Self-Referential Quantum Mechanics

David Hestenes

John Small

Simple self‐referential algorithms can model the essential logic of quantum systems and the quantum formalism is sufficiently rich to be able to model the output states of self‐referential alogrithms. We identify a key feature of self‐referentiality and show that both quantum mechanics and general relativity exhibit this feature in distinct yet complementary ways. This implies that self‐referentiality must be a foundational principle, but causality protection prohibits it being directly observed. Examining two facets of causality protection we find that quantum mechanics implements one and general relativity the other. The implication is that there can be no mathematically consistent theory for quantum gravity. However we can gain understanding of the constraints imposed on physical law when viewing a noncausal reality as if it were a causal sequence. We derive the 3+1 dimensionality of spacetime and quantum non‐locality and also possible rationale for the U(1) × SU(2) × SU(3) symmetry of the Standard Model. We also identify a number of key open problems.

Huping Hu, Maoxin Wu

We have recently theorized that consciousness is intrinsically connected to quantum mechanical spin since said spin is embedded in the microscopic structure of spacetime and is more fundamental than spacetime itself, that is, spin is the “mind-pixel.” Applying these ideas to the particular structures and dynamics of the brain, we have developed a qualitative model of quantum consciousness. In this paper, we express our fundamental view that spin is a primordial self-referential process driving quantum mechanics, spacetime dynamics and consciousness. To justify such a view, we will draw support from existing literatures, discuss from a reductionist perspective the essential properties said spin should possess as mind-pixel and explore further the nature of spin to see whether said properties are present. Our conclusion is that these properties are indeed endowed to spin by Nature. One of the implications from our fundamental view is that the probabilistic structure of quantum mechanics is due to the self-referential collapse of spin state that is contextual, non-local, non-computable and irreversible. Therefore, a complete theory of the self-referential spin process is necessarily semantic, that is, it should be based on internally meaningful information.

Mario Bunge

Jincheng Zhang

This paper explores the concept of self-referential quantum algorithms, proposing a novel framework for recursive computation using quantum mechanics. The core idea is to design algorithms where the output of a computation is fed back as input, allowing for iterative refinement and the potential to tackle problems that are computationally intractable for classical computers. We detail a theoretical mechanism involving feedback loops, emphasizing the creation of self-referential computations. The algorithm's efficiency hinges on leveraging quantum superposition and interference to explore multiple computational paths simultaneously. This approach offers a potential paradigm shift in quantum algorithm design, moving beyond sequential execution to embrace recursive processes. The theoretical framework presented here lays the groundwork for future research into self-referential quantum computation and its applications across diverse scientific and engineering domains. We investigate the mathematical underpinnings of this approach, focusing on the manipulation of quantum states and the design of iterative feedback mechanisms. The core of the algorithm is rooted in the principle of unitary transformations applied repeatedly, culminating in a state representing the solution. The key challenge lies in managing the complexity of these iterative processes and ensuring convergence to a desired outcome. The paper concludes by outlining potential future research directions and highlighting the significant implications of self-referential quantum algorithms for the advancement of computational science.

G. Feild