Category: Tutorial

Physics, Secondary ed level, Tutorial

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

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?

KJ Runia
A photoshopped image of an out-of-focus dude with a beard holding a little sphere between his thumb and index finger in front of his face. The little sphere has a plus-sign on it. There are multiple spheres floating around with a minus-sign on them. Have a lovely day today!
Mathematics, Secondary ed level, Tutorial

Just a minute: Minus minus and negative times negative

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

KJ Runia
A Hubble Space Telescope image of Galaxy cluster Abell 2537. The amount of gravity, that is, warping of spacetime, caused by this galaxy is visible through the bending of the light of stars and galaxies behind Abell. The galaxy works as a lens. All is predicted by Einstein's General Relativity.
Physics, Secondary ed level, Tutorial

Energy is neither fundamental nor conserved

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

KJ Runia
Level 1 Undergraduate, Level 2 Undergraduate, Physics, Tutorial

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

KJ Runia