Related papers: Emergent spacetime and the ergodic hierarchy
This is the first part in a series of two papers, where we consider a specific microscopic model of spacetime. In our model Planck size quantum black holes are taken to be the fundamental building blocks of space and time. Spacetime is…
The full causal ladder of spacetimes is constructed, and their updated main properties are developed. Old concepts and alternative definitions of each level of the ladder are revisited, with emphasis in minimum hypotheses. The implications…
We consider emergence from the perspective of dynamics: states of a system evolving with time. We focus on the role of a decomposition of wholes into parts, and attempt to characterize relationships between levels without reference to…
We investigate three aspects of the supposed problem of time: The disagreement between the treatments of time in general relativity and quantum theory, the problem of recovering time from within an isolated Universe and the prevalence of a…
At present we have only the very successful but phenomenological Einstein geometrical modelling of the spacetime phenomenon. This geometrical model provides a `container' for other theories, in particular the quantum field theories. Here we…
Astrophysical observations indicate the expansion of the universe is accelerating. Applying the holographic entropy conjecture to the cosmological horizon in an accelerating universe suggests the universe has only a finite number of degrees…
The IKKT matrix model yields an emergent space-time. We further develop these ideas and give a proposal for an emergent metric. Based on previous numerical studies of this model, we provide evidence that the emergent space-time is…
Given pseudo-random binary sequence of length $L$, assuming it consists of $k$ sub-sequences of length $N$. We estimate how $k$ scales with growing $N$ to obtain a {\it limiting} ergodic behaviour, to fulfill the basic definition of…
Theories of quantum gravity generically presuppose or predict that the reality underlying relativistic spacetimes they are describing is significantly non-spatiotemporal. On pain of empirical incoherence, approaches to quantum gravity must…
The mathematical definitions of distinct concepts that are needed in building an ergodicity detection algorithm are introduced in a framework. This algorithmic framework is expressed in a discrete setting in an accessible manner for broader…
These are intended to be review notes on emergent symmetries, i.e., symmetries which manifest themselves in specific sectors of energy in many systems. The emphasis is on the physical aspects rather than computation methods. We include some…
The thermodynamic arrow-of-time problem is thought to be resolved by the observation that our universe initially was---and still is---far from equilibrium. The psychological arrow-of-time problem is often attributed the same resolution, but…
We consider the emergence of large-scale cosmological expansion in scalar-tensor theories of gravity. This is achieved by modelling sub-horizon regions of space-time as weak-field expansions around Minkowski space, and then subsequently…
The quantum theory of Ur-alternatives of Carl Friedrich von Weizsaecker tries to constitute general quantum theory based on the concept of logical alternatives in time. Based on this interpretation of quantum theory the existence of free…
The renewed interest in the foundations of quantum statistical mechanics in recent years has led us to study John von Neumann's 1929 article on the quantum ergodic theorem. We have found this almost forgotten article, which until now has…
Any effort to localise an event in the vicinity of the Planck length scale, only where the quantum gravitational effects are predicted to be observed, will invariably result in gravitational collapse. One must postulate noncommutative (NC)…
Recently it has been proposed that the Bekenstein-Hawking formula for the entropy of spacetime horizons has a larger significance as the leading contribution to the entanglement entropy of general spacetime regions, in the underlying…
This paper examines two cosmological models of quantum gravity (from string theory and loop quantum gravity) to investigate the foundational and conceptual issues arising from quantum treatments of the big bang. While the classical…
Certain intriguing consequences of the discreteness of time on the time evolution of dynamical systems are discussed. In the discrete-time classical mechanics proposed here, there is an {\it arrow of time} that follows from the fact that…
We start from classical general relativity coupled to matter fields. Each configuration variable and its conjugate momentum, as also space-time points, are raised to the status of matrices [equivalently operators]. These matrices obey a…