The Catastrophic Consequences of Living in a Universe with a False Vacuum

Image by Kamil Szeląg from Pixabay.

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.

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A Clever Way to Quickly Take Derivatives Used by Richard Feynman

Image by Gerd Altmann from Pixabay.

Richard Feynman was an American theoretical physicist and co-recipient of the 1965 Nobel Prize in Physics (together with the American physicist Julian Schwinger and the Japanese physicist Shinichiro Tomonaga). He is one of the best-known scientists in the world. According to Wikipedia, “in a 1999 poll of 130 leading physicists worldwide by the British journal Physics World, he was ranked as one of the ten greatest physicists of all time”.

From Newton’s “Lion Claws” to the Modern Solution

Image by Gordon Johnson from Pixabay.

In June 1696, the renowned mathematician Johann Bernoulli published in the Acta Eruditorum, the first German scientific periodical, the following problem:

Given in a vertical plane two points A and B, assign to the moving [body] M, the path AMB, by means of which — descending by its own weight and beginning to be moved [by gravity] from point A — it would arrive at the other point B in the shortest time.”

It can be expressed in a more straightforward way as:

“Given two points A and B in a vertical plane, what is the curve traced out by…

An Introduction to Critical Phenomena in Physics

Image by Gerd Altmann from Pixabay.

In physics, events characterized by a significant difference in size (for example, the behavior of waves in the oceans and of their individual water molecules) have a small influence on one another (they do not communicate). Therefore we can independently study the physical properties corresponding to each order of magnitude. This scale independence is precisely what allows us to use hydrodynamics to model ocean waves, ignoring the behavior of individual water molecules. In other words, theories are only successful because physics at different scales can be modeled using different theoretical frameworks (see Wilson).

An Introduction to Cosmology and the Birth of the Universe

Image by Gerd Altmann from Pixabay.

Cosmology is the study of the dynamical behavior of the entire universe. Modern cosmology is currently dominated by the Big Bang theory, which attempts to put together in one framework (or model) astronomy and elementary particle physics. One example is the ΛCDM model (or Lambda cold dark matter model) which will be discussed in more detail below.

As its name says, this model includes many types of matter and energy such as:

Is Gravity Just an Average of the Behavior of Unknown “Atoms” of Spacetime?

Image by Bronisław Dróżka from Pixabay.

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 Space-Time Approach to Quantum Mechanics

Image by Gerd Altmann from Pixabay

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.

An Introduction to Geometrodynamics

Image by Gerd Altmann from Pixabay.

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 human-made labels, physical laws shouldn’t depend on the way they are chosen.

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:

Deriving Einstein’s Famous Mass-Energy Equivalence Formula

Image by SpaceX-Imagery from Pixabay.

The mass-energy equivalence formula E = mc² 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.

Why Moving Objects are Shortened

Image by Barbara A Lane from Pixabay.

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.

The Miracle Year

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…

Marco Tavora Ph.D.

Data Scientist | Physicist | Lover of unification, generalization & abstraction |

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