Chaotic Cracks
Classical Mechanics
Level
1
Two units of iPhone X have just been manufactured by a robotic assembly line. The testing team drops them one by one from the same height and angle on the same surface, which causes them to get cracked.
Will the same pattern of cracks emerge on their screens?
Yes
No
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
Intuitively (and as the problem name suggests), it seems like the cracks would be chaotic in nature. This is probably similar to lightning forming "streamers" on its way to ground. We can imagine this process being exquisitely sensitive to initial conditions.
Chaos: When the present determines the future, but the approximate present does not approximately determine the future.
Put another way, in a chaotic system, the output ( O ) is highly sensitive to changes in the input ( I ) :
d I d O = large
In this case, the inputs are both the manner in which the phone is dropped, and the particular crystalline structure of the glass. It is likely that both of these will vary slightly from phone to phone and drop to drop, despite efforts to control them. The (presumed) chaotic nature of the fracturing ensures that no two cracks develop the same way.