Variations on Symmetry

Symmetry

Symmetry review

Review the complete Symmetry section and its 31 animations. The packet includes the chapter, static images, exact surrounding context, generation source, and sampled frames decoded from the current movies. No review findings or grades are supplied.

Consider physical and mathematical correctness, support for the argument and its assumptions, teaching clarity, and the fidelity of the visuals to the stated mathematics.

What this evidence can establish

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.

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.

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  1. Animation 1

    Symmetry transforms don't change how pool balls behave

    Sample at 00:07.633 from symmetry-pool-table.mp4

    14 s · 12 decoded samples · 1 source file

  2. Animation 2

    A triangle's symmetries

    Sample at 00:10.889 from symmetry-triangle-actions.mp4

    20 s · 12 decoded samples · 1 source file

  3. Animation 3

    $D_3$ in 3-dimensional representation

    Sample at 00:03.542 from symmetry-d3-rotations-vs-flips.mp4

    6.5 s · 12 decoded samples · 2 source files

  4. Animation 4

    Reducing 3-dimensional representation to 2-dimensional

    Sample at 00:12.917 from symmetry-d3-irrep-collapse.mp4

    23.75 s · 12 decoded samples · 2 source files

  5. Animation 5

    Continuous symmetries

    Sample at 00:02.708 from symmetry-continuous-so2-translation.mp4

    5 s · 12 decoded samples · 2 source files

  6. Animation 6

    Symmetry flows provide a rich picture of symmetry transformations

    Sample at 00:04.750 from symmetry-so2-vector-field-flow.mp4

    8.75 s · 12 decoded samples · 1 source file

  7. Animation 7

    Metric structure

    Sample at 00:03.250 from symmetry-rotation-vector-invariants.mp4

    6 s · 12 decoded samples · 1 source file

  8. Animation 8

    Hyperbolic rotations

    Sample at 00:03.792 from symmetry-hyperbolic-rotation.mp4

    7 s · 12 decoded samples · 1 source file

  9. Animation 9

    Non-commuting operations of $SO_3$

    Sample at 00:04.333 from symmetry-so3-rotation-order.mp4

    8 s · 12 decoded samples · 2 source files

  10. Animation 10

    Shifting a number line is not a linear operation

    Sample at 00:03.542 from symmetry-translation-point-linearity-failure.mp4

    6.5 s · 12 decoded samples · 1 source file

  11. Animation 11

    A function representation is linear

    Sample at 00:03.542 from symmetry-translation-function-linearity.mp4

    6.5 s · 12 decoded samples · 1 source file

  12. Animation 12

    Translation of functions preserves their shape

    Sample at 00:02.958 from symmetry-function-translation-shape.mp4

    5.5 s · 12 decoded samples · 1 source file

  13. Animation 13

    A function value is translated by the function's slope

    Sample at 00:08.167 from symmetry-translation-tangent-zoom.mp4

    15 s · 12 decoded samples · 1 source file

  14. Animation 14

    Eigenvectors pictured

    Sample at 00:07.875 from symmetry-eigenbasis-stretch.mp4

    14.5 s · 12 decoded samples · 1 source file

  15. Animation 15

    The complex value rotates while its length stays fixed.

    Sample at 00:06.533 from symmetry-complex-plane-wave-v2.mp4

    12 s · 12 decoded samples · 1 source file

  16. Animation 16

    Three-tone chord packet and its Fourier decomposition

    Sample at 00:04.333 from symmetry-fourier-three-tone-packet.mp4

    8 s · 12 decoded samples · 1 source file

  17. Animation 17

    Wave Packet translated in position and momentum space

    Sample at 00:09.267 from symmetry-ccr-x-k-translations-symmetric.mp4

    17 s · 12 decoded samples · 1 source file

  18. Animation 18

    Unitarity of position and wave-number translations

    Sample at 00:09.267 from symmetry-ccr-unitarity.mp4

    17 s · 12 decoded samples · 1 source file

  19. Animation 19

    Visualizing Phase Change

    Sample at 00:09.800 from symmetry-complex-phase-modes.mp4

    18 s · 12 decoded samples · 2 source files

  20. Animation 20

    Phase as the $[\hat X,\hat K]$ commutator

    Sample at 00:08.700 from symmetry-ccr-loop-complex.mp4

    16 s · 12 decoded samples · 2 source files

  21. Animation 21

    Trading off spread in position for spread in wave number

    Sample at 00:06.533 from symmetry-xk-fourier-complex.mp4

    12 s · 12 decoded samples · 2 source files

  22. Animation 22

    Trade-off in uncertainty of position and wave number

    Sample at 00:06.542 from symmetry-xk-squared-magnitudes.mp4

    12 s · 12 decoded samples · 2 source files

  23. Animation 23

    Interference and Rays

    Sample at 00:10.900 from symmetry-short-wave-beams.mp4

    20 s · 12 decoded samples · 2 source files

  24. Animation 24

    Two Path Interference

    Sample at 00:05.433 from symmetry-double-slit-candidate-paths-shortwave-arcs.mp4

    10 s · 12 decoded samples · 2 source files

  25. Animation 25

    Seeing stationarity emerge in closely spaced paths

    Sample at 00:12.250 from symmetry-many-slit-paths-phasors-interference.mp4

    22.5 s · 12 decoded samples · 7 source files

  26. Animation 26

    Huygens–Fresnel principle

    Sample at 00:13.083 from symmetry-schematic-screens-v3-concise.mp4

    24 s · 12 decoded samples · 7 source files

  27. Animation 27

    Three trials accumulate a quarter turn at the longer wavelength while the shorter wavelength produces many rotations

    Sample at 00:09.267 from symmetry-phase-remainder-spinners.mp4

    17 s · 12 decoded samples · 2 source files

  28. Animation 28

    Matching colors connect candidate paths to their contributions in the tip-to-tail sum as wavelength decreases

    Sample at 00:19.633 from symmetry-spectrum-path-diamond-wavelength-scan.mp4

    36 s · 12 decoded samples · 4 source files

  29. Animation 29

    From intensity to position measurement probability density

    Sample at 00:15.267 from symmetry-amplitude-probability.mp4

    28 s · 12 decoded samples · 3 source files

  30. Animation 30

    A shared conversion factor makes phase and action select the same collision

    Sample at 00:16.333 from symmetry-collision-shared-scale.mp4

    30 s · 12 decoded samples · 1 source file

  31. Animation 31

    Three wave-number shells share the same proper-time interval while phase cycles and action accumulates at corresponding rates

    Sample at 00:13.071 from symmetry-action-phase-desktop.mp4

    24 s · 12 decoded samples · 7 source files