Simulation of Closed Timelike Curves in the Framework of an Information-Theoretic Darwinian Approach to Quantum Mechanics

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.

The D-CTC Condition is Generically Fulfilled in Classical (Non-quantum) Statistical Systems

The D-CTC condition, introduced by David Deutsch as a condition to be fulfilled by analogues for processes of quantum systems in the presence of closed timelike curves, is investigated for classical statistical (non-quantum) bi-partite systems. It is shown that the D-CTC condition can generically be fulfilled in classical statistical systems, under very general, model-independent conditions. The central property used is the convexity and completeness of the state space that allows it to generalize Deutsch’s original proof for q-bit systems to more general classes of statistically described systems. The results demonstrate that the D-CTC condition, or the conditions under which it can be fulfilled, is not characteristic of, or dependent on, the quantum nature of a bi-partite system.

Black hole microstates from the worldsheet

Recently an exact worldsheet description of strings propagating in certain black hole microstate geometries was constructed in terms of null-gauged WZW models. In this paper we consider a family of such coset models, in which the currents being gauged are specified by a set of parameters that a priori take arbitrary values. We show that consistency of the spectrum of the worldsheet CFT implies a set of quantisation conditions and parity restrictions on the gauging parameters. We also derive these constraints from an independent geometrical analysis of smoothness, absence of horizons and absence of closed timelike curves. This allows us to prove that the complete set of consistent backgrounds in this class of models is precisely the general family of (NS5-decoupled) non-BPS solutions known as the JMaRT solutions, together with their various (BPS and non-BPS) limits. We clarify several aspects of these backgrounds by expressing their six-dimensional solutions explicitly in terms of five non-negative integers and a single length-scale. Finally we study non-trivial two-charge limits, and exhibit a novel set of non-BPS supergravity solutions describing bound states of NS5 branes carrying momentum charge.

Type II Vacuum Spacetime Admitting Closed Timelike Curves

We present a cyclic symmetry type II vacuum spacetime admitting closed timelike curves (CTCs) which appear after a certain instant of time, i.e., a time-machine spacetime. The various authors in past have considered the 2D and 4D flat generalization of Misner space, but in the present work, we have considered the curved spacetime generalzations of 4D Misner space, and is asymptotically flat radially

A substrate for brane shells from $$ T\overline{T} $$

A solvable current-current deformation of the worldsheet theory of strings on AdS3 has been recently conjectured to be dual to an irrelevant deformation of the spacetime orbifold CFT, commonly referred to as single-trace $$ T\overline{T} $$ T T ¯ . These deformations give rise to a family of bulk geometries which realize a non-trivial flow towards the UV. For a particular sign of this deformation, the corresponding three-dimensional geometry approaches AdS3 in the interior, but has a curvature singularity at finite radius, beyond which there are closed timelike curves. It has been suggested that this singularity is due to the presence of “negative branes,” which are exotic objects that generically change the metric signature. We propose an alternative UV-completion for geometries displaying a similar singular behavior by cutting and gluing to a regular background which approaches a linear dilaton vacuum in the UV. In the S-dual picture, a singularity resolution mechanism known as the enhançon induces this transition by the formation of a shell of D5-branes at a fixed radial position near the singularity. The solutions involving negative branes gain a new interpretation in this context.

Pure Gauss–Bonnet NUT black hole with and without non-central singularity

It is known that NUT solution has many interesting features and pathologies like being non-singular and having closed timelike curves. It turns out that in higher dimensions horizon topology cannot be spherical but it has instead to be product of 2-spheres so as to retain radial symmetry of spacetime. In this letter we wish to present a new solution of pure Gauss–Bonnet $$\Lambda $$ Λ -vacuum equation describing a black hole with NUT charge. It has three interesting cases: (a) black hole with both event and cosmological horizons with singularity being hidden behind the former, (b) a regular spacetime free of both horizon and singularity, and (c) black hole with event horizon without singularity and cosmological horizon. Singularity here is always non-centric at $$r \ne 0$$ r ≠ 0 .

Axially symmetric Petrov type II general space–time and closed timelike curves

We present a Petrov type II general space–time which violates causality in the sense that it allows for the formation of closed timelike curves that appear after a definite instant of time. The metric, which is axially symmetric, admits an expansion-free, twist-free and shear-free null geodesic congruence. From the general metric, we obtain two particular type II metrics. One is a vacuum solution while the other represents a Ricci flat solution with a negative cosmological constant.

Closed Timelike Curves, Singularities and Causality: A Survey from Gödel to Chronological Protection

I give a historical survey of the discussions about the existence of closed timelike curves in general relativistic models of the universe, opening the physical possibility of time travel in the past, as first recognized by K. Gödel in his rotating universe model of 1949. I emphasize that journeying into the past is intimately linked to spacetime models devoid of timelike singularities. Since such singularities arise as an inevitable consequence of the equations of general relativity given physically reasonable assumptions, time travel in the past becomes possible only when one or another of these assumptions is violated. It is the case with wormhole-type solutions. S. Hawking and other authors have tried to “save” the paradoxical consequences of time travel in the past by advocating physical mechanisms of chronological protection; however, such mechanisms remain presently unknown, even when quantum fluctuations near horizons are taken into account. I close the survey by a brief and pedestrian discussion of Causal Dynamical Triangulations, an approach to quantum gravity in which causality plays a seminal role.