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Yes, they are different phases of the same thing, but suppose a scenario where the ice must remain solid and water must stay in it's the liquid form.

This is more of a philosophical question than a practical one, but suppose 2 scientists. one from the liquid planet and another from solid planet, where the rules of a game allows them to try anything as long as they do not change the states of the water and ice ( no gas form either ) to somehow agree that they are working with the same stuff.

In other words how can we establish that ice and water are one and the same thing without state transition?

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Please be precise about what it means to be the same. Ice and water are not the same. Do you mean that they are made of the same atoms with about the same binding? Are you allowed to do electrolysis on the solid planet? Are you allowed to use radioactive sources on planet solid (these might generate heat and melt or vaporize some of the ice)? Are you allowed to work with steam in either? I think the question is ill posed as it stands. –  Ron Maimon Dec 4 '11 at 9:47
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A properly designed experiment that excites the molecular levels of H2O and detects the ensuing spectrum should identify the same molecule by the characteristic lines without changing the phase it is in. That is how they identify water in space .

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I considered this but some of these experiments require single molecules (that is vapor/gas phase). Mass spectroscopy would be one useful technique. NMR another - that one might work with molecules in situ.. –  BjornW Dec 4 '11 at 15:36
    
@BjornWesen it is not my specialty, but from general knowledge reflection from an ice surface should work to give the molecular lines, as well as from water surface. Also absorption spectra of very thin films ( ice and water respectively)? –  anna v Dec 4 '11 at 16:25
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