The formalism of covariant quantum theory, introduced by Reisenberger and Rovelli, casts the description of quantum states and evolution into a framework compatable with the principles of general relativity. The leap to this covariant formalism, however, outstripped the standard interpretation used to connect quantum theory to experimental predictions, leaving the predictions of the RR theory ambiguous. Here we discuss in detail some implications of our recently proposed description of covariant quantum information (CQI), which addresses these problems. We show explicit agreement with standard quantum mechanics in the appropriate limit. In addition to compatability with general covariance, we show that our framework has other attractive and satisfying features -- it is fully unitary, realist, and self-contained. The full unitarity of the formalism in the presence of measurements allows us to invoke time-reversal symmetry to obtain new predictions closely related to the quantum Zeno effect.
The formalism of covariant quantum theory, introduced by Reisenberger and Rovelli, casts the description of quantum states and evolution into a framework compatable with the principles of general relativity. The leap to this covariant formalism, however, outstripped the standard interpretation used to connect quantum theory to experimental predictions, leaving the predictions of the RR theory ambiguous. Here we discuss in detail some implications of our recently proposed description of covariant quantum information (CQI), which addresses these problems. We show explicit agreement with standard quantum mechanics in the appropriate limit. In addition to compatability with general covariance, we show that our framework has other attractive and satisfying features -- it is fully unitary, realist, and self-contained. The full unitarity of the formalism in the presence of measurements allows us to invoke time-reversal symmetry to obtain new predictions closely related to the quantum Zeno effect.
The formalism of covariant quantum theory, introduced by Reisenberger and Rovelli, casts the description of quantum states and evolution into a framework compatible with the principles of general relativity. The leap to this covariant formalism, however, outstripped the standard interpretation used to connect quantum theory to experimental predictions, leaving the predictions of the theory ambiguous. In particular, the absence of a pre-defined time variable or background causal structure resulted in an ``order of projections" ambiguity, in which the usual rule for multiple-measurement probabilities (obtained by time-ordered projections) is not defined. Equally troublesome, the probability postulate of Reisenberger and Rovelli fails to reproduce the Born interpretation for the case of simple quantum mechanical systems. Here, we develop an alternative quantum measurement formalism, based on basic principles of quantum information. After reviewing how this can be done in the context of the traditional formulation of quantum mechanics and noting its implications for the quantum measurement problem, we find that this approach can be generalized to the covariant setting, where it essentially solves the correspondence problems of covariant quantum theory. We show explicit agreement with the Born interpretation of standard quantum mechanics in the context of simple systems. We also demonstrate the origin of the quantum mechanical arrow of time within our framework, and use this to solve the order of projections ambiguity. In addition to compatibility with general covariance, we show that our framework has other attractive and satisfying features - it is fully unitary, realist, and self-contained. The full unitarity of the formalism in the presence of measurements allows us to invoke time-reversal symmetry to obtain new predictions closely related to the quantum Zeno effect.
Due to the absence of an external, classical time variable, the probabilistic predictions of covariant quantum theory are ambiguous when multiple measurements are considered. Here, we introduce an information theoretic framework to the covariant formalism, and use it to interpret the measurement process. We find that the time ordering of measurements emerges as an entropy relationship in the state of the observers, giving unique probabilities for multiple measurements. This approach suggests a new, fully self-contained probability interpretation for generally covariant quantum physics, which makes use of a quantum mechanical description of the observer, in contrast to standard quantum mechanics which assumes an external, classical observer.
In this paper, we study implications of the geometrical nature of space- time for some of the basic tenets of quantum mechanics. That is, we study two different implications of the principle of general covariance; first we quantize a reparametrization invariant theory, the free particle in Minkowski spacetime and point out in detail where this theory fails (no- tably these comments appear to be missing in the literature). Second we study the covariance of quantum field theory and show how it connects to causality, the outcome of this study is that QFT is what we shall call ultra weakly covariant with respect to the background spacetime. Third, we treat the question of whether evolution in quantum theory (apart from the measurement act) needs to be unitary, it is easily shown that a per- fectly satisfying probabilistic interpretation exists which does not require unitary evolution. Fourth, we speculate on some modifications quantum theory should undergo in order for it to be generally covariant. The results in this paper hint at a profound change of the theory in which causality as a fundamental principle is abandonned.
The requirement of general covariance of quantum field theory (QFT) naturally leads to quantization based on the manifestly covariant De Donder-Weyl formalism. To recover the standard noncovariant formalism without violating covariance, fields need to depend on time in a specific deterministic manner. This deterministic evolution of quantum fields is recognized as a covariant version of the Bohmian hidden-variable interpretation of QFT. The reconcilation of quantum theory with general theory of relativity is still an unsolved problem. It is very likely that the successful reconcilation requires a radical reformulation of the basic principles of relativity, or that of quantum theory, or both. One obvious difference between quantum theory and general relativity is that quantum theory, in contrast with general relativity, is an undeterministic theory. Most 1 attempts towards the reconcilation start from the assumption that quantum gravity, just as any quantum theory, should also be an undeterministic theory. However, in contrast with this mainstream quantum-undeterministic paradigm, ’t Hooft suggests
Following the view of several leading quantum-information theorists, this paper argues that quantum phenomena, including those exhibiting quantum correlations (one of their most enigmatic features), and quantum mechanics may be best understood in quantum-informational terms. It also argues that this understanding is implicit already in the work of some among the founding figures of quantum mechanics, in particular W. Heisenberg and N. Bohr, half a century before quantum information theory emerged and confirmed, and gave a deeper meaning to, to their insights. These insights, I further argue, still help this understanding, which is the main reason for considering them here. My argument is grounded in a particular interpretation of quantum phenomena and quantum mechanics, in part arising from these insights as well. This interpretation is based on the concept of reality without realism, RWR (which places the reality considered beyond representation or even conception), introduced by this author previously, in turn, following Heisenberg and Bohr, and in response to quantum information theory.
In the well known Copenhagen interpretation of Quantum mechanics, advocated by N. Bohr, the physical objects and the experimental results can be described only in a macroscopic language, leaving any possible microscopic description as unspeakable. This point of view has been deepened by C. Rovelli in the relational interpretation of Quantum mechanics. Most of the alternative interpretations, which try a detailed microscopic description of physical phenomena and of their evolution, have in common the explicit introduction of the wave function as the basic element of the theory. These interpretations require the notion of quantum state as the fundamental concept of the theory, which is the typical unspeakable physical element according to the Copenhagen interpretation. The two basic physical entities are intimately bound together by the integrity of the wave function. These interpretations are usually indicated as realistic. It is well known that the use of the wave function and its time evolution in the description of the physical processes leads unavoidably to some difficulties or so-called paradoxes. The measurement problem is at the center of these difficulties, mainly because it requires the introduction of the reduction process of the wave function, which is not included explicitly within the mathematical formalism of Quantum Mechanics. In this paper we build up and propose a model which goes beyond the standard formalism and which is able to solve the measurement problem and all the other difficulties which, in a way or in another, are related to it.