Related papers: Reply to "A Comment on Singularities in Quantum Co…
We review the application of the consistent (or decoherent) histories formulation of quantum theory to canonical loop quantum cosmology. Conventional quantum theory relies crucially on "measurements" to convert unrealized quantum…
The initial conditions of our universe appear to us in the form of a classical probability distribution that we probe with cosmological observations. In the current leading paradigm, this probability distribution arises from a quantum…
Current theories of particle physics lead to the unavoidable conclusion that there must have been several phase transitions in the early universe. Further, in the context of these theories, it is possible that cosmological phase transitions…
Without wasting time and effort on philosophical justifications and implications, we write down the conditions for the Hamiltonian of a quantum system for rendering it mathematically equivalent to a deterministic system. These are the…
Classical defects (monopoles, vortices, etc.) are a characteristic consequence of many phase transitions of quantum fields. Most likely these include transitions in the early universe and such defects would be expected to be present in the…
The concept of correlation appears straightforward: measurement outcomes coincide, and patterns emerge. For any record of events, the coefficients are uniquely determined. Thus, if correlations change spontaneously, as seen in quantum…
As time passes, once simple quantum states tend to become more complex. For strongly coupled k-local Hamiltonians, this growth of computational complexity has been conjectured to follow a distinctive and universal pattern. In this paper we…
A recent claim by Bassi and Ghirardi that the consistent (decoherent) histories approach cannot provide a realistic interpretation of quantum theory is shown to be based upon a misunderstanding of the single-framework rule: they have…
Spacetime singularities in general relativity are commonly thought to be problematic, in that they signal a breakdown in the theory. We address the question of how to interpret this breakdown, restricting our attention to classical…
We argue that the conventional quantum field theory in curved spacetime has a grave drawback: The canonical commutation relations for quantum fields and conjugate momenta do not hold. Thus the conventional theory should be denounced and the…
We compare classical and quantum dynamics of a particle in the de Sitter spacetimes with different topologies to show that the result of quantization strongly depends on global properties of a classical system. We present essentially…
In his constructive and well-informed commentary, Andrei Khrennikov acknowledges a privileged status of classical probability theory with respect to statistical analysis. He also sees advantages offered by the Contextuality-by-Default…
Determining the initial state of the universe is a challenging problem in quantum cosmology and we argue that the issue is intractable if the basic postulates of quantum mechanics are not modified in a nontrivial way. Namely a "standard"…
General relativity allows a variety of future singularities to occur in the evolution of the universe. At these future singularities, the universe will end in a singular state after a finite proper time and geometrical invariants of the…
Quantum mechanics forces us to reconsider certain aspects of classical causality. The 'central mystery' of quantum mechanics manifests in different ways, depending on the interpretation. This mystery can be formulated as the possibility of…
In a previous paper [9], we proved the following singularity theorem applicable to cosmological models with a positive cosmological constant: if a four-dimensional spacetime satisfying the null energy condition contains a compact Cauchy…
A direct classical analog of quantum decoherence is introduced. Similarities and differences between decoherence dynamics examined quantum mechanically and classically are exposed via a second-order perturbative treatment and via a strong…
We review recent work on the existence and nature of cosmological singularities that can be formed during the evolution of generic as well as specific cosmological spacetimes in general relativity. We first discuss necessary and sufficient…
General relativity is a background-independent theory of a dynamical classical spacetime geometry. Quantum theory is formulated in a classical spacetime, as an intrinsically probabilistic, contextual theory of non-classical, interfering…
We show that a class of finite quantum non-local gravitational theories is conformally invariant at classical as well as at quantum level. This is actually a range of conformal anomaly-free theories in the spontaneously broken phase of the…