The main purpose of this short article is to give a brief overview of the development of the very interesting weak measurement protocol. I add some comments relating to the reality of weak values, and also comment on the allowed values of observables between measurements.
Homogeneous, periodic, quasiperiodic, irregular and disordered spatial structures have been at the heart of scientific interest and research for a long time and in many disciplines as diverse as chemistry, physics, biology and morphology. Some recent, spectacular achievements in experimental quantum optics have, however, made it possible to study quantum effects in a variety of spatial structures. The main aim of this Focus Issue is to present some of the most recent theoretical, numerical and experimental progresses in the area of Quantum Structures, i.e. spatial structures that display quantum features. A short background overview of Quantum Structures is provided at the beginning of this Focus Issue, in which individual authors' works are specifically commented. In brief, we can say that the articles can be catalogued into two main areas of research interest in Quantum Structures: quantum effects in spatial structures in nonlinear optics, and in atomic physics.
Despite their important applications in metrology and in spite of numerous experimental demonstrations, weak measurements are still confusing for part of the community. This sometimes leads to unjustified criticism. Recent papers have experimentally clarified the meaning and practical significance of weak measurements, yet in Kastner (Found Phys 47:697-707, 2017), Kastner seems to take us many years backwards in the the debate, casting doubt on the very term "weak value" and the meaning of weak measurements. Kastner appears to ignore both the basics and frontiers of weak measurements and misinterprets the weak measurement process and its outcomes. In addition, she accuses the authors of Aharonov et al. (Ann Phys 355:258-268, 2015) in statements completely opposite to the ones they have actually made. There are many points of disagreement between Kastner and us, but in this short reply I will leave aside the ontology (which is indeed interpretational and far more complex than that described by Kastner) and focus mainly on the injustice in her criticism. I shall add some general comments regarding the broader theory of weak measurements and the two-state-vector formalism, as well as supporting experimental results. Finally, I will point out some recent promising results, which can be proven by (strong) projective measurements, without the need of employing weak measurements.