To visually demonstrate why some systems need to be rotated 720 degrees instead of 360 degrees to return to their original state, Richard Feynman came up with the "Teacup Trick." After reading the steps of the "Teacup Trick," I suddenly remembered a scene featuring Bruce Leung (Liang Xiaolong) in the movie Tai Chi 0, where he carries a bowl of medicine. It corresponds exactly to Feynman’s "Teacup Trick," so I have clipped the footage for everyone to enjoy.
Please observe carefully: how many times does Bruce Leung’s hand rotate?
The general steps of the "Teacup Trick" are as follows:
Raise your right hand near your right shoulder, palm facing right, holding a teacup. Then, without turning your body, keep the cup upright and rotate your right hand counter-clockwise horizontally. Pass your right hand under your right ribs until it reaches waist height and becomes an underhand position, extending downwards and outwards. At this point, the cup is still upright and has rotated exactly one full turn. Although the cup has completed one rotation, the person’s posture has completely changed.
Then, starting from this state, bend and raise your elbow, pulling your right hand back slightly. Keeping the cup upright, continue rotating the cup counter-clockwise. Pass your right hand in front of your neck, then lower your elbow, and finally return to the original posture. At this point, the cup has rotated exactly two full turns counter-clockwise, and the person’s posture has finally returned to its original state.
Feynman used this to illustrate how this type of rotation requires two counter-clockwise turns for the system to return to its original state. (The second step is slightly difficult, but make no mistake—you do not need to dislocate your arm. If you did, it would be impossible for your body to return to its original state after two rotations.)
In The Road to Reality, Roger Penrose proposed a similar "Belt Trick" (this method can be used by friends whose joints are not particularly flexible ^_^). The general steps are:
Stretch a belt horizontally and fix one end.
Clamp the other end inside a book (it is not strictly necessary to use a book, but doing so makes it easier to keep the end from flipping over).
Keep the book horizontal, then rotate the book clockwise once. During the rotation, pass the book under the belt.
As a result, the book returns to its original orientation, but the belt is now twisted into a knot.
Continue rotating the book clockwise once more. During this rotation, pass the book over the belt.
As a result, the book returns to its original orientation again, and the twist in the belt disappears.
The key is the two rotations: one passing over and one passing under.
Of course, both of these metaphors are not strictly rigorous; they are merely illustrative because the two rotations are different (one passing over and one passing under). Therefore, it is a bit of a "cheat," but it is indeed very vivid.
Text sourced from: http://www.changhai.org/bbs/load_article.php?fid=3&aid=1131220903
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