Vacuum energy: Quantum hydrodynamics vs. quantum gravity

We compare quantum hydrodynamics and quantum gravity. They share many common features. In particular, both have quadratic divergences, and both lead to the problem of the vacuum energy, which, in quantum gravity, transforms to the cosmological constant problem. We show that, in quantum liquids, the vacuum energy density is not determined by the quantum zero-point energy of the phonon modes. The energy density of the vacuum is much smaller and is determined by the classical macroscopic parameters of the liquid, including the radius of the liquid droplet. In the same manner, the cosmological constant is not determined by the zero-point energy of quantum fields. It is much smaller and is determined by the classical macroscopic parameters of the Universe dynamics: the Hubble radius, the Newton constant, and the energy density of matter. The same may hold for the Higgs mass problem: the quadratically divergent quantum correction to the Higgs potential mass term is also cancelled by the microscopic (trans-Planckian) degrees of freedom due to the thermodynamic stability of the whole quantum vacuum.     

Bohm's quantum potentials and quantum gravity

A generally covariant theory, written in the spirit of Bohm's theory of quantum potentials, which applies to spinless, non interacting, gravitating systems, is formulated. In this theory the quantum state is coupled to the metric tensor g, and the effect of the quantum potential is absorbed in the geometry. At the same time, satisfies a covariant wave equation with respect to the very same g. This provides sufficient constraints to derive 11 coupled equations in the 11 unknowns: and the components of the metric tensor g_µv. The states of stable localized particles are identified, and vacuum-state solutions for both the Euclidean and the Lorentzian case are explicitly presented.     

Time and quantum gravity

The role of time in the interpretation of quantum mechanics and quantum gravity are analyzed, and changes to the form of quantum gravity to make it interpretable are suggested.     

Logics and quantum gravity

We consider the logic needed for models of quantum gravity, taking as our starting point a simple pregeometric toy model based on graph theory. First a discussion of quantum logic seen in the light of canonical quantum gravity is given, then a simple toy model is proposed and the logical structure underlying it exposed. It is then shown that this logic is nonclassical and in fact contains quantum logics as special cases. We then go on to show how Yang-Mills theory and quantum mechanics fits in. A single mathematical structure is proposed capable of containing all these subjects in a natural and elegant way. Causality plays an important role. The mere presence of a causal relation almost inevitably yields this kind of logic.     

Quantum integrals of motion and gravity wave experiment: Measurements in pure quantum states

Quantum limitations arising in measurements of a classical force acting on a quantum harmonic oscillator are studied in connection with the problem of increasing the sensitivity of gravity wave experiments. The physical nature of possible limits of sensitivity is elucidated. It originates in a degree of an uncertainty of an observable used for detecting an external force. This uncertainty can be made as small as desired for all moments of time for the observables corresponding to quantum integrals of motion. Advantages of integrals of motion with continuous spectra (like the operator of the initial coordinate) over integrals with discrete spectra (like energy) are discussed. An example of an observable suitable for exact continuous measurements of an external force independently on the initial state of the system—the difference link operator—is given. The general rule for constructing such “optimal observables” can be derived from the quantum optimal filtration theory. It is shown using Ehrenfest's theorem that no quantum limitations exist in principle for the accuracy of measurements of an external classical force acting on an arbitrary quantum system: limitations can appear only due to nonadequate measuring procedures. The general problem of finding the initial quantum states possessing the best sensitivity to an external force is formulated. The parametrically excited oscillator is briefly discussed, and it is shown that measuring the suitable integral of motion one can achieve the great gain in sensitivity. The role of quantum interference effects is emphasized.     

Continuum-regularized quantum gravity

The recent continuum regularization ofd-dimensional Euclidean gravity is generalized to arbitrary power-law measure and studied in some detail as a representative example of coordinate-invariant regularization. The weak-coupling expansion of the theory illustrates a generic geometrization of regularized Schwinger-Dyson rules, generalizing previous rules in flat space and flat superspace. The rules are applied in a non-trivial explicit check of Einstein invariance at one loop: The cosmological counterterm is computed and its contribution is included in a verification that the graviton mass is zero.     

Quantum gravity and dark matter

We propose a connection between global physics and local galactic dynamics via quantum gravity. The salient features of cold dark matter (CDM) and modified Newtonian dynamics (MOND) are combined into a unified scheme by introducing the concept of MONDian dark matter which behaves like CDM at cluster and cosmological scales but emulates MOND at the galactic scale.     

Foundational problems in quantum gravity and quantum cosmology

The conventionalistically based instrumentalist epistemology and methodology underlying the various approaches to the quantization of gravity is contrasted with the operationally based logical analysis practiced by the founders of relativity theory and quantum mechanics in developing their respective disciplines. The foundational problems to which they give rise are described. Their origins are traced to instrumentalist practices which have been in the past the objects of criticisms by Dirac, Heisenberg, Born, and others, but which have nevertheless prevailed in relativistic quantum physics after the emergence of the conventional renormalization program. The operationally based premises of a recently developed geometro-stochastic approach to the quantization of gravity are analyzed. It is shown that their roots lie in the epistemology adopted by the founders of relativity theory and quantum mechanics, and that they reflect a conceptualization of quantum reality which offers the possibility of a resolution of the main foundational problems encountered by the other approaches to quantum gravity.     

Einstein gravity emerging from quantum Weyl gravity

We advocate a conformal invariant world described by the sum of the Weyl, Dirac, and Yang-Mills action. Quantum fluctuations bring back Einstein gravity so that the long-distance phenomenology is as observed. Formulas for the induced Newton's constant and Eddington's constant are derived in quantized Weyl gravity. We show that the analogue of the trace anomaly for the Weyl action is structurally similar to that for the Yang-Mills action.