Coherence and contextuality in scattering experiments

Abstract

At a first sight, the description of a scattering experiment seems to be easy and unambiguous. A projectile, as for instance an electron or an ion, flies out of an accelerator with a given momentum p toward an atom or molecule, assumed to be at rest in the collision chamber, and interacts with it. This interaction might lead to different outcomes. For instance, the target might reach an excited bound state, or even loss an electron. These are only two examples of a myriad of options, which are usually called "channels". Thus, we can talk about the elastic channel, the excitation channel, the ionization channel, etc. Finally, one or some of the products of the collision are collected in order to investigate one of these channels.A closer look reveals that the description of any of these experiments is not quite as straight forward. More specifically, one major complication is that the Schrodinger equation is not analytically solvable for more than two mutually interacting particles, even when the underlying forces are precisely known. This is known as the few-body problem (FBP), which is formulated in the introduction to this book and theoretically discussed in other chapters. The FBP, in turn, is afflicted with an additional major complication which is usually overlooked. Addressing this drawback of the standard descriptions of the FBP is the main objective of the present chapter. Both the initial preparation of the projectiles and the final detection of the outgoing particles occur at macroscopic distances, and therefore it is assumed that they cannot have any effect on the scattering event, which occurs in a region of atomic dimensions. In other words, we might say that a scattering experiment is independent of its context. Furthermore, since both the beam of projectiles and the target gas can be described by pure quantum states, we are dealing with a purely coherent process.Unfortunately (or fortunately, depending on how each of us cope with uncertainties and broken paradigms), when we look deeper into this kind of experiments, we find out that they are trickier than expected. As we will discuss in the present chapter, all and every statement in the previous paragraph is false or at least doubtful. In what follows, we will discuss these issues, paying special attention to the assumption of coherence and lack of contextuality. But first, we will explore some basic ideas in very simple terms, which will pave the way for the discussion ahead.