Appendix/QED

Feynman's Path-Integral Formulation (QED)

A Couple of Relevant YouTube Videos

YouTube video: Richard P. Feynman's 1979 Lectures at the University of Auckland, NZ	YouTube video: Physics With Elliot
Book resulting from Auckland lectures QED: The Strange Theory of Light and Matter

Figures Similar to Feynmann's Fig. 24

Here are a few figures that we generated (in Excel) to explain Fig. 24 (on page 43) of Feynmann's Book, hereafter, [QED].

Following pp. 38-39 of [QED], the upper portion of our set of figures displays a mirror that, as labeled, extends from point "A" to point "M"; it is divided into 12 segments. Above the mirror is a source "that emits light of one color (red) at very low intensity"; the location of a detector is identified as well. "… there are millions of ways a photon could go" as it travels from the source to the detector: "it could go down to the left-hand part of the mirror at "A" — as indicated by a green arrow — or "B" (for example) and bounce up to the detector — as indicated by a red arrow; it could bounce off … at "G"; or it could go down to the right-hand part at K or M — as indicated by a longer green aroow — and bounce up to the detector (shorter red arrow).

Figure 1

Figure 24 in QED

Next, following pp. 41-42 of [QED], "let's draw a little arrow for each way the [photon] could go" as it travels from the source to the detector. "Although it is safe to assume that the length of all the arrows will be nearly the same" — the "amplitude" of each photon is the same — their directions will clearly differ because their timing is different — remember that the direction of a particular arrow is determined by the final position of an imaginary stop-watch that times a photon as it moves along that particular path."

Arrow Ensemble Part 1

Arrow Ensemble Part 2

Slit Aperture Instead of Mirror

Figure 2

Panel a:   Same as Figure 1, but with fewer photon trajectories displayed.
Panel b:   Positions of detector and source modified from Panel a.	Panel c:   Mirror replaced by slit; position of source flipped to position such that light passes through the slit rather than bouncing off of mirror.	Panel d:  If the source is a laser, then photon trajectories between the source and the slit are all in phase with, and parallel to one another.

See Also

• Computer-Generated Holography