Related papers: A note on the quantum of time
The Copenhagen interpretation of quantum mechanics assumes the existence of the classical deterministic Newtonian world. We argue that in fact the Newton determinism in classical world does not hold and in classical mechanics there is…
In quantum gravity there is no notion of absolute time. Like all other quantities in the theory, the notion of time has to be introduced "relationally", by studying the behavior of some physical quantities in terms of others chosen as a…
In the classical (non-quantum) relativity theory the course of the moving clock is dilated as compared to the course of the clock at rest (the Einstein dilation). Any unstable system may be regarded as a clock. The time evolution (e.g., the…
Non-relativistic quantum mechanics for a free particle is shown to emerge from classical mechanics through an invariance principle under transformations that preserve the Heisenberg position-momentum inequality. These transformations are…
We consider the evolution of quantum fields on a classical background space-time, formulated in the language of differential geometry. Time evolution along the worldlines of observers is described by parallel transport operators in an…
Quantum mechanical time operator is introduced following the parametric formulation of classical mechanics in the extended phase space. Quantum constraint on the extended quantum system is defined in analogy to the constraint of the…
Time is absolute in standard quantum theory and dynamical in general relativity. The combination of both theories into a theory of quantum gravity leads therefore to a "problem of time". In my essay I shall investigate those consequences…
Quantum theory does not only predict probabilities, but also relative phases for any experiment, that involves measurements of an ensemble of systems at different moments of time. We argue, that any operational formulation of quantum theory…
It is shown that the Schrodinger equation is a byproduct of more deterministic Boltzmann-like equation. All physical information is derived from the solution of this equation, which is a function of space and momentum. The additional terms…
We consider a number of aspects of the problem of defining time observables in quantum theory. Time observables are interesting quantities in quantum theory because they often cannot be associated with self-adjoint operators. Their…
A slight modification of one axiom of quantum theory changes a reversible theory into a time asymmetric theory. Whereas the standard Hilbert space axiom does not distinguish mathematically between the space of states (in-states of…
Both classical and respectively quantum observables can be modeled as somewhat similar examples of random variables. In such a model the associated measurements preserve the values spectrum of an observable but change the corresponding…
We discuss the classical and quantum mechanical evolution of systems described by a Hamiltonian that is a function of a solvable one, both classically and quantum mechanically. The case in which the solvable Hamiltonian corresponds to the…
The main distinction between classical mechanics and quantum mechanics is the lack in the latter of a full mechanical determinism: different final states can arise from the same physical state, after the measurement. No hidden variable is…
The one particle quantum mechanics is considered in the frame of a N-body classical kinetics in the phase space. Within this framework, the scenario of a subquantum structure for the quantum particle, emerges naturally, providing an…
I review basic principles of the quantum mechanical measurement process in view of their implications for a quantum theory of general relativity. It turns out that a clock as an external classical device associated with the observer plays…
Classical clocks measure proper time along their worldline, and Riemannian geometry provides tools for predicting the time shown by clocks in both flat and curved spacetimes. Common approaches to time in quantum systems, based for instance…
A practical way to deal with the problem of time in quantum cosmology and quantum gravity is proposed. The main tool is effective equations, which mainly restrict explicit considerations to semiclassical regimes but have the crucial…
Identifying the real and imaginary parts of wave functions with coordinates and momenta, quantum evolution may be mapped onto a classical Hamiltonian system. In addition to the symplectic form, quantum mechanics also has a positive-definite…
We study analytically the time evolution in decaying chaotic systems and discuss in detail the hierarchy of characteristic time scales that appeared in the quasiclassical region. There exist two quantum time scales: the Heisenberg time t_H…