Will Pearson, you can indeed summarily reject the possibility, and that's why I kept saying, "ignoring quantum". For quantumness, you would need a total description of the quantum state of the water, and this you can never obtain by any physical means. Though this is true even under classical mechanics: The third law of thermodynamics, on the impossibility of obtaining absolute zero, implies the impossibility of obtaining infinite-precision knowledge.

Silas, 'twas explicit: I said "sealed box".