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.
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.
Closed timelike curves (CTCs) are trajectories in spacetime that effectively travel backwards in time: a test particle following a CTC can interact with its former self in the past. A widely accepted quantum theory of CTCs was proposed by Deutsch. Here we analyze an alternative quantum formulation of CTCs based on teleportation and postselection, and show that it is inequivalent to Deutsch's. The predictions or retrodictions of our theory can be simulated experimentally: we report the results of an experiment illustrating how in our particular theory the "grandfather paradox" is resolved.
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.
Closed timelike curves (CTCs), non-intuitive theoretical solutions of general relativity field equations can be modelled in quantum mechanics in a way, known as Deutsch-CTCs, to circumvent one of their most paradoxical implications, namely, the so-called grandfather paradox. An outstanding theoretical result of this model is the demonstration that in the presence of a Deutsch-CTC a classical computer would be computationally equivalent to a quantum computer. In the present study, the possible implications of such a striking result for the foundations of quantum mechanics and the connections between classicality and quantumness are explored. To this purpose, a model for fundamental particles that interact in physical space exchanging carriers of momentum and energy is considered. Every particle is then supplemented with an information space in which a probabilistic classical Turing machine is stored. It is analysed whether, through the action of Darwinian evolution, both a classical algorithm coding the rules of quantum mechanics and an anticipation module might plausibly be developed on the information space from initial random behaviour. The simulation of a CTC on the information space of the particle by means of the anticipation module would imply that fundamental particles, which do not possess direct intrinsic quantum features from first principles in this information-theoretic Darwinian approach, could however generate quantum emergent behaviour in real time as a consequence of Darwinian evolution acting on information-theoretic physical systems.
Although general relativity allows the existence of closed timelike curves (CTCs), self-consistency problems arise (the ‘grandfather paradox’ among others). It is known that quantum mechanical consideration of the matter formally removes all the paradoxes, but the questions about causal structure remain. On the other hand, the idea of postselected CTCs (P-CTC) in quantum teleportation has know been put forward and experimentally implemented. We consider these problems with the aid of quantum causal analysis, where causality is defined without invoking the time relation. It implements the Cramer principle of weak causality, which admits time reversal in entangled states. We analyze Deutsch CTCs (D-CTC) with different kinds of interactions between the chronology-violating and chronology-respecting particles, with refined inferences about mixedness, quantum/classical correlations, entanglement and thermodynamics in the D-CTC. The main result is that time reversal causality can really exist, however, the final quantum state does not place retrospective constraints on the initial state, instead the final state can influence the state inside the D-CTC. This is effectively the implementation of Novikov self-consistency principle. The P-CTC has radically different properties; in particular, if the initial state was pure, the final state is always pure too. Self-consistency is controlled by the initial state-dependent traversability of the P-CTC.
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.
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.