The principle of cause and effect is deeply rooted in human experience, so much so that it is routinely and tacitly assumed throughout science, even by scientists working in areas where time symmetry is theoretically ingrained, as it is in both classical and quantum physics. Experiments are said to cause their results, not the other way around. In this informal paper, we argue that this assumption should be replaced with a more general notion of mutual influence-bi-directional relations or constraints on joint values of two or more variables. From an analysis based on quantum entropy, it is proposed that quantum measurement is a unitary three-interaction, with no collapse, no fundamental randomness, and no barrier to backward influence. Experimental results suggesting retrocausality are seen frequently in well-controlled laboratory experiments in parapsychology and elsewhere, especially where a random element is included. Certain common characteristics of these experiments give the appearance of contradicting well-established physical laws, thus providing an opportunity for deeper understanding and important clues that must be addressed by any explanatory theory. We discuss how retrocausal effects and other anomalous phenomena can be explained without major injury to existing physical theory. A modified quantum formalism can give new insights into the nature of quantum measurement, randomness, entanglement, causality, and time.