The observer effect in quantum physics is described as the collapse of the wave function and is as counterintuitive as Einstein's equivalence principle is a seeming bit of common sense.
Why quanta appear to behave differently when we aren't looking may be a category error that is nonsensical when rightly considered. But, even a clear definition of what constitutes an "observation" that triggers a wave function collapse is not well resolved theoretically in quantum physics despite its potential practical empirical importance and centrality to the discipline.
Whether an experimental setup constitutes, or does not constitute, "observation" has enough well enough established "safe harbor" cases that physicists can go about their business of studying quantum mechanics from day to day, but it takes considerable ingenuity and a better formulated set of possible definitions of "observation" to even devise experiments that could test those definitions to determine which ones best fit empirical reality.
Put another way, a fundamental unsolved problem of fundamental physics is "what causes the wave function to collapse?" This is sometimes called the "quantum measurement problem." Colloquially, this is sometimes described as the problem of Schrödinger's cat (surely one of the least animal friendly thought experiments in the scientific canon). This is closely related to the phenomena of quantum decoherence in the context of the consistent histories interpretation of quantum mechanics, which is a refinement of the old Copenhagen interpretation:
In Quantum Philosophy , Roland Omnès provides a less mathematical way of understanding this same formalism. The consistent histories approach can be interpreted as a way of understanding which sets of classical questions can be consistently asked of a single quantum system, and which sets of questions are fundamentally inconsistent, and thus meaningless when asked together. It thus becomes possible to demonstrate formally why it is that the questions which Einstein, Podolsky and Rosen assumed could be asked together, of a single quantum system, simply cannot be asked together. On the other hand, it also becomes possible to demonstrate that classical, logical reasoning often does apply, even to quantum experiments – but we can now be mathematically exact about the limits of classical logic.
Woit at Not Even Wrong notes several recent efforts to address that issue.