We analyse a proposition which considers quantum theory as a mere tool for calculating probabilities for sequences of outcomes of observations made by an Observer, who him/herself remains outside the scope of the theory. Predictions are possible, provided a sequence includes at least two such observations. Complex valued probability amplitudes, each defined for an entire sequence of outcomes, are attributed to Observer's reasoning, and the problem of wave function's collapse is dismissed as a purely semantic one. Our examples include quantum "weak values", and a simplified version of the "delayed quantum eraser". PACS numbers:...there must be a certain conformity between nature and our thought.
H. HertzUnlike classical mechanics, which has its conceptual issues largely settled by the end of the 19-th century [1], quantum theory appears to need an interpretation, which would go beyond mere statement of its mathematical apparatus. One of the reasons for this is the peculiar use of complex valued wave functions or, more generally, amplitudes, needed whenever one wishes to evaluate frequencies (probabilities) with which the observed events would occur under identical circumstances. Much depends upon how these amplitudes are considered mere computational tools, or essentials attributes of the physical world.. Present suggestions range from the pragmatic Copenhagen interpretation (see [2] and Refs. therein) to the highly subjective QBism (see [3]), and include the Bohmian mechanics (see [4]), Everett's many worlds theory (see [5]), and the consistent histories approach (see [6]), to name but a few. Among the issues at stake is the role and the place of a conscious Observer, famously brought into the discussion as "Wigner's friend" [7]. Another such issue is the "collapse" of the wave function (see [8] and Refs. therein), i.e., a sudden change in the observed system's state, apparently not described by the Schroedinger equation. While many of the mentioned interpretations, [2] -[6], each in its own way, aim at a global description of physical world, our objective is somewhat more modest. The purpose of this paper is to try to formulate a basic approach, consistent with the elementary quantum mechanics, as well as with particular assumptions about the general issues mentioned above. We would like the approach to be as simple as possible, and the assumptions to be few. A certain amount of philosophising is, therefore, unavoidable. We start by asking what could one expect from quantum theory? A possible answer can be found in Feynman's Lectures [9], and we reproduce it here in full: ' So at the present time we must limit ourselves to computing probabilities. We say at the "present time", but we suspect very strongly that it is something that will be with us forever -that it is impossible to beat this puzzle -that it is the way nature really' is.' In the above quote "we" clearly refers to conscious Observers. The probabilities, on the other hand, tend to be mentioned in literature in at lest three different contexts. Obje...