Observable and Unobservable in Quantum Mechanics

Guido Bacciagaluppi, Antony Valentini

Introduction Quantum mechanics is based on the intuition that the essential difference between atomic physics and classical physics is the occurrence of discontinuities (see in particular [1,4,58–63]). Quantum mechanics should thus be considered a direct continuation of the quantum theory founded by Planck, Einstein and Bohr. Bohr in particular stressed repeatedly, already before the birth of quantum mechanics, that the discontinuities must lead to the introduction of new kinematical and mechanical concepts, so that indeed classical mechanics and its corresponding conceptual scheme should be abandoned [1,4]. Quantum mechanics tries to introduce the new concepts through a precise analysis of what is ‘observable in principle’. In fact, this does not mean setting up the principle that a sharp division between ‘observable’ and ‘unobservable’ quantities is possible and necessary. As soon as a conceptual scheme is given, one can infer from the observations to other facts that are actually not observable directly, and the boundary between ‘observable’ and ‘unobservable’ quantities becomes altogether indeterminate. But if the conceptual scheme itself is still unknown, it will be expedient to enquire only about the observations themselves, without drawing conclusions from them, because otherwise wrong concepts and prejudices taken over from before will block the way to recognising the physical relationships [Zusammenhänge].

Nancy Delaney Cartwright

Roshan Raj

It presents the evolution of the quantum observables from their classical counterpart and distinctly analyses the meaning of observable in context to both the classical and the quantum realms, with an emphasis on W. Heisenberg's realization of observable and unobservable [1925]. It is stated that quantum observables are, in the first place, indeed distinctive to classical observables since each appears unobservable to the other; however, to associate physical essence as possessed by the latter, the expectation value of the former is determined. Further, the possibility of mapping quantum information to the classical ones through the action of the operator may be realized after re-interpreting analogies between the quantum commutator and Poisson brackets.

PEKKA J. LAHTI, Sylvia Pulmannová

Akira Tonomura

Fundamental aspects of quantum mechanics, which were discussed only theoretically as "thought experiments" in the 1920s and 1930s, have begun to frequently show up in nanoscopic regions owing to recent rapid progress in advanced technologies. Quantum phenomena were once regarded as the ultimate factors limiting further miniaturization trends of microstructured electronic devices, but now they have begun to be actively used as the principles for new devices such as quantum computers. To directly observe what had been unobservable quantum phenomena, we have tried to develop bright and monochromatic electron beams for the last 35 years. Every time the brightness of an electron beam improved, fundamental experiments in quantum mechanics became possible, and quantum phenomena became observable by using the wave nature of electrons.

Holger Neumann