Introduction In this chapter the modelling of spacetime is discussed, with the aim of maintaining a clear distinction between the local properties of a model and those attributes which are global. This separation of attributes (into local and global type) logically motivates the construction of the non-Hausdorff branched model for spacetime. Of course, much of the physical motivation for this construction is derived from the stochastic nature of quantum mechanics. The Many-World Interpretation is seen to be (at least, topologically) a consistent and complete interpretation of quantum mechanics. In any serious inquiry into the nature of spacetime (on either the quantum or cosmological level), mathematical models will be constructed which are in substantial agreement with the collective empiricism of experimental physics. If such a mathematical model is to be more than just a prescription for prediction, then it is necessary to give careful consideration to the appropriate level of mathematical generality of the model. Common sense, as well as the history of science, appear to indicate the need to maintain as general (i.e., unrestricted) a model as possible, constrained only by empirical data on one side, and the limits of our mathematical sophistication and imagination on the other. In the spirit of generalization, I will construct a model of the time parameter , which extends the usual concept of a time-line , and can be used to model spacetime locally, with the usual product structure of Minkowski spacetime. Our imagination will be constrained only by the mathematical discipline of topology and a clear view of all underlying assumptions.
Introduction In this chapter the modelling of spacetime is discussed, with the aim of maintaining a clear distinction between the local properties of a model and those attributes which are global. This separation of attributes (into local and global type) logically motivates the construction of the non-Hausdorff branched model for spacetime. Of course, much of the physical motivation for this construction is derived from the stochastic nature of quantum mechanics. The Many-World Interpretation is seen to be (at least, topologically) a consistent and complete interpretation of quantum mechanics. In any serious inquiry into the nature of spacetime (on either the quantum or cosmological level), mathematical models will be constructed which are in substantial agreement with the collective empiricism of experimental physics. If such a mathematical model is to be more than just a prescription for prediction, then it is necessary to give careful consideration to the appropriate level of mathematical generality of the model. Common sense, as well as the history of science, appear to indicate the need to maintain as general (i.e., unrestricted) a model as possible, constrained only by empirical data on one side, and the limits of our mathematical sophistication and imagination on the other. In the spirit of generalization, I will construct a model of the time parameter , which extends the usual concept of a time-line , and can be used to model spacetime locally, with the usual product structure of Minkowski spacetime. Our imagination will be constrained only by the mathematical discipline of topology and a clear view of all underlying assumptions.
Does time flow? It will be shown in this chapter that if the spacetime structure of the world has a certain branched dynamic form, then time flows. In addition to the flow and direction of time, two issues in quantum mechanics, those of non-locality and the definition of ‘measurement’, are shown to be illuminated by the hypothesis that the world has the spatio-temporal form described. I call the form the branched model , and the interpretation of quantum mechanics to which it gives rise I call the branched interpretation . Objective time flow The branched model is a four-dimensional spacetime model in the shape of a tree, each branch of which is a complete Minkowski manifold in which are located objects and events. The trunk represents the past, the first branch point is the present, and the branches constitute the set of all physically possible futures. The scheme is shown in figure 1. Of the many possible futures which split off at the first branch point, one and only one is selected to become part of the past. The unselected branches vanish, so that the first branch point moves up the tree in a stochastic manner and the tree ‘grows’ by losing branches. This progressive branch attrition is what in the model constitutes the flow of time. Suppose for example that 1000 lottery tickets have been sold to 1000 different purchasers. Then at the time of the draw, assuming the procedure is completely fair, there will be at least 1000 different kinds of branch at the first branch point: branches on which A wins, branches on which B wins, etc.
Abstract The chapter shows how local indeterminism underlying BST combines with relativistic space-times. First it defines particular BST structures in which histories are isomorphic to Minkowski space-times. It further argues that many general relativistic space-times are one-history structures of BST. It introduces the notion of non-Hausdorff differential manifolds and investigates if they can be interpreted modally, as structures of BST with multiple histories. It investigates bifurcating curves in non-Hausdorff manifolds, which are natural representations of alternative evolutions of point-like objects. As the required bifurcating curves are unlikely in General Relativity, whereas there are cases of indeterministic general relativistic space-times, the chapter concludes that General Relativity is globally indeterministic, but locally deterministic.
Abstract What does realism about the quantum state imply? What follows when quantum theory is applied without restriction, if need be, to the whole universe? These are the questions which are debated in this book. All the chapters start from the point of realism, and based on the need, or the aspiration, for a theory that unites micro- and macroworlds, at least in principle. But the further claim argued by some is that if you allow the Schrödinger equation unrestricted application, supposing the quantum state to be something physically real, then this universe is one of countlessly many others, constantly branching in time, all of which are real. The result is the many worlds theory, also known as the Everett interpretation of quantum mechanics. The contrary claim sees this picture of many worlds as in no sense inherent in quantum mechanics, even when the latter is allowed unrestricted scope and even given that the quantum state itself is something physically real. For this picture of branching worlds fails to make physical sense, let alone common sense, even on its own terms. The status of these worlds, what they are made of, is never adequately explained. Ordinary ideas about time and identity over time become hopelessly compromised. The concept of probability itself is brought into question. This picture of many branching worlds is inchoate, it is a vision, an error. There are realist alternatives to many worlds, some even that preserve the Schrödinger equation unchanged. Twenty chapters, accompanied by commentaries and discussions, examine these claims and counterclaims in depth. They focus first on the question of ontology, the existence of worlds, second on the interpretation of probability, and third on alternatives or additions to many worlds. The introduction offers a helpful guide to the arguments for the Everett interpretation, particularly as they have been formulated in the last two decades.
We propose a physical interpretation of quantum entanglement within the framework of the Superfluid Energy Field (SEF), in which the quantum vacuum is modeled as a coherent medium described by a complex scalar field. Within this approach, spacetime, matter, and interactions emerge as collective and topological properties of a single underlying field. We show that entanglement can be understood as a manifestation of long-range phase coherence in this medium. Spatially separated systems correspond to localized excitations embedded within a single, non-factorizable field configuration, and their correlations arise from the global structure of the phase rather than from dynamical nonlocal interactions. This interpretation provides a natural explanation for the violation of Bell inequalities while preserving relativistic causality. The no-signaling theorem is maintained through a clear distinction between global coherence and local dynamical evolution, while decoherence is reinterpreted as the loss of long-range phase coherence leading to the emergence of classical behavior. The framework is constructed to remain fully compatible with the empirical predictions of quantum mechanics at the effective level, while suggesting the possibility of small deviations associated with the finite coherence properties of the underlying field. These results support the view that quantum correlations may arise from the coherence of a continuous physical medium, thereby providing a unified hydrodynamic perspective on quantum phenomena.
Abstract This book develops a rigorous theory of indeterminism as a local and modal concept. Its crucial insight is that our world contains events or processes with alternative, really possible outcomes. The theory aims at clarifying what this assumption involves, and it does it in two ways. First, it provides a mathematically rigorous framework for local and modal indeterminism. Second, we support that theory by spelling out the philosophically relevant consequences of this formulation and by showing its fruitful applications in metaphysics. To this end, we offer a formal analysis of modal correlations and of causation, which is applicable in indeterministic and non-local contexts as well. We also propose a rigorous theory of objective single-case probabilities, intended to represent degrees of possibility. In a third step, we link our theory to current physics, investigating how local and modal indeterminism relates to issues in the foundations of physics, in particular, quantum non-locality and spatio-temporal relativity. The book also ventures into the philosophy of time, showing how the theory’s resources can be used to explicate the dynamic concept of the past, present, and future based on local indeterminism.
By taking into account the quantum aspects intrinsic to any operational definition of spatio-temporal relationships, a stochastic concept of spacetime emerges. In relation to its classical counterpart is realized as a stochastic mean around which quantum fluctuations become negligible only in the limit of macroscopic spacetime intervals. The test-particle propagators used in the proposed quantum concept of spacetime are derived by solving in a consistent manner the localizability problem for relativistic particles. This is achieved in the framework of the stochastic phase space formulation of quantum mechanics, which in the nonrelativistic context is shown to result from systems of imprimitivity related to phase space conserved probability currents derivable from bona fide convariant probability densities in stochastic phase spaces of one particle systems, which can be interpreted as due to measurements performed with extended rather than pointlike test particles. The associated particle propagators can be therefore consistently related to coordinate probability densities measurable by the exchange of photons in between test particles from a chosen standard. Quantum spacetime is defined as the family of propagators corresponding to all conceivable coherent flows of test particles. This family of free-fall propagators has to satisfy certain self-consistency conditions as well as consistent laws ofmore » motion which inplicitly determine the stochastic geometro-dynamics of quantum space-time. Field theory on quantum spacetime retains many of the formal features of conventional quantum field theory. On a fundamental epistemological level stochastic geometries emerge as essential prerequisites in the construction of spacetime models that would be operationally based and yet consistent with the relativity principle as well as with the uncertinty principle.« less