By: William Brown, scientist at the Resonance Science Foundation

Water is one of the most abundant molecules in the universe, and has a simple chemical composition of two atoms of hydrogen and one atom of oxygen. However, this abundant and seemingly simple molecule underlies astonishing properties arising from the peculiar molecular and intermolecular configurations of water. Starting at the molecular configuration where the hydrogen moieties and unbonded electron pairs of the oxygen atom form a tetrahedral molecule: naively, we might assume that the simplest binding arrangement would be a linear molecule, like carbon dioxide (which as a result does not exist as a liquid and goes straight from a solid to a gas via sublimation), however in a water molecule the hydrogen atoms bind to the single oxygen atom with a specific bond angle of 104.5°. This tetrahedral configuration of the water molecule produces a partial electric-dipole, which makes water ionically interactive and...

^{Credit: Courtesy of Charles Kane}

^{By Amal Pushp, Affiliate Physicist at the Resonance Science Foundation}

Topology is a branch of mathematics concerning the properties of geometric objects and their shapes. These properties are essentially invariant under continuous deformations such as stretching, twisting, etc. Entanglement on the other hand is purely a physical phenomenon wherein two particles can influence each other instantaneously irrespective of the spatial distance between them.

In new research published in the journal Physical Review X, Charles Kane, who is the Christopher H. Browne Distinguished Professor of Physics in U. Penn's School of Arts & Sciences established a conceptual duality between topology and entanglement along with his collaborators [1].

Consider a sphere and a donut. The difference between the two lies in the fact that a donut, which has a toroidal topology, is specified by a single hole whereas there are no holes in a sphere. In this sense, a coffee mug...

By: William Brown, Biophysicist at the Resonance Science Foundation

Scientists have measured an upper-bound to the size of the Universe using the Cosmic Microwave Background (CMB) temperature gradient field [1]. The results show that the universe is most likely multiply connected, which means that it is finite, and the topology is such that it closes back in on itself—such that on the largest scale the universe has the geometry of a torus (and has a global positive curvature). This is contrary to the conventional cosmological models of the universe that model it as spatially infinite and topologically flat—assumed parameters that the researchers of the latest study demonstrate do not match the CMB temperature gradient data.

If the universe were spatially infinite and topologically flat, then the temperature fluctuations seen in the CMB would occur across all size scales—however this is not what is observed in the data. If, instead, the universe has a finite size...