Quantization of the momentum of an electromagnetic field in atoms and selection rules for optical transitions

The existing methods for calculating the energy of stationary states relate it to the energy of the electron, considering it negative in the atom. Formally, choosing a point that corresponds to zero potential energy you can assign a negative value to the electron energy. However, this approach does not answer many other questions, for example, the actual value of the energy of stationary states is unknown, but only the difference in energies between stationary states is known; the concept of “minimum energy of the system” loses its meaning (choosing the origin of the energy reference, we replace the minimum with the maximum, or vice versa); the physical reason for the stability of stationary states is not clear; it is impossible to reveal the physical reason for the introduction of selection rules, since the Heisenberg uncertainty relations exclude the analysis of the transition mechanism, replacing it with the concept of a “quantum leap”. Let us show that the energy of stationary states is the energy of a spherical capacitor, the covers of which are spheres whose radii are equal to the radius of the nuclear and corresponding stationary state. The energy of the ground state in the hydrogen atom is 0.8563997 MeV. The presence of charges and a magnetic field presupposes the circulation of energy in the volume of the atom (the Poynting vector is not zero). Revealed quantization of the angular momentum of the electromagnetic field in stationary states is [Formula: see text]. The change in the angular momentum of the electromagnetic field during transitions between stationary states in atoms removes the physical grounds for introducing selection rules. The analysis shows that the Heisenberg uncertainty relations are not universal, and their application in each specific case must be justified.

A Contextual Planck Parameter and the Classical Limit in Quantum Cosmology

We propose that whatever quantity controls the Heisenberg uncertainty relations (for a given complementary pair of observables) it should be identified with an effective Planck parameter. With this definition it is not difficult to find examples where the Planck parameter depends on the region under study, varies in time, and even depends on which pair of observables one focuses on. In quantum cosmology the effective Planck parameter depends on the size of the comoving region under study, and so depends on that chosen region and on time. With this criterion, the classical limit is expected, not for regions larger than the Planck length, $$l_{P}$$ l P , but for those larger than $$l_{Q}=(l_{P}^{2}H^{-1})^{1/3}$$ l Q = ( l P 2 H - 1 ) 1 / 3 , where H is the Hubble parameter. In theories where the cosmological constant is dynamical, it is possible for the latter to remain quantum even in contexts where everything else is deemed classical. These results are derived from standard quantization methods, but we also include more speculative cases where ad hoc Planck parameters scale differently with the length scale under observation. Even more speculatively, we examine the possibility that similar complementary concepts affect thermodynamical variables, such as the temperature and the entropy of a black hole.

Zero–trade-off multiparameter quantum estimation via simultaneously saturating multiple Heisenberg uncertainty relations

Quantum estimation of a single parameter has been studied extensively. Practical applications, however, typically involve multiple parameters, for which the ultimate precision is much less understood. Here, by relating the precision limit directly to the Heisenberg uncertainty relation, we show that to achieve the highest precisions for multiple parameters at the same time requires the saturation of multiple Heisenberg uncertainty relations simultaneously. Guided by this insight, we experimentally demonstrate an optimally controlled multipass scheme, which saturates three Heisenberg uncertainty relations simultaneously and achieves the highest precisions for the estimation of all three parameters in SU(2) operators. With eight controls, we achieve a 13.27-dB improvement in terms of the variance (6.63 dB for the SD) over the classical scheme with the same loss. As an experiment demonstrating the simultaneous achievement of the ultimate precisions for multiple parameters, our work marks an important step in multiparameter quantum metrology with wide implications.

Determinism and Locality

This chapter discusses the conceptual relationship between determinism and locality, particularly in the context of quantum mechanics (QM). It first examines the connection between determinism and locality in abstract terms, and then in the context of QM. It then considers four possible combinations of locality and determinism: locality and determinism, nonlocality and determinism, locality and indeterminism, and nonlocality and indeterminism. It also explains how determinism and locality are linked to a central tenet of QM—the Heisenberg uncertainty relations. Three approaches that link uncertainty and nonlocality are explored: the first two, attributed to Erwin Schrödinger and I. Pitowsky, argue from the uncertainty relations to entanglement; the second, following S. Popescu and D. Rohrlich, from entanglement to the uncertainty relations. The chapter argues that determinism and locality are independent concepts but can offset each other under certain conditions, so that violation of the one permits satisfaction of the other.