Relational Approach To Quantum Physics - Mathematical Structure of Quantum Theory As A Conceptual Map

Mathematical Structure of Quantum Theory As A Conceptual Map

One can conclude that the Newtonian analysis of the world into constituent objects has been replaced in terms of a kind of interactive pattern between the fields and their detection by the observer. The implications of this approach avoids much of our confusion about the wave-particle duality, if we regard the quantum theory of light detection as a kind of conceptual map of the events in the world, in a similar manner to the Minkowski diagram in Einstein's theory of special relativity.

Because of the relativistic unification of the particle and wave pictures into the single expression of Eq. (1), there appears an illusion of co-existence of these two pictures. However, a little reflection shows that this view of the quantum theory of light detection is very far from the truth indeed. Let us say, for example, that an observer wants to measure the speed of a light signal. He or she must then construct a particle frame of detection that registers where, and when, a light signal is emitted and then absorbed. (We note that the propagation of a light signal is, in fact, what Einstein studied in the development of his special relativity theory). Such an observer cannot survey the whole of Eq. (1); he or she can only obtain the propagation details of the operators and . Therefore, the exact information of the phase factor is unknown to the observer; for this, an interference experiment is required.

Thus, the quantum theory of light detection can be envisioned as a conceptual map, having an invariant structure, containing the 'real' set of fields and their detection which can be observed experimentally. "In all maps (conceptual or otherwise) there arises the need for the user to locate and orient himself by seeing which point on the map represents his position and which line represents the direction in which he is looking". In doing this, one recognizes that every act of actualization yields a unique perspective on the world. But with the aid of the quantum theory of light detection, one can relate what is seen from one perspective (the particle frame) to what is seen from another (the wave frame). In this way one can abstract out what is invariant under a change of perspective, which leads to an ever-improving knowledge and understanding of the actual character of the radiation system under investigation. Therefore, when an observer, performing experiments with different frames of detection, tries to understand what is observed, he or she need not puzzle about which view is 'correct' and which view is 'wrong' (wave or particle). Rather, he or she consults the map provided by Eq. (1) and tries to come to a common understanding of why in each way detecting the same field has a different perspective. Different frames may be related to one another, for example, by employing the de Broglie relation, .