Is an infinite universe an open or closed system? Is an infinite universe a system in any sense at all?
Are there implications (scientific or philosophical) to seeing it one way or the other?
if a universe were truly infinite in space, it would necessarily be open. however, if it were infinite only in time (i.e. unending) but possessed finite spatial dimensions, then it would still be considered closed.
i think that a hypothetically infinite universe (in either spatial or temporal infinitude) would be considered a system, yes.
spatially infinite universes would be unending in size/energy, and would therefore imply an infinite amount of energy. this would mean that there would be no “end” or maximum amount of “stuff” in the universe. scientifically, this seems to violate thermodynamics. philosophically, it seems to violate the law of noncontradiction (although this is certainly debatable, depending on how you understand the ‘energy’ which is infinite).
temporally infinite universes (that are spatially finite) would be unending in their duration only, i.e. they would either reach a statis point where a state of zero movement or perfect balance is reached and remain that way forever, or they would cycle from one form to another, without end. this would mean that there would be no beginning or ending to the universe, despite that there would still be a finite quantity of “stuff” in it at any given time. scientifically, this satisfies thermodynamics. philosophically, this seems to generate an infinite causal regress, but considering the alternative to this regress is spontaneous noncausal causality of a “first” universe, a regress seems the lesser flawed view, since a regress does not TECHNICALLY entail a contradiction (but it is very counterintuitive), while noncausal causes do entail contradiction.
If it’s finite, then everything is in theory observable, if not, then not.
not quite, because the other side of the universe could be finite (not infinite) yet moving away from us at the speed of light, in which case it is theoretically impossible for us to observe it… yet it is still finite.