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A friend recently posed this question to me: let us take an arbitrary object and cut it into two pieces (not necessarily equal in any way). If we touch the two pieces back together so the object appears as it did originally, why do the bonds not reform and the object return to one solid piece?

I posed this question to some professors at a local university, and they believed that at the molecular level, the cut would be very jagged and it would become almost impossible to line up the two pieces perfectly at the molecular level as they once were. Nonetheless, they thought if we could somehow line them up, the bonds might reform on their own.

I feel van der Waals forces play an important role. Must we introduce energy into the system to form inter-molecular bonds and return the object to one piece again?

Also, I likely need some better tags for this.

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  • $\begingroup$ See also "galling" and "vacuum welding". $\endgroup$ – dmckee Mar 10 '15 at 16:42
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The confusing concept here is that before we cut the object in half, the object was not splitting on its own obviously, which means that being whole is more energetically favorable than splitting into pieces. Then why would the split system, which is a configuration we know to be of higher energy not want to go back to a configuration of lower energy? Isn't minimizing energy what every physical system longs for?

The answer is that sometimes a system finds itself in a local minimum of energy. Where even though there is a configuration which would bring it to a lower energy state, it costs some energy to cross that barrier!

This is what happens when you cut an object, the molecules on the surface realign themselves (now that there is a new energy expensive interface with air) to the best situation they can manage and end up in a local minimum of energy, separated from a better one by some energy gap. Maybe if you heated the surface (i.e. "welding") or provided some other form of energy to cross that barrier, the object will reattach!

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