One of the most profound insights of modern physics is called *duality. *Dualities were at the core of several breakthroughs in fundamental physics, considerably changing how physicists think about fundamental principles. Moreover, they provided unexpected mathematical results that are likely to help developing several branches of that subject, possibly for decades.

They also have identified completely unforeseen connections, thus eliminating previously hidden redundancies in physical theories. In the words of Joseph Polchinski (1954–2018), one of the preeminent physicists of the past 50 years (see link), “the existence of dualities points to a great unity in the structure of theoretical physics.”

Emergent gravity is an idea in quantum gravity according to which the fabric of spacetime *is not fundamental *but *emerges* as a coarse-graining approximation of underlying (still unknown) microscopic degrees of freedom (similarly to a gas emerging from a large sampling of atoms or molecules). In the words of Huggett and Wuthrich, emergent gravity is the view that gravity arises due to the “collective action of the dynamics of more fundamental non-gravitational degrees of freedom.”

The American theoretical physicist Richard Feynman is one of the best-known scientists in the world (see this link). Feynman made several contributions to theoretical physics. These include: a new formulation of quantum mechanics using path integrals, the theory of quantum electrodynamics (including the development of his famous pictorial representations known as Feynman diagrams), his contributions to the explanation of the phenomenon of superfluidity of supercooled liquid helium, and his pioneering work in quantum computing and nanotechnology. In 1965, he was one of the recipients of the Nobel Prize in Physics.

A vacuum is a space with as little energy in it as possible. However, a vacuum is not entirely empty. It contains quantum fields. Quantum fields are obtained after the quantization of classical fields, which are functions of spacetime coordinates (such as, for example, the electromagnetic field). Mathematically quantum fields are operator-valued functions of space and time.

In Albert Einstein’s original formulation of general relativity (his theory of gravity), the fundamental field is the metric tensor ** g **and the theory is covariant in spacetime. Covariance (more precisely general covariance) “consists of the invariance of the form of physical laws under arbitrary coordinate transformations.” The idea is that since coordinates are only

In general relativity, the action (“an attribute of the dynamics of a system from which its equations of motion can be derived”) is called Einstein–Hilbert action:

The mass-energy equivalence formula *E* = *mc*² defines a relationship between the mass *m* and the energy *E* of a body in its rest frame (the rest frame is the frame of reference where the body is at rest). The square of the speed of light is an enormous number, and therefore a small amount of rest mass is associated with a tremendous amount of energy.

Length contraction is the relativistic phenomenon where the length of a moving object is measured to be shorter than in its rest frame. It occurs only in the direction of motion, and its effect is significant only when the object is moving at speeds close to the speed of light.

In 1905, while still working as an assistant examiner at the Federal Office for Intellectual Property in Bern, Albert Einstein published four revolutionary papers in the scientific journal *Annals of Physics** *(*Annalen der Physik*). In our article, we will be interested specifically in one of those papers, namely, *On the…*

Superfluidity is a property of some fluids to flow apparently without any viscosity (with constant kinetic energy). Examples of superfluids include helium-3 (or ³He) and helium-4 (or ⁴He). For temperatures below 2.17 K, helium-4 becomes a superfluid. Helium-3 becomes a superfluid only below 0.0025 K. Also, when superfluids are stirred, they form vortices that “rotate indefinitely” (see Fig. 1). The appearance of the superfluid phase in ⁴He, which is a boson, is related to Bose condensation, where a macroscopic fraction of the atoms occupies the lowest-energy state. The mechanism that generates the superfluid behavior in ³He is different since ³He…

The discovery of the form of the tautochrone, “the curve for which the time taken by an object sliding (without friction) in a uniform gravitational field to its lowest point is independent of its starting point,” was made in 1659 by the Dutch physicist, mathematician, astronomer, and inventor Christiaan Huygens. Huygens is widely regarded as one of the greatest scientists in history.

In this article, I will consider the problem of finding the shape of the free surface of the water inside a half-full bucket rotating with constant angular speed. Since I will work with systems moving with speeds much smaller than the speed of light, relativistic effects can be safely neglected. The derivation will be based on the Newtonian laws of motion, first enunciated in Newton’s *magnum opus*, the *Principia*.

The *Principia* was first published in 1687, followed by two expanded editions in 1713 and 1726. An American edition appeared in 1846. …

I’m a physicist. For me, nothing is more magical than uncovering connections between domains of knowledge that seem, at first, to be entirely unrelated.