L.I. Mandelstam, the outstanding Soviet physicist, leader of a prominent and productive scientific community, was educated as a physicist and started as a researcher and an university teacher at Strasbourg University. We consider the intellectual influence of the main currents in contemporary German science on Mandelstam's work in science.

In his 1939 Lectures, the prominent Soviet physicist L. I. Mandelstam proposed an interpretation of quantum mechanics that was understood in different ways. To assess Mandelstam's interpretation, we classify contemporary interpretations of quantum mechanics and compare his interpretation with others developed in the 1930s. We conclude that Mandelstam's interpretation belongs to the family of minimal statistical interpretations and has much in common with interpretations developed by American physicists. Mandelstam's characteristic message was his theory of indirect measurement, which influenced his discussion (...) of the "reduction of the wave packet" and the Einstein, Podolsky, and Rosen argument. This article also reconstructs what lay behind Mandelstam's interpretation of quantum mechanics. This was his operationalism, by virtue of which his interpretation resembled Kemble's, in which the statistical and Copenhagen views had been combined. Like Popper and Margenau, Mandelstam followed R. von Mises's empirical conception of probability. Mandelstam, like the other proponents of the statistical approach to quantum mechanics, was affected by the culture of macroscopic experimentation with its emphasis on statistical measurement. (shrink)

A quantization procedure without Hamiltonian is reported which starts from a statistical ensemble of particles of mass m and an associated continuity equation. The basic variables of this theory are a probability density ρ, and a scalar field S which defines a probability current j=ρ ∇ S/m. A first equation for ρ and S is given by the continuity equation. We further assume that this system may be described by a linear differential equation for a complex-valued state variable χ. Using (...) these assumptions and the simplest possible Ansatz χ(ρ,S), for the relation between χ and ρ,S, Schrödinger’s equation for a particle of mass m in a mechanical potential V(q,t) is deduced. For simplicity the calculations are performed for a single spatial dimension (variable q). Using a second Ansatz χ(ρ,S,q,t), which allows for an explicit q,t-dependence of χ, one obtains a generalized Schrödinger equation with an unusual external influence described by a time-dependent Planck constant. All other modifications of Schrödinger’ equation obtained within this Ansatz may be eliminated by means of a gauge transformation. Thus, this second Ansatz may be considered as a generalized gauging procedure. Finally, making a third Ansatz, which allows for a non-unique external q,t-dependence of χ, one obtains Schrödinger’s equation with electrodynamic potentials A,φ in the familiar gauge coupling form. This derivation shows a deep connection between non-uniqueness, quantum mechanics and the form of the gauge coupling. A possible source of the non-uniqueness is pointed out. (shrink)

This paper makes a collective biographical profile of a sample of physicists who were protagonists in the research on the foundations of quantum physics circa 1970. We study the cases of Zeh, Bell, Clauser, Shimony, Wigner, Rosenfeld, d’Espagnat, Selleri, and DeWitt, analyzing their training and early career, achievements, qualms with quantum mechanics, motivations for such research, professional obstacles, attitude towards the Copenhagen interpretation, and success and failures. Except for Rosenfeld, they were all dissidents, fighting against the dominant attitude among physicists (...) at the time according to which foundational issues had already been solved by the founding fathers of the discipline. Theirs is a story of success as the foundations of quantum mechanics finally entered the physics mainstream despite the fact that their expectations of breaking down quantum mechanics were not fulfilled. (shrink)

By probability theory the probability space to underlie the set of statistical data described by the squared modulus of a coherent superposition of microscopically distinct (sub)states (CSMDS) is non-Kolmogorovian and, thus, such data are mutually incompatible. For us this fact means that the squared modulus of a CSMDS cannot be unambiguously interpreted as the probability density and quantum mechanics itself, with its current approach to CSMDSs, does not allow a correct statistical interpretation. By the example of a 1D completed scattering (...) and double slit diffraction we develop a new quantum-mechanical approach to CSMDSs, which requires the decomposition of the non-Kolmogorovian probability space associated with the squared modulus of a CSMDS into the sum of Kolmogorovian ones. We adapt to CSMDSs the presented by Khrennikov (Found. Phys. 35(10):1655, 2005) concept of real contexts (complexes of physical conditions) to determine uniquely the properties of quantum ensembles. Namely we treat the context to create a time-dependent CSMDS as a complex one consisting of elementary (sub)contexts to create alternative subprocesses. For example, in the two-slit experiment each slit generates its own elementary context and corresponding subprocess. We show that quantum mechanics, with a new approach to CSMDSs, allows a correct statistical interpretation and becomes compatible with classical physics. (shrink)

Reichenbach's interpretation of quantum mechanics has been narrowly reduced to the advocacy of a three‐valued logic. His interpretation rests, though, on the same rich epistemological framework that shapes his influential analysis of space‐time theories. Different interpretations of the quantum formalism, with their conflicting ontologies and causes, emerge in this view as “equivalent descriptions”. One casualty of the conventionalist approach is the measurement problem. I give reasons for why Reichenbach's view on the nature of interpretations of quantum theory cannot be defended.

Quantum mechanics notoriously faces the measurement problem, the problem that if read thoroughly, it implies the nonexistence of definite outcomes in measurement procedures. A plausible reaction to this and to related problems is to regard a system's quantum state |ψ> merely as an indication of our lack of knowledge about the system, i.e., to interpret it epistemically. However, there are radically different ways to spell out such an epistemic view of the quantum state. We here investigate recent developments in the (...) branch that introduces hidden variables λ in addition to the quantum state |ψ> and has its roots in Einstein's views. In particular, we confront purported achievements of a concrete model that has been considered to serve as evidence for an epistemic view of the envisioned kind, as well as specific no-go results and their import. It will be argued that while an epistemic account of the particular kind is not straightforwardly ruled out by the no-go results, they demonstrate that the evidential character of the model(s) discussed rests on a rather shaky foundation, and that they make some achievements widely recognized in the literature appear worthy of doubt. (shrink)