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.
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.
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.