All animations · In the chapter · Open full MP4
Animation 23
Interference and Rays
symmetry-short-wave-beams.mp4
These are sparse samples decoded from the current MP4, not newly rendered illustrations. They can support checks of the sampled states and labels, but cannot establish continuous motion, timing, transitions, or the absence of problems between samples. Use the full MP4 when judging those properties.
1440 × 1120 · 30 fps · 20 s · 600 frames · 12 samples
MP4 SHA-256 0fdf04ec716792f0956e939ca3f6aac349cb0f3315b200b2a6eb8d07c46634bd
Frame manifest · Context markdown · Download complete review packet
Chapter context
Section: Wave Propagation and Interference. Excerpts are verbatim; line numbers refer to the included chapter markdown.
Caption
Interference and Rays
Image description
Waves through fixed openings becoming narrow beams as the wavelength decreases
Before the animation
Chapter lines 1071–1073
Chapter lines 1075–1075
Such "physically valid" paths in the macroscopic world have a fascinating quality that can be leveraged to find the laws of motion that predict them. They are such that some quantity associated with possible paths, which is called action, is extremized at the valid path. In the next sections, we will explore the relationship between objects following paths and wave propagation. Just as an object following a definite path extremizes action, a wave, in the regime where it behaves like a ray, follows a path that extremizes accumulated phase. We will establish how contributions from many possible paths combine to produce this behavior, giving us a bridge between wave propagation and action extremization. We will then see how this stationary-path limit connects the quantum wave description we have alluded to with the well-defined paths that action extremization predicts for everyday macroscopic objects.
After the animation
Chapter lines 1083–1083
Thus far we have described the symmetry group of a wave with a single translation direction $x$ and wave number, $k$. If the wave is to propagate, we also require that the wave represent time translation. We also need to require that time translation commute with spatial translation, for otherwise, it would change the mode composition over time, and spatial translation would no longer be a symmetry of nature. A single-mode travelling wave is then given by:
Chapter lines 1085–1087
Generation source
Main script --render computes finite-opening angular-spectrum fields and encodes their frames. generate_symmetry_widening_apertures supplies shared visual helpers and imported libraries. --check and --encoded-check write the companion reports; no input movie is used.
Mapping evidence and limits
Exact NAME match. Matching validation records fixed opening 0.5, centers -2.4/+2.4, wavelengths 0.5 down to 0.001, and 1440 x 1120, 30 fps, 20 s. Matching encoded-validation.json records all 600 decoded frames and source-frame comparison errors.
Source SHA-256 values identify the exact downloadable bytes in this packet. The source mapping and recorded checks explain the likely generation pipeline; they do not prove that these exact source bytes produced the movie. A GitHub link pinned to a commit is provided only when the delivered source bytes exactly match that path at the build's Git HEAD.
- scripts/generate_symmetry_short_wave_beams.py · GitHub at 974f9de35254
SHA-256 aa81d6b00bd42d01531e20b7231a663092d69a81bde399fbec577b9038719cb8 - scripts/generate_symmetry_widening_apertures.py · GitHub at 974f9de35254
SHA-256 2850a5c705823e498af5ef6180f0639cde6955631a763bc735e3d8992bb35127
Existing generator checks (2 reports)
These are existing author-produced generator reports, copied without changes. Their checks were not rerun for this packet and are not independent certification. A report may describe an earlier generation run; inspect its contents before applying its claims to the current movie.
- symmetry-short-wave-beams-validation.json
SHA-256 49603b342c08ee1d2c9d69254ae9aa80d2b7beae9dab12e1d2f8ed256c5a5a2f - symmetry-short-wave-beams-encoded-validation.json
SHA-256 6ffc80015366476539ee23aca3149aea5a2b1ab7134d04053cfbdb90849f3c88
Decoded contact sheet
Extraction method: Twelve evenly spaced decoded frame indices, including first and last. Native-resolution JPEGs from the encoded MP4; timestamps read from FFmpeg showinfo. No source rerendering. Frame indices are zero-based. Sparse samples do not establish continuous motion or capture every transition.. Frame indices are zero-based.
Full-size sampled frames
