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?
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".
|show 3 more comments|
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.