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Does anyone know why they called the momentum-position space the phase space in the first place?
To clarify what I mean a bit more, I'll give you an example:
The name configuration space for the position space makes perfect sense to me as it represents the configuration of individual particles of a system. But what type of phase does the phase space represent?
See this article on the history of phase space.
Assuming the article is to be trusted, Boltzmann noted that in a 2-D system the trajectories looked like Lissajous figures, and the shape of the Lissajous figure is determined by the relative phase of the two input signals. He then used the work phase to refer to that part of the configuration that was external i.e. excluding rotation and vibration of molecules. Maxwell picked up on the word and the rest is history.
