Despite various parallels between quantum states and ordinary information, quantum no-go-theorems have convinced many that there is no realistic framework that might underly quantum theory, no reality that quantum states can represent knowledge about. This paper develops the case that there is a plausible underlying reality: one actual spacetime-based history, although with behavior that appears strange when analyzed dynamically (one time-slice at a time). By using a simple model with no dynamical laws, it becomes evident that this behavior is actually quite natural when analyzed “all-at-once” (as in classical action principles). From this perspective, traditional quantum states would represent incomplete information about possible spacetime histories, conditional on the future measurement geometry. Without dynamical laws imposing additional restrictions, those histories can have a classical probability distribution, where exactly one history can be said to represent an underlying reality.
Despite various parallels between quantum states and ordinary information, quantum no-go-theorems have convinced many that there is no realistic framework that might underly quantum theory, no reality that quantum states can represent knowledge about. This paper develops the case that there is a plausible underlying reality: one actual spacetime-based history, although with behavior that appears strange when analyzed dynamically (one time-slice at a time). By using a simple model with no dynamical laws, it becomes evident that this behavior is actually quite natural when analyzed “all-at-once” (as in classical action principles). From this perspective, traditional quantum states would represent incomplete information about possible spacetime histories, conditional on the future measurement geometry. Without dynamical laws imposing additional restrictions, those histories can have a classical probability distribution, where exactly one history can be said to represent an underlying reality.
We propose a realistic, spacetime interpretation of quantum theory in which reality constitutes a *single* history obeying a "law of motion" that makes definite, but incomplete, predictions about its behavior. We associate a "quantum measure" |S| to the set S of histories, and point out that |S| fulfills a sum rule generalizing that of classical probability theory. We interpret |S| as a "propensity", making this precise by stating a criterion for |S|=0 to imply "preclusion" (meaning that the true history will not lie in S). The criterion involves triads of correlated events, and in application to electron-electron scattering, for example, it yields definite predictions about the electron trajectories themselves, independently of any measuring devices which might or might not be present. (So we can give an objective account of measurements.) Two unfinished aspects of the interpretation involve *conditonal* preclusion (which apparently requires a notion of coarse-graining for its formulation) and the need to "locate spacetime regions in advance" without the aid of a fixed background metric (which can be achieved in the context of conditional preclusion via a construction which makes sense both in continuum gravity and in the discrete setting of causal set theory).
If Richard Feynman's path integral formulation had been proposed not merely as a computational tool for probability amplitudes, but as a fundamental physical ontology—namely, that "all histories collectively constitute reality"—the foundational paradigm of physics would have undergone a profound transformation. Traditional physics treats a single trajectory of a system in spacetime as the primary object and path integration as a summation technique over possible paths. This paper systematically develops an alternative framework: Physics of History Space, where the ensemble of all possible histories serves as the irreduceable primary object of physical description. Within this paradigm, physical reality is defined by the topology, measure, and algebraic structures over the space of histories, rather than being restricted to a single actualized trajectory. We establish the mathematical formulation of history space and re-examine the measurement problem in quantum mechanics, the problem of initial conditions in cosmology, and the philosophy of time. We demonstrate that classical single-trajectory spacetime emerges merely as a low-dimensional projection of history space under decoherence and stationary phase limits.
Ever since quantum mechanics was first developed, it has been unclear what it really tells us about reality. A novel framework, based on 5 axioms, is presented here which offers an interpretation of quantum mechanics unlike any considered thus far: It is postulated that physical objects can exist in one of two distinct modes, based on whether they have an intrinsic actual spacetime history or not. If they do, their mode of existence is actual and they can be described by classical physics. If they do not, then their mode of existence is called actualizable and they must be described in terms of an equal-weight superposition of all possible actualizable (not actual) histories. The distinction is based on an axiom according to which there exists a limit in which spacetime reduces to a one-dimension reduced version, called areatime, and that objects which merely actualizably exist in spacetime actually exist in areatime. The operational comparison of the passage of time for such objects to the passage of time for a spacetime observer is postulated to be made possible by what is called an angular dual bilateral symmetry. This symmetry can be decomposed into the superposition of two imaginary phase angles of opposite sign. To mathematically describe the spacetime manifestation of objects which actually exist in areatime, each actualizable spacetime history is associated with an actualizable path, which in turn is associated with the imaginary phases. For a single free particle, the complex exponent is identified with a term proportional to its relativistic action, thus recovering the path integral formulation of quantum mechanics. Although based on some highly unfamiliar ideas, this framework appears to render at least some of the usual mysteries connected with quantum mechanics amenable to simple conceptual understanding. It also appears to connect the foundations of quantum theory to the foundation of the special theory of relativity while clarifying its relationship to the general theory of relativity and yields a testable prediction about a type of experiment, as yet unperformed, which under the current paradigm is utterly unexpected, namely, that the gravitational field of radiation is zero. The paper concludes with some speculations about how the theory may be extended to a metatheory of nature.(Note the paper was edited on 3-October-2011 to remove one sentence on page 7)
In usual quantum theory, the information available about a quantum system is defined in terms of the density matrix describing it on a spacelike surface. This definition must be generalized for extensions of quantum theory which neither require, nor always permit, a notion of state on a spacelike surface. In particular, it must be generalized for the generalized quantum theories appropriate when spacetime geometry fluctuates quantum mechanically or when geometry is fixed but not foliable by spacelike surfaces. This paper introduces a four-dimensional notion of the information available about a quantum system's boundary conditions in the various sets of decohering, coarse-grained histories it may display. This spacetime notion of information coincides with the familiar one when quantum theory is formulable in terms of states on spacelike surfaces but generalizes this notion when it cannot be so formulated. The idea of spacetime information is applied in several contexts: When spacetime geometry is fixed the information available through alternatives restricted to a fixed spacetime region is defined. The information available through histories of alternatives of general operators is compared to that obtained from the more limited coarse grainings of sum-over-histories quantum mechanics that refer only to coordinates. The definition of information is considered in generalized quantum theories. We consider as specific examples time-neutral quantum mechanics with initial and final conditions, quantum theories with nonunitary evolution, and the generalized quantum frameworks appropriate for quantum spacetime. In such theories complete information about a quantum system is not necessarily available on any spacelike surface but must be searched for throughout spacetime. The information loss commonly associated with the ``evolution of pure states into mixed states'' in black hole evaporation is thus not in conflict with the principles of generalized quantum mechanics.
Since its emergence, quantum mechanics has been a challenge for an understanding of reality which is based on our intuition in a classical world. Nevertheless, it has often been tried to impose this understanding of reality on quantum theory - with limited success. Instead, it might be a better alternative to redefine the meaning of physical reality. This is the objective of the paper. A consideration of the quantum measurement process, conditional probabilities and some well-known typical quantum physical experiments provides the reasoning for the following three hypotheses: (1) Prior to a first measurement, a physical system is not in a quantum state. (2) Physical reality is all that and only that about which (classical) information is available in the universe. (3) Information creation is an independent process and is not covered by the Schroedinger equation. It is the first step of the quantum measurement process and does not have a classical counterpart. The first hypothesis makes sense only if the quantum measurement process can be described without presupposing an initial state for the system under consideration. This becomes possible by the objective conditional probabilities which represent the transition probabilities between the outcomes of successive quantum measurements and have been introduced by the author in some recent papers. The second hypothesis holds as well in the classical case, but a certain incompleteness of reality is typical of quantum mechanics and the origin of many quantum phenomena. Classically, the existence of a complete reality is presumed, and hypothesis 3 has no meaning then.
Ever since quantum mechanics was first developed, it has been unclear what it really tells us about reality. A novel framework, based on 5 axioms, is presented here which offers an interpretation of quantum mechanics unlike any considered thus far: It is postulated that physical objects can exist in one of two distinct modes, based on whether they have an intrinsic actual spacetime history or not. If they do, their mode of existence is actual and they can be described by classical physics. If they do not, then their mode of existence is called actualizable and they must be described in terms of an equal-weight superposition of all possible actualizable (not actual) histories. The distinction is based on an axiom according to which there exists a limit in which spacetime reduces to a one-dimension reduced version, called areatime, and that objects which merely actualizably exist in spacetime actually exist in areatime. The operational comparison of the passage of time for such objects to the passage of time for a spacetime observer is postulated to be made possible by what is called an angular dual bilateral symmetry. This symmetry can be decomposed into the superposition of two imaginary phase angles of opposite sign. To mathematically describe the spacetime manifestation of objects which actually exist in areatime, each actualizable spacetime history is associated with an