This question has had me thinking for a while. If I have two large panes of glass and a rock or similar item is thrown in exactly the same place on the glass, would the two panes break in the same way. Does the shattering of glass follow any rules or is it always random and subject to other variables? Could you predict the shattering of glass down to the smallest shards or again, is it random?
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3$\begingroup$ Do you consider quantum effects? Inhomogeneities in the glass? $\endgroup$– jinaweeMay 13, 2014 at 16:47
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2$\begingroup$ One can't even reliably throw a couple of fair dice to repeatedly end up showing the same pips without severely constraining the throw (and even then maybe not), much less a situation involving two+ dimensional propogation of a stress fracture. $\endgroup$– MichaelMay 13, 2014 at 20:57
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2 Answers
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The answer is sort of yes and no.
YES: If you have two perfectly identical panes of glass and two perfectly identical projectiles, and you throw the two projectiles in a perfectly identical way, then the two panes will shatter in a perfectly similar fashion. This is really just by construction, you did the same thing twice.
NO: Shattering glass involves breaking bonds between atoms/molecules. This leads to two important conclusions. First, two "identical" panes of glass for this experiment must be identical at least down to the arrangement of the atoms (including the placement of any impurities), and possibly as far as the internal configuration of each atom (as the strength of the bonds can depend on the electron configuration, for instance). In practice this means that it is impossible, given current technological constraints, to construct two macroscopic identical panes of glass. Second, predicting the shattering of a given pane of glass would require both a detailed description of the microscopic structure of the pane (which is impractical because of the large amount of data storage required, and because the structure varies quickly enough in time that any measurement would quickly become obsolete), and solving the relevant dynamical equations. I imagine the equations would be reasonably easy to write down, we're talking about a bunch of particles connected by bonds and reasonably well defined forces, after all. But solving them would be computationally prohibitive, given the size of the system.
Still, some characteristics of the shattering can be predicted, for instance under suitable conditions the glass will begin to break at the location of the projectile impact, and the smallest shards will form near the impact site, larger shards further away, etc. The coarse properties of the process can be predicted, but we're stuck describing the fine properties as "random".
answered May 13, 2014 at 16:54
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$\begingroup$ I'm wondering if your statement "...and because the structure varies quickly enough in time that any measurement would quickly become obsolete" is true. After all, glass is a solid, so the arrangement of molecules stays pretty much the same. I know that due to heat, solids have some amount of "wiggling" around, but is this relevant when asking, "how will it shatter"? $\endgroup$– Tim S.May 13, 2014 at 20:53
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$\begingroup$ @TimS. Agreed that as a solid (technically supercooled liquid for glasses I think) the molecules don't move around that much, but (1) they move a bit, and (2) the internal properties definitely change rapidly (not necessarily dramatically), like electron configurations, which will have an effect on the bond strengths. Since roughly speaking the weakest bonds will break first, this matters... $\endgroup$ May 13, 2014 at 21:00
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$\begingroup$ Glass isn't a solid. Technically it is a (very) viscous liquid. A pane of glass mounted vertically will (after 100's of years) flow out at the bottom. Go look closely at the windows in a very old building (stained glass in an old church for example). If you look closely you will see that the panes are thicker at the bottom than at the top. The larger (higher) the pane (due to added weight) and the older the more pronounced the effect will be. $\endgroup$– TonnyMay 13, 2014 at 22:38
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1$\begingroup$ @Tonny Sorry, but that is a Debunked Urban Myth. io9.com/… dwb.unl.edu/Teacher/NSF/C01/C01Links/www.ualberta.ca/~bderksen/… tl;dr glass is thicker at the bottom because the production process made it thicker on one side than the other, and they were inserted thicker side on the bottom because that was more structurally stable! $\endgroup$– PatashuMay 13, 2014 at 23:02
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I believe the breaking itself will be fairly deterministic. Since I would expect that quantum mechanical uncertainty will play only a very small roll at those scales.
However I do suspect that the results will be different. But this would be due to the structure of the glass. By this I mean the imperfections within it. Because these will be the spots where the glass will fail first.
I think the location of these imperfections can be called random and are formed during fabrication. One source would be uneven cooling, which could add internal stresses. Other sources I can think of are impurities and air bubbles. All of these should be able to be modeled, however not knowing the exact initial and boundary conditions should give plenty of room for uncertainty.
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$\begingroup$ Not only imperfections: glass is amorphous, so even a perfect piece of glass is microscopically different from any other. $\endgroup$– DavidmhMay 13, 2014 at 20:06
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$\begingroup$ And the glass's history makes a difference. Any scratch will concentrate stress -- which is why glass-cutters work. $\endgroup$– keshlamMay 14, 2014 at 4:43