Related papers: Causal Sets and an Emerging Continuum
The model is a particular case of causal set. This is a discrete model of spacetime in a microscopic level. In paper the most general properties of the model are investigated without any reference to a dynamics. The dynamics of the model is…
The theory of causal fermion systems is an approach to describe fundamental physics. Giving quantum mechanics, general relativity and quantum field theory as limiting cases, it is a candidate for a unified physical theory. We here give a…
The configuration space of causal sets is vast. It is a critical goal to map out this space. Here, we take a practical step towards this goal. We investigate nine classes of causal sets, most of them not studied before. These include…
The theory of causal fermion systems is a recent approach to fundamental physics. Giving quantum mechanics, general relativity and quantum field theory as limiting cases, it is a candidate for a unified physical theory. The dynamics is…
We begin with a brief summary of issues encountered involving causality in quantum theory, placing careful emphasis on the assumptions involved in results such as the EPR paradox and Bell's inequality. We critique some solutions to the…
A recently proposed algebraic representation of the causal set model of the small-scale structure of space-time of Sorkin et al. is briefly reviewed and expanded. The algebraic model suggested, called quantum causal set, is physically…
The possibility of non-causal signal propagation is examined for various theories of dense matter. This investigation requires a discussion of definitions of causality, together with interpretations of spacetime position. Specific examples…
A precise definition of a black hole has long been absent in causal set theory. I first show that the local finiteness of the theory cannot be interpreted as a complete discretization condition, and the theory still admits continua, which I…
Popular wisdom amongst theoretical physicists says that the continuum structure of spacetime is probably not elementary, but rather emergent. While many arguments to support that view arise from speculative ideas, the argument can also be…
General Relativity traces the evolution of our Universe back to a Big Bang singularity. To probe physics before the singularity -- if indeed there is a ``before'' -- we must turn to quantum gravity. The Causal Set approach to quantum…
The proposed theory of causally structured discrete fields studies integer values on directed edges of a self-similar graph with a propagation rule, which we define as a set of valid combinations of integer values and edge directions around…
In causal set theory, there are three ambiguous concepts that this article tries to provide a solution to resolve these ambiguities. These three ambiguities in Planck's scale are: the causal relationship between events, the position of the…
I describe the history of my attempts to arrive at a discrete substratum underlying the spacetime manifold, culminating in the hypothesis that the basic structure has the form of a partial-order (i.e. that it is a causal set).
We briefly survey open questions in cosmology that either have been or could potentially be addressed with the help of the causal set theory approach to quantum gravity. Our discussion includes topics ranging from dark matter and dark…
A mathematical definition of classical causality over discrete spacetime dynamics is formulated. The approach is background free and permits a definition of causality in a precise way whenever the spacetime dynamics permits. It gives a…
A reflexive relation on a set can be a starting point in defining the causal structure of a spacetime in General Relativity and other relativistic theories of gravity. If we identify this relation as the relation between lightlike separated…
A large class of the dynamical laws for causal sets described by a classical process of sequential growth yield a cyclic universe, whose cycles of expansion and contraction are punctuated by single `origin elements' of the causal set. We…
In this paper we consider a claim that in the natural world there is no fact of the matter about the spatio-temporal separation of events. In order to make sense of such a notion and construct useful models of the world, it is proposed to…
The ``generic'' family of classical sequential growth dynamics for causal sets provides cosmological models of causal sets which are a testing ground for ideas about the, as yet unknown, quantum theory. In particular we can investigate how…
Causal set theory provides a model of discrete spacetime in which spacetime events are represented by elements of a causal set---a locally finite, partially ordered set in which the partial order represents the causal relationships between…