Equivalence of Approaches to Relational Quantum Dynamics in Relativistic Settings

We have previously shown that three approaches to relational quantum dynamics—relational Dirac observables, the Page-Wootters formalism and quantum deparametrizations—are equivalent. Here we show that this “trinity” of relational quantum dynamics holds in relativistic settings per frequency superselection sector. Time according to a clock subsystem is defined via a positive operator-valued measure (POVM) that is covariant with respect to the group generated by its (quadratic) Hamiltonian. This differs from the usual choice of a self-adjoint clock observable conjugate to the clock momentum. It also resolves Kuchař's criticism that the Page-Wootters formalism yields incorrect localization probabilities for the relativistic particle when conditioning on a Minkowski time operator. We show that conditioning instead on the covariant clock POVM results in a Newton-Wigner type localization probability commonly used in relativistic quantum mechanics. By establishing the equivalence mentioned above, we also assign a consistent conditional-probability interpretation to relational observables and deparametrizations. Finally, we expand a recent method of changing temporal reference frames, and show how to transform states and observables frequency-sector-wise. We use this method to discuss an indirect clock self-reference effect and explore the state and temporal frame-dependence of the task of comparing and synchronizing different quantum clocks.

Fixing the non-relativistic expansion of the 1PM potential

We obtain a first order post-Minkowskian two-body effective potential whose post-Newtonian expansion directly reproduces the Einstein-Infeld-Hoffmann potential. Post-Minkowskian potentials can be extracted from on-shell scattering amplitudes in a quantum field theory of scalar matter coupled to gravity. Previously, such potentials did not reproduce the Einstein-Infeld-Hoffmann potential without employing a suitable canonical transformation. In this work, we resolve this issue by obtaining a new expression for the first-order post-Minkowskian potential. This is accomplished by exploiting the reference frame dependence that arises in the scattering amplitude computation. Finally, as a check on our result, we demonstrate that our new potential gives the correct scattering angle.

Minimal Frames and Transparent Frames for Risk, Time, and Uncertainty

Behavior differs between transparent and nontransparent presentations of decisions, but “transparent presentation” has not been precisely defined. We formally define “transparent frames” for risk and time, establish their uniqueness, provide algorithms for constructing them, and compare them with “standard” presentation formats. A logic emerges for predicting systematic shifts in choice under risk and over time, and how violations of rational choice theory will depend on frames. An experiment verifies most of those predictions in choice under risk. We extend results to choice under uncertainty and also predict frame dependence of ambiguity aversion, a result supported by recent experimental evidence. This paper was accepted by Elke Weber, judgment and decision making.

Inflation in f(R,ϕ) Gravity with Exponential Model

We are taking action of f(R) gravity with a nonminimal coupling to a massive inflaton field. A f(R,ϕ) model is chosen which leads to the scalar-tensor theory which can be transformed to Einstein frame by conformal transformation. To avoid the vagueness of the frame dependence, we evaluate the exact analytical solutions for inflationary era in Jordan frame and find a condition for graceful exit from inflation. Furthermore, we calculate the perturbed parameters (i.e., number of e-folds, slow-roll parameters, scalar and tensor power spectra, corresponding spectral indices, and tensor to scalar ratio). It is showed that the tensor power spectra lead to blue tilt for this model. The trajectories of the perturbed parameters are plotted to compare the results with recent observations.