Christian Wüthrich

Do the Laws of Physics Forbid the Operation of Time Machines

We address the question of whether it is possible to operate a time machine by manipulating matter and energy so as to manufacture closed timelike curves. This question has received a great deal of attention in the physics literature, with attempts to prove no-go theorems based on classical general relativity and various hybrid theories serving as steps along the way towards quantum gravity. Despite the effort put into these no-go theorems, there is no widely accepted definition of a time machine. We explain the conundrum that must be faced in providing a satisfactory definition and propose a resolution. Roughly, we require that all extensions of the time machine region contain closed timelike curves; the actions of the time machine operator are then sufficiently “potent” to guarantee that closed timelike curves appear. We then review no-go theorems based on classical general relativity, semi-classical quantum gravity, quantum field theory on curved spacetime, and Euclidean quantum gravity. Our verdict on the question of our title is that no result of sufficient generality to underwrite a confident “yes” has been proven. Our review of the no-go results does, however, highlight several foundational problems at the intersection of general relativity and quantum physics that lend substance to the search for an answer.

To Quantize or Not to Quantize: Fact and Folklore in Quantum Gravity

Does the need to find a quantum theory of gravity imply that the gravitational field must be quantized? Physicists working in quantum gravity routinely assume an affirmative answer, often without being aware of the metaphysical commitments that tend to underlie this assumption. The ambition of this article is to probe these commitments and to analyze some recently adduced physical—as opposed to metaphysical—arguments pertinent to the issue of quantization. While there exist good reasons to quantize gravity, as this analysis will show, alternative approaches to gravity challenge the received wisdom. These renegade approaches do not regard gravity as a fundamental force, but rather as effective, i.e., as merely supervening on fundamental physics. I will urge that these alternative accounts at least prove the tenability of an opposition to quantization.Does the need to find a quantum theory of gravity imply that the gravitational field must be quantized? Physicists working in quantum gravity routinely assume an affirmative answer, often without being aware of the metaphysical commitments that tend to underlie this assumption. The ambition of this article is to probe these commitments and to analyze some recently adduced physical—as opposed to metaphysical—arguments pertinent to the issue of quantization. While there exist good reasons to quantize gravity, as this analysis will show, alternative approaches to gravity challenge the received wisdom. These renegade approaches do not regard gravity as a fundamental force, but rather as effective, i.e., as merely supervening on fundamental physics. I will urge that these alternative accounts at least prove the tenability of an opposition to quantization.

Challenging the Spacetime Structuralist

Structural realist interpretations of generally relativistic spacetimes have recently come to enjoy a remarkable degree of popularity among philosophers. I present a challenge to these structuralist interpretations that arises from considering cosmological models in general relativity. As a consequence of their high degree of spacetime symmetry, these models resist a structuralist interpretation. I then evaluate the various strategies available to the structuralist to react to this challenge.

The Structure of Causal Sets

More often than not, recently popular structuralist interpretations of physical theories leave the central concept of a structure insufficiently precisified. The incipient causal sets approach to quantum gravity offers a paradigmatic case of a physical theory predestined to be interpreted in structuralist terms. It is shown how employing structuralism lends itself to a natural interpretation of the physical meaning of causal set theory. Conversely, the conceptually exceptionally clear case of causal sets is used as a foil to illustrate how a mathematically informed rigorous conceptualization of structure serves to identify structures in physical theories. Furthermore, a number of technical issues infesting structuralist interpretations of physical theories such as difficulties with grounding the identity of the places of highly symmetrical physical structures in their relational profile and what may resolve these difficulties can be vividly illustrated with causal sets.More often than not, recently popular structuralist interpretations of physical theories leave the central concept of a structure insufficiently precisified. The incipient causal sets approach to quantum gravity offers a paradigmatic case of a physical theory predestined to be interpreted in structuralist terms. It is shown how employing structuralism lends itself to a natural interpretation of the physical meaning of causal set theory. Conversely, the conceptually exceptionally clear case of causal sets is used as a foil to illustrate how a mathematically informed rigorous conceptualization of structure serves to identify structures in physical theories. Furthermore, a number of technical issues infesting structuralist interpretations of physical theories such as difficulties with grounding the identity of the places of highly symmetrical physical structures in their relational profile and what may resolve these difficulties can be vividly illustrated with causal sets.

No Presentism in Quantum Gravity

This essay offers a reaction to the recent resurgence of presentism in the philosophy of time. What is of particular interest in this renaissance is that a number of recent arguments supporting presentism are crafted in an untypically naturalistic vein, breathing new life into a metaphysics of time with a bad track record of co-habitation with modern physics. Against this trend, the present essay argues that the pressure on presentism exerted by special relativity and its core lesson of Lorentz symmetry cannot easily be shirked. A categorization of presentist responses to this pressure is offered. As a case in point, I analyze a recent argument by Monton (Presentism and quantum gravity, 263–280, 2006) presenting a case for the compatibility of presentism with quantum gravity. Monton claims that this compatibility arises because there are quantum theories of gravity that use fixed foliations of spacetime and that such fixed foliations provide a natural home for a metaphysically robust notion of the present. A careful analysis leaves Monton’s argument wanting. In sum, the prospects of presentism to be alleviated from the stress applied by fundamental physics are faint.

A twist in the geometry of rotating black holes: seeking the cause of acausality

We investigate Kerr–Newman black holes in which a rotating charged ring-shaped singularity induces a region which contains closed timelike curves (CTCs). Contrary to popular belief, it turns out that the time orientation of the CTC is opposite to the direction in which the singularity or the ergosphere rotates. In this sense, CTCs “counter-rotate” against the rotating black hole. We have similar results for all spacetimes sufficiently familiar to us in which rotation induces CTCs. This motivates our conjecture that perhaps this counter-rotation is not an accidental oddity particular to Kerr–Newman spacetimes, but instead there may be a general and intuitively comprehensible reason for this.

No Categorial Support for Radical Ontic Structural Realism

Radical ontic structural realism (ROSR) asserts an ontological commitment to ‘free-standing’ physical structures understood solely in terms of fundamental relations, without any recourse to relata that stand in these relations. Bain ([2013], pp.1621–35) has recently defended ROSR against the common charge of incoherence by arguing that a reformulation of fundamental physical theories in category-theoretic terms (rather than the usual set-theoretic ones) offers a coherent and precise articulation of the commitments accepted by ROSR. In this essay, we argue that category theory does not offer a more hospitable environment to ROSR than set theory. We also show that the application of category-theoretic tools to topological quantum field theory and to algebraic generalizations of general relativity do not warrant the claim that these theories describe ‘object-free’ structures. We conclude that category theory offers little if any comfort to ROSR. 1 Introduction: Ridding Structures of Objects 2 The Set-theoretic Peril for Radical Ontic Structural Realism 3 Bain’s Categorial Strategy to Save Radical Ontic Structural Realism 4 Throwing out the Relations with the Relata 5 Categorial and Set-theoretical Structures 6 Radical Suggestions from Topological Quantum Field Theory? 7 Sheaves of Einstein Algebras as Radical Structures? 8 Conclusions 1 Introduction: Ridding Structures of Objects 2 The Set-theoretic Peril for Radical Ontic Structural Realism 3 Bain’s Categorial Strategy to Save Radical Ontic Structural Realism 4 Throwing out the Relations with the Relata 5 Categorial and Set-theoretical Structures 6 Radical Suggestions from Topological Quantum Field Theory? 7 Sheaves of Einstein Algebras as Radical Structures? 8 Conclusions

Raiders of the Lost Spacetime

Spacetime as we know and love it is lost in most approaches to quantum gravity. For many of these approaches, as inchoate and incomplete as they may be, one of the main challenges is to relate what they take to be the fundamental non-spatiotemporal structure of the world back to the classical spacetime of general relativity (GR). The present essay investigates how spacetime is lost and how it may be regained in one major approach to quantum gravity, loop quantum gravity.

What Becomes of a Causal Set

Unlike the relativity theory it seeks to replace, causal set theory (CST) has been interpreted to leave space for a substantive, though perhaps ‘localized’, form of ‘becoming’. The possibility of fundamental becoming is nourished by the fact that the analogue of Stein’s theorem from special relativity does not hold in CST. Despite this, we find that in many ways, the debate concerning becoming parallels the well-rehearsed lines it follows in the domain of relativity. We present, however, some new twists and challenges. In particular, we show that a novel and exotic notion of becoming is compatible with causal sets. In contrast to the localized becoming considered compatible with the dynamics of CST by its advocates, our novel kind of becoming, while not answering to the typical A-theoretic demands, is global and objective. 1 Introduction 2 The Basics of Causal Set Theory 3 Facing the Same Dilemma? 4 Taking Growth Seriously 5 Conclusion 1 Introduction 2 The Basics of Causal Set Theory 3 Facing the Same Dilemma? 4 Taking Growth Seriously 5 Conclusion

A quantum-information-theoretic complement to a general-relativistic implementation of a beyond-Turing computer

There exists a growing literature on the so-called physical Church–Turing thesis in a relativistic spacetime setting. The physical Church–Turing thesis is the conjecture that no computing device that is physically realizable (even in principle) can exceed the computational barriers of a Turing machine. By suggesting a concrete implementation of a beyond-Turing computer in a spacetime setting, Németi and Dávid (Appl Math Comput 178:118–142, 2006) have shown how an appreciation of the physical Church–Turing thesis necessitates the confluence of mathematical, computational, physical, and indeed cosmological ideas. In this essay, I will honour István’s seventieth birthday, as well as his longstanding interest in, and his seminal contributions to, this field going back to as early as 1987 by modestly proposing how the concrete implementation in Németi and Dávid (Appl Math Comput 178:118–142, 2006) might be complemented by a quantum-information-theoretic communication protocol between the computing device and the logician who sets the beyond-Turing computer a task such as determining the consistency of Zermelo–Fraenkel set theory. This suggests that even the foundations of quantum theory and, ultimately, quantum gravity may play an important role in determining the validity of the physical Church–Turing thesis.There exists a growing literature on the so-called physical Church–Turing thesis in a relativistic spacetime setting. The physical Church–Turing thesis is the conjecture that no computing device that is physically realizable (even in principle) can exceed the computational barriers of a Turing machine. By suggesting a concrete implementation of a beyond-Turing computer in a spacetime setting, Nemeti and David (Appl Math Comput 178:118–142, 2006) have shown how an appreciation of the physical Church–Turing thesis necessitates the confluence of mathematical, computational, physical, and indeed cosmological ideas. In this essay, I will honour Istvan’s seventieth birthday, as well as his longstanding interest in, and his seminal contributions to, this field going back to as early as 1987 by modestly proposing how the concrete implementation in Nemeti and David (Appl Math Comput 178:118–142, 2006) might be complemented by a quantum-information-theoretic communication protocol between the computing device and the logician who sets the beyond-Turing computer a task such as determining the consistency of Zermelo–Fraenkel set theory. This suggests that even the foundations of quantum theory and, ultimately, quantum gravity may play an important role in determining the validity of the physical Church–Turing thesis.