I'm asking if space space is subject to change, if not, why not, and if so, then would it be subject to a subsequent phase space that describes that? Let us make a phase space for a deterministic time evolved dynamic system of three spatial dimensions. Since the actions of the system and the phase space are totally correlated, is there a sense in which one is the cause of the other? It looks to me like the system, being deterministic, cannot independently deviate from its time evolution, so it cannot change its phase space; but if the phase space itself were subject to change, this would alter the system (changing the system's evolution throughout all time)... First, are there any concepts of phase space that allow itself to be subject to change? I know this raises questions about what kind of "time" within which the phase space would change, being a different concept of time from the system's time. If phase space were subject to change, it would seem that the next step would be to make a higher phase space "II" to describe the "time" evolution of the first phase space. And if this phase space II were also subject to change, this process might be indefinitely iterative up to phase space "c" where no further changes occur (as in taking the derivative of a function over and over that reaches a point where all subsequent higher derivatives return zero...) Anyone ever look at this or is it fundamentally preempted by the problem of defining a concept of "time" for a phase space? Is there anything that just prevents a phase space from being subject to change?