We study large families of theories of interacting spin 2 particles from the point of view of causality. Although it is often stated that there is a unique Lorentz invariant effective theory of massless spin 2, namely general relativity, other theories that utilize higher derivative interactions do in fact exist. These theories are distinct from general relativity, as they permit any number of species of spin 2 particles, are described by a much larger set of parameters, and are not constrained to satisfy the equivalence principle. We consider the leading spin 2 couplings to scalars, fermions, and vectors, and systematically study signal propagation in all these other families of theories. We find that most interactions directly lead to superluminal propagation of either a spin 2 particle or a matter particle, and interactions that are subluminal generate other interactions that are superluminal. Hence, such theories of interacting multiple spin 2 species have superluminality, and by extension, acausality. This is radically different to the special case of general relativity with a single species of minimally coupled spin 2, which leads to subluminal propagation from sources satisfying the null energy condition. This pathology persists even if the spin 2 field is massive. We compare these findings to the analogous case of spin 1 theories, where higher derivative interactions can be causal. This makes the spin 2 case very special, and suggests that multiple species of spin 2 is forbidden, leading us to general relativity as essentially the unique internally consistent effective theory of spin 2.
Motivated by the recent attention on superluminal phenomena, we investigate the compatibility between faster-than-c propagation and the fundamental principles of relativity and causality. We first argue that special relativity can easily accommodate -- indeed, does not exclude -- faster-than-c signalling at the kinematical level. As far as causality is concerned, it is impossible to make statements of general validity, without specifying at least some features of the tachyonic propagation. We thus focus on the Scharnhorst effect (faster-than-c photon propagation in the Casimir vacuum), which i…
We examine the role of consistency with causality and quantum mechanics in determining the properties of gravitation. We begin by examining two different classes of interacting theories of massless spin 2 particles -- gravitons. One involves coupling the graviton with the lowest number of derivatives to matter, the other involves coupling the graviton with higher derivatives to matter, making use of the linearized Riemann tensor. The first class requires an infinite tower of terms for consistency, which is known to lead uniquely to general relativity. The second class only requires a finite nu…
We start from the well-known form of the interval of the special relativity, stare it, and build up an attempt to implement the causality from it. Some features appear to be new, they involve the mass of the particle and the structure of space-time.
We give a new, wave-like solution of the field equations of five-dimensional relativity. In ordinary three-dimensional space, the waves resemble de Broglie or matter waves, whose puzzling behaviour can be better understood in terms of one or more extra dimensions. Causality is appropriately defined by a null higher-dimensional interval. It may be possible to test the properties of these waves in the laboratory.
To confront relativity theory with observation, it is necessary to split spacetime into its temporal and spatial components. The (1+3) timelike threading approach involves restrictions on the gravitational potentials $(g_{μν})$, while the (3+1) spacelike slicing approach involves restrictions on $(g^{μν})$. These latter coordinate conditions protect chronology within any such coordinate patch. While the threading coordinate conditions can be naturally integrated into the structure of Lorentzian geometry and constitute the standard coordinate conditions in general relativity, this circumstance …
The k-essence theories admit in general the superluminal propagation of the perturbations on classical backgrounds. We show that in spite of the superluminal propagation the causal paradoxes do not arise in these theories and in this respect they are not less safe than General Relativity.
We show that quantum mechanics and general relativity imply the existence of a minimal length. To be more precise, we show that no operational device subject to quantum mechanics, general relativity and causality could exclude the discreteness of spacetime on lengths shorter than the Planck length. We then consider the fundamental limit coming from quantum mechanics, general relativity and causality on the precision of the measurement of a length.
Theories with a curved momentum space, which became recently of interest in the quantum-gravity literature, can in general violate many apparently robust aspects of our current description of the laws of physics, including relativistic invariance, locality, causality and global momentum conservation. We here explore some aspects of the particularly severe pathologies arising in generic theories with curved momentum space for what concerns causality and momentum conservation. However, we also report results suggesting that when momentum space is maximally symmetric, and the theory is formulated…
We develop the General Theory of Relativity in a formalism with extended causality that describes physical interaction through discrete, transversal and localized pointlike fields. The homogeneous field equations are then solved for a finite, singularity-free, point-like field that we associate to a ``classical graviton". The standard Einstein's continuous formalism is retrieved by means of an averaging process, and its continuous solutions are determined by the chosen imposed symetry. The Schwarzschild metric is obtained by the imposition of spherical symmetry on the averaged field.
We derive causality constraints on the simplest scalar-tensor theories in which black holes differ from what General Relativity predicts, a scalar coupled to the Gauss-Bonnet or the Chern-Simons terms. Demanding that time advances are unobservable within the regime of validity of these effective field theories, we find their cutoff must be parametrically of the same size as the inverse Schwarzschild radius of the black holes for which the non-standard effects are of order one. For astrophysical black holes within the range of current gravitational wave detectors, this means a cutoff length at …
We analyze properties of the Sp(2M) conformally invariant field equations in the recently proposed generalized $\half M(M+1)$-dimensional space-time $\M_M$ with matrix coordinates. It is shown that classical solutions of these field equations define a causal structure in $\M_M$ and admit a well-defined decomposition into positive and negative frequency solutions that allows consistent quantization in a positive definite Hilbert space. The effect of constraints on the localizability of fields in the generalized space-time is analyzed. Usual d-dimensional Minkowski space-time is identified with …
Causality constrains the gravitational interactions of massive higher spin particles in both AdS and flat spacetime. We explore the extent to which these constraints apply to composite particles, explaining why they do not rule out macroscopic objects or hydrogen atoms. However, we find that they do apply to glueballs and mesons in confining large $N$ gauge theories. Assuming such theories contain massive bound states of general spin, we find parametric bounds in $(3+1)$ spacetime dimensions of the form $N\lesssim \frac{M_{Pl}}{Λ_{\text{QCD}}}$ relating $N$, the QCD scale, and the Planck scale…
Gravitational Faraday rotation, gravitational spin Hall effect, and spin-refined causality analysis from Magnusian matrix in effective field theories of gravity
It is well known that non-local theories of gravity have been a flourish arena of studies for many reasons, for instance, the UV incompleteness of General Relativity (GR). In this paper we check the consistency of ST-homogeneous Gödel-type metrics within the non-local gravity framework. The non-local models considered here are ghost-free but not necessarily renormalizable since we focus on the classical solutions of the field equations. Furthermore, the non-locality is displayed in the action through transcendental entire functions of the d'Alembert operator $\Box$ that are mathematically repr…
The causal properties of curved spacetime, which underpin our sense of time in gravitational theories, are defined by the null cones of the spacetime metric. In classical general relativity, it is assumed that these coincide with the light cones determined by the physical propagation of light rays. However, the quantum vacuum acts as a dispersive medium for the propagation of light, since vacuum polarisation in QED induces interactions which effectively violate the strong equivalence principle (SEP). For low frequencies the phenomenon of gravitational birefringence occurs and indeed, for some …
The $f(R)$ gravity theories provide an alternative way to explain the current cosmic acceleration without a dark energy matter component. If gravity is governed by a $f(R)$ theory a number of issues should be reexamined in this framework, including the violation of causality problem on nonlocal scale. We examine the question as to whether the $f(R)$ gravity theories permit space-times in which the causality is violated. We show that the field equations of these $f(R)$ gravity theories do not exclude solutions with breakdown of causality for a physically well-motivated perfect-fluid matter cont…
The gravity/gauge theory duality has provided us a way of studying QCD at short distances from straightforward calculations in classical general relativity. Among numerous results obtained so far, one of the most striking is the universality of the ratio of the shear viscosity to the entropy density. For all gauge theories with Einstein gravity dual, this ratio is η/s=1/4π. However, in general higher-curvature gravity theories, including two concrete models under discussion - the Gauss-Bonnet gravity and the (Riemann)^2 gravity - the ratio η/s can be smaller than 1/4π(thus violating the conjec…
Reflective equilibrium between physics and philosophy, and between GR and particle physics, is fruitful and rational. I consider the virtues of simplicity, conservatism, and conceptual coherence, along with perturbative expansions. There are too many theories to consider. Simplicity supplies initial guidance, after which evidence increasingly dominates. One should start with scalar gravity; evidence required spin 2. Good beliefs are scarce, so don't change without reason. But does conservatism prevent conceptual innovation? No: considering all serious possibilities (Feynman, Weinberg, etc.) co…
William H. Miller III Department of Physics & Astronomy, Johns Hopkins University（约翰斯·霍普金斯大学）；International Centre for Theoretical Sciences, Tata Institute of Fundamental Research（塔塔基础研究所国际理论科学中心）；Chennai Mathematical institute（金奈数学研究所）；Indian Institute of Technology, Gandhinagar（印度理工学院甘地纳格尔分校）
A theory governing the metric and matter fields in spacetime is {\it locally causal} if the probability distribution for the fields in any region is determined solely by physical data in the region's past, i.e. it is independent of events at space-like separated points. General relativity is manifestly locally causal, since the fields in a region are completely determined by physical data in its past. It is natural to ask whether other possible theories in which the fundamental description of space-time is classical and geometric -- for instance, hypothetical theories which stochastically coup…
Higher-derivative gravity theories, such as Lovelock theories, generalize Einstein's general relativity (GR). Modifications to GR are expected when curvatures are near Planckian and appear in string theory or supergravity. But can such theories describe gravity on length scales much larger than the Planck cutoff length scale? Here we find causality constraints on Lovelock theories that arise from the requirement that the equations of motion (EOM) of perturbations be hyperbolic. We find a general expression for the "effective metric" in field space when Lovelock theories are perturbed around so…
In an attempt to clarify what is the velocity of a particle in doubly special relativity, we solve Maxwell's equations invariant under the position-space nonlinear Lorentz transformation proposed by Kimberly, Magueijo, and Medeiros. We show that only the amplitude of the Maxwell wave, not the phase, is affected by the nonlinearity of the transformation. Thus, although the Maxwell wave appears to have infinitely large energy near the Planck time, the wave velocity is the same as the conventional light velocity. Surprisingly, the velocity of the Maxwell wave is not the same as the maximum signal…
This work explores a Standard Model (S.M.) extension possibility, that violates Lorentz invariance, preserving the space-time isotropy and homogeneity. In this sense HMSR represents an attempt to introduce an isotropic Lorentz Invariance Violation in the elementary particle S.M. The theory is constructed starting from a modified kinematics, that takes into account supposed quantum effects due to interaction with the space-time background. The space-time structure itself is modified, resulting in a pseudo-Finsler manifold. The S.M. extension here provided is inspired by the effective fields the…
After reviewing recently suggested operational "principles of the quantumness", I address the problem on whether Quantum Theory (QT) and Special Relativity (SR) are unrelated theories, or instead, if the one implies the other. I show how SR can be indeed derived from causality of QT, within the computational paradigm "the universe is a huge quantum computer", reformulating QFT as a Quantum-Computational Field Theory (QCFT). In QCFT SR emerges from the fabric of the computational network, which also naturally embeds gauge invariance. In this scheme even the quantization rule and the Planck cons…
