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AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit (JPC)

Cyclic Entanglements for Complex Superpositions

Allan Goff

Published Jul 9, 2006• 7 citations
Publisher

Abstract

In previous work, the case has been made that the nonlocality of quantum systems implies some kind of spacelike causal connection, and that for this connection to be physically real, it must meet several very rigid constraints. Step by step, a reformulation of quantum mechanics has been developed that meets these constraints. These constraints include relativistic consistency, causality, and some way to avoid temporal paradox. The reformulation of quantum mechanics to meet these criteria has yielded a hypothesis that cyclically entangled quantum systems provide an objective measurement mechanism. This hypothesis has stood up well in abstract quantum systems where the superpositions are unweighted. This paper continues the effort by considering the case for cyclic entanglements when the superpositions have complex weights. It is shown that in general, a cyclic entanglement is self-referential in only one basis and it is in this basis that collapse occurs. Thus, cyclic entanglements provide both the nonlinearity and the symmetry breaking necessary for a quantum system to self-collapse. This removes the confusing and ambiguous requirement for an outside observer (which ultimately is just another quantum system) to perform the measurement act. This reformulation of quantum mechanics permits relativistically consistent superluminal communications and paradox-free backwards-intime causality.

DOI
10.2514/6.2006-4732

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In previous work, the case has been made that the nonlocality of quantum systems implies some kind of spacelike causal connection, and that for this connection to be physically real, it must meet several very rigid constraints. Step by step, a reformulation of quantum mechanics has been developed that meets these constraints. These constraints include relativistic consistency, causality, and some way to avoid temporal paradox. The reformulation of quantum mechanics to meet these criteria has yielded a hypothesis that cyclically entangled quantum systems provide an objective measurement mechanism. This hypothesis has stood up well in abstract quantum systems where the superpositions are unweighted. This paper continues the effort by considering the case for cyclic entanglements when the superpositions have complex weights. It is shown that in general, a cyclic entanglement is self-referential in only one basis and it is in this basis that collapse occurs. Thus, cyclic entanglements provide both the nonlinearity and the symmetry breaking necessary for a quantum system to self-collapse. This removes the confusing and ambiguous requirement for an outside observer (which ultimately is just another quantum system) to perform the measurement act. This reformulation of quantum mechanics permits relativistically consistent superluminal communications and paradox-free backwards-intime causality.
We propose an information-centric interpretation of quantum mechanics. According to this interpretation, a quantum mechanical system, AAA, can always choose a basis in which its own state is an eigenstate; it never sees itself in a superposition. This holds true even if, from the perspective of another system BBB, AAA is entangled with system SSS. In this case, AAA and SSS are in eigenstates (in their own systems) with their counterpart subsystem wave functions collapsed in the entangled degrees of freedom, but they are entangled according to BBB. This interpretation does not introduce new physics, and is consistent with the experimental predictions of quantum mechanics. At the same time, it avoids many ambiguities and potential inconsistencies associated with other interpretations. We further clarify concepts of measurement, macroscopic superposition, entanglement, and the dichotomy between the classical and quantum realms, in accordance with our interpretation.
This paper surveys a research effort to explore the potential for quantum nonlocality to support superluminal signaling. The emphasis is on the issue of temporal paradox. Through the metaphor of Quantum Tic-Tac-Toe, it is shown how superposition leads to a Many Worlds variant called the Classical Ensemble. As a quantum system evolves, superposition branches off new classical realities, but contradictory ones are pruned from the ensemble. The pruning results in nonseparable states and thus to entangling of the quantum system. When these entanglements become cyclic, they introduce nonlinearities into the quantum system that result in self-collapse. Since cyclic entanglements are in general self-referential in only one basis, collapse occurs only in the self-referential basis. Cyclic entanglements are thus a viable candidate as the measurement mechanism. Collapse is made consistent with relativity by introducing the symmetric spacetime interval. The resulting closed loops in spacetime entangle the near future with the recent past so collapse of quantum systems offers a potential means for achieving superluminal signaling (FTL) and something very like time travel. The pruning in the classical ensemble acts as the censor mechanism that prevents temporal paradox while allowing backwards-in-time causality. This removes the logical objections to FTL and time travel.
Quantum entanglement appears nonlocal: measuring one particle instantaneously determines outcomes for its distant partner, seemingly defying relativistic causality. Building on prior work, we propose that this "paradox" dissolves when particles are recognized not as point-objects but as spatial termini of single, extended correlation sequences. These sequences remain genuinely incomplete – indeterminate in any measurement basis – until measurement supplies the boundary conditions that complete the entire pattern. No information propagates between termini because they were never separate entities. Measurement doesn't reveal hidden properties; it finishes an incomplete structure through the enforcement of local invariants via irreversible interaction with macroscopic systems. This framework explains why superposition exists, why certain observables become classical (position, momentum, and energy), and why quantum behavior dominates at small scales while classical behavior emerges at large scales. The approach eliminates longstanding paradoxes without exotic ontology: no hidden variables, no parallel worlds, no consciousness-dependent collapse, no violation of relativity. We derive testable predictions and resolve the measurement problem: there is no discontinuous collapse, only thermodynamically irreversible completion of correlation sequences. Most provocatively, this analysis reinforces a claim from prior work: if laws are emergent attractors rather than eternal axioms, the search for a "theory of everything" unifying quantum mechanics and general relativity may rest on a category error.
We take it for granted that our physical environment communicates information, making things observable and measurable. However, there are very strong constraints on the fundamental physics of any universe that can do this. Measuring or communicating any kind of information always requires an appropriate interactive context, and these contexts are necessarily complex, involving other kinds of information determined in different contexts. This makes measurement hard to grasp theoretically, since every measurement depends on other kinds of measurements. Even so, we can identify some basic functional requirements for a physics that determines and communicates facts. These are sufficient to explain the peculiar features of quantum mechanics, combining the unitary evolution of superpositions with the mysterious "collapse" that occurs whenever the context allows new facts to be defined. Moreover, the precise determinism of classical physics can be understood on the same basis. It seems likely, in fact, that most of the complexity and fine-tuning we see in our most fundamental theories is needed to make any kind of information measurable.
Abstract Quantum mechanics and relativity are two of the most successful theoretical frameworks in modern physics, yet their conceptual foundations remain difficult to reconcile at the deepest level. Quantum theory describes physical systems through states, observables, probabilities, measurement contexts, superposition, entanglement, and nonclassical correlations. Relativity describes physical processes through space-time structure, causal order, invariant physical law, observer-dependent decomposition of time and space, and constraints on signal propagation. This article examines the conceptual relationship between quantum measurement, relativistic causality, and space-time description. The purpose is not to present a mathematical unification but to analyze how the two frameworks organize physical explanation differently and where their interpretive tensions arise. Special attention is given to the measurement problem, the status of quantum states, the role of observers and reference frames, the meaning of locality, the distinction between correlation and causal influence, and the challenge of describing quantum processes without privileging a single global time. The article argues that many apparent conflicts between quantum theory and relativity result from importing classical intuitions into domains where they no longer apply. Quantum entanglement does not permit controllable faster-than-light communication, yet it challenges classical separability. Relativity forbids superluminal signaling, yet it does not require that all physically meaningful correlations be reducible to local classical properties. Measurement introduces another difficulty because standard quantum theory often describes state update in a way that appears instantaneous, while relativistic space-time does not provide a universal present. The discussion develops a conceptual framework in which quantum measurement is treated as a physical interaction, relativistic causality as a constraint on operational influence, and space-time description as an organizing structure for events rather than a simple background stage. This analysis is relevant for quantum field theory, quantum information, relativistic quantum foundations, and future approaches to quantum gravity.
Quantum mechanics is mathematically complete but conceptually burdened by a discrete‑state ontology that the formalism itself does not require. This paper reframes superposition, measurement, and nonlocality as structural features of unresolved and resolved constraint geometry in continuous fields. In this interpretation, a quantum state is not a catalogue of simultaneous possibilities but the orientation of an unresolved constraint region; measurement is the stabilization of that region under new constraints; and entanglement reflects a single unresolved region spanning multiple subsystems. The standard Hilbert‑space formalism remains unchanged—linearity, projection, the Born rule, and tensor structure all arise naturally from the geometry of unresolved continuity. This framework dissolves the paradoxes associated with collapse, wavefunction ontology, and nonlocal influence, yielding a unified, minimal, and physically intuitive account of quantum behavior that preserves the full empirical power of quantum mechanics while eliminating its metaphysical burdens.