Related papers: A note on the quantum of time
In quantum mechanics, time is introduced as a non-measurable quantity, as there is no possibility to build a hermitian operator canonically conjugated to the Hamiltonian. We cannot have, therefore, the time operator, which means that the…
Discussions of quantum mechanics often loosely claim that time evolution logically must be unitary, in order for the probabilistic interpretation of the amplitudes of the state vector to make sense at all times. We discuss from first…
In two articles, the authors claim that the Heisenberg uncertainty principle limits the precision of simultaneous measurements of the position and velocity of a particle and refer to experimental evidence that supports their claim. It is…
If there exists a classical, i.e. deterministic theory underlying quantum mechanics, an explanation must be found of the fact that the Hamiltonian, which is defined to be the operator that generates evolution in time, is bounded from below.…
Quantum mechanics postulates the existence of states determined by a particle position at a single time. This very concept, in conjunction with superposition, induces much of the quantum-mechanical structure. In particular, it implies the…
Due to the inevitable existence of quantum effects, a classical description generically breaks down after a finite quantum break-time $t_q$. We aim to find criteria for determining $t_q$. To this end, we construct a new prototype model that…
A method based off of operator consideration for solving the time evolution of a wave function is developed. The method is applied to free space, constant force and harmonic oscillator potentials where general solutions are derived for the…
The application of quantum theory to cosmology raises a number of conceptual questions, such as the role of the quantum-mechanical notion of "observer" or the absence of a time variable in the Wheeler-DeWitt equation. I point out that a…
Frauchiger and Renner recently cast doubt on the universal applicability of Quantum Mechanics [1]. In the following, it is pointed out that their conclusion of one of three common-sense conditions, demanded for Quantum Mechanics, being…
It is expected that a quantum theory of gravity will radically alter our current notion of spacetime geometry. However, contrary to what was commonly assumed for many decades, quantum gravity effects could manifest in scales much larger…
The mechanism of the transition of a dynamical system from quantum to classical mechanics is one of the remaining challenges of quantum theory. Currently, it is considered to occur via decoherence caused by entanglement and/or stochastic…
We have previously presented a version of the Weak Equivalence Principle for a quantum particle as an exact analog of the classical case, based on the Heisenberg picture analysis of free particle motion. Here, we take that to a full…
Do scientific theories limit human knowledge? In other words, are there physical variables hidden by essence forever? We argue for negative answers and illustrate our point on chaotic classical dynamical systems. We emphasize parallels with…
Time evolution operator in quantum mechanics can be changed into a statistical operator by a Wick rotation. This strict relation between statistical mechanics and quantum evolution can reveal deep results when the thermodynamic limit is…
The problem of time operator in quantum mechanics is revisited. The unsharp measurement model for quantum time based on the dynamical system-clock interaction, is studied. Our analysis shows that the problem of the quantum time operator…
I propose a new and direct connection between classical mechanics and quantum mechanics where I derive the quantum mechanical propagator from a variational principle. This variational principle is Hamilton's modified principle generalized…
Different quantum mechanical operators can correspond to the same classical quantity. Hermitian operators differing only by operator ordering of the canonical coordinates and momenta at one moment of time are the most familiar example.…
The treatment of time in relativity does not conform to that in quantum theory. To resolve the discrepancy, a formalization of time is introduced in an accompanying paper, starting from the assumption that the treatment of time in physics…
In a previous paper a formalism to analyze the dynamical evolution of classical and quantum probability distributions in terms of their moments was presented. Here the application of this formalism to the system of a particle moving on a…
I consider in this book a formulation of Quantum Mechanics. Usually QM is formulated based on the notion of time and space, both of which are thought a priori given quantities or notions. However, when we try to define the notion of…