Related papers: Whose Projection Postulate?
The mathematics of classical probability theory was subsumed into classical measure theory by Kolmogorov in 1933. Quantum theory as nonclassical probability theory was incorporated into the beginnings of noncommutative measure theory by von…
The Von Neumann quantum measurement theory and Zurek reformulation are based on an assumption that the quantum system, apparatus and environment obey the quantum mechanics rules. According to the Zurek theory the observers typically…
A geometric approach to formulate the uncertainty principle between quantum observables acting on an $N$-dimensional Hilbert space is proposed. We consider the fidelity between a density operator associated with a quantum system and a…
The von Neumann interaction between a particle and an apparatus has been considered in the measurement of the position of a particle when the interaction lasts for a finite amount of time. When the measurement has finite duration, both the…
John von Neumann's spectral theorem for self-adjoint operators is a cornerstone of quantum mechanics. Among other things, it also provides a connection between expectation values of self-adjoint operators and expected values of real-valued…
Paul A. M. Dirac has been undoubtedly one of the central figures of the last century physics, contributing in several and remarkable ways to the development of Quantum Mechanics (QM); he was also at the centre of an active community of…
According to quantum theory, the outcomes of future measurements cannot (in general) be predicted with certainty. In some cases, even with a complete physical description of the system to be measured and the measurement apparatus, the…
The conventional postulate for the probabilistic interpretation of quantum mechanics is asymmetric in preparation and measurement, making retrodiction reliant on inference by use of Bayes' theorem. Here, a more fundamental symmetric…
The inference of a hidden variable's historical value, based on observations before and after the fact, is a controversial subject in quantum mechanics. Here I address the controversy by proposing a formalism that unifies and generalizes…
We derive differential equations for the modified Feynman propagator and for the density operator describing time-dependent measurements or histories continuous in time. We obtain an exact series solution and discuss its applications.…
Heisenberg's uncertainty principle was originally posed for the limit of the accuracy of simultaneous measurement of non-commuting observables as stating that canonically conjugate observables can be measured simultaneously only with the…
New insight to the principles of the quantum physics development is given. The correct ways for the construction of new versions of quantum mechanics on the second main postulate base are discussed. The conclusion on the status of the…
The quantum measurement problem is formulated in the form of an insolubility theorem that states the impossibility of obtaining, for all available object preparations, a mixture of states of the compound object and apparatus system that…
In 1971 Feynman, Kislinger and Ravndal [1] proposed Lorentz-invariant differential equation capable to describe relativistic particle with mass and internal space-time structure. By making use of new variables that differentiate between…
Gleason's theorem [A. Gleason, J. Math. Mech., \textbf{6}, 885 (1957)] is an important result in the foundations of quantum mechanics, where it justifies the Born rule as a mathematical consequence of the quantum formalism. Formally, it…
The Born rule may be stated mathematically as the rule that probabilities in quantum theory are expectation values of a complete orthogonal set of projection operators. This rule works for single laboratory settings in which the observer…
Quantum mechanics allows for multiple predictions for the outcome of an EPR experiment. The correct calculation must be used, guided by the physical conditions of the experiment. The quantum joint prediction for EPR correlation is derived…
Influence theory is a foundational theory of physics that is not based on traditional empirically defined concepts, such as positions in space and time, mass, energy, or momentum. Instead, the aim is to derive these concepts, and their…
Physical observation is made relative to a reference frame which is essentially a quantum system. Thus, a quantum system must be described relative to a quantum reference frame (QRF). Further requirements on QRF include using only…
This paper gives new foundations of quantum state reduction without appealing to the projection postulate for the probe measurement. For this purpose, the quantum Bayes principle is formulated as the most fundamental principle for…