First, we point out that the present applied superposition principle is linear, it must be developed into a generality. Next, the linear operators and equations should be developed nonlinearly. They will include nonlinear Klein-Gordon equation and Dirac equations, and corresponding Heisenberg equation. The quantum commutation and anticommutation should be developed. This theory may include the renormalization, which is the correction of Feynman rules of curved closed loops. We think the interaction equations are nonlinear. Many theories, models and phenomena are all nonlinear, for instance, soliton, nonabelian gauge field, and the bag model, etc. The superluminal entangled state, which relates the nonlocal quantum teleportation and nonlinearity, should be a new fifth interaction. Moreover, the NL effects exist possibly for four interactions, for single particle, for high energy, and for small space-time, etc. The relations among NL theory and electroweak unified theory, and QCD, and CP nonconservation, etc., are expounded. Finally, some known and possible tests are discussed. The NL theory relates the possible decrease of entropy in isolated system.
First, we point out that the present applied superposition principle is linear, it must be developed into a generality. Next, the linear operators and equations should be developed nonlinearly. They will include nonlinear Klein-Gordon equation and Dirac equations, and corresponding Heisenberg equation. The quantum commutation and anticommutation should be developed. This theory may include the renormalization, which is the correction of Feynman rules of curved closed loops. We think the interaction equations are nonlinear. Many theories, models and phenomena are all nonlinear, for instance, soliton, nonabelian gauge field, and the bag model, etc. The superluminal entangled state, which relates the nonlocal quantum teleportation and nonlinearity, should be a new fifth interaction. Moreover, the NL effects exist possibly for four interactions, for single particle, for high energy, and for small space-time, etc. The relations among NL theory and electroweak unified theory, and QCD, and CP nonconservation, etc., are expounded. Finally, some known and possible tests are discussed. The NL theory relates the possible decrease of entropy in isolated system.
First, based on the uncertainty principle in quantum theory and new generalized uncertainty principle, we research uncertain relations of entropy, information and thermodynamics, and propose the speed of light and some fundamental constants should be uncertain. Next, in the quantum entangled states, velocities of different phases may be superluminal, and obey possibly general Lorentz transformation (GLT). Third, we search its possible development in superstring, and the extensive quantum theory, various matters and different phases, etc. Fourth, the duality exists probably only under interactions. Some nonlinear quantum equations and wave equations have soliton solutions, which correspond to particles. This is mathematical description of wave-particle duality. Fifth, based on the soliton-chaos double solutions of nonlinear equations, we propose the field-particle duality, and field (wave)-quantum-chaos ternary. Sixth, the irreversibility and statistics are discussed, and we derive operators of entropy, etc. New measuring technology and some developed theories already challenge the uncertainty principle and duality, which may not be held under certain conditions, and must be modified and developed.
Nonlinear Dirac equations (NLDE) are derived through a group N^2 of nonlinear (gauge) transformation acting in the corresponding state space. The construction generalises a construction for nonlinear Schrödinger equations. To relate N^2 with physically motivated principles we assume: locality (i.e. it contains no explicit derivative and no derivatives of the wave function), separability (i.e. it acts on product states componentwise) and Poincaré invariance. Furthermore we want that a positional density is invariant under N^2. Such nonlinear transformations yield NLDE which describe physically equivalent systems. To get 'new' systems, we extend this NLDE (gauge extension) and present a family of NLDE which is a slight nonlinear generalisation of the Dirac equation. We discuss and comment the fact that nonlinear evolutions are not consistent with the usual framework of quantum theory. To develop a corresponding extended framework one needs models for nonlinear evolutions which also indicate possible physical consequences of nonlinearities.
The basic principles of quantum mechanics, which is the foundations of model science, and, its difficulties and contradictions are exhibited and confirmed in detail and systematically by plenty of the experimental facts and theoretical results obtained from the solutions of basic Schrödinger equation through their comparisons of the intrinsic features of wave and corpuscle of the microscopic particles between the theoretical results and experimental facts. A basic difficulty is that the microscopic particles described by this linear theory have only a wave, not wave and corpuscle duality, which is inherent of quantum mechanics and cannot all be changed in the framework of the linear theory no matter what variations of investigated ways and methods, i.e., these difficulties and contradictions determinate and affirm that original quantum mechanics must be remoulded completely and developed forward. Its only direction of development is to establish nonlinear quantum mechanics, its some ideas and principles were proposed and suggested by a great number of researchers and authors over the past few decades, but they are not successful. But new nonlinear quantum mechanics proposed by Pang gave a perfect wave-corpuscle dulauty of microscopc particles and established a complete and systematical principle and theory. Thus, we afformed and confirmed the correctness of the new nonlinear quantum theory. In order to verify further the validity of the new nonlinear theory we elucodate and explain again that the nonlinear interactions existed in the new theory are wide and real existences in all physical systems, they were generated by virtue of five mechanisms for self-interaction, self-trapping, self-forcusing, self-considering and self-localizing. At the same time, we researched and exhibiteed fully the concrete representions of nonlear interaction for commom microscopic particles such as the electron, exciton, proton, plaron, photon, phonon and magneton, which are all consistent from those in Pang’s nonlinear quantum mechanics. These investigations and results proved also that Pang’s nonlinear quantum mechanics is correct and exact. Finally, we verified and confirmed completely the correctness of Pang’s new nonlinear theory using the experimental results of the property of movements of nonlinear solitons occurred in water and light fibers, in which the n, the dynamic equations of the water soliton and photon solito are all described by the nonlinear Schrödiger equation. Hence, their results and experimental evidences of wave-corpuscle duality of microscopic particles veried the correctness of Pang’s nonlinear quantum mechanics. Then we can use Pang’s theory to research the properties of microscopic particles in differet systems. These problems, the rules of motion of the particles as well as 396 reference papers are contained in the e-book for the reders. The concrete content his involved by e-book are described the follows. Chapter 1. The basic principles of quantum mechanism and its dificults and contradictions; Chapter 2. The necessarity remoulding quantum mechanics and establishment of nonlinear quantum mechanics; Chapter 3. The wave-corpuscle duality of microscopic particles in Pang’s nonlinear quantum mechanics; Chapter 4. Real and wide existences of nonlinear interactions as well as their mechanisms of generation in physical systems; Chapter 5. The nonlinear dynamic properities of common microscopic particles in different physical systems; Chapter 6. The experimental evidences for the correctness of nonlinear quantum mechanics. This e-book is intended and learned for researchers, teachers, graduate students and upper level undergraduate students.
Two fundamental, and unsolved problems in physics are: i) the resolution of the "measurement problem" in quantum mechanics ii) the quantization of strongly nonlinear (nonabelian) gauge theories. The aim of this paper is to suggest that these two problems might be linked, and that a mutual, simultaneous solution to both might exist. We propose that the mechanism responsible for the "collapse of the wave function" in quantum mechanics is the nonlinearities already present in the theory via nonabelian gauge interactions. Unlike all other models of spontaneous collapse, our proposal is, to the best of our knowledge, the only one which does not introduce any new elements into the theory. A possible experimental test of the model would be to compare the coherence lengths - here defined as the distance over which quantum mechanical superposition is still valid - for, \textit{e.g}, electrons and photons in a double-slit experiment. The electrons should have a finite coherence length, while photons should have a much longer coherence length (in principle infinite, if gravity - a very weak effect indeed unless we approach the Planck scale - is ignored).
We propose that the mechanism responsible for the ``collapse of the wave function" (or "decoherence" in its broadest meaning) in quantum mechanics is the nonlinearities already present in the theory via nonabelian gauge interactions. Unlike all other models of spontaneous collapse, our proposal is, to the best of our knowledge, the only one which does not introduce any new elements into the theory. Indeed, unless the gauge interaction nonlinearities are not used for exactly this purpose, one must then explain why the violation of the superposition principle which they introduce does not destroy quantum mechanics. A possible experimental test of the model would be to compare the coherence lengths for, e.g., electrons and photons in a double-slit experiment. The electrons should have a finite coherence length, while photons should have a much longer (in principle infinite) coherence length.
Standard quantum mechanics requires six independent axioms of the Copenhagen interpretation, all formulated in a non-relativistic framework lacking Lorentz invariance and thus fundamentally inconsistent with Minkowski spacetime. This paper argues that the measurement problem, wave-function collapse, Schrödinger's cat, and the non-locality of entanglement share a common root: non-relativistic quantum mechanics is an approximation of a more fundamental theory, and interpretations built upon an approximation cannot be fully correct. We propose Spacetime Wave Quantum Theory (SWQ theory), which takes Minkowski spacetime as its sole geometric premise and proceeds from two axioms: Axiom 1 (Quantum nature): A quantum exists in spacetime with finite extent and behaves as a wave whose action changes only in discrete multiples of h. Axiom 2 (Superposition principle): Superposition on multiple paths holds if and only if no difference arises in the state of external quanta between those paths — a purely physical condition with no role for observer consciousness. From these two axioms, the Klein–Gordon and Dirac equations are derived directly, with the Schrödinger equation recovered as their non-relativistic limit. The six Copenhagen axioms are replaced by two. Central concept — the Spacetime Action Packet (SAP): Every quantum occupies a finite four-dimensional spacetime region. For energy E, the temporal thickness satisfies Δt ≳ h/E. The SAP has a minimum size but no upper bound; quantum interactions are described as overlap integrals over the spacetime volume where two SAPs coincide. A key consequence is that different quanta — including three quarks inside a nucleon and neutrinos traversing the Earth — can occupy the same spacetime region without restriction; the Pauli exclusion principle applies only to identical fermions in identical states. Principal results of v2.0: Wave-function collapse is dissolved as the physical end and beginning of a quantum wave (wave-terminating interaction); the projection postulate is unnecessary. Feynman spacetime integration and virtual particles acquire a natural physical basis; finite SAP size provides an intrinsic UV cutoff without renormalization. Zero-point energy (ħω/2) is diagnosed as an artifact of operator ordering in quantization — not a physical entity — rendering the cosmological constant problem a structural consequence of summing a quantity that was never real. A first-order extension to a-ECG curved spacetime shows that gravitational redshift, gravitational mass deficit, and the increase in SAP temporal thickness all scale as √A(r), unifying classical and quantum descriptions of energy conservation under gravity. These results are supported by quantitative tests obtained without renormalization: the electron anomalous magnetic moment ae = α/2π (1-loop) and 2-loop coefficient C4 to 0.0015%; the Compton cross-section to within 0.07% of the Klein–Nishina formula; and nucleon magnetic moments to ∼1.5%. Details appear in the series papers on the Rotating Spinor Wave (RSW) model. Series context: SWQ theory forms the foundational framework for the RSW model (unified description of fermion spin, g-factors, and hadron mass spectra) and the Energy-Conserving Gravity theory (a-ECG, a modification of general relativity incorporating full energy-momentum conservation). These three papers constitute an interconnected series. Note: Generative AI tools (Claude Sonnet 4.6, Anthropic; Grok, xAI) were used for drafting and language checking. All scientific content and responsibility rest solely with the author.