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In line with previous editions, the Time Machine Factory [unspeakable, speakable] on Time Travel - 2024 conference focuses on causality and non-locality in physics, and the insurgence of situations where causality or chronology can potentially be violated, and how this relates to the existence of “time machines”.
The conference has the following aims
Although violations of chronology might seem to contradict common sense and lead to logical paradoxes, “time machines” are not ruled out by the current laws of physics.
The conference will highlight new horizons in physics and astrophysics associated with the possible existence of a Time Machine. Examining these fundamental issues provides an opportunity to initiate new ideas and investigations, which explore the role of causality and the interplay between General Relativity and Quantum Mechanics, two theories that on their own have been extensively verified by experiment but have not yet been successfully combined into a single unified theory.
A screening of three short films about time travel by Michele Reilly, Andrey Kezzin, and Seth Lloyd:
Steeplechase
Stag Hunt, and
Pope Bans Time Travel Pilgrimages,
All three films won multiple prizes at Cannes and film festivals around the world.
Screening of the movie Primer by Shane Carruth.
In this talk we will start by reviewing the structure of some model spacetimes containing closed timelike curves (CTCs) such as Misner space, and spacetimes with moving or rotating cosmic strings. In general such spacetimes contain both a chronal and non-chronal region separated by a Cauchy horizon. We give initial data for the wave equation on a partial Cauchy surface in the chronal region and show that the Cauchy problem is well-posed up to and on the chronology horizon. We then consider extending the solution beyond the chronology horizon. In the model spacetimes we can first pass to an covering space and then introduce coordinates so that the identifying isometries are manifest in one periodic coordinate. Factoring out this coordinate we obtain a reduction of the wave equation which turns out to be of mixed type, changing from hyperbolic to elliptic on the horizon. The well-posedness of the solution then turns out to be similar to that of the classical Tricomi problem which is also a PDE which changes type on a hypersurface. We end by discussing the situation in more general spacetimes.
A central result within mathematical relativity is the well-posedness of the initial value formulation of GR for initial data satisfying Einstein constraint equations, where uniqueness of maximal globally hyperbolic developments of initial data is consistent with the type of determinism expected from classical physical theories. In this context, isolated gravitational systems are modelled by asymptotically Euclidean initial data sets, and there are physically reasonable expectations about the asymptotic behaviour of these systems. It turns out that a rigorous mathematical understanding of the conditions that guarantee these expectations is still an open problem. This is crucial to make canonically conserved quantities carrying physical information well-defined. In the case of the ADM energy and linear momentum, precise geometric criteria making them well-defined are well-known, but for the finer ADM center of mass and angular momentum this is not the case, and ad-hoc asymptotic conditions, expected to hold for reasonable physical systems, tend to be demanded. In this talk, we will comment on recent advances related to regularity theory and asymptotic analysis of geometric partial differential equations which allow one to partially characterise in pure geometric terms those initial data sets which indeed obey these expected asymptotic properties.
We review several recent low regularity versions of the singularity theorems of General Relativity. Following a brief recap of the classical theorems of Penrose and Hawking we focus on the analytical aspects of their proofs. In particular, we discuss focusing results for causal geodesics in the case of merely locally Lipschitz spacetime metrics and present corresponding recent extensions of the classical theorems. We also address the interrelation of these result to versions of the singularity theorems in the settings of closed cone structures due to Ettore Minguzzi and of metric measure geometry due to Fabio Cavalletti and Andrea Mondino.
This talk investigates the practical applications of projective closed timelike curves (PCTCs).
Because PCTCs can be realized in the laboratory via post-selected experiments, some of the more counter-intuitive effects of closed timelike curves can actually be implemented. We discuss the enhancement of measurement accuracy via PCTCs, the application of closed timelike curves to game theory, and possible near-term experimental realizations.
In General Relativity, time travel is associated with the existence of closed timelike curves. Such trajectories model the history of point particles, and so in this description, the body travelling into its own past is devoid of any structure. In order to begin the process of describing time-travelling extended bodies, we consider the motion of gyroscopes and spinning particles along closed timelike curves. We argue that such motion generically involves contradictions that are enforced by the laws of physics - as expressed in the equations of motion of these bodies. This presents a challenge to Novikov's self-consistency principle of time travel.
It is well known that (static) regular black hole spacetimes can be sourced by appropriately chosen theories of non-linear electrodynamics. More recently, it was shown that many such models can also be obtained as solutions of vacuum gravity equations, upon considering an infinite series of quasi-topological higher curvature corrections. After reviewing both these approaches, I will show that the latter construction can be upgraded
to yield regular black holes with vanishing inner horizon surface gravity. In four dimensions, such a condition is necessary for the absence of classical instabilities associated with mass inflation on the inner horizon.
In my talk I will review the idea of pseudo-density matrices (PDMs), which are states of physical systems "stretching across" time. They arise by treating different instances of time as different Hilbert spaces connected by the usual tensor product structure that is normally used for spatial modes (i.e., different instances of time become different modes in this formulation). I will then talk about entropic measures of correlation as functions of PDMs. Various comparisons will be made with the traditional spatial measures of entanglement, discord and classical correlations.
The area of spatially stable marginally trapped surfaces (MTS) has a bound that depends on the minimum of a particular component of the Einstein tensor. I will prove that any spacetime containing spatially stable MTSs with area approaching the bound acquire universal properties generically. In particular, they possess marginally trapped tubes foliated by MTS of spherical topology, composed of a dynamical horizon portion and a timelike membrane portion that meet at a preferred round sphere $S$ with constant Gaussian curvature and the maximal area. All such marginally trapped tubes change signature at $S$, and they develop towards the past with increasing area without limitation. A future singularity also arises. This has particular relevance in the presence of a positive cosmological constant $\Lambda$, as then the minimum value is universal and given by $\Lambda$ itself. These "ultra-massive" spacetimes are more powerful than black holes, as they produce a collapsing universe with no event horizon. They can even overcome the repulsive force of the cosmological constant. Examples and implications will be discussed.
We investigate a Schwarzschild metric exhibiting a signature change across the event horizon, which gives rise to what we term a Lorentzian-Euclidean black hole. The resulting geometry is regularized by employing the Hadamard partie finie technique, which allows us to prove that the metric represents a solution of vacuum Einstein equations. In this framework, we introduce the concept of atemporality as the dynamical mechanism responsible for the transition from a regime with a real-valued time variable to a new one featuring an imaginary time. We show that this mechanism prevents the occurrence of the singularity and, by means of the regularized Kretschmann invariant, we discuss in which terms atemporality can be considered as the characteristic feature of this black hole. The physical foundation of the approach can be related to the conservation laws. In fact, the black hole is singularity free if Noether symmetries, related to the size and the mass of the gravitational system, are not violated. In other words, the emergence of imaginary time is the signature of a symmetry breaking. In this perspective, it is not possible to enter the black hole and the event horizon becomes the limit of our knowledge according to the standard laws of physics. Future challenges are related to the observational signatures of atemporality which actually means that the information comes only from the external black hole solution and, in addition, it is conserved. Other open issues are related to the quantum counterpart of the model. In fact, we could conceive the event horizon as a sort of potential barrier and the investigation of quantum particles impacting against it could open an interesting phenomenology to be explored.
In this talk I analyze the construction of quantum field theory in spacetimes that contain regions with closed timelike curves (CTCs). Additionally, I explore how particle detectors can discern the presence of CTCs in causally disconnected regions and differentiate between various spacetime topologies.
Before we can begin manufacturing time machines in our factory, we must consider whether those time machines could create time travel paradoxes, and if so, how these paradoxes might be resolved by existing or new laws of physics. We will first review the different types of time travel paradoxes and their proposed resolutions. Then we will present the results of our 3 recent papers (1911.11590, 2110.02448, 2303.07635) discussing different aspects of time travel paradoxes from the perspectives of both general relativity and quantum mechanics. We will argue that generic time travel paradoxes can only be resolved using the concept of parallel timelines, and suggest possibilities for how such timelines may manifest themselves.
The “problem of time” that approaches to quantum gravity have to either tackle or circumvent should, naturally, also occur in models of time travel trying to move beyond (semi-)classical gravity. From a viewpoint of canonical gravity a first hurdle to time travel is that the underlying quantization procedure relies on global hyperbolicity of the space-time to be quantized. As with any new theory, it is to be expected that expectations of earlier theories (like in this case, global hyperbolicity) would have to be tempered, changed, or let go in the successor theory. Recent advances in the understanding of relational dynamics in quantum theory have greatly propelled the field of time in quantum theories forward. In this talk we will present our recent efforts to combine such relational quantum dynamics and periodic clocks in the service of toy models for time travel. The goal will be to build a collection of toy models of varying degrees of complexity that should provide a view of quantum gravity beyond global hyperbolic space-times, and thus potentially new arguments against time travel.
In the extreme mass ratio limit, the evolution of the event horizon in a merging event between a large black hole and a small compact object can be computed exactly with elementary ray-tracing techniques. I will describe what happens when the small body is an Ellis-Bronnikov traversable wormhole. A double-mouth wormhole within the same universe is obtained by gluing two such geometries --- in this setting the ratio of the distance between the two mouths to the distance traversed through the wormhole plays an important role.
At scales comparable to the wormhole, its geometry drastically distorts the planar horizon of the large black hole. When a `short' wormhole falls in, the horizon wraps around it and an island is formed, representing a region of spacetime that is spatially disconnected from the exterior of the black hole, but in causal contact with future null infinity (through the wormhole). This region shrinks as time evolves and eventually disappears. The lifetime of the island essentially grows linearly with the inter-mouth distance, but also decreases linearly with the length of the wormhole throat. Imposing physically reasonable energy conditions severely restricts the duration of the open communication channel with the interior of the black hole.
The flaring-out condition at a wormhole’s throat is a fundamental aspect of wormhole physics, which, in the context of classical general relativity, leads to a violation of the null energy condition. In this work, we explore the broadest possible conditions under modified gravity, where the matter threading the wormhole throat satisfies the energy conditions. In fact, it is the higher-order curvature effects, interpreted as a gravitational fluid, that sustain these non-standard wormhole geometries. Our analysis demonstrates that wormholes can theoretically exist without requiring exotic matter, but rather within the framework of modified gravity. Interestingly, these non-trivial geometries have the potential to generate closed timelike curves, thus posing challenges to the concept of causality. Given that causality is central to the formulation of physical theories, the prospect of time travel and the resulting paradoxes demands careful scrutiny. This presentation will address these critical issues in detail.
The possibility that the topology of space can change even at a classical level in General Relativity necessitates abandoning either the causality conditions or the equivalence principle. If the causal structure is regarded as fundamental, topology changes are possible by allowing singularities, degenerate tetrads, or gravitational instantons, i.e., Riemannian solutions of the Einstein equations with interesting geometrical and topological properties. Conversely, if the equivalence principle is considered fundamental, spacetime is described by an everywhere non-degenerate Lorentzian geometry, requiring the existence of closed time-like curves for topology transitions to occur. Specifically, the formation of a wormhole from a topologically trivial configuration of space is constrained in the Lorentzian case by topological invariants of the spacetime manifold, even allowing for causality violations. Such topological restrictions are kinematical, independent of the equations of motion, and arise only from global requirements on spacetime. In this session, these topological constraints are presented in the case where the transition occurs in a finite region of space and is mediated by a Lorentzian cobordism. Special emphasis will be given to the nucleation of a wormhole by 3-dimensional topological surgery and the maintenance of the Lorentzian structure by employing Misner's trick of taking connected sums with closed 4-manifolds.
We describe the connection between a traversable wormhole and the Casimir effect. With the help of an equation of state we also discuss different forms of solutions related to the Casimir source. The effect of including an electromagnetic field, temperature and rotations to the original energy density are also discussed.
In 1917 Tullio Levi-Civita exactly solved the Einstein-Maxwell equations for the artificial and very tiny gravitational field created by the energy of a static and extremely intense magnetic or electric field.
In 1995 Claudio Maccone extended that Levi-Civita solution so as to check its validity by virtue of the Z_machine existing at Sandia Labs in the USA.
In 2000 Dr. Slutz’s reply from Sandia Labs was that not even the Z_machine would be powerful enough to carry on the experimental verification of the theory.
Thus, the only hope we have as of 2024 is to devise some new astronomical method allowing the measurement of artificial gravity in the proximity of magnetars.
Finally, some speculations are made to see if these theoretical results may be related to Wormhole Theory.
Wormhole solutions in general relativity have some spectacular local and global properties. An invariant characterisation of a wormhole's throat presents it as an outer marginal trapped surface subject to additional conditions. The requirement that this trapped surface forms within a finite time from the perspective of a distant observer leads to unusual properties of black and white holes and may be contentious. However, it is mandatory if a wormhole is to be traversable.
The paradigmatic traversable wormholes are described by static, spherically symmetric Ellis-Morris-Thorne and Simpson-Visser metrics. We show that no dynamical solution of the semiclassical Einstein equations can have these metrics as their static limit. Conversely, possible static limits of the allowed dynamical solutions are not traversable and result in the breach of a quantum energy inequality that limits the null energy condition violations by quantum fields and/or divergent tidal forces. This finding holds irrespective of the specific properties of fields suggested for wormhole construction, indicating that spherically symmetric wormholes are not feasible in semiclassical gravity. This conclusion does not depend on specific properties of fields that may be proposed for wormhole construction. As a result, spherically symmetric wormholes cannot exist in semiclassical gravity.
As was shown by Ellis in gr-qc/0411096, one can establish a
correspondence between the Schwarzschild metric and a warp drive-type
metric, making it possible to consider a warp drive in a black hole
background. We elaborate upon this result and demonstrate that the
black hole's gravitational field can alleviate the violations of
energy conditions, reducing the amount of negative energy required to
sustain a warp bubble. Besides, we demonstrate that the black hole
horizon is effectively absent for the observers inside the bubble,
making it possible for them to send a light signal from the inside to
the outside.
We also generalize the Ellis scheme to the case of Morris-Thorne
wormholes and prove that Alcubierre warp drives cannot traverse
humanly traversable wormholes and can only pass through those that
either have a horizon or violate the flare-out condition. However,
this "no-go" theorem does not apply to another class of warp drive
solutions, the spherically symmetric warp drives, that are not
localized in space, and have the form of spherical waves.
Numerical solutions of the Dirac equation show that, post-selected for tunneling, relativistic electrons can exhibit transit time distributions with a peak corresponding to superluminal effective velocity. However, a non-negligible effect is seen only when tunneling probability is very small. If one attempts to send a signal using many electrons to compensate for the low tunneling probability, a distribution of signaling times is obtained with superluminal effective speed. However, we find that the signal always arrives slightly earlier if carried by the same number of photons traveling in a vacuum. The effective superluminality that is seen results from the uncertainty in the initial particle - electron or photon - position.
Thirty years after Alcubierre introduced the concept of the warp drive spacetime in General Relativity (GR), extensive literature has emerged on his model and its generalizations. However, these models, which we refer to as "restricted warp drive" models, are limited within the context of GR. In contrast, we propose a new approach called the "tilted warp drive," which incorporates essential elements missing from previous models, such as covariant descriptions of motion, including tilted, accelerated, and vortical motions.
In this talk, I will discuss the major significance of the tilt in advancing towards a feasible physical warp drive model. I will present the key concepts and an example demonstrating the potential of this new proposal, which opens a new avenue of research. This approach, not previously explored in the literature, may lead the way towards a deeper understanding of a physical warp drive. If time permits, I will also link these spacetimes to cosmological models.
This is joint work with Thomas Buchert.
Warp drives are exotic solutions in general relativity that allow inertial observers to accelerate and reach subluminal or superluminal speeds relative to other inertial observers. The field of warp drives was defined three decades ago with the famous Alcubierre metric and its generalization, the Natário metric. Both classes of warp drives feature propulsion-less acceleration, zero ADM mass, and shift-only metrics. Moreover, both these classes violate all the energy conditions, which made these solutions perceived as historically quirky and unphysical. Recently, a new wave of warp drive research has emerged, with several new metrics proposed by us and other groups. It has become clear that there are many more warp drive spacetimes than initially conceived, not necessarily limited to the earlier constraints. To explore these spacetimes, we have introduced a new software tool called Warp Factory (which can also be turned into a Time Machine Factory), capable of rapidly numerically evaluating the physicality of arbitrarily complex metrics and visualizing warp drives. With it, we have already found an unambiguously physical constant velocity solution and an accelerating hovering solution. Remarkably, the field seems to be invigorated, with novel ideas proposed by many groups around the world. These include collapsing warp drives, their gravitational wave signatures, and the first explorations into mechanisms of physical acceleration. What does the future of warp drive research look like? It appears remarkably bright as the field is still in its infancy.
Warp drives offer intriguing possibilities for novel transportation methods. This study presents a groundbreaking solution for a constant velocity subluminal warp drive that satisfies all energy conditions. Our approach combines a stable matter shell with a shift vector distribution resembling established warp drive solutions, such as the Alcubierre metric. We numerically generate the spacetime metric and rigorously evaluate the energy conditions. Importantly, we demonstrate that the shift vector distribution cannot be reduced to a mere coordinate transformation, confirming the physical significance of our solution. This research marks a significant advancement in warp drive theory by showing that classic warp drive spacetimes can be modified to satisfy energy conditions through the addition of a regular matter shell with a positive ADM mass. Our findings open new avenues for theoretical explorations of faster-than-light travel within the constraints of general relativity and provide a foundation for future studies in this exciting field.
In this talk I will use the Page-Wootters "timeless" framework for analyzing dynamics from the perspective of inertial and non-inertial quantum clocks. I will derive a new time-energy uncertainty relation indicating that the duration of an energy measurement carried out by an external system cannot be performed arbitrarily fast from the perspective of the internal clock [1]. In addition, when using the relativistic mass-energy equivalence to study an accelerating massive quantum particle with an internal clock I will show that the evolution from the perspective of that clock is non-Hermitian [2]. As a particular consequence, I will prove that the effective Hamiltonian of two gravitationally interacting particles is non-Hermitian from the perspective of the clock of either particle [2]. If time lets me, I will discuss some related results addressing dynamical nonlocality [3] and spatiotemporal quantum reference frames [4] in light of the relativistic independence principle [5].
References
[1] I.L. Paiva, A.C. Lobo, and E. Cohen, Quantum 6 (2022) 683.
[2] I.L. Paiva, A. Te’eni, B.Y. Peled, E. Cohen, and Y. Aharonov, Commun. Phys. 5 (2022) 298.
[3] I.L. Paiva, M. Nowakowski, and E. Cohen, Phys. Rev. A 105 (2022) 042207.
[4] M. Suleymanov, I.L. Paiva, and E. Cohen, Phys. Rev. A 109 (2024) 032205.
[5] A. Carmi, and E. Cohen, Sci. Adv. 5 (2019) eaav8370
A general entanglement-based witness of non-classicality has recently been proposed, which can be applied to testing quantum effects in gravity. This witness is based on generating entanglement between two quantum probes via a mediator. We provide a "temporal" variant of this witness, using a single quantum probe to assess the non-classicality of the mediator. Within the formalism of quantum theory, we show that if a system $M$ can induce a coherent dynamical evolution of a quantum system $Q$, in the presence of a conservation law, then $M$ must be non-classical. We shall explore the possibility of interpreting this temporal witness of non-classicality as the equivalent of generating entanglement in time between the single probe $Q$ before and after the evolution mediated by $M$, provided that a global quantity is conserved in the evolution. This creates a temporal parallel to the previously proposed entanglement-based witness of non-classicality, offering intriguing perspectives on locality in time and the connections between quantum correlation in space and time. Moreover, this argument supports witnesses of non-classicality relying on a single quantum probe, which can be applied to several open issues, notably in quantum gravity or quantum biology.
We demonstrate that a matter field with proper time oscillations has the properties of a quantum field. The particles observed are oscillators propagating back and forth in time. We also find that the internal time of the field is self-adjoint. The proper time oscillation of an observed particle satisfies an uncertainty relation analogous to that between spatial position and momentum. To test the theory, we propose to study the effects of the oscillations on a particle’s decaying time and arrival time.
In contemporary physics, there is a quest to unite quantum theory and general relativity. Recently, there has been discussion about using the observation of gravity-induced entanglement to demonstrate the quantum nature of gravity. While some experimental proposals have been in this direction, the extreme technological requirements make their implementation quite challenging. We present a table-top interferometer that could enable less demanding quantum gravity tests. This interferometer relies on quantum superpositions of steady massive objects. It is compact and requires only short-range electromagnetic. Additionally, it allows for the re-use of the quantum probes involved
We quantify the difference between classical and quantum counterfactual effects, where an output distribution is somehow changed by the removal of signal (``blocking'') at some point. We show that there is a counterfactual gain in quantum counterfactual communication, which quantifies the effect it has above and beyond any classical counterfactual effect, and that this counterfactual gain comes from coherences. This counterfactual gain contains a term proportional to a Kirkwood-Dirac quasiprobability term---when this is positive or zero, this counterfactual gain can only distribute probability more equitably over a the set of outputs; however, if this Kirkwood-Dirac term is negative, blocking can cause output probability to focus on a specific outcome. We show that this difference between quantum and classical counterfactual effects results from the measurement backaction caused by this blocking. We show that we cannot explain quantum counterfactual effects simply by removing detection events. We link this to attempts to argue from counterfactuals in quantum mechanics (e.g. when forming noncontextual and Bell inequalities), and show that this backaction effect forms a natural explanation for the violation of the statistical, or measurement, independence assumption used to form these inequalities.
Carroll symmetries arise generically on null hypersurfaces, such as black hole event horizons or null infinity in asymptotically flat spacetimes. Carroll gravity is a gravitational theory based on Carroll symmetries. Carroll black holes are solutions of Carroll gravity that exhibit Carroll thermal properties and have a Carroll extremal surface. I review, motivate, and explain all these notions and address recent results on the Carroll Hawking effect.
In this talk, I review the Deutsch-Politzer spacetime, the related teleporter spacetime, and the quasiregular singularities necessarily present in such spacetimes. Such singularities, characterized by points with multiple future-directed and past-directed light cones, are generalizations of conical singularities and can reveal insights into topology change and the termination point of an evaporating black hole horizon. I then describe a gravity theory that can in principle provide a microscopic description for such singularities.
Thermodynamics of local causal horizons binds together gravity, quantum entanglement and the Unruh effect in a relatively simple setting. Moreover, it offers an elegant way to derive the equations governing the gravitational dynamics. A central role in this derivation is played by the causal structure of the spacetime and the equivalence principle(s). In my talk, I explore how the quasi-local energy of the gravitational field affects the thermodynamics of local causal horizons, and whether it can lead to corrections to the Einstein field equations. I also comment on the role of the energy conditions in this approach.
An extension of standard nonequilibrium thermodynamics is presented, where the gravitational potential is a thermodynamic state variable, (P. Ván & S. Abe, Physica A 588 (2022) 126505). Then standard and rigorous methods of Rational Mechanics and nonequilibrium thermodynamic framework allow a set of evolution equations to be derived for the gravitational field and the derivation of thermodynamic forces and fluxes. The method effectively substitutes variational principles for ideal systems without dissipation, and provides the evolution equations for dissipative continua at the same time. An important aspect of this framework is the application of $\beta$-, or thermometer flow-frame (F. Becattini, Acta Physica Polonica B, (2016) 47:1819--1832), i.e. tying the flow of the continuum, the flow-frame, to the temperature four-vector, compared to the usual Landau-Lifshitz (or energy) or Eckart (conserved particle) flow-frames, which have been proved unstable.
With certain straightforward assumptions for the gravitating system, a nondissipative gravitational field equation can be derived in the form of a modified Poisson equation:
$$ \Delta \varphi = 4 \pi G \rho + K (\nabla \varphi)^2, $$
resulting in modified gravity. Analytical solutions show a double crossover, allowing for different gravitational behaviour on different size scales (S. Abe & P. Ván, Symmetry 2022, 14, 1048(7)). This property presents a possible approach to explain Dark Matter-related phenomena on galactic scales, and different dynamics on extragalactic scales. Moreover, a direct connection to quantum mechanics is presented, as well, (P. Ván, Physics of Fluids, (2023) 35(5).).
I will present a detailed introduction to my Mathematica package, OGRe: (O)bject-Oriented (G)eneral (Re)lativity, and its Python port OGRePy, both of which would be of great interest to anyone doing research in general relativity. I will demonstrate the package's usage and features, including its ability to calculate arbitrary tensor formulas involving any combination of addition, multiplication, trace, contraction, and partial and covariant derivatives, while automatically figuring out the proper index configuration and coordinate system to use for each tensor. I will discuss how this package has been used in research so far, as well as future plans.