## This is not an atom

The standard cartoon of an atom is incorrect. An atom is not like a tiny planetary system. Quantum mechanics is all about the wave function. Let’s observe this carefully. Continue reading This is not an atom

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# Category: Tutorial

## This is not an atom

## Proof that the square root of 2 is irrational

## The meaning of E=mc²

## Einstein’s special relativity in under 6.999 minutes for people on the move

## Rainbows: Alexander’s band

## A radioactive smoking gun

## Just a minute: how do polarized sunglasses work?

## The Eagle has landed

## Is microwave oven radiation unhealthy?

## Why, exactly, do glass and liquids refract light?

## Finding the normal force in planar non-uniform circular motion using polar coordinates

## Why do wet clothes dry?

## Deriving the volume of the inside of a sphere using spherical coordinates

## Just a minute: what is a black hole?

## Simple problems on relativistic energy and momentum

## Just a minute: how big is the universe?

## Happy birthday mister Einstein, happy Pi Day to you!

## The formula that got Albert Einstein the Nobel Prize and should stop us getting sunburn all the time

## Just a minute: why do large and heavy ships not sink?

## Mirror, mirror, what’s up with the mirror writing?

## Why your coffee does not have tides

## Just a minute: Minus minus and negative times negative

## Energy is neither fundamental nor conserved

## When and why do you multiply probabilities?

## The riddle of birthdays

## Simple problems on relativistic energy and momentum

## What is a spacetime interval?

## Deriving the Lorentz transformations from a rotation of frames of reference about their origin with real time Wick-rotated to imaginary time

## Real eigenvalues and eigenvectors of 3×3 matrices, example 3

## Real eigenvalues and eigenvectors of 3×3 matrices, example 2

## Real eigenvalues and eigenvectors of 3×3 matrices, example 1

The standard cartoon of an atom is incorrect. An atom is not like a tiny planetary system. Quantum mechanics is all about the wave function. Let’s observe this carefully. Continue reading This is not an atom

We will provide the proof that the square root of 2 is irrational through a proof of contradiction. We will show no valid ratio of integers exists. Continue reading Proof that the square root of 2 is irrational

The most famous equation may not be what you think it is. For example, it’s not about converting mass into energy. And, it’s only a part of the whole thing. Continue reading The meaning of E=mc²

Especially for people on the move, we discuss as briefly as possible the intricacies of Einstein’s special relativity. Continue reading Einstein’s special relativity in under 6.999 minutes for people on the move

The band between the primary and the secondary rainbow is darker. The area underneath the primary rainbow is lighter. We explain Alexander’s band. Continue reading Rainbows: Alexander’s band

Even physics tells us that smoking is bad. We briefly discuss what radioactivity is, what ionising radiation is, and how radioactive lungs become. Continue reading A radioactive smoking gun

We briefly discuss how polarized sunglasses work, quantum fields, pilots, and 3D cinema. Continue reading Just a minute: how do polarized sunglasses work?

We celebrate our 50th lunar anniversary. On this day, the Eagle landed. Continue reading The Eagle has landed

We discuss what electromagnetic radiation is and why ionising radiation is dangerous. We discuss how a microwave oven heats up food, and vitamins too. Continue reading Is microwave oven radiation unhealthy?

We provide a semi-in-depth look into why glass and liquids bend light. We discuss quantum fields, Maxwell’s equations, and vectors. No calculations. Continue reading Why, exactly, do glass and liquids refract light?

We find an expression for the normal force on a mass which is in planar non-uniform circular motion using polar coordinates. Continue reading Finding the normal force in planar non-uniform circular motion using polar coordinates

We discuss the second law of thermodynamics, the notion of entropy, the statistical nature of the situation, and why wet clothes dry. Continue reading Why do wet clothes dry?

Using a volume integral and spherical coordinates, we derive the formula of the volume of the inside of a sphere, the volume of a ball. Continue reading Deriving the volume of the inside of a sphere using spherical coordinates

What is a black hole? We briefly discuss the Schwarzschild radius. Continue reading Just a minute: what is a black hole?

We will focus on a few simple problems where we will manipulate Einstein’s equations for relativistic energy and momentum. Continue reading Simple problems on relativistic energy and momentum

In case your child asks how big the universe is, this is something you quickly might want to read. Continue reading Just a minute: how big is the universe?

Pi Day is the day on which we commemorate Albert Einstein’s birthday. Also, people celebrate the existence of pi. Here are some cool ways to calculate pi. Continue reading Happy birthday mister Einstein, happy Pi Day to you!

Albert Einstein didn’t win the Nobel Prize with his famous formula from the special theory of relativity. What formula did he win the Prize with then? Continue reading The formula that got Albert Einstein the Nobel Prize and should stop us getting sunburn all the time

Until they do due to a mistake, ships do not sink, not even the large and heavy ones. Now and then, textbooks say this is because of dissimilar density. Though not a a wrong statement, it is also not a fundamental one. While ships may sink to the bottom of the ocean thanks to gravity, they also float thanks to gravity. Continue reading Just a minute: why do large and heavy ships not sink?

Ever wondered why sentences, words, and letters always exclusively seem to have their left and right reversed in the mirror, while they are almost never projected upside down? Probably, because mirrors do something else than you would expect. For starters, mirrors don’t reverse left and right. Continue reading Mirror, mirror, what’s up with the mirror writing?

The moon orbits the earth and its gravity is causing the tides. But why don’t swimming pools have tides? Or a cup of coffee? Human bodies consist of water, mostly. Aren’t they tidally influenced by the moon? If you’re asking all these beautiful questions, then what you thought is causing the tides is probably wrong, and here’s why. Continue reading Why your coffee does not have tides

Minus minus is plus. And negative times negative is positive. Two negatives make a positive. You may have heard or uttered these expressions many times. Even though you will know this already, here you will find an algebraic proof, just for your reference. Requirements: simple algebra from the second year in secondary, high or grammar school. Continue reading Just a minute: Minus minus and negative times negative

Sometimes you may have heard someone say that, ‘in the end, everything is energy. Einstein himself said that mass equals energy, we are energy ourselves, light is energy, and everything in this universe is energy.’ Often, it is represented as the fundamental substance everything is made out of. And energy is conserved. Both statements are incorrect. Continue reading Energy is neither fundamental nor conserved

At high school you may have been taught that, sometimes, you have to multiply probabilities. We briefly discuss when and why you do this. Continue reading When and why do you multiply probabilities?

Probabilities can be hard to grasp. For instance, what are the chances that among a birthday party’s attendants two or more people will have their birthdays on the same day? Probably better than you might expect. Continue reading The riddle of birthdays

We will focus on a couple of simple problems where we will manipulate the equations for relativistic energy en momentum. Continue reading Simple problems on relativistic energy and momentum

Einstein and collaborators taught us that space and time are not fixed quantities. They can stretch and contract. They vary. There is one thing, though, that does not vary. It is the invariance of the spacetime interval. Continue reading What is a spacetime interval?

Well-known for their central role in Einstein’s Special Relativity, the Lorentz transformations are derived from the rotation of two frames of reference in standard configuration while time is taken to be an imaginary unit of spacetime. This is rarely seen in the wild. Not many undergraduate textbooks or online texts show the details of the working. Hence, this article. Continue reading Deriving the Lorentz transformations from a rotation of frames of reference about their origin with real time Wick-rotated to imaginary time

In these examples, the eigenvalues of matrices will turn out to be real values. In other words, the eigenvalues and eigenvectors are in real number space. Continue reading Real eigenvalues and eigenvectors of 3×3 matrices, example 3

In these examples, the eigenvalues of matrices will turn out to be real values. In other words, the eigenvalues and eigenvectors are in real number space. Continue reading Real eigenvalues and eigenvectors of 3×3 matrices, example 2

In these examples, the eigenvalues of matrices will turn out to be real values. In other words, the eigenvalues and eigenvectors are in real number space. Continue reading Real eigenvalues and eigenvectors of 3×3 matrices, example 1