Murray Gell-Mann and James Hartle have made an original proposal for a version of decoherent histories quantum mechanics which is specifically tailored so as not to imply the emergence of multiple quasi-classical worlds. I argue that there is an explanatory gap in the proposal but that there remains an important insight which might be used to tackle what can be seen as an outstanding problem for Hugh Everett III’s “relative state” interpretation of quantum mechanics, if it is understood as giving ontic priority to the wavefunction. The argument employs a recent novel analysis of self-location within any sort of multiverse.
Murray Gell-Mann and James Hartle have made an original proposal for a version of decoherent histories quantum mechanics which is specifically tailored so as not to imply the emergence of multiple quasi-classical worlds. I argue that there is an explanatory gap in the proposal but that there remains an important insight which might be used to tackle what can be seen as an outstanding problem for Hugh Everett III’s “relative state” interpretation of quantum mechanics, if it is understood as giving ontic priority to the wavefunction. The argument employs a recent novel analysis of self-location within any sort of multiverse.
I review the decoherent (or consistent) histories approach to quantum mechanics, due to Griffiths, to Gell-Mann and Hartle, and to Omnes. This is an approach to standard quantum theory specifically designed to apply to genuinely closed systems, up to and including the entire universe. It does not depend on an assumed separation of classical and quantum domains, on notions of measurement, or on collapse of the wave function. Its primary aim is to find sets of histories for closed systems exhibiting negligble interference, and therefore, to which probabilities may be assigned. Such sets of histories are called consistent or decoherent, and may be manipulated according to the rules of ordinary (Boolean) logic. The approach provides a framework from which one may predict the emergence of an approximately classical domain for macroscopic systems, together with the conventional Copenhagen quantum mechanics for microscropic subsystems. In the special case in which the total closed system naturally separates into a distinguished subsystem coupled to an environment, the decoherent histories approach is closed related to the quantum state diffusion approach of Gisin and Percival.
This paper shows how to treat quantum field theory as a modern, locally Lorentz covariant quantum version of the classical, mechanical universe suggested by Laplace over 200 years ago. The result is a fairly common-sense single-history, single-world alternative to decoherent histories (Gell-Mann and Hartle) and many-worlds interpretations (Everett, DeWitt). From the assumption that there is a single universal Heisenberg state whose N-point functions uniquely describe all physical details of our universe, everything is rigorously deduced in a way showing that the mathematical formalism is capable of yielding its own interpretation. Probabilities arise from the neglect of the environment in approximate models. By giving the collapse of the wave function at a double slit a natural unitary explanation, new light is shed on the quantum measurement problem and the origin of the Born rule.
I briefly review the "decohering histories" or "consistent histories" formulation of quantum theory, due to Griffiths, Omnès, and Gell-Mann and Hartle (and the subject of my graduate work with George Sudarshan). I also sift through the many meanings that have been attached to decohering histories, with an emphasis on the most basic one: Decoherence of appropriate histories is needed to establish that quantum mechanics has the correct classical limit. Then I will describe efforts to find physical mechanisms that do this. Since most work has focused on density matrix versions of decoherence, I'll consider the relation between the two formulations, which historically has not been straightforward. Finally, I'll suggest a line of research that would use recent results by Sudarshan to illuminate this aspect of the classical limit of quantum theory.
Recent years have seen a good deal of work done on one of the most mind blowing and conceptually radical views in quantum mechanics, namely the ‘many worlds’ interpretation of quantum mechanics. Many worlds was first proposed by Hugh Everett III in his long Ph.D. dissertation, which only some years later, and after significant shortening, came to be published as the ‘Relative State Formulation of Quantum Mechanics’ (Everett 1957). To commemorate the 50th anniversary of the first publication of Everett's ideas, two conferences were held at Oxford University and the Perimeter Institute, which brought together some of the most active researchers in the field. The works presented in these two conferences have now been compiled in the volume Many Worlds? Everett, Quantum Theory and Reality, edited by Simon Saunders, Jonathan Barrett, Adrian Kent and David Wallace.1 This is then a comprehensive collection of papers – 23 papers altogether – where the reader will find virtually anything that can be said about the many worlds interpretation today.
Everett's relative-state construction in quantum theory has never been satisfactorily expressed in the Heisenberg picture. What one might have expected to be a straightforward process was impeded by conceptual and technical problems that we solve here. The result is a construction which, unlike Everett's one in the Schrödinger picture, makes manifest the locality of Everettian multiplicity, its inherently approximative nature and its origin in certain kinds of entanglement and locally inaccessible information. (By Everettian , we are referring not only to Everett's own work, but also to versions of quantum theory that elaborate and refine his. The notion of relative states first appeared in Everett (Everett 1973 In The many worlds interpretation of quantum mechanics (eds BS DeWitt, N Graham)). We are proposing a formalism for relative states that is more detailed and more illuminating than Everett's.) Our construction also allows us to give a more precise definition of an Everett ‘universe’, under which it is fully quantum, not quasi-classical, and we compare the Everettian decomposition of a quantum state with the foliation of a space–time.
We introduce and review the consistent (decoherent) histories approach to quantum mechanics due to Griffiths, to Gell-Mann and Hartle, and to Omnes. We will not attempt an in depth look at this approach as it would be impossible to treat it in such a short review. The emphasis is on understanding the broader meaning of the consistency and decoherence. The consistent history approach to quantum mechanics provides a precise conceptual framework for describing how a closed quantum system develops in time. The approach also provides a framework from which we may observe the emergence of an approximately classical domain for macroscopic systems, together with the conventional Copenhagen quantum mechanics for microscopic subsystems. We will study the formalism of decoherence and look at several approaches to decoherence. In examining a system of quantum Brownian motion and using the methods of Feynman and Vernon, we derive an equation of motion for the density matrix, the master equation of the system. This leads us to a brief overview of decoherence. PACS Nos.: 03.65.Ta, 03.65.w, 03.65.Yz, 04.60.m, 05.30.d