If you'll forgive me for belaboring the point....
I'm not convinced that, "...that which is not objectively perceptible is irrelevant to our lives..."
Therefore, and purely for argument's sake, I propose that there exists a ghost-type being, a "spiritual emanation" with no directly measurable physical properties. This ghost is not bound by the laws of space or time that exist in our physical universe. We humans cannot perceive the ghost, nor can it perceive us.
The ghost
can perceive an entire "spiritual universe" filled with other spiritual beings of various types. These other beings cannot in any way affect or perceive our material universe, nor can we affect or perceived them and theirs. The ghost in question, however, is unique in that it
can affect us. Specifically, it can cause spontaneous human combustion (SHC). That is the
only effect it can have on our physical universe.
The ghost does not simply burn anyone who comes into its proximity (which after all, exists outside of what we perceive as space and time). It burns humans according to subtle fluctuations its emotional and intellectual state, in response primarily to stimuli generated not within our physical universe, but within its own spiritual reality. In other words, the ghost kills us by accident without ever knowing it or of us.
Human science could certainly collect the dates, times and locations of deaths resulting from SHC, as well as information about the victims. But given the nature of the phenomena as I've described it, I suggest that science could not learn enough from the available information to test and validate any even partially accurate hypotheses about its true cause - much less accurately model the ghost and its universe.
I would argue that the ghost's passing thoughts and feelings, though they are not objectively perceptible to us, are relevant to our lives, in that they can trigger our deaths. They remain relevant to us whether or not we know of them (warning: semantics).
That's a fair response not only to the "God problem" I proposed before, but also to the hypothetical "ghost problem" above. In the ghost version of the problem, I've tried to constrict the one-way "information leak" from the ghost's reality to our own so as to confound scientific inquiry, but I do concede that where information exists, things can be learned. Nevertheless, while an infinite timeframe would make all understandings possible, I believe that the ghost problem as formulated would prove impervious to human science on a human-scale, practical level.
I say this because science does not deal in absolute truth or falsehood. It concerns itself only with what seems to be true (or at least reliable) and that which is yet unknown. I mean by this that scientific "truths" and principles are inherently provisional. They attempt to account for what we have observed but say nothing about anything else. Logic and other valid forms of human understanding are similar. Therefore, we can't ever rule anything out in an inviolably absolute sense. We can only speak of what seems reliably to be. Put more simply, I'm splitting ghost hairs