In this paper I argue that the consistency condition from the Deutsch's influential model for closed timelike curves (CTCs) differs significantly from the classical consistency condition found in Lewis (1976) and Novikov (2002), as well as from the consistency condition found in the P-CTC model, the major rival to Deutsch's approach. Both the CCC and the P-CTC consistency condition are formulable in the context of a single history of the world. Deutsch's consistency condition relies on the existence of a structure of parallel worlds. I argue that Deutsch's commitment to realism about parallel worlds puts his solutions to the information paradox in jeopardy. I argue that, because of Deutsch's commitment to this metaphysical picture, he is committed to the existence of physical situations that are in every way indistinguishable from the paradoxes he attempts to rule out by adopting the model in the first place. Deutsch's proposed solution to the Knowledge Paradox, in particular his commitment to the actuality of the many worlds of the Everett interpretation (on which he relies to solve the paradoxes), guarantees the existence of worlds that are indistinguishable from worlds in which the genuine Knowledge Paradox arises.
In this paper I argue that the consistency condition from the Deutsch's influential model for closed timelike curves (CTCs) differs significantly from the classical consistency condition found in Lewis (1976) and Novikov (2002), as well as from the consistency condition found in the P-CTC model, the major rival to Deutsch's approach. Both the CCC and the P-CTC consistency condition are formulable in the context of a single history of the world. Deutsch's consistency condition relies on the existence of a structure of parallel worlds. I argue that Deutsch's commitment to realism about parallel worlds puts his solutions to the information paradox in jeopardy. I argue that, because of Deutsch's commitment to this metaphysical picture, he is committed to the existence of physical situations that are in every way indistinguishable from the paradoxes he attempts to rule out by adopting the model in the first place. Deutsch's proposed solution to the Knowledge Paradox, in particular his commitment to the actuality of the many worlds of the Everett interpretation (on which he relies to solve the paradoxes), guarantees the existence of worlds that are indistinguishable from worlds in which the genuine Knowledge Paradox arises.
This dissertation is an exploration of several issues surrounding David Deutsch’s CTC model first introduced in his 1991 paper “Quantum Mechanics Near Closed Timelike Lines”. Deutsch developed his model to account for the effects of quantum theory, which had been left out of classical discussions of time travel paradoxes. Deutsch’s formulation of his model in terms of quantum computational circuits lends itself to being adopted in the quantum information community. The dissertation argues that the adoption of the D-CTC model entails the existence of Nonlocal Signaling, which is in conflict with a fundamental principle of the quantum information approach. In order to motivate this argument, in Chapter 2 I introduce a distinction between Nonlocal Signaling, and Superluminal Information Transfer. In the latter case, a carrier of information physically traverses the space between the distant communicating parties faster than the speed of light. Exploiting quantum entanglement to signal, however, need not have this feature. I term this Nonlocal Signaling. Chapter 3 is where I present the argument that D-CTCs entail Nonlocal Signaling, and examine the controversy surrounding this and related results. I argue that the resistance to these kinds of predictions in the literature is motivated by a commitment to the principles of quantum information theory, which are inappropriately applied here. Chapters 4 and 5 examine details of Deutsch’s model. Chapter 4 argues that it presupposes a significant metaphysical picture that, when explicitly stated, makes a much less comfortable fit between D-CTCs and quantum information theory. Chapter 5 argues that, because of Deutsch’s commitment to this metaphysical picture, he is committed to the existence of physical situations that are in every way indistinguishable from the paradoxes he attempts to rule out by adopting the model in the first place. In Chapter 6, I make some observations about the relationship between the quantum information-theoretic approach to the interpretation of quantum theory, and the approaches focused primarily on arguing for one or another underlying ontology. Deutsch’s model is situated squarely in the latter camp. It serves as a useful example in pulling apart the implications of the two approaches. In conclusion, I argue that the quantum information-theoretic interpretation of quantum theory, in denying the fundamentality of any particular ontology, in favor of kinematical principles, is in tension with the metaphysical commitments of the Deutsch model. Deutsch’s interpretational stance is among the metaphysically-motivated positions. I argue that this element of the Deutsch model is essential to the solutions it offers to the paradoxes of time travel, and therefore the D-CTC model cannot be adopted without implicitly endorsing Deutsch’s metaphysical commitments. This feature makes the D-CTC model an uncomfortable fit with QIT.
For time travel to be consistent with the known laws of physics, the resulting paradoxes must be resolved. It has been suggested that parallel timelines (a.k.a. multiple histories) may provide a resolution. However, so far, a concrete mechanism by which parallel timelines can be created has never been satisfactorily formulated. In this paper we propose such a mechanism based on the Everett (many-worlds) interpretation of quantum mechanics, together with a linear pure-state CTC consistency condition. The timelines in our model are emergent, like the "worlds" of the Everett interpretation; they are created by the entanglement of the time machine with the environment and the resulting decoherence. Therefore, we call them "entangled timelines" or E-CTCs. As the entanglement gradually spreads out to additional systems, the timelines spread out as well, providing a local and well-defined alternative to the naive "branching timelines" picture often presented in the literature. The E-CTC model is similar to Deutsch's familiar D-CTC model, but differs from it mainly by keeping the entangled state explicit and imposing a different consistency condition. These differences allow us to create a clearer practical definition of the resulting parallel timelines.
David Deutsch provided us one possible solution to the grandfather paradox, Deutsch's closed timelike curves, or simply Deutsch CTC. Deutsch states that this gives us a tool to test many-worlds (Everettian) hypothesis since Deutsch CTC requires Everettian understanding. This paper explores the possibility of co-existence of Deutsch CTC with contextual/epistemic understanding of quantum mechanics. Then this paper presents the irrelevance hypothesis and the hypothetical application to quantum complexity theory.
How should we think about subjective states vs. objective states? Is it a question of the meaning associated with a state? Recent work on this question arose in consideration of closed timelike curves (CTCs) and their possible role in quantum computers. The issue of ontic and epistemic states is particularly important when considering CTCs because, as one may argue, the interpretation of quantum states as either ontic or epistemic will naturally lead to different assumptions about how quantum systems behave in the presence of CTCs. For example, David Deutsch studied various time travel scenarios in a classical model and then in a quantum model motivated by a strictly ontic interpretation of quantum states. While in the classical model, CTCs could produce paradoxes, however Deutsch argued that no paradoxes can occur in his parallel universes (modified Everett interpretation) quantum treatment. Although all paradoxes are resolved in this way, the resulting theory is not standard quantum theory, but a new nonlinear theory. Many implications can arise using Deutsch's model and I shall discuss some of them in particular. These assumptions are particularly unconventional in part because they require that mixed quantum states are ontic. Pure quantum states can be interpreted as ontic, however most interpretations view mixed states as epistemic, i.e., reflecting an observer's lack of knowledge. I shall here consider an alternative proposal-pure quantum states, represented by density matrices containing off-diagonal elements, are possibly epistemic (since we never actually see them) while mixed quantum states arising in CTCs are always ontic representing the action of consciousness in observers (we do see them). Paradoxically my argument is based on the well-known experiences of gaining knowledge in classical physics; couching this in quantum physics terms, classical mixed states (represented by diagonal density matrices in quantum physics) are just what arise when an "observation" is said to occur resulting in a so-called reduction of the quantum wave function and the appearance of a classical world. In brief, Deutsch's CTC nonlinear post quantum physics model may represent the action of a conscious mind.
Abstract This study examines closed timelike curves (CTCs) in quantum mechanics, focusing on the Deutsch model, one of the most widely studied frameworks for describing quantum systems in the presence of time loops. In this model, a quantum state ∣ψ⟩|\psi\rangle∣ψ⟩ interacts unitarily with its past version, effectively forming a two-qubit system where the chronologically consistent qubit interacts with a qubit ρCTC\rho_{\text{CTC}}ρCTC trapped in a closed timelike curve. The state ρCTC\rho_{\text{CTC}}ρCTC is determined by the Deutsch consistency condition, ensuring self-consistent evolution along the CTC. This approach allows for rigorous modeling of quantum systems under non-classical temporal structures, providing insights into temporal correlations, causality violations, and the potential computational advantages offered by CTC-assisted quantum operations. While alternative CTC models based on postselection have been proposed, the Deutsch model remains a foundational reference for studying quantum evolution in non-linear temporal frameworks. Its analysis informs research in quantum information, retrocausality, and the theoretical limits of computation in exotic spacetime geometries.
Closed timelike curves (CTCs) are non-intuitive theoretical solutions of general relativity field equations. The main paradox associated with the physical existence of CTCs, the so-called grandfather paradox, can be satisfactorily solved by a quantum model named Deutsch-CTC. An outstanding theoretical result that has been demonstrated in the Deutsch-CTC model is the computational equivalence of a classical and a quantum computer in the presence of a CTC. In this article, in order to explore the possible implications for the foundations of quantum mechanics of that equivalence, a fundamental particle is modelled as a classical-like system supplemented with an information space in which a randomizer and a classical Turing machine are stored. The particle could then generate quantum behavior in real time in case it was controlled by a classical algorithm coding the rules of quantum mechanics and, in addition, a logical circuit simulating a CTC was present on its information space. The conditions that, through the action of evolution under natural selection, might produce a population of such particles with both elements on their information spaces from initial sheer random behavior are analyzed.