KJ Runia

Reads for a joint honours degree in mathematics and theoretical physics (final year) in England, at the School of Mathematics and Statistics and the School of Physical Sciences at The Open University, Walton Hall, Milton Keynes.

Spaces and dimensions

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What do mathematicians and physicists mean with phrases like higher and/or extra dimensions? Let’s travel through a Universe of spaces and dimensions!

Quantum entanglement: the EPR paradox and Bell’s Theorem

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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

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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.

A little bit: mirror writing

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Sometimes we post a ‘little bit’ to highlight the main message of a previous article. This time it’s about mirror writing. Do mirrors switch left and right?

Is microwave oven radiation unhealthy?

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A modern kitchen with a microwave oven. Is the radiation of a microwave oven unhealthy?

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

Why, exactly, do glass and liquids refract light?

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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.

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

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

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

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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?

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

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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.

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

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We see a monkey holding a mirror and looking in it, looking at itself.

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.

Why your coffee does not have tides

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A computer-generated 3D image of a cup of coffee. The coffee, however, looks like a moderately turbulent sea. There's a tiny sailboat trying to avoid a lighthouse. All in this cup.

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.

Just a minute: Minus minus and negative times negative

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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!

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.

Energy is neither fundamental nor conserved

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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.

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.

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

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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.