Heisenberg uncertainty relations and average space curvature in geometric quantum mechanics

1988 ◽  
Vol 130 (4-5) ◽  
pp. 199-202 ◽  
Author(s):  
E. Santamato
Author(s):  
Yemima Ben-Menahem

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.


2012 ◽  
Vol 86 (2) ◽  
Author(s):  
Iwo Bialynicki-Birula ◽  
Zofia Bialynicka-Birula

Author(s):  
S. A. Pyroha

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.


Author(s):  
M. Suhail Zubairy

The laws of quantum mechanics were formulated in the year 1925 through the work of Werner Heisenberg, followed by Max Born, Pascual Jordan, Paul Dirac, and Wolfgang Pauli. A separate but equivalent approach was independently developed by Erwin Schrödinger in early 1926. The laws governing quantum mechanics were highly mathematical and their aim was to explain many unresolved problems within the framework of a formal theory. The conceptual foundation emerged in the subsequent 2–3 years that indicated how radically different the new laws were from classical physics. In this chapter some of these salient features of quantum mechanics are discussed. The topics include the quantization of energy, wave–particle duality, the probabilistic nature of quantum mechanics, Heisenberg uncertainty relations, Bohr’s principle of complementarity, and quantum superposition and entanglement. This discussion should indicate how different and counterintuitive its fundamentals are from those of classical physics.


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