Observer dependence is central to Quantum Mechanics; in particular if we associate consistent sets with observer worldviews we can think of the Consistent Histories (CH) interpretation as a formalisation of observer dependence. However we lack a theory of the observers themselves. In this paper we begin by building such a theory within General Relativity (GR), and find that this framework bears close mathematical resemblance to the treatment of consistent sets in CH. We therefore adapt the CHSH framework to identify the `gap' between the classical and quantum theories. We find that the CHSH argument does not hold on a curved background, so that the inequality may be violated by classical theories.
Observer dependence is central to Quantum Mechanics; in particular if we associate consistent sets with observer worldviews we can think of the Consistent Histories (CH) interpretation as a formalisation of observer dependence. However we lack a theory of the observers themselves. In this paper we begin by building such a theory within General Relativity (GR), and find that this framework bears close mathematical resemblance to the treatment of consistent sets in CH. We therefore adapt the CHSH framework to identify the `gap' between the classical and quantum theories. We find that the CHSH argument does not hold on a curved background, so that the inequality may be violated by classical theories.
The Consistent Histories (CH) formalism attempts to construct a quantum framework which can be used without the need to introduce observers external to the studied system. The prime motivation in mind is the application of the formalism to the universe as a whole. In order to achieve this, CH maintains that a formulation of quantum mechanics should allow for the assignment of probabilities to alternative histories of a system. Therefore, it provides an observer-independent criterion to decide which sets of histories can be given probabilities and states rules to determine them. The framework establishes that each realm, that is, each set of histories to which probabilities can be assigned, provides a valid quantum-mechanical account of a system. Furthermore, the version of CH first presented in [1, 2] proposes an "evolutionary" explanation of our existence in the universe and of our preference for quasiclassical descriptions of nature. The present work critically evaluates claims to the effect that the formalism offered in [1, 2] solves many interpretational problems in quantum mechanics. In particular, it is pointed out that the interpretation of the proposed framework leaves vague two crucial points, namely, whether realms are fixed or chosen and the link between measurements and histories. The claim of this work is that by doing so, CH overlooks the main interpretational problems of quantum mechanics. Furthermore, we challenge the evolutionary explanation offered and we critically examine the proposed notion of a realm-dependent reality.
This paper discusses the fundamental assumptions and background of the consistent histories (CH) approach to quantum mechanics. The focus of the paper is on the concept of frameworks. It is proposed that frameworks should be interpreted objectively as observer-independent realities. Two further options are considered: a hidden-variables variant of the CH approach, and a many-worlds version, which considers each individual history belonging to a given family as describing a separate world. The latter interpretation is subsequently compared and contrasted with the standard many-worlds interpretation. Finally, the solution to the measurement problem offered by the many-worlds variant of CH is analyzed and amended.
Abstract: The Consistent Histories (CH) formalism aims at a quantum mechani-cal framework which could be applied even to the universe as a whole. CH stresses the importance of histories for quantum mechanics, as opposed to measurements, and maintains that a satisfactory formulation of quantum mechanics allows one to assign probabilities to alternative histories of a quantum system. It further proposes that each realm, that is, each set of histories to which probabilities can be assigned, provides a valid quantum-mechanical account, but that different realms can be mutually incom-patible. Finally, some of its proponents offer an “evolutionary ” explanation of our existence in the universe and of our preference for quasiclassical descriptions of nature. The present work questions the validity of claims offered by CH proponents asserting that it solves many interpretational problems in quantum mechanics. In particular, we point out that the interpretation of the framework leaves vague two crucial points, namely, whether realms are fixed or chosen and the link between measurements and histories. Our claim is that by doing so, CH overlooks the main interpretational prob-lems of quantum mechanics. Furthermore, we challenge the evolutionary explanation offered and we critically examine the proposed notion of a realm-dependent reality. 1
A measurement-independent formulation of quantum mechanics called ‘regular histories’ (RH) is presented, able to reproduce the predictions of the standard formalism without the need to for a quantum-classical divide or the presence of an observer. It applies to closed systems and features no wave-function collapse. Weights are assigned only to histories satisfying a criterion called ‘regularity’. As the set of regular histories is not closed under the Boolean operations this requires a new con- cept of weight, called ‘likelihood’. Remarkably, this single change is enough to overcome many of the well-known obstacles to a sensible interpretation of quantum mechanics. For example, Bell’s theorem, which makes essential use of probabilities, places no constraints on the locality properties of a theory based on likelihoods. Indeed, RH is both counter- factually definite and free from action-at-a-distance. Moreover, in RH the meaningful histories are exactly those that can be witnessed at least in principle. Since it is especially difficult to make sense of the concept of probability for histories whose occurrence is intrinsically indeterminable, this makes likelihoods easier to justify than probabilities. Interaction with the environment causes the kinds of histories relevant at the macroscopic scale of human experience to be witnessable and indeed to generate Boolean algebras of witnessable histories, on which likelihoods reduce to ordinary probabilities. Further- more, a formal notion of inference defined on regular histories satisfies, when restricted to such Boolean algebras, the classical axioms of implication, explaining our perception of a largely classical world. Even in the context of general quantum histories the rules of reasoning in RH are remark- ably intuitive. Classical logic must only be amended to reflect the fundamental premise that one cannot meaningfully talk about the occurrence of unwitnessable histories. Crucially, different histories with the same ‘physical content’ can be interpreted in the same way and independently of the family in which they are expressed. RH thereby rectifies a critical flaw of its inspiration, the consistent histories (CH) approach, which requires either an as yet unknown set selection rule or a paradigm shift towards an un- conventional picture of reality whose elements are histories-with-respect-to-a-framework. It can be argued that RH compares favourably with other proposed interpretations of quantum mechanics in that it resolves the measurement problem while retaining an essentially classical worldview without parallel universes, a framework-dependent reality or action-at-a-distance.
Classical mechanics and standard Copenhagen quantum mechanics respect subspace implications. For example, if a particle is confined in a particular region R of space, then in these theories we can deduce that it is confined in regions containing R. However, subspace implications are generally violated by versions of quantum theory that assign probabilities to histories, such as the consistent histories approach. I define here a new criterion, ordered consistency, which refines the criterion of consistency and has the property that inferences made by ordered consistent sets do not violate subspace relations. This raises the question: do the operators defining our observations form an ordered consistent history? If so, ordered consistency defines a version of quantum theory with greater predictive power than the consistent histories formalism. If not, and our observations are defined by a non-ordered consistent quantum history, then subspace implications are not generally valid.
General Relativity (GR) and Quantum Mechanics (QM) are the theories dependent on the observer/detector so they are not the theories of the independent from observer Nature. In GR it follows from the fact that each act of observation (the photon-detector interaction via exchanges of the invisible superluminal particles responsible for quantum entanglement i.e. there are exchanged the spin-1 entanglons) sets the speed of light in “vacuum” c in relation to the detector (the speed c is in relation to the emitter or a last-interaction object - sometimes it is a detector). In QM it results from the fact that we cannot observe the entanglons directly and because time of observation lasts much longer than the time of exchanges of the invisible superluminal entanglons so there appear wavefunctions, superposition of states, and probabilities to find a particle in different states. Simultaneity of different states of the same particle is an illusion that appears only in the theories dependent on the observer. There must be in existence a more fundamental theory, which should be a theory of Nature independent on the observer - it is the Scale-Symmetric Theory (SST). SST leads to the initial conditions applied in GR and QM and shows that these theories are dependent on the observer. Moreover, SST shows that we cannot unify GR and QM within the same methods. SST shows that Nature behaves classically in a deterministic way but it does not mean that the free will is not in existence.