measurement is a disruptive act
by measuring a thing, you force it to take a definite value in some frame of reference. you subsequently deal with that thing as having that snapshot value, thereby forcing it to respond as if it had that value - and forwarding that value to other things that go on to cause more reality to happen based on it.
the problem is that measurement is made against a set of attributes of a thing, but that set is always bound to be a subset of all the possible attributes of any real thing, both in breadth and in depth. reality is infinite and infinitesimal. so the measurement must be missing parts of reality - we're aware of this, and the practice of modelling explicitly aims at choosing only "relevant" dimensions to track and measure, but looking at the track record of our global modelling efforts so far (the economy, foreign relations, social organization, software production, etc.) we're doing a fantastically poor job.
maybe the problem lies with discretization, aka digitization. If we allowed our sensors to capture analog signals and process them analogically, we would lose less fidelity. the first example is the cursed boolean bit which forces the values 0 or 1. we need an analog equivalent which may represent any value between 0 and 1, including an unknown value. building our logic on top of such a different basic element would yield totally different algorithms.
but the central problem of measurement would remain. can we observe without interaction? that may be a zen question - but can it be done in hardware? we'd have to know how to do it ourselves first!