From Strings to Loops: A Journey Through Modern Physics' Biggest Questions

The unification of quantum principles with Einstein's geometric conception of spacetime and gravity into a consistent theory of quantum gravity is one of the main open challenges at the foundations of modern theoretical physics. Among several approaches developed over the years, the two main candidates are string theory and loop quantum gravity (LQG). Both theories are characterized by their own achievements and open issues so that the solution to the problem of quantum gravity remains still elusive. In lack of experimental guidance, in order to make progress, it becomes important to single out common features shared by different approaches allowing to merge tools and ideas, thus providing indirect tests to potentially overcome current limitations. In this respect, one of the major recent developments is the so-called holographic principle and its string theory-based realization within the Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence, a conjectured duality between string theory in asymptotically AdS spacetime and a SU(N) gauge theory thought of as living on its conformal boundary. As such it provides a promising arena to look for possible connections between non-perturbative LQG and string theory non-perturbatively defined via its dual field theory. With this motivation in mind, in this thesis we focus on effective symmetry-reduced models for resolved cosmological and black hole singularities to which lot of effort has been devoted within the LQG community and their possible embedding within the AdS/CFT framework. First of all, we focus on the field theory signatures of the singularity resolution in the bulk of Kasner-AdS spacetimes and show via several examples of quantum corrected effective geometries that the finite-distance pole in the boundary two-point correlator previously interpreted as the holographic signature of the bulk singularity is smoothed out by quantum gravity effects. The time dependence of the boundary spacetime however prevents us from setting up an independent field theory computation to compare with the bulk gravity results. We move then to black hole (BH) singularities whose asymptotic boundary is Minkowski or AdS. Since no fully satisfactory effective LQG model is available already for the simplest static spherically symmetric case with zero cosmological constant, we consider the case of a 4-dimensional Schwarzschild BH as a necessary preparation for higher dimensional extensions to AdS BHs. New models based on new sets of canonical variables directly related to the Kretschmann scalar are thus introduced to take the onset of quantum effects under control, and the resulting quantum corrected spacetime structure is discussed in detail. A key ingredient of our analysis is the study of Dirac observables for the asymptotic ADM masses and their relation with admissible initial conditions for the effective dynamics compatibly with the requirement of a unique upper bound on curvature invariants resolving the central singularity. Finally, quantum corrections to thermodynamic quantities are also analyzed and, coming back to the original motivation of using LQG techniques for AdS/CFT, a possible extension to arbitrary dimensions and negative cosmological constant is sketched.

This special issue is devoted to the proceedings of the workshops Peyresq Physics 11 and Peyresq Physics 12 on 'Micro and Macro Structure of Spacetime', which were held on the 17–23 June 2006 and 16–22 June 2007, respectively, in Peyresq, Alpes de Haute Provence, France, and organized by E Gunzig, B-L Hu and one of us (EV). These workshops are part of a series of annual meetings which bring together around 20 physicists active in different areas of theoretical physics.Uncovering the microscopic structures of spacetime is the goal of quantum gravity and string theory. It is often considered as the 'holy grail' of theoretical physics because it is believed that all fundamental forces are unified at that level of description. Macroscopic spacetime refers to astrophysical and cosmological structures and processes in the observable physical world, from black holes to the cosmos, from the second law to the arrow of time. The challenge theoretical physicists now face is to infer the micro structure of spacetime from the observed macro phenomena, and to deduce the multifarious manifestations of our world from any such candidate theory. To do so demands a careful re-examination of the foundational issues of quantum physics and general relativity (such as intrinsic and quantum gravity decoherence), the origin and nature of symmetries in spacetime (such as Lorentz symmetry) and the conditions where they may be violated, as well as their intersections (such as the physics of the early universe and the end states of black hole evolution).One asks how and why these two pillars of modern physics appear to be so incongruous with each other. Is it because their basic tenets and assumptions are at odds to each other? For these quests one needs to draw upon concepts and techniques from close disciplines such as those found in topology and geometry, or other subdisciplines of physics such as particle physics, strings and loops, statistical mechanics and mesoscopic phenomena, atomic-optical and condensed matter physics. The richness of this theme spans a diverse spectrum of current topics which can be gleaned from the titles of the talks presented in these two meetings.Peyresq is a medieval Provençal village situated 100km from Nice at an altitude of 1528m. The village was founded in the early 13th century. At thebeginning of the 17th century there were around 50 houses and by 1851 the village counted 208 inhabitants distributed among 53 families. Like many othervillages of Haute Provence, it was almost completely deserted after the Second World War. During the 1950s the village was progressively entirely rebuilt inits original spirit and style by students of Belgian universities, mainly the Université Libre de Bruxelles, under the guidance of Mady and Toine Smets.The aim was to create a 'Foyer d'Humanisme', an international humanistic center for cultural, artistic, and scientific pursuits.The workshops were financed by the Fondation Peyresq, Foyer d'Humanisme, the Fondation Nicolas Claude Fabri de Peyresq, and OLAM (Association pour laRecherche Fondamentale, Brussels). We would like to thank all these institutions for their help and financial support. We extend our warm appreciation to Madame Mady Smets without whom none of this work could have come to light. We would like to thank all the participants for the many lively discussions that we have enjoyed and for their effort in preparing written contributions. We would also like to thank the editorial staff of Classical and Quantum Gravity, especially Tom Spicer, Joseph Tennant and Eirini Messaritaki, for their support and efficiency in preparing this volume. Finally, we thank Edgar Gunzig and Bei-Lok Hu as the main driving forces behind the organization of these workshops.

In this work, we will show that a deeper understanding of space-time provided by both quantum physics and general relativity can lead to a new way to understand string theory. This new way of understanding and applying string theory, the universal wave function interpretation of string theory (UWFIST), may yield to a more powerful string theory and testable prediction. We will show how to derive UWFIST and what new result we can obtain from UWFIST. We will demonstrate that UWFIST indicates that the observed space-time and all phenomena are the projections from the world-sheet hologram. UWFIST provides the possible source for dark energy and dark matter and the explanation about why the dark energy and dark matter is beyond the detection of our current detector. We will show that UWFIST may also yield correct prediction of the cosmological constant to be of the order 10-121 in the unit of Planck scale. It may also help us understand and derive the energy source for inflation and the flatness of our observed 4-dimensional universe. UWFIST may also make other testable predictions that may be detected by interferometers.We conclude that UWFIST has the potential to make string theory a more powerful physics theory that can yield testable predictions. It is worth further investigation by more physicists.

Modern Canonical Quantum General Relativity

We apply common gravitational wave inference procedures on binary black hole merger waveforms beyond general relativity. We consider dynamical Chern-Simons gravity, a modified theory of gravity with origins in string theory and loop quantum gravity. This theory introduces an additional parameter $\ell$, corresponding to the length-scale below which beyond-general-relativity effects become important. We simulate data based on numerical relativity waveforms produced under an approximation to this theory, which differ from those of general relativity in the strongly nonlinear merger regime. We consider a system with parameters similar to GW150914 with different values of $\ell$ and signal-to-noise ratios. We perform two analyses of the simulated data. The first is a template-based analysis that uses waveforms derived under general relativity and allows us to identify degeneracies between the two waveform morphologies. The second is a morphology-independent analysis based on BayesWave that does not assume that the signal is consistent with general relativity. The BayesWave analysis faithfully reconstructs the simulated signals. However, waveform models derived under general relativity are unable to fully mimic the simulated modified-gravity signals and such a deviation would be identifiable with existing inference tools. Depending on the magnitude of the deviation, we find that the templated analysis can under perform the morphology-independent analysis in fully recovering simulated beyond-GR waveforms even for achievable signal-to-noise ratios $\gtrsim 20{-}30$.

The so-called Geometric Trinity of Gravity includes General Relativity (GR), based on spacetime curvature; the Teleparallel Equivalent of GR (TEGR), which relies on spacetime torsion; and the Symmetric Teleparallel Equivalent of GR (STEGR), grounded in nonmetricity. Recent studies demonstrate that GR, TEGR, and STEGR are dynamically equivalent, raising questions about the fundamental structure of spacetime, the under-determination of these theories, and whether empirical distinctions among them are possible. The aim of this work is to show that they are equivalent in many features but not exactly in everything. In particular, their relationship with the Equivalence Principle (EP) is different. The EP is a deeply theory-laden assumption, which is assumed as fundamental in constructing GR, with significant implications for our understanding of spacetime. However, it introduces unresolved conceptual issues, including its impact on the nature of the metric and connection, its meaning at the quantum level, tensions with other fundamental interactions and new physics, and its role in dark matter and dark energy problems. In contrast, TEGR and STEGR recover the EP, in particular in its strong formulation, but do not rely on it as a foundational principle. The fact that GR, TEGR, and STEGR are equivalent in non-trivial predictions, but the EP is not necessary for TEGR and STEGR, suggests that it may not be a fundamental feature but an emergent one, potentially marking differences in the empirical content of the three theories. Thus, the developments within the Geometric Trinity framework challenge traditional assumptions about spacetime and may help to better understand some of the unresolved foundational difficulties related to the EP.

Theory of everything must include consciousness. In Part I (Vimal, 2010b) of this series of 3 articles, the subjective experience (SE) aspect of consciousness was introduced in classical physics by examining the invariance of various components of theories under PE-SE transformations, where PEs (proto-experiences) are precursors of SEs. We found that (i) classical physics is invariant under the PE-SE transformation, (ii) SEs are embedded in spacetime geometry for the structure of spacetime in superposed form, (iii) SEs can move with spatiotemporal coordinates of matter for matter field because both mental and material aspects are always together in the dual-aspect-dual-mode optimal PE-SE framework, and (iv) our specific SE is the result of matching and selection processes and can change with space and time. For example, experiencing redness has neural correlates of V4/V8/VO-red-green neural-net with redness state. When a subject moves, the specific SE redness also moves with the subject’s correlated neural-net. In the current Part II, the SE aspect of consciousness is introduced in orthodox quantum physics by examining its invariance under the PE-SE transformations. We found that the followings are invariant under the PE-SE transformations: Schrodinger equation, current, Dirac Lagrangian, the Lagrangian for a charged self-interacting scalar field, and Standard Model (the Lagrangian for free gauge field and Lagrangian for the electromagnetic interaction of a charged scalar field (Higgs Mechanism)). In Part III (Vimal, 2010c), the SE aspect of consciousness will be introduced to unify it with fundamental forces in loop quantum gravity and string theory of modern quantum physics. All parts together lead us towards the theory of everything.

The two fundamental pillars of physics for over 100 years have been quantum theory and general relativity, but their unification at short distances remains elusive, both technically and conceptually. This work is a philosophical investigation of the second kind of problem, and in particular of the striking fact that in many approaches to ‘quantum gravity’ classical spacetime structures are not merely quantized, but arguably absent—so that spacetime is not merely a classical limit, but ‘emergent’. This issue is not only central to the problem of quantum gravity, but of deep significance for our philosophical understanding of physical reality, promising a conceptual revolution at least as profound as Einstein’s. We give an introduction to the question of spacetime emergence in general, for philosophers of metaphysics and science, and argue that spacetime functionalism explains how something non-spatiotemporal could ever appear as space and time. More technical chapters investigate the issue in detail for causal set theory, loop quantum gravity, and string theory, and the book also serves as a philosophical introduction to those theories for philosophers of physics. Our results help physicists clarify what new conceptual framework—not resting on space and time—may be necessary to achieve a theory of quantum gravity; and show philosophers how the world may not be spatiotemporal at root, and what kind of a world we might then live in.

Alternatives to Einstein’s General Relativity Theory

Loop quantum gravity is a physical theory that aims at unifying general relativity and quantum mechanics. It takes general relativity very seriously and modifies it via quantisation. General relativity describes gravity in terms of geometry; therefore, quantising such theory must be equivalent to quantising geometry and that is what loop quantum gravity does. This sounds like a mathematical task as well, thus, in this paper we will present the mathematics of loop quantum gravity. We will do it from a mathematician’s point of view. This paper is intended to be an introduction to loop quantum gravity for postgraduate students of physics and mathematics. In this work we will restrict ourselves to the three-dimensional case.

Following recent assumptions to unify quantum mechanics and general relativity, the structure of spacetime is suppose to be a consequence of the relations among some fundamental objects, and its concept can be formulated without the reference to the intuition. As physical consequences the continuous laws should be translated in to difference equations and the lattice field theories should be interpreted as a realistic model.

I take non-locality to be the Michelson–Morley experiment of the early 21st century, assume its universal validity, and try to derive its consequences. Spacetime, with its locality, cannot be fundamental, but must somehow be emergent from entangled coherent quantum variables and their behaviors. There are, then, two immediate consequences: (i). if we start with non-locality, we need not explain non-locality. We must instead explain an emergence of locality and spacetime. (ii). There can be no emergence of spacetime without matter. These propositions flatly contradict General Relativity, which is foundationally local, can be formulated without matter, and in which there is no “emergence” of spacetime. If these be true, then quantum gravity cannot be a minor alteration of General Relativity but must demand its deep reformulation. This will almost inevitably lead to: matter not only curves spacetime, but “creates” spacetime. We will see independent grounds for the assertion that matter both curves and creates spacetime that may invite a new union of quantum gravity and General Relativity. This quantum creation of spacetime consists of: (i) fully non-local entangled coherent quantum variables. (ii) The onset of locality via decoherence. (iii) A metric in Hilbert space among entangled quantum variables by the sub-additive von Neumann entropy between pairs of variables. (iv) Mapping from metric distances in Hilbert space to metric distances in classical spacetime by episodic actualization events. (v) Discrete spacetime is the relations among these discrete actualization events. (vi) “Now” is the shared moment of actualization of one among the entangled variables when the amplitudes of the remaining entangled variables change instantaneously. (vii) The discrete, successive, episodic, irreversible actualization events constitute a quantum arrow of time. (viii) The arrow of time history of these events is recorded in the very structure of the spacetime constructed. (ix) Actual Time is a succession of two or more actual events. The theory inevitably yields a UV cutoff of a new type. The cutoff is a phase transition between continuous spacetime before the transition and discontinuous spacetime beyond the phase transition. This quantum creation of spacetime modifies General Relativity and may account for Dark Energy, Dark Matter, and the possible elimination of the singularities of General Relativity. Relations to Causal Set Theory, faithful Lorentzian manifolds, and past and future light cones joined at “Actual Now” are discussed. Possible observational and experimental tests based on: (i). the existence of Sub- Planckian photons, (ii). knee and ankle discontinuities in the high-energy gamma ray spectrum, and (iii). possible experiments to detect a creation of spacetime in the Casimir system are discussed. A quantum actualization enhancement of repulsive Casimir effect would be anti-gravitational and of possible practical use. The ideas and concepts discussed here are not yet a theory, but at most the start of a framework that may be useful.

In daily life, we can transmit and obtain information through mechanical waves and electromagnetic waves. For example, judging where the fish swims from the flooded water waves, and learns from the wonderful music to know what kind of instrument the musicians are playing and communicating through the radio waves. Gravitational waves, a fundamental prediction of Einstein's theory of general relativity, have revolutionized our understanding of the universe. This essay explores the background of research on gravitational waves, tracing their theoretical origins to the early 20th century and highlighting their recent detection in 2015. The research technique employed involves highly sensitive interferometers, such as LIGO and Virgo, which can detect the minuscule distortions in space-time caused by these elusive waves. By observing the gravitational waves emitted during cataclysmic cosmic events, scientists can now delve deeper into the nature of black holes, neutron stars, and the origin of our universe. In conclusion, the discovery of gravitational waves opens up new avenues for exploring the cosmos, providing unprecedented insights into the fabric of space-time itself.

Gravitational waves are basically ripples in spacetime predicted by Einstein's General Theory of Relativity (1915), have revolutionized our understanding of the universe since their first detection in 2015 by the LIGO. These waves are typically generated by extreme cosmological events such as the mergers of two or more black holes, neutron stars, and other compact objects. Black holes, regions of spacetime where gravity is so intense that not even light can escape, are both significant sources and subjects of gravitational wave studies. The observation of gravitational waves from binary black hole mergers has provided unprecedented insights into the nature of black holes, their mass distribution, and the environments in which they form. This paper reviews the current state of research on gravitational waves and black holes, focusing on their astrophysical origins, the mechanisms of wave generation, and the information encoded in the wave signals. I have discussed how gravitational wave detections have confirmed the existence of stellar-mass black hole binaries, revealed new populations of black holes, and provided tests of general relativity in the strong-field regime. Additionally, this study highlights the potential of gravitational wave astronomy to address unresolved questions, such as the formation channels of black hole binaries, the detection of primordial black holes, and the role of black holes in galaxy evolution. By bridging observational data with theoretical models, gravitational wave observations are opening new frontiers in our understanding of both black holes and the fundamental nature of gravity.

Since its conception in the 1960s, string theory has been hailed as one of the most promising routes we have to unify quantum mechanics and general relativity. This book provides a concise introduction to string theory explaining central concepts, mathematical tools and covering recent developments in physics including compactifications and gauge/string dualities. With string theory being a multidisciplinary field interfacing with high energy physics, mathematics and quantum field theory, this book is ideal for both students with no previous knowledge of the field and scholars from other disciplines who are looking for an introduction to basic concepts.