Abstract:
In a series of papers [1,2,3], Lawrence Schulman presented examples which demonstrate the compatibility of opposite arrows of time in various situations. In a previous letter to this journal [4] I questioned some of them for not being realistic in spite of being logically correct. Schulman replied [5] to these objections in a letter directly succeeding my one. I am here trying to clarify some aspects of the dispute, thereby further explaining and supporting my previous conclusions.

Abstract:
I argue that opposite arrows of time, while being logically possible, cannot realistically be assumed to exist during one and the same epoch of our universe.

Abstract:
A historically important but little known debate regarding the necessity and meaning of macroscopic superpositions, in particular those containing different gravitational fields, is discussed from a modern perspective.

Abstract:
Conceptual problems regarding the arrow of time in classical physics, quantum physics, cosmology, and quantum gravity are discussed. Particular attention is paid to the dynamical role of the quantum indeterminism, and to various concepts of timelessness.

Abstract:
A short critical review of the concept of decoherence, its consequences, and its possible implications for the interpretation of quantum theory is given.

Abstract:
The concept of decoherence is defined, and discussed in a historical context. This is illustrated by some of its essential consequences which may be relevant for the interpretation of quantum theory. Various aspects of the formalism are also reviewed for this purpose. Contents: 1. Definition of concepts. 2. Roots in nuclear physics. 3. The quantum-to-classical transition. 4. Quantum mechanics without observables. 5. Rules versus tools. 6. Nonlocality. 7. Information loss (paradox?). 8. Dynamics of entanglement. 9. Irreversibility. 10. Concluding remarks.

Abstract:
I review arguments demonstrating how the concept of "particle" numbers arises in the form of equidistant energy eigenvalues of coupled harmonic oscillators representing free fields. Their quantum numbers (numbers of nodes of the wave functions) can be interpreted as occupation numbers for objects with a formal mass (defined by the field equation) and spatial wave number ("momentum") characterizing classical field modes. A superposition of different oscillator eigenstates, all consisting of n modes having one node, while all others have none, defines a nondegenerate "n-particle wave function". Other discrete properties and phenomena (such as particle positions and "events") can be understood by means of the fast but smooth process of decoherence: the irreversible dislocalization of superpositions. Any wave-particle dualism thus becomes obsolete. The observation of individual outcomes of this decoherence process in measurements requires either a subsequent collapse of the wave function or a "branching observer" in accordance with the Schr\"odinger equation - both possibilities applying clearly after the decoherence process. Any probability interpretation of the wave function in terms of local elements of reality, such as particles or other classical concepts, would open a Pandora's box of paradoxes, as is illustrated by various misnomers that have become popular in quantum theory.

Abstract:
Introduction to the theory of decoherence. Contents: 1. The phenomenon of decoherence: superpositions, superselection rules, decoherence by "measurements". 2. Observables as a derivable concept. 3. The measurement problem. 4. Density matrix, coarse graining, and "events". 5. Conclusions.

Abstract:
The existence of spacetime singularities is irrelevant for the irreversible appearance of black holes. However, confirmation of the latter's unitary dynamics would require the preparation of a coherent superposition of a tremendous number of appropriate ``Everett worlds''.