"Hot-spotting" to improve vaccine allocation by harnessing digital contact tracing technology: An application of percolation theory.

Vaccinating individuals with more exposure to others can be disproportionately effective, in theory, but identifying these individuals is difficult and has long prevented implementation of such strategies. Here, we propose how the technology underlying digital contact tracing could be harnessed to boost vaccine coverage among these individuals. In order to assess the impact of this "hot-spotting" proposal we model the spread of disease using percolation theory, a collection of analytical techniques from statistical physics. Furthermore, we introduce a novel measure which we call the efficiency, defined as the percentage decrease in the reproduction number per percentage of the population vaccinated. We find that optimal implementations of the proposal can achieve herd immunity with as little as half as many vaccine doses as a non-targeted strategy, and is attractive even for relatively low rates of app usage.

Interaction-Free Effects Between Distant Atoms.

A Gedanken experiment is presented where an excited and a ground-state atom are positioned such that, within the former's half-life time, they exchange a photon with 50% probability. A measurement of their energy state will therefore indicate in 50% of the cases that no photon was exchanged. Yet other measurements would reveal that, by the mere possibility of exchange, the two atoms have become entangled. Consequently, the "no exchange" result, apparently precluding entanglement, is non-locally established between the atoms by this very entanglement. This quantum-mechanical version of the ancient Liar Paradox can be realized with already existing transmission schemes, with the addition of Bell's theorem applied to the no-exchange cases. Under appropriate probabilities, the initially-excited atom, still excited, can be entangled with additional atoms time and again, or alternatively, exert multipartite nonlocal correlations in an interaction free manner. When densely repeated several times, this result also gives rise to the Quantum Zeno effect, again exerted between distant atoms without photon exchange. We discuss these experiments as variants of interaction-free-measurement, now generalized for both spatial and temporal uncertainties. We next employ weak measurements for elucidating the paradox. Interpretational issues are discussed in the conclusion, and a resolution is offered within the Two-State Vector Formalism and its new Heisenberg framework.

Anomalous cosmic-microwave-background polarization and gravitational chirality.

We consider the possibility that gravity breaks parity, with left and right-handed gravitons coupling to matter with a different Newton's constant and show that this would affect their zero-point vacuum fluctuations during inflation. Should there be a cosmic background of gravity waves, the effect would translate into anomalous cosmic microwave background polarization. Nonvanishing temperature-magnetic (TB) mode [and electric-magnetic mode] components emerge, revealing interesting experimental targets. Indeed, if reasonable chirality is present a TB measurement would provide the easiest way to detect a gravitational wave background. We speculate on the theoretical implications of such an observation.

The self-organization of space and time.

Self-organization is clearly relevant to biology, chemistry, Earth science, economics and other sciences that have to deal with big and complicated issues. This paper shows that self-organization also has a great deal to do with fundamental physics, including quantum mechanics, relativity, quantum gravity and cosmology. This paper also aims to give some insight into what self-organization means and discusses questions such as the kinds of methods that can be used to understand self-organization and how self-organization relates to other modes of explanation such as reductionism.

Lorentz invariance with an invariant energy scale.

We propose a modification of special relativity in which a physical energy, which may be the Planck energy, joins the speed of light as an invariant, in spite of a complete relativity of inertial frames and agreement with Einstein's theory at low energies. This is accomplished by a nonlinear modification of the action of the Lorentz group on momentum space, generated by adding a dilatation to each boost in such a way that the Planck energy remains invariant. The associated algebra has unmodified structure constants. We also discuss the resulting modifications of field theory and suggest a modification of the equivalence principle which determines how the new theory is embedded in general relativity.