needed|date=September 2020}}
[[File:Compton Scattering.svg|thumb|left|200px|[[Compton scattering]] ]]
But there are other ways in which the result could come about. The electron might move to a place and time ''E'', where it absorbs the photon; then move on before emitting another photon at ''F''; then move on to ''C'', where it is detected, while the new photon moves on to ''D''. The probability of this complex process can again be calculated by knowing the probability amplitudes of each of the individual actions: three electron actions, two photon actions and two vertexes – one emission and one absorption. We would expect to find the total probability amplitude by multiplying the probability amplitudes of each of the actions, for any chosen positions of ''E'' and ''F''. We then, using rule a) above, have to add up all these probability amplitudes for all the alternatives for ''E'' and ''F''. (This is not elementary in practice and involves [[Integral|integration]].) But there is another possibility, which is that the electron first moves to ''G'', where it emits a photon, which goes on to ''D'', while the electron moves on to ''H'', where it absorbs the first photon, before moving on to ''C''. Again, we can calculate the probability amplitude of these possibilities (for all points ''G'' and ''H''). We then have a better estimation for the total probability amplitude by adding the probability amplitudes of these two possibilities to our original simple estimate. Incidentally, the name given to this process of a photon interacting with an electron in this way is [[Compton scattering]].{{Citation needed|date=September 2020}}

There is an ''infinite number'' of other intermediate "virtual" processes in which more and more photons are absorbed and/or emitted. For each of these processes, a Feynman diagram could be drawn describing it. This implies a complex computation for the resulting probability amplitudes, but provided it is the case that the more complicated the diagram, the less it contributes to the result, it is only a matter of time and effort to find as accurate an answer as one wants to the original question. This is the basic approach of QED. To calculate the probability of ''any'' interactive process between electrons and photons, it is a matter of first noting, with Feynman diagrams, all the possible ways in which the process can be constructed from the three basic elements. Each diagram involves some calculation involving definite rules to find the associated probability amplitude.

That basic scaffolding remains when one moves to a quantum description, but some conceptual changes are needed. One is that whereas we might expect in our everyday life that there would be some constraints on the points to which a particle can move, that is ''not'' true in full quantum electrodynamics. There is a nonzero probability amplitude of an electron at ''A'', or a photon at ''B'', moving as a basic action to ''any other place and time in the universe''. That includes places that could only be reached at speeds greater than that of light and also ''earlier times''. (An electron moving backwards in time can be viewed as a [[positron]] moving forward in time.)<ref name=feynbook/>{{rp|89, 98–99}}