Related papers: Whose Projection Postulate?
Quantum mechanics is usually presented starting from a series of postulates about the mathematical framework. In this work we show that those same postulates can be derived by assuming that measurements are discrete interactions: that is,…
The cognitive state of mind concerning a range of choices to be made can effectively be modelled in terms of an element of a high-dimensional Hilbert space. The dynamics of the state of mind resulting form information acquisition is…
As is well known, in quantum mechanics, the calculation rule of the probability that an eigen-value a_n is observed when the physical quantity A is measured for a state described by the state vector |> is P(a_n)=<|A_n><A_n|> . However, in…
Understanding the invasive nature of quantum measurement and its implications in quantum foundations and information science demands a mathematically rigorous and physically well-grounded characterization of intrinsic back-action in general…
Projective measurement is used as a fundamental axiom in quantum mechanics, even though it is discontinuous and cannot predict which measured operator eigenstate will be observed in which experimental run. The probabilistic Born rule gives…
The problem of measurement in quantum mechanics is that the quantum particle in the course of evolution, as described by the linear Schrodinger equation, exists in all of its possible states, but in measuring, the particle is always…
Measurement in quantum mechanics is generally described as an irreversible process that perturbs the wavefunction describing a quantum system. In this work we establish a formal connection between the measurement description within the…
In quantum theory general measurements are described by so-called Positive Operator-Valued Measures (POVMs). We show that in $d$-dimensional quantum systems an application of depolarizing noise with constant (independent of $d$) visibility…
The space discreteness hypothesis asserts that the nature of space at short distances is radically different from that at large distances. Based on the Bronstein inequality, here, we use a totally disconnected topological space…
It is well known that the pointer state |{\Phi}> resulting from the von Neumann measurement of a projection operator A performed upon an ensemble of quantum systems in the preselected state |{\psi}> depends upon A|{\psi}>. Here it is shown…
We review the famous no-hidden-variables theorem in John von Neumann's 1932 book on the mathematical foundations of quantum mechanics. We describe the notorious gap in von Neumann's argument, pointed out by Grete Hermann in 1935 and, more…
In 1929 Szilard pointed out that the physics of the observer may play a role in the analysis of experiments. The same year, Bohr pointed out that complementarity appears to arise naturally in psychology where both the objects of perception…
Bohmian mechanics, also known as pilot-wave theory or de Broglie-Bohm theory, is a formulation of quantum mechanics whose fundamental axioms are not about what observers will see if they perform an experiment but about what happens in…
One of the concepts of Relativity theory that challenges conventional intuition the most is time dilation and length contraction. Usual approaches for describing relativistic effects in quantum systems merely postulate the consequences of…
The argument is re-examined that the program of deriving the rule of state reduction from the Schroedinger equation holding for the object-apparatus composite system falls into a vicious circle or an infinite regress called the von Neumann…
From an analysis of projective measurements, it is shown that the Wigner rule is the unique operational quasi-probability for the post-measurement state. A unique pre-measurement quasi-probability is derived from a principle of invariance…
In this paper we are going to introduce a new dynamical postulate in Quantum Mechanics. This new principle is defined using path integrals over the set of normalized wave functions. We will show in a qualitative way that this postulate is…
In two papers entitled "On a new foundation [Neue Begr\"undung] of quantum mechanics," Pascual Jordan (1927b,g) presented his version of what came to be known as the Dirac-Jordan statistical transformation theory. As an alternative that…
It is shown that, although correct mathematically, the celebrated 1932 theorem of von Neumann which is often interpreted as proving the impossibility of the existence of "hidden variables" in Quantum Mechanics, is in fact based on an…
We give an explicit formula for the time projection in an arbitrary von Neumann algebra from which all its basic properties can be easily derived. The analysis of the situation when this time projection is a conditional expectation is also…