Computationalism provides a framework for understanding how a mathematically describable physical world could give rise to conscious observations without the need for dualism. A criterion is proposed for the implementation of computations by physical systems, which has been a problem for computationalism. Together with an independence criterion for implementations this would allow, in principle, prediction of probabilities for various observations based on counting implementations. Applied to quantum mechanics, this results in a Many Computations Interpretation (MCI), which is an explicit form of the Everett style Many Worlds Interpretation (MWI). Derivation of the Born Rule emerges as the central problem for most realist interpretations of quantum mechanics. If the Born Rule is derived based on computationalism and the wavefunction it would provide strong support for the MWI; but if the Born Rule is shown not to follow from these to an experimentally falsified extent, it would indicate the necessity for either new physics or (more radically) new philosophy of mind.
Computationalism provides a framework for understanding how a mathematically describable physical world could give rise to conscious observations without the need for dualism. A criterion is proposed for the implementation of computations by physical systems, which has been a problem for computationalism. Together with an independence criterion for implementations this would allow, in principle, prediction of probabilities for various observations based on counting implementations. Applied to quantum mechanics, this results in a Many Computations Interpretation (MCI), which is an explicit form of the Everett style Many Worlds Interpretation (MWI). Derivation of the Born Rule emerges as the central problem for most realist interpretations of quantum mechanics. If the Born Rule is derived based on computationalism and the wavefunction it would provide strong support for the MWI; but if the Born Rule is shown not to follow from these to an experimentally falsified extent, it would indicate the necessity for either new physics or (more radically) new philosophy of mind.
A non-relativistic quantum mechanical theory is proposed that describes the universe as a continuum of worlds whose mutual interference gives rise to quantum phenomena. A logical framework is introduced to properly deal with propositions about objects in a multiplicity of worlds. In this logical framework, the continuum of worlds is treated in analogy to the continuum of time points; both “time” and “world” are considered as mutually independent modes of existence. The theory combines elements of Bohmian mechanics and of Everett’s many-worlds interpretation; it has a clear ontology and a set of precisely defined postulates from where the predictions of standard quantum mechanics can be derived. Probability as given by the Born rule emerges as a consequence of insufficient knowledge of observers about which world it is that they live in. The theory describes a continuum of worlds rather than a single world or a discrete set of worlds, so it is similar in spirit to many-worlds interpretations based on Everett’s approach, without being actually reducible to these. In particular, there is no splitting of worlds, which is a typical feature of Everett-type theories. Altogether, the theory explains (1) the subjective occurrence of probabilities, (2) their quantitative value as given by the Born rule, and (3) the apparently random “collapse of the wavefunction” caused by the measurement, while still being an objectively deterministic theory.
The Everett (or relative-state, or many-worlds) interpretation of quantum mechanics has come under fire for inadequately dealing with the Born rule (the formula for calculating quantum probabilities). Numerous attempts have been made to derive this rule from the perspective of observers within the quantum wavefunction. These are not really analytic proofs, but are rather attempts to derive the Born rule as a synthetic a priori necessity, given the nature of human observers (a fact not fully appreciated even by all of those who have attempted such proofs). I show why existing attempts are unsuccessful or only partly successful, and postulate that Solomonoff's algorithmic approach to the interpretation of probability theory could clarify the problems with these approaches. The Sleeping Beauty probability puzzle is used as a springboard from which to deduce an objectivist, yet synthetic a priori framework for quantum probabilities, that properly frames the role of self-location and self-selection (anthropic) principles in probability theory. I call this framework "algorithmic synthetic unity" (or ASU). I offer no new formal proof of the Born rule, largely because I feel that existing proofs (particularly that of Gleason) are already adequate, and as close to being a formal proof as one should expect or want. Gleason's one unjustified assumption--known as noncontextuality--is, I will argue, completely benign when considered within the algorithmic framework that I propose. I will also argue that, to the extent the Born rule can be derived within ASU, there is no reason to suppose that we could not also derive all the other fundamental postulates of quantum theory, as well. There is nothing special here about the Born rule, and I suggest that a completely successful Born rule proof might only be possible once all the other postulates become part of the derivation. As a start towards this end, I show how we can already derive the essential content of the fundamental postulates of quantum mechanics, at least in outline, and especially if we allow some educated and well-motivated guesswork along the way. The result is some steps towards a coherent and consistent algorithmic interpretation of quantum mechanics.
This unpublished 1990 preprint argues that a crucial distinction in discussions of the many-worlds interpretation of quantum mechanics (MWI) is that between versions of the interpretation positing a physical multiplicity of worlds, and those in which the multiplicity is merely psychological, and due to the splitting of consciousness upon interaction with amplified quantum superpositions. It is argued that Everett's original version of the MWI belongs to the latter class, and that most of the criticisms leveled against the MWI, in particular that it is illogical or incoherent, are not valid against such "psychological-multiplicity" versions. Attempts to derive the quantum-mechanical probabilities from the many-worlds interpretation are reviewed, and Everett's initial derivation is extended in an attempt to show that these are the unique possible probabilities. But there remains a challenge for proponents of the MWI: to show that their interpretation requires probabilities, rather than merely nonprobabilistic indeterminacy. A 2002 preface, revised in 2004, briefly discusses the extent to which I still agree with the claims in the paper. While its derivation of probabilities used, and failed to justify, noncontextuality, I still agree with the paper's general interpretation of the MWI, though not with the MWI itself.
Subjective aspects of quantum mechanics (QM) are most radically expressed in the (EI) of QM which suggests coexisting macroscopically distinct configurations of the world in the form of a superposition of the (quasi-)classical state vectors. The components of such a superposition are often verbally denoted as Everett's worlds, hence the name Many-Worlds Interpretation (MWI) for EI. Explicit accounting the correlation of each classical configuration of the world with the corresponding state of an observer's mind yields the so-called Many-Minds interpretation (MMI). This is maximum that may be done in the context of EI if the restriction by pure physics is implied. In the author's Extended Everett Concept (EEC) the observer's consciousness is defined in the spirit of psycho-physical parallelism, i.e. as going beyond pure physics. As a consequence, according to EEC, an observer, if he/she weakens or turns off his/her consciousness (perception), obtains the ability of super-intuition (obtaining seemingly unavailable information) and even of controlling the subjective reality (a picture of classical reality as it will be subjectively perceived). This may be interpreted as a realization of the Jung's collective unconscious as well as an explanation of the mystical elements in Oriental philosophies, world religions and deep psychological practices.
NeuroQuantology | March 2013 | Vol 11 | Issue 1 | Suppl 1 | Page 85-96
The Many-worlds Interpretation (MWI) of quantum mechanics has captivated physicists and philosophers alike since its inception in the mid-20th century. This paper explores the historical roots, evolution, and implications of the MWI within the context of quantum theory. Beginning with an overview of early developments in quantum mechanics and the emergence of foundational interpretations, we delve into the origins of the MWI through the groundbreaking work of physicist Hugh Everett III. Everett's doctoral thesis proposed a radical solution to the measurement problem, positing the existence of multiple branching universes to account for quantum phenomenon. We trace the evolution of the MWI, examining its refinement and elaboration by subsequent physicists such as John Wheeler. Furthermore, we discuss the MWI's impact on contemporary physics, including its connections to quantum information theory and ongoing experimental tests. By providing a comprehensive analysis of the MWI's historical development and current relevance, this paper offers insights into one of the most provocative interpretations of quantum mechanics and its implications for our understanding of the universe.
A non-relativistic quantum mechanical theory is proposed that combines elements of Bohmian mechanics and of Everett's "many-worlds" interpretation. The resulting theory has the advantage of resolving known issues of both theories, as well as those of standard quantum mechanics. It has a clear ontology and a set of precisely defined postulates from where the predictions of standard quantum mechanics can be derived. Most importantly, the Born rule can be derived by straightforward application of the Laplacian rule, without reliance on a "quantum equilibrium hypothesis" that is crucial for Bohmian mechanics, and without reliance on a "branch weight" that is crucial for Everett-type theories. The theory describes a continuum of worlds rather than a single world or a discrete set of worlds, so it is similar in spirit to many-worlds interpretations based on Everett's approach, without being actually reducible to these. In particular, there is no "splitting of worlds", which is a typical feature of Everett-type theories. Altogether, the theory explains 1) the subjective occurrence of probabilities, 2) their quantitative value as given by the Born rule, 3) the identification of observables as self-adjoint operators on Hilbert space, and 4) the apparently random "collapse of the wavefunction" caused by the measurement, while still being an objectively deterministic theory.