Complex numbers: an introduction
We will leave the domain of real numbers behind us and start exploring the plane of complex numbers. An introduction to a realm beyond imagination.
Level 1 Undergraduate
Heisenberg’s uncertainty principle
Heisenberg’s uncertainty principle is famous in quantum mechanics. However, it doesn’t have its roots in quantum mechanics. Let’s look at Fourier transform pairs.
Quantum entanglement: the EPR paradox and Bell’s Theorem
Einstein didn’t like that quantum entanglement seemed to imply information travelling faster than the speed of light. We discuss Bell’s Theorem.
Quantum entanglement: non-locality and the state of a two-particle system
In this two-parter, we discuss quantum entanglement, non-locality, and some mathematics. In the next post, we discuss the EPR paradox and Bell’s Theorem.
Lab centrifuges and prime numbers
Lab centrifuges are crucial in e.g. coronavirus research. It’s vital the test tubes are balanced. There is an easy method to know if that’s possible.
Finding the normal force in planar non-uniform circular motion using polar coordinates
We find an expression for the normal force on a mass which is in planar non-uniform circular motion using polar coordinates.
Why do wet clothes dry?
We discuss the second law of thermodynamics, the notion of entropy, the statistical nature of the situation, and why wet clothes dry.
The formula that got Albert Einstein the Nobel Prize and should stop us getting sunburn all the time
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?
What is a spacetime interval?
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.
Deriving the Lorentz transformations from a rotation of frames of reference about their origin with real time Wick-rotated to imaginary time
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.