Abstract This chapter explains the many-worlds interpretations, particularly the DeWitt–Graham interpretation — the splitting-worlds interpretation. The splitting-worlds theory proposes that one must choose what physical quantities one wants to be determinate in a world, which amounts to choosing a physically preferred basis. It discusses several traditional and real problems encountered with the splitting-worlds theory. It also describes another theory, where one might stipulate that the global state always evolves in the usual linear way, selects a preferred basis that makes observers' records always determinate in each local state, and then chooses a connection rule that will link local states at different times into trajectories — the many threads theory.
Abstract This chapter explains the many-worlds interpretations, particularly the DeWitt–Graham interpretation — the splitting-worlds interpretation. The splitting-worlds theory proposes that one must choose what physical quantities one wants to be determinate in a world, which amounts to choosing a physically preferred basis. It discusses several traditional and real problems encountered with the splitting-worlds theory. It also describes another theory, where one might stipulate that the global state always evolves in the usual linear way, selects a preferred basis that makes observers' records always determinate in each local state, and then chooses a connection rule that will link local states at different times into trajectories — the many threads theory.
Next year, there will be a 100-year celebration of quantum mechanics, but there is no consensus on the interpretation of this theory. This reprint presents recent works on one of the most intriguing interpretations, the many-worlds interpretation, presented at a workshop in October 2022 at Tel Aviv University. The many-worlds interpretation solves the measurement problem, avoids action at a distance and indeterminism, and does not contradict empirical evidence. The main question discussed in the workshop was as follows: why is it not in the consensus? Major issues such as preferred basis, the meaning of probability, non-locality, and alternative approaches were discussed, which are increasingly drawing attention in physics and philosophy. The contributions demonstrated a striking diversity in understanding the basic concepts. What are the worlds in the many-worlds interpretation? Do the worlds diverge or split? Is probability objective or subjective, or is it just an illusion? Can we avoid the non-separability of quantum mechanics? Many questions were raised and significant progress in understanding was achieved, but the papers showed that consensus is still far away. This reprint describes the current status of the research and will be invaluable for physicists and philosophers who want to resolve the long-standing problem of the interpretation of quantum mechanics.
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.
Abstract We consider a number of radically different ways that Everett’s pure wave mechanics has been understood. Each of these reconstructions aims to provide a stronger variety of empirical adequacy than Everett’s own formulation of the theory. Among the alternative formulations of quantum mechanics we consider are splitting worlds, decohering worlds, many minds, many threads, and many maps. Each of these differs in its metaphysical commitments and, hence, in how it explains determinate measurement records and probabilities. We focus, in particular, on the problem of accounting for the standard quantum probabilities. To this end, we consider the relationship between typicality and probability and contrast synchronic and forward-looking probabilities. We conclude with a brief discussion of epistemological, pragmatic, and information-theoretic formulations of quantum mechanics. A recurring issue in this chapter concerns what it should mean for a physical theory to be empirically adequate.
This paper systematically elaborates on the structural interpretations of sixemerging mathematical physics frameworks for Everett’s many-worlds interpretation, including the branching structure of dynamic time algebra, the logical parallelism of the post-Markovian paradigm, the historical bifurcation of temporal layercausal evolution, the representation splitting of the time group framework, the section bundling of chronological fiber categories, and the stability selection in theorigin of order theory. These theories, from different perspectives, demonstratethe global unitarity of quantum state evolution, reinterpreting ”world splitting”as representation branching, logical parallelism, or fiber bundling on mathematical structures, thereby providing a mathematical foundation for the many-worldsinterpretation independent of philosophical assumptions. By comparing the coremechanisms, mathematical structures, and physical predictions of each theory, thispaper proposes a unified view: the many-worlds is not ”splitting” but a naturalresult of structural degeneration, and all branches are mathematically equal andco-existent. At the same time, this paper discusses feasible paths for experimentalverification and introduces the category of potential worlds to unify the six theories,clarifying how the condition of observer self-consistency leads to the Born rule.
It is emphasized that a many-worlds interpretation of quantum theory exists only to the extent that the associated basis problem is solved. The core basis problem is that the robust enduring states specified by environmental decoherence effects are essentially Gaussian wave packets that form continua of non-orthogonal states. Hence they are not a discrete set of orthogonal basis states to which finite probabilities can be assigned by the usual rules. The natural way to get an orthogonal basis without going outside the Schrödinger dynamics is to use the eigenstates of the reduced density matrix, and this idea is the basis of some recent attempts by many-worlds proponents to solve the basis problem. But these eigenstates do not enjoy the locality and quasi-classicality properties of the states defined by environmental decoherence effects, and hence are not satisfactory preferred basis states. This core problem is obscured by approaches that treat the universe as a quantum computer, but it needs to be addressed and resolved before a many-worlds-type interpretation can be said to exist. PACS No.: 03.65Bz
It is emphasized that a many-worlds interpretation of quantum theory exists only to the extent that the associated basis problem is solved. The core basis problem is that the robust enduring states specified by environmental decoherence effects are essentially Gaussian wave packets that form continua of non-orthogonal states. Hence they are not a discrete set of orthogonal basis states to which finite probabilities can be assigned by the usual rules. The natural way to get an orthogonal basis without going outside the Schroedinger dynamics is to use the eigenstates of the reduced density matrix, and this idea is the basis of some recent attempts by many-worlds proponents to solve the basis problem. But these eigenstates do not enjoy the locality and quasi-classicality properties of the states defined by environmental decoherence effects, and hence are not satisfactory preferred basis states. This core problem is obscured by approaches that treat the universe as a quantum computer, but it needs to be addressed and resolved before a many-worlds-type interpretation can be said to exist.