There is a 1 square meter of glass in front of me, I am holding a quarter inch steel ball bearing. I thow the ball bearing at the glass and the glass breaks into many pieces. I examine the pieces and look at there differnt shapes. I assume that they are in that shape because of:
Tiny defects in the glass that cant be detected
The angle the ball hit
Any kind of spin to the ball
etc
Now lets say I have another square meter of glass infront of me. Now this glass is PERFECT, it was put together molecule by molecule by tiny aliens, it is perfect in everyway, not one side is one molecule longer then the other. It has no defects of any kind. Now I have another ball bearing, again pefect, a perfect sphear, which was put together molecule by molecule. I launch the ball at the plate of glass hitting it exactly in the center, the ball has no spin to it at all.
Now how would the glass break? Would it break into little squares or what? I am not sure how the molecules fit together and what shape they make? triagles? For sake of the argument assume that the glass is common everday glass.
I think it’s reasonable to assume that a (theoretically) perfect sheet of fragile material(not glass*) in a perfect way by a perfect object would (in the absence of all other confounding factors, such as air curents and vibration) break in a completely symmetrical pattern. I’m not sure what the pattern would be, but it would be created by cracks radiating out from the point of impact along the weakest lines.
*The reason glass wouldn’t work is that glass is an amorphous solid anyway - it doesn’t have a regular crystal lattice structure, so your tiny aliens could put it together in a number of different ways and each of these ways could break in a different pattern.
This all assumes that uncaused quantum effects do not affect the experiment.
In reality though, it never happens this way; there is *always some kind of tiny asymmetry, imperfection, imbalance, etc - indeed, the reason our universe isn’t just a dispersed homogenous field of hydrogen atoms may well be that perfection just can’t happen - in order for things to start clumping together to form stars, there has to be a nucleation point that is different in some way from the others elsewhere.
I second the amorphous solid. Using some type of mineral sheet would probably give better results, both for this hypothetical example, and in practice.
Your glass and ball would have to be at absolute zero, or thermal variation in bond strength/length would screw up all that perfect symmetry.
Even then, shockwaves from the impact would probably move out to the edges of the glass, and reflect back to create a nonsymetric region of maximal stress.
Well in your magic scenario, I would assume the general rule for “exact equality” would be completely symmetric response in some cases (weakest line, point, etc.) and utterly random in others (choice of two or more equally weak lines, points, etc.