Since the suggestion of relativistic shocks as the origin of gamma-ray bursts (GRBs) in the early 1990s, the mathematical formulation of this process has stayed at a phenomenological level. One of ...the reasons for the slow development of theoretical works has been the simple power-law behaviour of the afterglows hours or days after the prompt gamma-ray emission. It was believed that they could be explained with these formulations. Nowadays, with the launch of the Swift satellite and implementation of robotic ground follow-ups, GRBs and their afterglow can be observed at multi-wavelengths from a few tens of seconds after trigger onwards. These observations have led to the discovery of features unexplainable by the simple formulation of the shocks and emission processes used up to now. Some of these features can be inherent in the nature and activities of the GRBs' central engines which are not yet well understood. On the other hand, the devil is in the detail and others may be explained with a more detailed formulation of these phenomena and without ad hoc addition of new processes. Such a formulation is the goal of this work. We present a consistent formulation of the kinematics and dynamics of the collision between two spherical relativistic shells, their energy dissipation and their coalescence. It can be applied to both internal and external shocks. Notably, we propose two phenomenological models for the evolution of the emitting region during the collision. One of these models is more suitable for the prompt/internal shocks and late external shocks, and the other for the afterglow/external collisions as well as the onset of internal shocks. We calculate a number of observables such as flux, lag between energy bands and hardness ratios. One of our aims has been a formulation complex enough to include the essential processes, but simple enough such that the data can be directly compared with the theory to extract the value and evolution of physical quantities. To accomplish this goal, we also suggest a procedure for extracting parameters of the model from data. In a companion paper, we numerically calculate the evolution of some simulated models and compare their features with the properties of the observed GRBs.
In Paper I, we presented a detailed formulation of the relativistic shocks and synchrotron emission in the context of gamma-ray burst (GRB) physics. To see how well this model reproduces the observed ...characteristics of the GRBs and their afterglows, here we present the results of some simulations based on this model. They are meant to reproduce the prompt and afterglow emissions in some intervals of time during a burst. We show that this goal is achieved for both short and long GRBs and their afterglows, at least for part of the parameter space. Moreover, these results are evidence of the physical relevance of the two phenomenological models we have suggested in Paper I for the evolution of the active region– synchrotron emitting region in a shock. The dynamical active region model seems to reproduce the observed characteristics of prompt emissions and late afterglow better than the quasi-steady model which is more suitable for the onset of afterglows. Therefore, these simulations confirm the arguments presented in Paper I about the behaviour of these models based on their physical properties.
Since the early days of search for a quantum theory of gravity the attempts have been mostly concentrated on the quantization of an otherwise classical system. The two most contentious candidate ...theories of gravity, string theory and quantum loop gravity are based on a quantum field theory – the latter is a quantum field theory of connections on a SU(2) group manifold and the former is a quantum field theory in two dimensional spaces. Here we argue that there is a very close relation between quantum mechanics (QM) and gravity. Without gravity, QM becomes ambiguous. We consider this observation as the evidence for an intrinsic relation between these fundamental laws of nature. We suggest a quantum role and definition for gravity in the context of a quantum Universe, and present a preliminary formulation for gravity in a system with a finite number of particles.
Our Universe is ruled by quantum mechanics and should be treated as a quantum
system. {$SU(\infty)$-QGR is a recently proposed quantum model for the
Universe, in which gravity is associated to ...$SU(\infty)$ symmetry of its
Hilbert space. Clustering/blockization of its infinite dimensional state due to
random quantum fluctuations divides the Universe to approximately isolated
subsystems. In addition to parameters of their {\it internal} finite rank
symmetries, states and dynamics of subsystems are characterized by 4 continuous
parameters, and the perceived classical spacetime is their effective
representation, reflecting quantum states of subsystems and their relative
evolution. At lowest order the effective Lagrangian of {$SU(\infty)$-QGR has
the form of Yang-Mills gauge theories for both $SU(\infty)$ - gravity - and
internal symmetries defined on the aforementioned 4D parameter space. In the
present work we study more thoroughly some of the fundamental aspects of
{$SU(\infty)$-QGR. Specifically, we clarify impact of the degeneracy of
$\mathcal{SU}(\infty)$; describe mixed states of subsystems and their
purification; calculate measures of their entanglement to the rest of the
Universe; and discuss their role in the emergence of local gauge symmetries. We
also describe the relationship between what is called {\it internal space} of
$SU(\infty)$ Yang-Mills with the 4D parameter space, and analytically
demonstrate irrelevance of the geometry of parameter space for physical
observables. Along with these topics, we demonstrate the equivalence of two
sets of criteria for compositeness of a quantum system, and show uniqueness of
the limit of various algebras leading to $\mathcal{SU}(\infty)$.
$SU(\infty)$-QGR is a quantum approach to Universe and gravity. Its main
assumption is infinite mutually commuting observables in the Universe, leading
to representation of $SU(\infty)$ by its ...Hilbert spaces and those of its
subsystems. The Universe as a whole is static, topological, and characterized
by two continuous parameters. Nonetheless, quantum fluctuations induce
clustering and finite rank internal symmetries, which approximately divide the
Universe to infinite interacting subsystems. Their Hilbert space depends on an
additional dimensionful parameter, and selection of a subsystem as clock
induces a relative dynamics, with $SU(\infty)$ sector as gravity. The
Lagrangian defined on the (3+1)-dimensional parameter space is Yang-Mills for
both symmetries. When quantumness of gravity is undetectable, it is perceived
as curvature of an effective spacetime.
$SU(\infty)$-QGR is a foundationally quantum approach to gravity. It assumes
that the Hilbert space of the Universe as a whole represents the symmetry group
$SU(\infty)$, and demonstrates this ...symmetry for Hilbert spaces of infinite
number of subsystems that randomly emerge and represent arbitrary finite rank
internal symmetries. It is shown that their states depend on a dimensionful
parameter arising due to the breaking of a global $U(1)$ symmetry, and a
relative dynamics can be defined by selection of a subsystem as clock. The
action has the form of a Yang-Mills quantum field theory defined on the
(3+1)-dimensional parameter space for both $SU(\infty)$ - gravity - and
internal symmetries. Therefore, $SU(\infty)$-QGR is renormalizable, but
predicts a spin-1 mediator for quantum gravity. Nonetheless, it is proved that
when quantum gravity effects are not detectable, dynamics is similar to the
Einstein-Hilbert action. The aim of present work is in depth study of the
foundation and properties of this model. In particular, we show that the global
$SU(\infty)$ symmetry manifests itself through the entanglement of subsystems
with the rest of the Universe, and demonstrate irrelevance of geometry of the
parameter space for observables. Hence, $SU(\infty)$-QGR deviates from
gauge-gravity duality models, because the classical spacetime is an emergent
effective geometry with negative signature, reflecting relative variation of
quantum states of subsystems and quantum uncertainties. We also briefly discuss
$SU(\infty)$-QGR specific models for dark energy.
So far, none of attempts to quantize gravity has led to a satisfactory model that not only describe gravity in the realm of a quantum world, but also its relation to elementary particles and other ...fundamental forces. Here, we outline the preliminary results for a model of quantum universe, in which gravity is fundamentally and by construction quantic. The model is based on three well motivated assumptions with compelling observational and theoretical evidence: quantum mechanics is valid at all scales; quantum systems are described by their symmetries; universe has infinite independent degrees of freedom. The last assumption means that the Hilbert space of the Universe has \(SU(N\rightarrow \infty) \cong \text{area preserving Diff.} (S_2)\) symmetry, which is parameterized by two angular variables. We show that, in the absence of a background spacetime, this Universe is trivial and static. Nonetheless, quantum fluctuations break the symmetry and divide the Universe to subsystems. When a subsystem is singled out as reference -- observer -- and another as clock, two more continuous parameters arise, which can be interpreted as distance and time. We identify the classical spacetime with parameter space of the Hilbert space of the Universe. Therefore, its quantization is meaningless. In this view, the Einstein equation presents the projection of quantum dynamics in the Hilbert space into its parameter space. Finite dimensional symmetries of elementary particles emerge as a consequence of symmetry breaking when the Universe is divided to subsystems/particles, without having any implication for the infinite dimensional symmetry and its associated interaction - perceived as gravity. This explains why gravity is a universal force.
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