Editing Quantum electrodynamics (section)

===Introduction===
Near the end of his life, [[Richard Feynman]] gave a series of lectures on QED intended for the lay public. These lectures were transcribed and published as Feynman (1985), ''[[QED: The Strange Theory of Light and Matter]]'',<ref name=feynbook/> a classic non-mathematical exposition of QED from the point of view articulated below.

The key components of Feynman's presentation of QED are three basic actions.<ref name=feynbook/>{{rp|85}}
: A [[photon]] goes from one place and time to another place and time.
: An [[electron]] goes from one place and time to another place and time.
: An electron emits or absorbs a photon at a certain place and time.

[[File:Feynman Diagram Components.svg|thumb|right|300px|[[Feynman diagram]] elements]]
These actions are represented in the form of visual shorthand by the three basic elements of [[Feynman diagram|diagrams]]: a wavy line for the photon, a straight line for the electron and a junction of two straight lines and a wavy one for a vertex representing emission or absorption of a photon by an electron. These can all be seen in the adjacent diagram.

As well as the visual shorthand for the actions, Feynman introduces another kind of shorthand for the numerical quantities called [[Quantum electrodynamics#Probability amplitudes|probability amplitudes]]. The probability is the square of the absolute value of total probability amplitude, <math>\text{probability} = | f(\text{amplitude}) |^2</math>. If a photon moves from one place and time <math>A</math> to another place and time <math>B</math>, the associated quantity is written in Feynman's shorthand as <math>P(A \text{ to } B)</math>, and it depends on only the momentum and polarization of the photon. The similar quantity for an electron moving from <math>C</math> to <math>D</math> is written <math>E(C \text{ to } D)</math>. It depends on the momentum and polarization of the electron, in addition to a constant Feynman calls ''n'', sometimes called the "bare" mass of the electron: it is related to, but not the same as, the measured electron mass. Finally, the quantity that tells us about the probability amplitude for an electron to emit or absorb a photon Feynman calls ''j'', and is sometimes called the "bare" charge of the electron: it is a constant, and is related to, but not the same as, the measured [[Elementary charge|electron charge]] ''e''.<ref name=feynbook/>{{rp|91}}

QED is based on the assumption that complex interactions of many electrons and photons can be represented by fitting together a suitable collection of the above three building blocks and then using the probability amplitudes to calculate the probability of any such complex interaction.  It turns out that the basic idea of QED can be communicated while assuming that the square of the total of the probability amplitudes mentioned above (''P''(''A'' to ''B''), ''E''(''C'' to ''D'') and ''j'') acts just like our everyday [[probability]] (a simplification made in Feynman's book). Later on, this will be corrected to include specifically quantum-style mathematics, following Feynman.

The basic rules of probability amplitudes that will be used are:<ref name=feynbook/>{{rp|93}}
{{Ordered list|list_style_type = lower-alpha
|If an event can occur via a number of ''indistinguishable'' alternative processes (a.k.a. "virtual" processes), then its probability amplitude is the '''sum''' of the probability amplitudes of the alternatives.
|If a virtual process involves a number of independent or concomitant sub-processes, then the probability amplitude of the total (compound) process is the '''product''' of the probability amplitudes of the sub-processes. 
}}

The indistinguishability criterion in (a) is very important: it means that there is ''no observable feature present in the given system'' that in any way "reveals" which alternative is taken. In such a case, one cannot observe which alternative actually takes place without changing the experimental setup in some way (e.g. by introducing a new apparatus into the system). Whenever one ''is'' able to observe which alternative takes place, one always finds that the ''probability'' of the event is the sum of the ''probabilities'' of the alternatives. Indeed, if this were not the case, the very term "alternatives" to describe these processes would be inappropriate. What (a) says is that once the ''physical means'' for observing which alternative occurred is ''removed'', one cannot still say that the event is occurring through "exactly one of the alternatives" in the sense of adding probabilities; one must add the amplitudes instead.<ref name=feynbook/>{{rp|82}}

Similarly, the independence criterion in (b) is very important: it only applies to processes which are not "entangled".