File:Shadow faster than light.webm
Summary
| Description |
English: Can shadows move faster than light?
Not really. There is nothing moving sideways, so nothing is moving faster than light (which, incidentally, mean you can't use shadows to communicate faster than light). But the edges of the projection of the shadow can indeed appear to move arbitrarily fast. |
| Date | |
| Source | https://twitter.com/j_bertolotti/status/1679091197397139457?s=20 |
| Author | Jacopo Bertolotti |
| Permission (Reusing this file) |
https://twitter.com/j_bertolotti/status/1030470604418428929 |
Mathematica 13.1 code
smoothstep[t_, t0_, t1_] := With[{tt = (t - t0)/(t1 - t0)}, If[tt < 0, 0, If[tt > 1, 1, 6 tt^5 - 15 tt^4 + 10 tt^3]]];
r0 = 1; r1 = 3; c = 1; t =.;
\[Theta]vst[t_] := 4 \[Pi]*smoothstep[t, 0, 10]; \[Theta]range = \[Pi]/10;
frames = Table[
dots = DeleteCases[ Flatten[Table[ If[And[r + c t > 0, r + c t < r1], {r + c t, \[Theta]}], {r, -4*r1, 2*r1, 0.1}, {\[Theta], -\[Pi] + 0.00001, \[Pi], (2 \[Pi])/50}], 1], Null];
selecteddots = Select[dots, Nand[(#[[1]] > r0), Mod[\[Theta]vst[t - (#[[1]] - r0)/c] - \[Theta]range - #[[2]], 2 \[Pi], -\[Pi]] < 0, Mod[\[Theta]vst[t - (#[[1]] - r0)/c] + \[Theta]range - #[[2]], 2 \[Pi], -\[Pi]] > 0] & ];
Graphics[{
LightGray, Disk[{0, 0}, r0],
Table[Circle[{0, 0}, r, {\[Theta]vst[t - (r - r0)/c] + \[Theta]range, 2 \[Pi] + \[Theta]vst[t - (r - r0)/c] - \[Theta]range}], {r, r0, r1, 0.01}],
Thick, Black, Circle[{0, 0}, r0, {\[Theta]vst[t] + \[Theta]range, \[Theta]vst[t] - \[Theta]range}],
Point[FromPolarCoordinates@selecteddots],
Gray, Circle[{0, 0}, r1]
}]
, {t, -0.5, 12, 0.025}];
ListAnimate[frames, 10]
Licensing
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This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication. |
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