The Fundamental Paradox of the Quantum Theory

Ronald F. Peierls

George Frederick James Temple

George Frederick James Temple

Jun Yan

To date in the development of modern physics, relativity and quantum mechanics can precisely agree with experimental observations within their respective scopes of application. However, the underlying logics of the two theoretical systems remain incompatible, giving rise to a host of intractable paradoxes and puzzles. This paper investigates nine representative problems: the quantum grandfather paradox, Hawking's chronology protection conjecture, the causality paradox of quantum fluctuations, the black hole information loss paradox, the quantum Maxwell's demon, the Boltzmann brain paradox, the ultraviolet catastrophe, the quantum tunnelling paradox, and the quantum no-cloning and identical particle paradox. This research is built upon the original Two-Dimensional Linear Matrix Wave Theory. It holds that the objective ontology of the universe consists of a one-dimensional propagation substrate and a global two-dimensional linear matrix wave field. A free two-dimensional linear matrix wave is defined as a travelling wave, while stable structures formed by constrained superposition of energy are standing waves. Electrons, protons and neutrons are the only three fundamental primitive standing waves in the universe, and all macroscopic matter in nature is composed of their combinations. Time is not an independent spacetime dimension; essentially, it refers to the intrinsic oscillation frequency inside fundamental standing waves. The basic equations and theorems of the Two-Dimensional Linear Matrix Wave Theory are not rederived herein, and are directly adopted as an established original theoretical framework. The research reveals that all the aforementioned paradoxes stem from cognitive biases in conventional physics: regarding the three-dimensional space perceived by humans as the primordial structure of the universe, treating time as an independently flowing dimension, and misinterpreting microscopic wave phenomena as random particle behaviours. Within the framework of the Two-Dimensional Linear Matrix Wave Theory, all these paradoxes can be fundamentally resolved based on the fundamental laws of wave propagation, standing wave evolution and wave field superposition, without introducing additional hypotheses or ad hoc theories. This paper focuses on constructing a complete physical interpretation system, and relevant detailed mathematical formulas can be supplemented and refined by subsequent researchers. The original intellectual property rights of the core theory are clearly defined. This study provides a new perspective for fundamental physics to break through existing theoretical constraints.

Coelho de Araujo Dórea, Roberto José

We present a universal framework showing that all physical measurements return values from the ternary set {-1, 0, +1}. This is not a choice but a fundamental constraint emerging from quantum mechanics, relativity, and information theory. The state 0 represents the non-measurable transition state—mathematically necessary for continuous transformation between +1 and -1. This framework resolves 58 fundamental paradoxes spanning mathematics, logic, quantum mechanics, and philosophy. We demonstrate connections to the singular present (T=1) and zero crossing mechanisms, providing a unified foundation for measurement theory. All paradoxes reduce to misidentification of state 0 as measurable, when it represents the pre-measurement or transitional state that enables physical existence.

Felix M. Lev

The postulate that coordinate and momentum representations are related to each other by the Fourier transform has been accepted from the beginning of quantum theory. As a consequence, coordinate wave functions of photons emitted by stars have cosmic sizes. This results in a paradox because predictions of the theory contradict observations. The reason of the paradox and its resolution are discussed.