A Bayesian View on the Dr. Evil Scenario.

In Defeating Dr. Evil with Self-Locating Belief, Adam Elga proposes and defends a principle of indifference for self-locating beliefs: if an individual is confident that his world contains more than one individual who is in a state subjectively indistinguishable from his own, then he should assign equal credences to the hypotheses that he is any one of these individuals. Through a sequence of thought experiments, Elga in effect claims that he can derive the credence function that should apply in such situations, thus justifying his principle of indifference. Here we argue, using a Bayesian approach, that Elga's reasoning is circular: in analyzing the third of his thought experiments, he uses an assertion that is justifiable only if one assumes, from the start, the principle of indifference that he is attempting to justify. We agree with Elga that the assumption of equal credences is a very reasonable principle, in the absence of any reason to assign unequal credences, but we do not agree that the equality of credences can be so derived.

Cosmic Bell Test Using Random Measurement Settings from High-Redshift Quasars.

In this Letter, we present a cosmic Bell experiment with polarization-entangled photons, in which measurement settings were determined based on real-time measurements of the wavelength of photons from high-redshift quasars, whose light was emitted billions of years ago; the experiment simultaneously ensures locality. Assuming fair sampling for all detected photons and that the wavelength of the quasar photons had not been selectively altered or previewed between emission and detection, we observe statistically significant violation of Bell's inequality by 9.3 standard deviations, corresponding to an estimated p value of ≲7.4×10^{-21}. This experiment pushes back to at least ∼7.8 Gyr ago the most recent time by which any local-realist influences could have exploited the "freedom-of-choice" loophole to engineer the observed Bell violation, excluding any such mechanism from 96% of the space-time volume of the past light cone of our experiment, extending from the big bang to today.

Cosmic Bell Test: Measurement Settings from Milky Way Stars.

Bell's theorem states that some predictions of quantum mechanics cannot be reproduced by a local-realist theory. That conflict is expressed by Bell's inequality, which is usually derived under the assumption that there are no statistical correlations between the choices of measurement settings and anything else that can causally affect the measurement outcomes. In previous experiments, this "freedom of choice" was addressed by ensuring that selection of measurement settings via conventional "quantum random number generators" was spacelike separated from the entangled particle creation. This, however, left open the possibility that an unknown cause affected both the setting choices and measurement outcomes as recently as mere microseconds before each experimental trial. Here we report on a new experimental test of Bell's inequality that, for the first time, uses distant astronomical sources as "cosmic setting generators." In our tests with polarization-entangled photons, measurement settings were chosen using real-time observations of Milky Way stars while simultaneously ensuring locality. Assuming fair sampling for all detected photons, and that each stellar photon's color was set at emission, we observe statistically significant ≳7.31σ and ≳11.93σ violations of Bell's inequality with estimated p values of ≲1.8×10^{-13} and ≲4.0×10^{-33}, respectively, thereby pushing back by ∼600 years the most recent time by which any local-realist influences could have engineered the observed Bell violation.

Inflationary cosmology: exploring the universe from the smallest to the largest scales.

Understanding the behavior of the universe at large depends critically on insights about the smallest units of matter and their fundamental interactions. Inflationary cosmology is a highly successful framework for exploring these interconnections between particle physics and gravitation. Inflation makes several predictions about the present state of the universe-such as its overall shape, large-scale smoothness, and smaller scale structure-which are being tested to unprecedented accuracy by a new generation of astronomical measurements. The agreement between these predictions and the latest observations is extremely promising. Meanwhile, physicists are busy trying to understand inflation's ultimate implications for the nature of matter, energy, and spacetime.

Inflationary spacetimes are incomplete in past directions.

Many inflating spacetimes are likely to violate the weak energy condition, a key assumption of singularity theorems. Here we offer a simple kinematical argument, requiring no energy condition, that a cosmological model which is inflating--or just expanding sufficiently fast--must be incomplete in null and timelike past directions. Specifically, we obtain a bound on the integral of the Hubble parameter over a past-directed timelike or null geodesic. Thus inflationary models require physics other than inflation to describe the past boundary of the inflating region of spacetime.