This post was prompted by something written in the art magazine Universal Colours (http://www.eu-man.org/magazine/issue903.df). The article states that, “Modern science uses mathematics … for proving … suppositions in science”. Mathematics is not used to prove scientific ideas; it is used to develop new ideas from ideas that we believe to be true. This is not… Continue reading 20.1 Mathematical proof and science

Maxwell’s demon is an early example of a “thought experiment” (see post 19.26). The Scottish physicist James Clerk Maxwell thought about two samples of a gas, each containing containing fast (red in the picture) and slow (blue) molecules, separated by a wall. He supposed that the wall contained a tiny door that could be opened… Continue reading 19.30 Maxwell’s demon

My posts on quantum mechanics have made a number of statements that not everyone would agree with: That particles, like electrons, can behave as particles or waves (wave-particle duality, post 19.25) That we cannot simultaneously know the position and the energy of a particle, like an electron (Heisenberg’s uncertainty principle, post 19.26) That a wavefunction… Continue reading 19.29 Interpreting quantum mechanics

Before you read this, I suggest you read post 19.27. Schrödinger’s equation, above, describes the motion of a particle (like an electron) in terms of its wavefunction, ψ (post 18.10), and energy, E. Here ∇ is the Laplacian operator (post 19.12), m is the mass of the particle, h is Planck’s constant (post 19.19) and… Continue reading 19.28 Solving Schrödinger’s equation

Before you read this, I suggest you read posts 19.12 and 19.24. If you’ve heard of “Schrödinger’s cat”, and didn’t understand what it was about, I suggest that you forget it – it won’t help you to understand how quantum theory (post 16.2) is used to explain things. But Schrödinger’s equation is very important –… Continue reading 19.27 Schrödinger’s equation

Before you read this, I suggest you read post 19.24. The uncertainty principle is named after Werner Heisenberg (picture above), the German physicist who suggested it in 1927. Heisenberg was awarded the Nobel prize in Physics in 1932. He was the first director of the Max Planck Institute for Physics; the Max Planck Institutes are… Continue reading 19.26 Heisenberg’s uncertainty principle

Before you read this, I suggest you read posts 19.23 and 19.24. In post 19.23 we saw that electromagnetic waves (post 19.9) could behave as particles, called photons, and in post 19.24 that particles, like electrons, could behave as waves. People often try to imagine what these things are “really” like and then the first… Continue reading 19.25 Wave-particle duality

Before you read this, I suggest you read post 19.23. In post 19.23, I explained the idea that light could behave as a stream of particles, as well as being a wave. So, do particles (or any other objects) behave as waves? This question was explored by the French physicist Louis de Broglie in his… Continue reading 19.24 Electron waves

When light shines on some materials, mostly metals, electrons may be emitted. This effect is called the photoelectric effect and the electrons emitted are called photoelectrons. Presumably, light energy overcomes the energy that attracts the electrons to the atomic nuclei in the metal (post 16.29) and gives them kinetic energy (post 16.21). The moving electrons… Continue reading 19.23 Photoelectric effect and photons

Research that identifies other planets that may be capable of sustaining life sometimes leads to the suggestion that we may soon be communicating with alien life forms. Recently such a planet was identified that is 111 light years away from earth (https://www.bbc.com/news/science-environment-49648746). What is a light year? It is the distance that light travels in… Continue reading 19.22 Light years away