Related papers: ``Weighing'' a closed system and the time-energy u…
We consider the situation in which an observer internal to an isolated system wants to measure the total energy of the isolated system (this includes his own energy, that of the measuring device and clocks used, etc...). We show that he can…
Quantum measurement is a physical process. A system and an apparatus interact for a certain time period (measurement time), and during this interaction, information about an observable is transferred from the system to the apparatus. In…
Measurements are ordinarily described with respect to absolute "Newtonian" time. In reality however, the switching-on of the measuring device at the instance of the measurement requires a timing device. Hence the classical time $t$ must be…
Suppose that the Hamiltonian acting on a quantum system is unknown and one wants to determine what is the Hamiltonian. We show that in general this requires a time $\Delta t$ which obeys the uncertainty relation $\Delta t \Delta H \gtrsim…
We propose a method to continually monitor the energy of a quantum system. We show that by having some previous knowledge of the system's dynamics, but not all of it, one can use the measured energy to determine many other quantities, such…
The celebrated Takens' embedding theorem provides a theoretical foundation for reconstructing the full state of a dynamical system from partial observations. However, the classical theorem assumes that the underlying system is deterministic…
In quantum systems, a plausible definition of work is based on two energy measurement scheme. Considering that energy change of quantum system obeys a time-energy uncertainty relation, it shall be interesting to see whether such type of…
Observations in Quantum Mechanics are subject to complex restrictions arising from the principle of energy conservation. Determining such restrictions, however, has been so far an elusive task, and only partial results are known. In this…
All energy measurements of a quantum system are prone to inaccuracies. In particular, if such measurements are carried over a finite period of time the accuracy of the result is affected by the length of that period. Here I show an upper…
The result of a physical measurement depends on the timescale of the experimental probe. In solid-state systems, this simple quantum mechanical principle has far-reaching consequences: the interplay of several degrees of freedom close to…
A simplified Heisenberg spin model is studied in order to examine the idea of decoherence in closed quantum systems. For this purpose, we present a quantifiable definition to quantum coherence $\Xi$, and discuss in some detail a general…
Heisenberg's uncertainty principle in application to energy and time is a powerful heuristics. This statement plays the important role in foundations of quantum theory and statistical physics. If some state exists for a finite interval of…
In this paper, we extend the standard formalism of quantum mechanics to a quantum theory for a total system including one internal measuring apparatus. The internality of the measuring apparatus implies that different decomposition of a…
We critically discuss the measure of very short time intervals. By means of a "gedankenexperiment", we describe an ideal clock based on the occurrence of completely random events. We show that the minimum time interval Delta t that this…
Textbook quantum mechanics treats time as a classical parameter, and not as a quantum observable with an associated Hermitian operator. For this reason, to make sense of usual time-energy uncertainty relations such as $\Delta {t}\Delta…
Energy has an ambiguous status in general relativity. For systems embedded in asymptotically flat space-times it is possible to construct an integral invariant that corresponds to total energy, however there is no local differential…
We prove an uncertainty relation for energy and arrival time, where the arrival of a particle at a detector is modeled by an absorbing term added to the Hamiltonian. In this well-known scheme the probability for the particle's arrival at…
The uncertainty principle is a cornerstone of modern physics, and its implications have a fundamental impact on theoretical and applied quantum mechanics. The aim of this thesis is to study and apply the uncertainty relations between time…
Measurement is a fundamental notion in the usual approximate quantum mechanics of measured subsystems. Probabilities are predicted for the outcomes of measurements. State vectors evolve unitarily in between measurements and by reduction of…
We review Bohr's reasoning in the Bohr-Einstein debate on the photon box experiment. The essential point of his reasoning leads us to an uncertainty relation between the proper time and the rest mass of the clock. It is shown that this…