Michael Esfeld, Against the disappearance of spacetime in quantum gravity, Arxiv.Org, 2019 1903.06637, physics.hist-ph.
This paper argues against the proposal to draw from current research into a physical theory of quantum gravity the ontological conclusion that spacetime or spatiotemporal relations are not fundamental. As things stand, the status of this proposal is like the one of all the other claims about radical changes in ontology that were made during the development of quantum mechanics and quantum field theory. However, none of these claims held up to scrutiny as a consequence of the physics once the theory was established and a serious discussion about its ontology had begun. Furthermore, the paper argues that if spacetime is to be recovered through a functionalist procedure in a theory that admits no fundamental spacetime, standard functionalism cannot serve as a model: all the known functional definitions are definitions in terms of a causal role for the motion of physical objects and hence presuppose spatiotemporal relations.
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A T Hyman, A new interpretation of Whitehead’s theory, Il Nuovo Cimento B (1971-1996), 104 (2007) 387-398.
A new interpretation is given of Afred N. Whitehead's 1922 theory of gravity, which was considered a viable alternative to Einstein's theory until 1971. The strong equivalence principle is satisfied...
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Sinya Aoki et al., Conserved charges in general relativity, Arxiv.Org, 2020.
We present a precise definition of a conserved quantity from an arbitrary covariantly conserved current available in a general curved spacetime. This definition enables us to define energy and momentum for matter by the volume integral. As a result we can compute charges of well-known black holes just as an electric charge of an electron in electromagnetism by the volume integration of a delta function singularity. As a byproduct we show that the definition leads to a correction to the known mass formula of a compact star in the Oppenheimer-Volkoff equation. We finally comment on a definition of generators associated with a vector field on a general curved manifold.
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Luboš Motl, A serious critique of the real-world Asymptotic Safety program for quantum gravity, Motls.Blogspot.Com, 2019 pp. 1-3.
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Erik Curiel, On geometric objects, the non-existence of a gravitational stress-energy tensor, and the uniqueness of the Einstein field equation, Studies In History And Philosophy Of Science Part B: Studies In History And Philosophy Of Modern Physics, 66 (2019) 90-102.
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Thibault Damour, Theoretical aspects of the equivalence principle, Classical And Quantum Gravity, 29 (2012) 184001-17.
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S Deser, Energy in Gravitation and Noether's Theorems, Arxiv.Org, 2019 1902.05105v2, gr-qc.
I exhibit the conflicting roles of Noether's two great theorems in defining conserved quantities, especially Energy in General Relativity and its extensions: It is the breaking of coordinate invariance through boundary conditions that removes the barrier her second theorem otherwise poses to the applicability of her first. There is nothing new here, except the emphasis that General must be broken down to Special Relativity in a special, but physically natural, way in order for the Poincare or other global groups such as (A)dS to "re-"emerge.
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John F Donoghue, A Critique of the Asymptotic Safety Program, Arxiv.Org, 2019 1911.02967, hep-th.
The present practice of Asymptotic Safety in gravity is in conflict with explicit calculations in low energy quantum gravity. This raises the question of whether the present practice meets the Weinberg condition for Asymptotic Safety. I argue, with examples, that the running of Λ and G found in Asymptotic Safety are not realized in the real world, with reasons which are relatively simple to understand. A comparison/contrast with quadratic gravity is also given, which suggests a few obstacles that must be overcome before the Lorentzian version of the theory is well behaved. I make a suggestion on how a Lorentzian version of Asymptotic Safety could potentially solve these problems.
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Patrick M Duerr, Fantastic Beasts and where (not) to find them: Local gravitational energy and energy conservation in general relativity, Studies In History And Philosophy Of Modern Physics, 65 (2019) 1-14.
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Astrid Eichhorn et al., Quantum-gravity predictions for the fine-structure constant, Physics Letters B, 782 (2018) 198-201.
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Kris Krogh, Gravitation Without Curved Space-time, , 2006.
A quantum-mechanical theory of gravitation is presented, where the motion of particles is based on the optics of de Broglie waves. Here the large-scale geometry of the universe is inherently flat, and its age is not constrained to < 13 Gyr. While this theory agrees with the standard experimental tests of Einstein's general relativity, it predicts a different second-order deflection of light, and measurement of the Lense-Thirring effect in the upcoming NASA experiment Gravity Probe B.
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Niels S Linnemann and Manus R Visser, Hints towards the emergent nature of gravity, Studies In History And Philosophy Of Science Part B: Studies In History And Philosophy Of Modern Physics, 64 (2018) 1-13.
A possible way out of the conundrum of quantum gravity is the proposal that general relativity (GR) is not a fundamental theory but emerges from an underlying microscopic description. Despite recent interest in the emergent gravity program within the physics as well as the philosophy community, an assessment of the theoretical evidence for this idea is lacking at the moment. We intend to fill this gap in the literature by discussing the main arguments in favour of the hypothesis that the metric field and its dynamics are emergent. First, we distinguish between microstructure inspired from GR, such as through quantization or discretization, and microstructure that is not directly motivated from GR, such as strings, quantum bits or condensed matter fields. The emergent gravity approach can then be defined as the view that the metric field and its dynamics are derivable from the latter type of microstructure. Subsequently, we assess in how far the following prop- erties of (semi-classical) GR are suggestive of underlying microstructure: (1) the metric’s universal coupling to matter fields, (2) perturbative non-renormalizability, (3) black hole thermodynamics, and (4) the holographic principle. In the conclusion we formalize the general structure of the plausibility arguments put forward.
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James Mattingly, Studies in History and Philosophy of Modern Physics, Studies In History And Philosophy Of Modern Physics, 44 (2013) 329-337.
I focus on the stochastic gravity program, a program that conceptualizes spacetime as the hydrodynamic limit of the correlation hierarchy of an underlying quantum theory, that is, a theory of the microscopic theory of gravity. This approach is relatively obscure, and so I begin by outlining the stochastic gravity program in enough detail to make clear the basic sense in which, on this approach, spacetime emerges from more fundamental physical structures. The theory, insofar as it is a univocal theory, is quite clear in its basic features, and so issues of philosophical interpretation can be readily isolated.
The most obvious reason to investigate the theory as a model for the emergence of spacetime structure is how close it is to the stage at which the behavior that we recognize as spacetime actually emerges from the micro gravitational system. Approaches that begin with fully quantum gravity (insofar as there is such a thing) treat a system that is conceptually quite far removed from the stage at which emergence is relevant. The stochastic approach however begins by identifying the point at which spacetime emerges as a phenomena of interest.
I begin with an analysis of the emergence question generally and ask how best we should understand it, especially from the point of view of thinking of spacetime as emergent. A nice feature of the stochastic program is how clear the question of emergence is on this approach. In part this is because of its similarity by design to the kinetic theory of gases and solid state physics. And so many of the analyses of the emergence of macroscopic variables in the thermodynamic limit can be repurposed to understand how an apparently continuous metrical space emerges from the behavior of a non-spatial system.
A serious interpretive problem looms however. The problem is that there is no clear connection between features of the kinetic theory of gravity, as a quantum theory, and any final theory of gravity. In the third part of the paper I will argue that as far as questions of emergence are concerned, we need not begin with a final, underlying theory, and I attempt to identify general issues connected to the emergence of spacetime that can be addressed in isolation from our certainty about that final theory. I will argue that this is a common way in which we treat our other, after all, provisional theories. We begin with the theories we have and ask about their implications without assuming that they are final theories, and yet also without explicitly downplaying the significance of the results we derive. Moreover I will attempt to show that, whatever character a (or the) final theory of micro gravity has, spacetime as an emergent structure in that theory is likely to be similar in important respects to the way it manifests in the stochastic gravity program. Briefly this is precisely because of the metaphysical neutrality of the kinetic theory. I will expand, in this section, on the nature of the emergence of the spacetime structure in the context of the stochastic gravity program and explain how the emergence is tied not to the particular model of interactions appealed to, but rather to the generic features of quantum fields with correlated fluctuations at all orders.
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Tim Maudlin et al., On the Status of Conservation Laws in Physics: Implications for Semiclassical Gravity, Arxiv.Org, 2019 1910.06473v1, gr-qc.
We start by surveying the history of the idea of a fundamental conservation law and briefly examine the role conservation laws play in different classical contexts. In such contexts we find conservation laws to be useful, but often not essential. Next we consider the quantum setting, where the conceptual problems of the standard formalism obstruct a rigorous analysis of the issue. We then analyze the fate of energy conservation within the various viable paths to address such conceptual problems; in all cases we find no satisfactory way to define a (useful) notion of energy that is generically conserved. Finally, we focus on the implications of this for the semiclassical gravity program and conclude that Einstein's equations cannot be said to always hold.
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J Menezes et al., Cosmic strings in Bekenstein-type models, Journal Of Cosmology And Astroparticle Physics, 2005 (2005) 003-003.
We study static cosmic string solutions in the context of Bekenstein-type models. We show that there is a class of models of this type for which the classical Nielsen–Olesen vortex is still a valid solution. However, in general, static string solutions in Bekenstein-type models strongly depart from the standard Nielsen–Olesen solution with the electromagnetic energy concentrated along the string core seeding spatial variations of the fine structure constant, α. We consider models with a generic gauge kinetic function and show that the equivalence …
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Clésio E Mota et al., Generalized Rastall's gravity and its effects on compact objects, Arxiv.Org, 2020.
We present a generalization of Rastall's gravity in which the conservation law of the energy-moment tensor is altered, and as a result, the trace of the energy-moment tensor is taken into account together with the Ricci scalar in the expression for the covariant derivative. Afterwards, we obtain the field equation in this theory and solve it by considering a spherically symmetric space-time. We show that the external solution has two possible classes of solutions with spherical symmetry in the vacuum in generalized Rastall's gravity. The first class of solutions is completely equivalent to the Schwarzschild solution, while the second class of solutions has the same structure as the Schwarzschild--de Sitter solution in general relativity. The generalization, in contrast to constant value $k=8πG$ in general relativity, has a gravitational parameter $k$ that depends on the energy density $ρ$. As an application, we perform a careful analysis of the effects of the theory on neutron stars using realistic equations of state (EoS) as inputs. Our results show that important differences on the profile of neutron stars are obtained within two representatives EoS.
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J Brian Pitts, Einstein׳ s physical strategy, energy conservation, symmetries, and stability:“But Grossmann & I believed that the conservation laws were not satisfied”, Studies In History And Philosophy Of Science Part B, 54 (2016) 52-72.
Recent work on the history of General Relativity by Renn, Sauer, Janssen et al. shows that Einstein found his field equations partly by a physical strategy including the Newtonian limit, the electromagnetic analogy, and energy conservation. Such themes are similar to those later used by particle physicists. How do Einstein’s physical strategy and the particle physics deriva- tions compare? What energy-momentum complex(es) did he use and why? Did Einstein tie conservation to symmetries, and if so, to which? How did his work relate to emerging knowledge (1911-14) of the canonical energy-momentum tensor and its translation-induced conservation?
After initially using energy-momentum tensors hand-crafted from the gravitational field equa-
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tions, Einstein used an identity from his assumed linear coordinate covariance xμ = Mμxν to ν
relate it to the canonical tensor. Usually he avoided using matter Euler-Lagrange equations and so was not well positioned to use or reinvent the Herglotz-Mie-Born understanding that the canonical tensor was conserved due to translation symmetries, a result with roots in Lagrange, Hamilton and Jacobi. Whereas Mie and Born were concerned about the canonical tensor’s asymmetry, Einstein did not need to worry because his Entwurf Lagrangian is modeled not so much on Maxwell’s theory (which avoids negative-energies but gets an asymmetric canonical tensor as a result) as on a scalar theory (the Newtonian limit). Einstein’s theory thus has a symmetric canonical energy-momentum tensor. But as a result, it also has 3 negative-energy field degrees of freedom (later called “ghosts” in particle physics). Thus the Entwurf theory fails a 1920s-30s a priori particle physics stability test with antecedents in Lagrange’s and Dirichlet’s stability work; one might anticipate possible gravitational instability.
This critique of the Entwurf theory can be compared with Einstein’s 1915 critique of his Entwurf theory for not admitting rotating coordinates and not getting Mercury’s perihelion right. One can live with absolute rotation but cannot live with instability.
Particle physics also can be useful in the historiography of gravity and space-time, both in assessing the growth of objective knowledge and in suggesting novel lines of inquiry to see whether and how Einstein faced the substantially mathematical issues later encountered in particle physics. This topic can be a useful case study in the history of science on recently reconsidered questions of presentism, whiggism and the like. Future work will show how the history of General Relativity, especially Noether’s work, sheds light on particle physics.
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David E Rowe, Emmy Noether on Energy Conservation in General Relativity, Arxiv.Org, 2019.
During the First World War, the status of energy conservation in general relativity was one of the most hotly debated questions surrounding Einstein's new theory of gravitation. His approach to this aspect of general relativity differed sharply from another set forth by Hilbert, even though the latter conjectured in 1916 that both theories were probably equivalent. Rather than pursue this question himself, Hilbert chose to charge Emmy Noether with the task of probing the mathematical foundations of these two theories. Indirect references to her results came out two years later when Klein began to examine this question again with Noether's assistance. Over several months, Klein and Einstein pursued these matters in a lengthy correspondence, which culminated with several publications, including Noether's now famous paper "Invariante Variationsprobleme". The present account focuses on the earlier discussions from 1916 involving Einstein, Hilbert, and Noether. In these years, a Swiss student named R.J. Humm was studying relativity in Göttingen, during which time he transcribed part of Noether's lost manuscript on Hilbert's invariant energy vector. By making use of this 9-page manuscript, it is possible to reconstruct the arguments Noether set forth in response to Hilbert's conjecture. Her results turn out to be closely related to the findings Klein published two years later, thereby highlighting, once again, how her work significantly deepened contemporary understanding of the mathematical underpinnings of general relativity.
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J Brian Pitts, Progress and Gravity: Overcoming Divisions Between General Relativity and Particle Physics and Between Physics and HPS, The Philosophy Of Cosmology, Chapter 13, 263-282. Cambridge.
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Peter W Shor, Scheme for reducing decoherence in quantum computer memory, Physical Review A, 52 (1995) R2493-R2496.
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J Brian Pitts, What Are Observables in Hamiltonian Einstein-Maxwell Theory?, Arxiv.Org, 2019 1907.09473v1, gr-qc.
Is change missing in Hamiltonian Einstein-Maxwell theory? Given the most common definition of observables (having weakly vanishing Poisson bracket with each first-class constraint), observables are constants of the motion and nonlocal. Unfortunately this definition also implies that the observables for massive electromagnetism with gauge freedom (Stueckelberg) are inequivalent to those of massive electromagnetism without gauge freedom (Proca). The alternative Pons-Salisbury-Sundermeyer definition of observables, aiming for Hamiltonian-Lagrangian equivalence, uses the gauge generator G, a tuned sum of first-class constraints, rather than each first-class constraint separately, and implies equivalent observables for equivalent massive electromagnetisms. For General Relativity, G generates 4-dimensional Lie derivatives for solutions. The Lie derivative compares different space-time points with the same coordinate value in different coordinate systems, like 1 a.m. summer time vs. 1 a.m. standard time, so a vanishing Lie derivative implies constancy rather than covariance. Requiring equivalent observables for equivalent formulations of massive gravity confirms that G must generate the 4-dimensional Lie derivative (not 0) for observables. These separate results indicate that observables are invariant under internal gauge symmetries but covariant under external gauge symmetries, but can this bifurcated definition work for mixed theories such as Einstein-Maxwell theory? Pons, Salisbury and Shepley have studied G for Einstein-Yang-Mills. For Einstein-Maxwell, both Fμν and gμν are invariant under electromagnetic gauge transformations and covariant (changing by a Lie derivative) under 4-dimensional coordinate transformations. Using the bifurcated definition, these quantities count as observables, as one would expect on non-Hamiltonian grounds.
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Steven Weinberg, The Cosmological Constant Problem, Reviews Of Modern Physics, 61 (1989) 1-23.
Astronomical observations indicate that the cosmological constant is many orders of magnitude smaller than estimated in modern theories of elementary particles. After a brief review of the history of this problem, five different approaches to its solution are described.
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