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arXiv:1806.00134

An exploration of the limits of control using quantum superpositions

Holger Friedrich Hofmann

Published May 31, 2018• 0 citations
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Abstract

Quantum interferences between non-orthogonal states are the best approximation of a joint realization of the non-commuting physical properties represented by the two states. As I have shown recently, such interferences can be used to demonstrate that quantum physics deviates from classical causality in the limit of small action. Here, I point out that this proof constitutes a failure of the principle of least action and consider possible implications for our understanding of fundamental physics.

DOI
10.48550/arxiv.1806.00134

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Quantum interferences between non-orthogonal states are the best approximation of a joint realization of the non-commuting physical properties represented by the two states. As I have shown recently, such interferences can be used to demonstrate that quantum physics deviates from classical causality in the limit of small action. Here, I point out that this proof constitutes a failure of the principle of least action and consider possible implications for our understanding of fundamental physics.
We propose a novel and interdisciplinary conceptual framework that bridges Feynman’s path integral formulation of quantum mechanics with reinforcement learning (RL) in artificial intelligence. In the path integral approach, a quantum system does not follow a single predetermined trajectory but instead explores all possible paths simultaneously, assigning each a complex amplitude weighted by eiS/h, where S represents the classical action. Constructive and destructive interference across these paths acts as a natural filter, amplifying trajectories of stationary action and suppressing suboptimal ones, thereby leaving paths of least action as the observable outcomes. We argue this process is strongly analogous to a quantum agent evaluating an entire policy space in superposition, where interference effectively encodes a reward mechanism that eliminates non-optimal policies. This perspective not only deepens our understanding of light’s propagation in complex refractive media but also inspires the design of quantum-inspired Reinforcement learning architectures capable of leveraging the intrinsic parallelism of quantum mechanics. Furthermore, the advent of quantum computing, with its inherent properties of superposition, entanglement, and quantum interference, provides a tangible pathway for implementing such algorithms in practice. To illustrate this paradigm, we propose a toy model wherein policies are encoded as quantum states, rewards are mapped to phase shifts, and measurement collapses the superposed state into an optimal policy. The implications of this framework extend beyond algorithmic innovation, offering insights into the possibility that nature itself operates as a quantum learning system, with physical laws emerging from a process akin to reinforcement learning.
This work presents a conceptual and interdisciplinary framework exploring parallels between quantum measurement theory, human cognition, and metaphysical causality. Rather than proposing an experimental or testable physical model, the paper develops a theoretical interpretation that uses established quantum concepts—such as superposition, collapse, observation, and tunneling—as structural analogies for understanding human decision-making, regret, and the perceived limits of self-driven agency. The framework introduces the notion of a “Divine Collapse Point (DCP)” as a metaphysical boundary condition, representing the moment at which intentional effort and analytical reasoning reach their conceptual limits. At this point, the model suggests a transition beyond classical notions of control and causality, interpreted philosophically rather than physically. Regret is reframed as a cognitive indicator of collapse, marking the exhaustion of internally generated possibilities rather than a psychological failure. This paper is positioned within the domains of philosophy of science, consciousness studies, and conceptual interpretations of quantum mechanics. It does not claim empirical validation, predictive power, or experimental confirmation. Instead, it aims to provide a coherent language for discussing observation, limitation, and surrender across scientific, cognitive, and metaphysical contexts. The work also contributes to the ongoing development of Javed’s Quantum Thought, a conceptual approach that interprets quantum principles as reflective structures within human cognition and existential experience.
The investigation of quantum foundations has historically focused on spatial non-locality, entanglement, and the superposition of states within a fixed background spacetime. However, the nature of causality itself in the quantum regime remains a profound open question, particularly concerning whether causal relations can exist in quantum superpositions or whether causal influences leave persistent temporal signatures that can be manipulated and interfered with. This paper introduces the theoretical framework of Quantum Causal Echo Interferometry, designated as QCEI. Rather than exploring passive vacuum memory effects, QCEI addresses a fundamental question: whether the causal impact of a quantum event can propagate into the future and manifest as an interfering causal echo when manipulated through multi-path quantum control. We formalize the concept of quantum causal echoes through an integral propagation kernel relating past actions to future echoes, and construct a comprehensive multi-path control architecture that forces distinct causal pathways to reconverge. By evaluating the resulting interference observables defined by the intensity equation I = |A_1 + A_2 + A_echo|^2, we demonstrate that QCEI provides a rigorous analytical framework for probing the dynamical structure of quantum causality. This work establishes the mathematical and conceptual foundations for what may ultimately serve as a transformative diagnostic tool for probing non-classical causal structures in fundamental physics.
In quantum mechanics it is well known that, if any two states are superposed, they interfere with each other. It is true, we should not deny such interference in principle, but we may assert what follows. When two states different from each other in a great many degrees of freedom are superposed, the interference effect becomes obscure. If they are different in an infinitely many degrees of freedom, they do not interfere at all, and their superposition is nothing but a mere probability function. This assertion enables us to understand how the probability amplitude for a micro-system is converted into a probability function for a measuring apparatus in the cource of measurement.