I will propose that the reality to which the quantum formalism implicitly refers is a kind of generalized history, the word history having here the same meaning as in the phrase sum-over-histories. This proposal confers a certain independence on the concept of event, and it modifies the rules of inference concerning events in order to resolve a contradiction between the idea of reality as a single history and the principle that events of zero measure cannot happen (the Kochen-Specker paradox being a classic expression of this contradiction). The so-called measurement problem is then solved if macroscopic events satisfy classical rules of inference, and this can in principle be decided by a calculation. The resulting conception of reality involves neither multiple worlds nor external observers. It is therefore suitable for quantum gravity in general and causal sets in particular. Quantum gravity and quantal reality Why, in our attempts to unify our theories of gravity and the quantum, has progress been so slow? One reason, no doubt, is that it's simply a very hard problem. Another is that we lack clear guidance from experiments or astronomical observations. But I believe that a third thing holding us back is that we haven't learned how to think clearly about the quantum world in itself, without reference to “observers” and other external agents. Because of this we don't really know how to think about the Planckian regime where quantum gravity is expected to be most relevant. We don’t know how to think about the vacuum on small scales, or about the inside of a black hole, or about the early universe. Nor do we have a way to pose questions about relativistic causality in such situations.
I will propose that the reality to which the quantum formalism implicitly refers is a kind of generalized history, the word history having here the same meaning as in the phrase sum-over-histories. This proposal confers a certain independence on the concept of event, and it modifies the rules of inference concerning events in order to resolve a contradiction between the idea of reality as a single history and the principle that events of zero measure cannot happen (the Kochen-Specker paradox being a classic expression of this contradiction). The so-called measurement problem is then solved if macroscopic events satisfy classical rules of inference, and this can in principle be decided by a calculation. The resulting conception of reality involves neither multiple worlds nor external observers. It is therefore suitable for quantum gravity in general and causal sets in particular. Quantum gravity and quantal reality Why, in our attempts to unify our theories of gravity and the quantum, has progress been so slow? One reason, no doubt, is that it's simply a very hard problem. Another is that we lack clear guidance from experiments or astronomical observations. But I believe that a third thing holding us back is that we haven't learned how to think clearly about the quantum world in itself, without reference to “observers” and other external agents. Because of this we don't really know how to think about the Planckian regime where quantum gravity is expected to be most relevant. We don’t know how to think about the vacuum on small scales, or about the inside of a black hole, or about the early universe. Nor do we have a way to pose questions about relativistic causality in such situations.
Quantum mechanics is the physics of a superposed class of relativistic worlds. The direct evidence is the formalism itself: it is class arithmetic throughout. All worlds that share the same correlation record are indistinguishable, and by that principle constitute one world. The result is a 'class-of-worlds-as-a-world': literally a metaworld. This is the ontology of the quasi-classical world, and the explanation of the physics. The term quantum gravity becomes an ontological description of the quasi-classical world. This is quantum-gravity reality: the quantum superposition of gravitational spacetime worlds. As quantum mechanics is the superposition of the relativistic operation of all the worlds, the science is unified. The cycle of the standard von Neumann formulation is thus the operation of one causal principle, effective alternately at the two levels of logical type. In addition to Process 1, collapse, and Process 2, linear evolution, this framework identifies Process 0: the determinate relativistic dynamics of each world in the class. Process 2 is then the class-level superposition of Process 0; Process 1 is its class-level consequence when it causes the correlation record to change. Thus the formalisms are fully unified, together forming a single causal order. No new equations or dynamics are required. The same physical unification is exposed geometrically in the Compton-Schwarzschild crossing. In the standard resolving experiment, the same physical process operates at the two levels of logical type: the class-level Compton localisation scale contracts as the energy rises, while the element-level Schwarzschild radius expands, the two becoming equal at Planck order. At the crossing, the higher-logical-type quantum description loses its physical referent and the physically instantiated resolving scale becomes Schwarzschild geometry. The crossing is not a merger of the two formalisms at the Planck scale, but the transition for the enclosed region to element-level reality alone. The higher-logical-type class-of-worlds-as-a-world ceases to be constituted there, while relativistic physics continues. In reverse, the same transition is the genesis of the quantum universe in the Big Bang.
Introduction ‘The term “3-geometry” makes sense as well in quantum geometrodynamics as in classical theory. So does superspace. But space-time does not. Give a 3-geometry, and give its time rate of change. That is enough, under typical circumstances to fix the whole time-evolution of the geometry; enough in other words, to determine the entire four-dimensional space-time geometry, provided one is considering the problem in the context of classical physics. In the real world of quantum physics, however, one cannot give both a dynamic variable and its time-rate of change. The principle of complementarity forbids. Given the precise 3-geometry at one instant, one cannot also know at that instant the time-rate of change of the 3-geometry. … The uncertainty principle thus deprives one of any way whatsoever to predict, or even to give meaning to, “the deterministic classical history of space evolving in time”. No prediction of spacetime, therefore no meaning for spacetime , is the verdict of the quantum principle’. (Misner, Thorne, and Wheeler 1973) One of the few propositions about quantum gravity that most physicists in the field would agree upon, that our notion of spacetime must, at best, be altered considerably in any theory conjoining the basic principles of quantum mechanics with those of general relativity, will be questioned in this chapter. We will argue, in fact, that most, if not all, of the conceptual problems in quantum gravity arise from the sort of thinking on display in the preceding quotation.
Many attempts have been made at the unification of General Relativity (GR) and Quantum Theory (QT), but there is a fundamental error made with these attempts, as we will discuss. What is the point of such theories? Well, obviously to describe the physical world we live in. QT describes what happens on the tiny scale, and GR describes what happens to bodies on a large scale. The fundamental error in unifying the two subjects is that QT doesn’t provide the physical happenings for GR to work, or in other words, QT describes why the world is the way it is, but not how, and this does not philosophically suffice in GR. Must we simply give up, in that the subjects are two different entities? I think the answer is that we mustn't. I think that we should put one theory in terms of the basic mechanics of the other, perhaps by simplifying, or perhaps by taking the physical reality to be our guide. Do I believe QT describes the world? Accurately. Do I believe that QT is the physical truth? Of course not… it is simply a mathematical construct to provide a model that allows for us to predict future outcomes. I will begin very simplistic, but the goal for the first part of the paper is to Classically describe the physical mechanics of QT. I will stick with particles in their ground state, and hence no translational motion.
The problem of time in quantum gravity is often presented as a consequence of applying quantum theory to general relativity. These notes adopt a broader perspective. We first examine how time enters classical mechanics, relativity, quantum theory, and quantum field theory, distinguishing three principal aspects: causal order, temporal duration, and the present. This analysis shows that the conceptual difficulties associated with time do not arise only when gravity is quantised. Tensions between causal structure, clocks, observables, and measurement are already present in the theories from which quantum gravity is constructed. We then survey responses to the problem of time across the principal approaches to quantum gravity. These include canonical and Wheeler-DeWitt quantisation, path-integral and histories formulations, perturbative and background-dependent approaches, causal sets, and twistor theory. The programmes are compared according to whether they retain an external time, render time problematic through quantisation, or incorporate causal or temporal structure into their foundations. Particular emphasis is placed on questions arising from quantum foundations and relativistic quantum information. We conclude by examining linearised gravity and weak-gravity quantum systems. This regime shows that the problem of time is not confined to Planck-scale physics, but arises already in attempts to provide a predictive and operationally meaningful quantum description of spacetime near flat geometry.
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.
Where does what happens happen in a quantum system? The standard textbook formulation of quantum mechanics provides a strange, imprecise and yet successful-in-practice answer to this question. In the struggle to unify our understanding of gravity with quantum theory, though, the textbook answer no longer suffices, and an alternative approach is needed. The Feynman Sum Over Histories approach provides an alternative that is particularly suited to quantum gravity because the Sum Over Histories and General Relativity are built on the same fundamental concepts of `event' and `history'.