The Traveling Minds interpretation of Quantum Mechanics is a no-collapse interpretation on which the wavefunction evolves deterministically like in the Everett branching multiple-worlds interpretation. As in the Many Minds interpretation, minds navigate the Everett branching structure following the probabilities given by the Born rule. However, in the Traveling Minds interpretation (a variant by Squires and Barrett of the single-mind interpretation), the minds are guaranteed to all travel together—they are always found in the same branch. The Traveling Forms interpretation extends the Traveling Minds interpretation in an Aristotelian way by having forms of non-minded macroscopic entities that have forms, such as plants, lower animals, bacteria, and planets, travel along the branching structure together with the minds. As a result, while there is deterministic wavefunction-based physics in the branches without minds, non-reducible higher-level structures like life are found only in the branch with minds.
The Traveling Minds interpretation of Quantum Mechanics is a no-collapse interpretation on which the wavefunction evolves deterministically like in the Everett branching multiple-worlds interpretation. As in the Many Minds interpretation, minds navigate the Everett branching structure following the probabilities given by the Born rule. However, in the Traveling Minds interpretation (a variant by Squires and Barrett of the single-mind interpretation), the minds are guaranteed to all travel together—they are always found in the same branch. The Traveling Forms interpretation extends the Traveling Minds interpretation in an Aristotelian way by having forms of non-minded macroscopic entities that have forms, such as plants, lower animals, bacteria, and planets, travel along the branching structure together with the minds. As a result, while there is deterministic wavefunction-based physics in the branches without minds, non-reducible higher-level structures like life are found only in the branch with minds.
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 interpretation of quantum mechanics is, inter alia, an interpretation of objective probability: an account of what probability really is. Everett called his work “wave mechanics without probability” for good reason: it provides a non-chancy base level of categorical properties and relations. The objection may concern justification rather than understanding, particularly if decoherence theory is used to derive the Born rule. The branch-counting rule makes nonsense of quantum mechanics but it appears to be suggested by the picture of branching. Branch counting is hardly a rival to the branch-weight rule as an interpretation of branching structure, if it brings that branching structure crashing down. Denizens of anomalous branches, or of anomalous stretches of history in one-world theories, will be misled by the observed statistics of measurements.
A group of philosophers and physicists at Oxford have recently crafted, in light of developments in the theory of decoherence, a new version of the Everett or Many Worlds interpretation of quantum mechanics. I will focus on the work of David Wallace, who identifies the quasi-classical domains making up the various “worlds” or “branches” of the interpretation with macroscopic patterns that are functionally realized (to an approximate degree good enough for practical purposes) by the quantum wavefunction of the universe. I argue that Wallace’s reliance on Savage’s pragmatic account of probability fails, due to the unreasonableness of Savage’s Sure Thing Principle in a many-worlds setting. I also argue that Wallace’s program is vulnerable to a version of Putnam’s model-theoretic indeterminacy argument, with the result that almost any conceivable macroscopic “world” is in fact realized by that function and so is (by Wallace’s light) as real as our own. I offer a hylomorphic revision of the many-worlds model, the “traveling forms” interpretation of Alexander Pruss, and I argue that this revision solves both the indeterminacy problem and the problem of interpreting quantum probabilities.
A complete reappraisal of the philosophical meaning of Everett's interpretation of quantum mechanics is carried out, by analysing carefully the role of the concept of "observer" in physics. It is shown that Everett's interpretation is the limiting case of a series of conceptions of the measurement problem which leave less and less of the observer out of the quantum description of the measuring interaction. This limiting case, however, should not be considered as one wherein nothing is left outside the description. Something is still needed besides this description: pure cognitive capacity, the subject, or, in a very abstract sense: "mind". The set of branches which arise, according to Everett, from a measuring interaction, gain a renewed signification. They do not refer to distinct "worlds", but to the points of view "mind" can identify itself to. This idea is compared and contrasted with Squires' "selection" of a branch by the mind (without quotation marks). Finally, the notion of indeterminism in quantum mechanics gains an unexpected and new light from a strict application of the previous ideas.
An increasingly popular interpretation of quantum mechanics holds that in any genuinely chancy situation, all possible outcomes occur.1 For example, if the spin of a typical electron is measured in a given direction, then both 'up' and 'down' results will be registered. (True, 'up' and 'down' won't occur within the same 'branch of reality', for that would be inconsistent. Rather, the idea is that reality comes to contain two elements, with 'up' registered relative to one, and 'down' registered relative to the other.) This kind of 'many worlds' or 'many minds' interpretation of quantum mechanics has advantages and disadvantages. The main advantage is that it avoids any 'collapse of the wave function' and so avoids the measurement problem, mysterious non-local interactions, and the like. The most obvious disadvantage is that its burgeoning world of duplicate histories seems repugnant to common sense. Some commentators think that there is another disadvantage. They argue that this interpretation undermines itself by destroying any notion of objective probability. Quantum mechanics is, if anything, a theory which specifies the objective probabilities of certain results. But in what sense is there an objective probability for 'up' and 'down' in a spin measurement, if both results always happen? (Albert [1]; Albert and Loewer [3], [4]; Healey [5]; Squires [9]; Stein [8].) This looks like a good objection. But I shall show in this note that it is not. The proposed interpretation does leave objective probability as a rather mysterious notion. But it is no more mysterious on the proposed interpretation than on the conventional view of the world. This is not the place to go into details about the 'many minds'2 interpretation of quantum mechanics, but one point may help readers. If both the 'up' and 'down' results occur, why do we experience only one?
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.