相关论文: Axiom System and Completeness Expression for Quant…
Conditional probabilities in quantum systems which have both initial and final boundary conditions are commonly evaluated using the Aharonov-Bergmann-Lebowitz rule. In this short note we present a seemingly disturbing paradox that appears…
Contrary to general relativity, quantum theory treats space and time in fundamentally different ways. In particular, while joint probabilities associated with spacelike separated measurements are defined in terms of the Born rule, joint…
The notion that any physical quantity is defined and measured relative to a reference frame is traditionally not explicitly reflected in the theoretical description of physical experiments where, instead, the relevant observables are…
The quantum theory of decoherence plays an important role in a pragmatist interpretation of quantum theory. It governs the descriptive content of claims about values of physical magnitudes and offers advice on when to use quantum…
In a companion paper (hereafter referred to as Paper I), we have presented an attempt to derive the finite-dimensional abstract quantum formalism from a set of physically comprehensible assumptions. In this paper, we formulate a…
A recent concept in theoretical physics, motivated in string duality and M-theory, is the notion that not all quantum theories arise from quantising a classical system. Also, a given quantum model may possess more than just one classical…
We study the construction of probability densities for time-of-arrival in quantum mechanics. Our treatment is based upon the facts that (i) time appears in quantum theory as an external parameter to the system, and (ii) propositions about…
It is the matter of fact that quantum mechanics operates with notions that are not determined in the frame of the mechanics' formalism. Among them we can call the notion of "wave-particle" (that, however, does not appear in both classical…
The additivity of classical probabilities is only the first in a hierarchy of possible sum-rules, each of which implies its successor. The first and most restrictive sum-rule of the hierarchy yields measure-theory in the Kolmogorov sense,…
Quantum metrology is a general term for methods to precisely estimate the value of an unknown parameter by actively using quantum resources. In particular, some classes of entangled states can be used to significantly suppress the…
We propose a complete proof of the Born rule using an additional postulate stating that for a short enough time {\Delta}t between two measurements, a property of a particle will keep its values fixed. This dynamical postulate allows us to…
The ``evolving constants'' method of defining the quantum dynamics of time-reparametrization-invariant theories is investigated for a particular implementation of parametrized non-relativistic quantum mechanics (PNRQM). The wide range of…
We use sets of assignments, a.k.a. teams, and measures on them to define probabilities of first-order formulas in given data. We then axiomatise first-order properties of such probabilities and prove a completeness theorem for our…
In standard quantum mechanics (QM), a state vector $| \psi \rangle$ may belong to infinitely many different orthogonal bases, as soon as the dimension $N$ of the Hilbert space is at least three. On the other hand, a complete physical…
The Born rule postulates that the probability of measurement in quantum mechanics is related to the squared modulus of the wave function $\psi$. We rearrange the equation for energy eigenfunctions to define the energy as the real part of…
A rigorous general definition of quantum probability is given, which is valid for elementary events and for composite events, for operationally testable measurements as well as for inconclusive measurements, and also for non-commuting…
It is argued that the three main quantum interpretations, Copenhagen, de Broglie-Bohm, and Many-Worlds, support the Principle Q (Quantum): Not all what matters for physical phenomena is contained in space-time. This principle underpins…
We discuss the axiomatic basis of quantum mechanics and show that it is neither general nor consistent, since its axioms are incompatible with each other and moreover it does not incorporate the magnetic quantization as in the cyclotron…
The probabilistic predictions of quantum theory are conventionally obtained from a special probabilistic axiom. But that is unnecessary because all the practical consequences of such predictions follow from the remaining, non-probabilistic,…
The quantum mechanics of closed systems such as the universe is formulated using an extension of familiar probability theory that incorporates negative probabilities. Probabilities must be positive for sets of alternative histories that are…