Related papers: Born rule and Schr\"odinger equation from first pr…
The functional Schr\"odinger equation in curved space-time is derived from the manifestly covariant precanonical Schr\"odinger equation. The Schr\"odinger wave functional is expressed as the trace of the multidimensional product integral of…
The notion of probability plays a crucial role in quantum mechanics. It appears in quantum mechanics as the Born rule. In modern mathematics which describes quantum mechanics, however, probability theory means nothing other than measure…
Without Niels Bohr, QBism would be nothing. But QBism is not Bohr. This paper attempts to show that, despite a popular misconception, QBism is no minor tweak to Bohr's interpretation of quantum mechanics. It is something quite distinct.…
To apply the abstract quantum formalism to a particular physical system, one must specify the precise form of the relevant measurement and symmetry transformation operators. These operators are determined by a set of rules, the…
The Born rule asserts the probability distribution of eigenstates observed in unbiased quantum measurements, but the reason it holds remains elusive. This manuscript discusses how the Born rule might be explained by Schrodinger equation…
Starting from the guiding principles of spacetime locality and operationalism, a general framework for a probabilistic description of nature is proposed. Crucially, no notion of time or metric is assumed, neither any specific physical…
One of the advantages of a reconstruction of quantum mechanics based on transparent physical axioms is that it may offer insight to naturally generalize quantum mechanics by relaxing the axioms. Here, we discuss possible extensions of…
Modern experiments using nanoscale devices come ever closer to bridging the divide between the quantum and classical realms, bringing experimental tests of objective collapse theories that propose alterations to Schr\"{o}dinger's equation…
It has been suggested by Diosi and Penrose that the occurrence of quantum state reduction in macroscopic objects is related to a manifestation of gravitational effects in quantum mechanics. Although within Penrose's framework the dynamics…
The kinematical foundations of Schwinger's algebra of selective measurements were discussed in a previous paper (arXiv:1905.12274) and, as a consequence of this, a new picture of quantum mechanics based on groupoids was proposed. In this…
We reconstruct the explicit formalism of qubit quantum theory from elementary rules on an observer's information acquisition. Our approach is purely operational: we consider an observer O interrogating a system S with binary questions and…
The Schr\"odinger equation is universally accepted due to its excellent predictions aligning with observed results within its defined conditions. Nevertheless, it does not seem to possess the simplicity of fundamental laws, such as Newton's…
When a conscious observer is part of a quantum mechanical system, rule (4) cuts off solutions to the Schrodinger equation. It is important to show that this interruption of the Hamiltonian dynamics does not effect the statistical…
This paper presents a novel explanation of the cause of quantum probabilities and the Born rule based on the intuitionistic interpretation of quantum mechanics where propositions obey constructive (intuitionistic) logic. The use of…
The introduction of nonlinearities in the Schr\"odinger equation has been considered in the literature as an effective manner to describe the action of external environments or mean fields. Here, in particular, we explore the nonlinear…
The generalized Schrodinger equation deduced in the earlier papers is compared with conventional constructions of quantum field theory. In particular, it yields the usual Schrodinger equation of quantum field theory written without normal…
We deduce the Born rule. No use is required of quantum postulates. One exploits only rudimentary quantum mathematics--a linear, not Hilbert', vector space--and empirical notion of the statistical length of a state. Its statistical nature…
Quantum theory is usually formulated in terms of abstract mathematical postulates, involving Hilbert spaces, state vectors, and unitary operators. In this work, we show that the full formalism of quantum theory can instead be derived from…
Feynman's formulation of quantum theory is remarkable in its combination of formal simplicity and computational power. However, as a formulation of the abstract structure of quantum theory, it is incomplete as it does not account for most…
We consider the special and general relativistic extensions of the action principle behind the Schr\"odinger equation distinguishing classical and quantum contributions. Postulating a particular quantum correction to the source term in the…