Related papers: Nonlinear Quantum Theory, Development of the Super…
There are four reasons why our present knowledge and understanding of quantum mechanics could be regarded as incomplete. Firstly, the principle of linear superposition has not been experimentally tested for position eigenstates of objects…
The linear superposition principle in quantum mechanics is essential for several no-go theorems such as the no-cloning theorem, the no-deleting theorem and the no-superposing theorem. It remains an open problem of finding general forbidden…
Clarifying the nature of the quantum state $|\Psi\rangle$ is at the root of the problems with insight into counter-intuitive quantum postulates. We provide a direct-and math-axiom free-empirical derivation of this object as an element of a…
We propose a list of conditions that consistency with thermodynamics imposes on linear and nonlinear generalizations of standard unitary quantum mechanics that assume a set of true quantum states without the restriction $\rho^2=\rho$ even…
There are still no interacting models of the Wightman axioms, suggesting that the axioms are too tightly drawn. Here a weakening of linearity for quantum fields is proposed, with the algebra still linear but with the quantum fields no…
Unitary and dissipative models of quantum dynamics are linear maps on the space of states or density matrices. This linearity encodes the superposition principle, a key feature of quantum theory. However, this principle can break down in…
We add non-linear and state-dependent terms to quantum field theory. We show that the resulting low-energy theory, non-linear quantum mechanics, is causal, preserves probability and permits a consistent description of the process of…
The limits of linear electrodynamics are reviewed, and possible directions of nonlinear extension are explored. The central theme is that the qualitative character of the empirical successes of quantum electrodynamics must be used as a…
Nonlinear modifications of quantum mechanics have a troubled history. They were initially studied for many promising reasons: resolving the measurement problem, testing the limits of standard quantum mechanics, and reconciling it with…
The interaction between two parts in a compound quantum system may be reconsidered more completely than before and some new understandings and conclusions different from current quantum mechanics are obtained, including the conservation law…
Quantum mechanics is an extremely successful theory that agrees with every experiment. However, the principle of linear superposition, a central tenet of the theory, apparently contradicts a commonplace observation: macroscopic objects are…
Generalizations of the three main equations of quantum physics, namely, the Schr\"odinger, Klein-Gordon, and Dirac equations, are proposed. Nonlinear terms, characterized by exponents depending on an index $q$, are considered in such a way…
The ordinary linear quantum theory predicts the quantum correlations at any distance (the universal superposition principle). It creates the decoherence problem since quantum interactions entangle states into non-separable combination. On…
The superposition principle is a very basic ingredient of quantum theory. What may come as a surprise to many students, and even to many practitioners of the quantum craft, is tha superposition has limitations imposed by certain…
Quantum theory is compatible with special relativity. In particular, though measurements on entangled systems are correlated in a way that cannot be reproduced by local hidden variables, they cannot be used for superluminal signalling. As…
This paper follows recent steps towards a nonassociative quantum theory and points out the mathematical structure behind the proposed modifications to conventional quantum theory. An N=1 supersymmetry model and a strong force glueball…
Nonlinear modifications of quantum theory are considered potential candidates for the theory of quantum gravity, with the intuitive argument that since Einstein field equations are nonlinear, quantum gravity should be nonlinear as well.…
Principle of ``Superrelativity'' has been proposed in order to avoid the contradiction between principle of relativity and foundations of quantum theory. Solutions of a newly derived non-linear Klein-Gordon equation presumably may be…
Basing on the theory of Feynman's influence functional and its hierarchical equations of motion, we develop a linear response theory for quantum open systems. Our theory provides an effective way to calculate dynamical observables of a…
We study nonlinear dynamics of superposition of quantum wavepackets in various systems such as Kerr medium, Morse oscillator and bosonic Josephson junction. The prime reason behind this study is to find out how the superposition of states…