A tutorial on the “three polarizer paradox”. Actually the stuff we see in this tutorial won’t be all that paradoxical, just a little unexpected perhaps. The real “paradox” will emerge in the next tutorial when we look at photons. Nevertheless, we need to know how things look classically before we start messing about with semi-hypothetical particles …
A tutorial on Malus’ law and where it comes from. Malus’ law enables us to predict how the intensity of a beam of polarized light will change as it passes through polarizing filters. Even if basic old optical laws don’t interest you, it’s worth studying this stuff, since we’re going to move on to looking at how this whole thing works when we start claiming that light is made up of photons, which is going to be quite interesting.
This is the first tutorial I’ve published in a while … thanks for your patience if you’ve been waiting for it, and many thanks to those few who emailed me and asked when the next tutorial was due!
How the energy carried by a wave relates to its electric field strength.
A tutorial on angular frequency in the plane wave equation.
In this tutorial we’ll look at the wave number; which is the name given to the constant k in the plane wave equation. Wave number turns out to have a pretty simple physical significance.
It’s interesting to model the electric component of EM radiation as a plane wave. Although this isn’t a fully realistic model and neglects such important aspects as electric flux density, nevertheless it captures some aspects of light and it’ll get us started with waves, which there is going to be a lot more of later on.
How light came to be thought of as consisting of electric and magnetic fields, and the history of the strange relationship between electric and magnetic fields.
Light is made up of magnetic fields and electric fields, intertwined — at least from a certain point of view. While every child knows what a magnetic field is, sort of, less know what an electric field is, even though they are just as easy to demonstrate. We’ll look at electric fields in this tutorial.
Since light is, from a certain point of view, made up of electric and magnetic fields, it behoves us to study them a little. This is a tutorial on the history and mysterious nature of magnetic fields. Next time we’ll look at electric fields, before putting the two together.
Stuff that moves has energy by virtue of the fact that it’s moving. Although it’s hard to say what energy really is, we know it when we see it, and movement definitely counts. In this tutorial we’ll do a little bit of algebra to get from our basic definition of energy to figuring out how much energy a moving thing has, exactly. This is really going to help a lot when we get on to looking at light and photons. Honest.
Before we start looking at light, let’s break down some of the key concepts involved in understanding light. We’ll start here with energy; a term that is rigorously defined in physics and yet nevertheless impossible to fully grasp. In fact, it’s surprising how many things in physics, or indeed in life, are possible to define and yet impossible to grasp. At least being able to define a thing is better than bandying about words without having any clear agreed definition — we’ll leave that to philosophers. At least for now.
Photos are weird. Fact. Once we start thinking that light is made up of photons, we’re left with some pretty strange conundrums just as soon as we start to think it through. It’s almost enough to make you give up and start arguing that photons don’t exist …. except that they’re so darned useful. By considering the weird nature of polarized photons, we can start to see what kind of mathematical theorem we might be looking for exactly, when we’re trying to formulate a mechanics of the quantum realm.
The physicist Michio Kaku on free will:
I came across this short video on YouTube and couldn’t resist posting it. To be honest, the fact that Michio Kaku would defend free will surprises me. I had him pegged (for no reason but idle prejudice) as a “free will is an illusion” guy.
In this video he doesn’t really bring out the aspect of quantum physics which is really the most supportive of the whole idea of free will, though. He talks about randomness, and it’s true that the random nature of small things shows us that there is no iron mechanism that determines our actions, as some (such as Susan Blackmore) seem to think. But of course it’s still possible to argue that, if small things behave in a random fashion, that still doesn’t mean they are guided by some mysterious “will”.
We need to dig deeper into QM (quantum mechanics) to understand why it leaves the door wide open for free will without conflicting in any way with the known laws of physics. The behaviour of small objects seems to depend on the actual observations that we choose to make, and that’s what’s really so interesting about QM.
Quantum physics is an incomplete science, and I just know this article is going to come across as me searching for loopholes in physics that would allow free will, when in actual fact the case for free will is far stronger than it might initially appear from this brief summary.
What can I say? I can only implore you to check out the Quantum Mindcast, where I’ll be explaining episode by episode why the world is not quite as it appears and why we really do have free will.
A tutorial on polarized light. Polarized light behaves according to rules that we could think of as belong to classical physics. Nothing too weird happens, and we can make concrete predictions about future observations on the same ray of light. But don’t worry, things are going to get very crazy when we start to look at photos in the next tutorial. This tutorial just paves the way for the vile monstrous insanity that is to follow.
A tutorial on observables and compatibility, using some examples drawn from every day life.
When we’re looking at very small objects, we can’t observe them without disturbing them. The process of measuring the value of a property that we consider them to have, becomes an active process that causes them to manifest that property — a bit like measuring how violent a person is by punching him in the face and seeing if he attacks you or not. One side effect of this is that often measuring one “observable” will disturb the measurement of another observable, in which case we say the two observables are incompatible.
The Quantum Mindcast is here: a podcast about consciousness and quantum physics.
In this episode:
The world is a projection of the mind – Introducing the Quantum Mindcast – The mind-body problem – Why there’s little point discussing stuff like telepathy – Schrödinger’s Paradox – Are we machines? – How the brain works – Three common responses to the mind-body problem – Philosophical zombies – We don’t need to throw rationality out the window.
Featured music: Illumination by Action Davis, featuring Emmalyne Braswell
Note: Francis Crick apparently died in 2004. His work, however, lives on.
A lightning overview of what quantum mechanics is about, when it started and why it’s worth looking at.