It can be hard to grasp that radio waves, deadly radiation, and the light we can see are all the same thing. How can electromagnetic (EM) radiation – photons – sometimes penetrate walls and sometimes not? How can some forms of EM radiation be perfectly safe and others damage our DNA? How can radio waves travel so much further than gamma rays in air, but no further through concrete?

It all comes down to wavelength. But before we get into that, we should at least take a glance at what EM radiation really is.

Electromagnetic radiation takes the form of two orthogonal waves. In one direction, you have an oscillating magnetic field. In the other, an oscillating electric field. Both of these fields are orthogonal to the direction of travel.

These oscillations take a certain amount of time to complete, a time which is calculated by observing the peak value of one of the fields and then measuring how long it takes for the field to return to that value. Luckily, we only need to do this once, because the time an oscillation takes (called the period) will stay the same unless acted on by something external. You can invert the period to get the frequency – the number of times oscillations occur in a second. Frequency uses the unit Hertz, which are just inverted seconds. If something has the frequency 60Hz, it happens 60 times per seconds.

EM radiation has another nifty property: it always travels at the same speed, a speed commonly called “the speed of light” [1] (even when applied to EM radiation that isn’t light). When you know the speed of an oscillating wave and the amount of time it takes for the wave to oscillate, you can calculate the wavelength. Scientists like to do this because the wavelength gives us a lot of information about how radiation will interact with world. It is common practice to represent wavelength with the Greek letter Lambda (λ).

Put in a more mathy way: if you have an event that occurs with frequency f to something travelling at velocity v, the event will have a spatial periodicity λ (our trusty wavelength) equal to v / f. For example, if you have a sound that oscillates 34Hz (this frequency is equivalent to the lowest C♯ on a standard piano) travelling at 340m/s (the speed of sound in air), it will have a wavelength of (340 m/s)/(34 s-1) = 10m. I’m using sound here so we can use reasonably sized numbers, but the results are equally applicable to light or other forms of EM radiation.

Wavelength and frequency are inversely related to each other. The higher the frequency of something, the smaller its wavelength. The longer the wavelength, the lower the frequency. I’m used to people describing EM radiation in terms of frequency when they’re talking about energy (the quicker something is vibrating, the more energy it has) and wavelength when talking about what it will interact with (the subject of the rest of this post).

With all that background out of the way, we can actually “look” at electromagnetic radiation and understand what we’re seeing.

Wavelength is very important. You know those big TV antennas houses used to have?

Turns out that they’re about the same size as the wavelength of television signals. The antenna on a car? About the same size as the radio waves it picks up. Those big radio telescopes in the desert? Same size as the extrasolar radio waves they hope to pick up.

Even things we don’t normally think of as antennas can act like them. The rod and cone cells in your eyes act as antennas for the light of this very blog post [2]. Chains of protein or water molecules act as antennas for microwave radiation, often with delicious results. The bases in your DNA act as antennas for UV light, often with disastrous results.

These are just a few examples, not an exhaustive list. For something to be able to interact with EM radiation, you just need an appropriately sized system of electrons (or electrical system; the two terms imply each other). You get this system of electrons more or less for free with metal. In a metal, all of the electrons are delocalized, making the whole length of a metal object one big electrical system. This is why the antennas in our phones or on our houses are made of metal. It isn’t just metal that can have this property though. Organic substances can have appropriately sized systems of delocalized electrons via double bonding [3].

EM radiation can’t really interact with things that aren’t the same size as its wavelength. Interaction with EM radiation takes the form of the electric or magnetic field of a photon altering the electric or magnetic field of the substance being interacted with. This happens much more readily when the fields are approximately similar sizes. When fields are the same size, you get an opportunity for resonance, which dramatically decreases the loss in the interaction. Losses for dissimilar sized electric fields are so high that you can assume (as a first approximation) that they don’t really interact.

In practical terms, this means that a long metal rod might heat up if exposed to a lot of radio waves (wavelengths for radio waves vary from 1mm to 100km; many are a few metres long due to the ease of making antennas in that size) because it has a single electrical system that is the right size to absorb energy from the radio waves. A similarly sized person will not heat up, because there is no single part of them that is a unified electrical system the same size as the radio waves.

Microwaves (wavelengths appropriately micron-sized) might heat up your food, but they won’t damage your DNA (nanometres in width). They’re much larger than individual DNA molecules. Microwaves are no more capable of interacting with your DNA than a giant would be of picking up a single grain of rice. Microwaves can hurt cells or tissues, but they’re incapable of hurting your DNA and leaving the rest of the cell intact. They’re just too big. Because of this, there is no cancer risk from microwave exposure (whatever paranoid hippies might say).

Gamma rays do present a cancer risk. They have a wavelength (about 10 picometres) that is similar in size to electrons. This means that they can be absorbed by the electrons in your DNA, which kick these electrons out of their homes, leading to chemical reactions that change your DNA and can ultimately lead to cancer.

Wavelength explains how gamma rays can penetrate concrete (they’re actually so small that they miss most of the mass of concrete and only occasionally hit electrons and stop) and how radio waves penetrate concrete (they’re so large that you need a large amount of concrete before they’re able to interact with it and be stopped [4]). Gamma rays are stopped by the air because air contains electrons (albeit sparsely) that they can hit and be stopped by. Radio waves are much too large for this to be a possibility.

When you’re worried about a certain type of EM radiation causing cancer, all you have to do is look at its wavelength. Any wavelength smaller than that of ultraviolet light (about 400nm) is small enough to interact with DNA in a meaningful way. Anything large is unable to really interact with DNA and is therefore safe.

Epistemic Status: Model. Looking at everything as antenna will help you understand why EM radiation interacts with the physical world the way it does, but there is a lot of hidden complexity here. For example, eyes are far from directly analogous to antennas in their mechanism of action, even if they are sized appropriately to be antennas for light. It’s also true that at the extreme ends of photon energy, interactions are based more on energy than on size. I’ve omitted this in order to write something that isn’t entirely caveats, but be aware that it occurs.

##### Footnotes:

[1] You may have heard that the speed of light changes in different substances. Tables will tell you that the speed of light in water is only about ¾ of the speed of light in air or vacuum and that the speed of light in glass is even slower still. This isn’t technically true. The speed of light is (as far as we know) cosmically invariant – light travels the same speed everywhere in the galaxy. That said, the amount of time light takes to travel between two points can vary based on how many collisions and redirections it is likely to get into between two points. It’s the difference between how long it takes for a pinball to make its way across a pinball table when it hits nothing and how long it takes when it hits every single bumper and obstacle. ^

[2] This is a first approximation of what is going on. Eyes can be modelled as antennas for the right wavelength of EM radiation, but this ignores a whole lot of chemistry and biophysics. ^

[3] The smaller the wavelength, the easier it is to find an appropriately sized system of electrons. When your wavelength is the size of a double bond (0.133nm), you’ll be able to interact with anything that has a double bond. Even smaller wavelengths have even more options for interactions – a wavelength that is well sized for an electron will interact with anything that has an electron (approximately everything). ^

[4] This interaction is actually governed by quantum mechanical tunneling. Whenever a form of EM radiation “tries” to cross a barrier larger than its wavelength, it will be attenuated by the barrier. The equation that describes the probability distribution of a particle (the photons that make up EM radiation are both waves and particles, so we can use particle equations for them) is approximately  (I say approximately because I’ve simplified all the constants into a single term, k), which becomes  (here I’m using k1 to imply that the constant will be different), the equation for exponential decay, when the energy (to a first approximation, length) of the substance is higher than the energy (read size of wavelength) of the light.

This equation shows that there can be some probability – occasionally even a high probability – of the particle existing on the other side of a barrier.  All you need for a particle to traverse a barrier is an appropriately small barrier. ^

# An Update on a Prediction

Back in February, I predicted that the slew of scandals Trudeau was facing wouldn’t decrease his approval ratings. To put numbers on this, I gave my confidence intervals for Trudeau’s approval ratings in April.

Thanks to the “Leader Meter“, it’s easy for me to check up on how Trudeau is doing. As of right now, the most recent poll has him at 48% approval (this is conveniently the first poll since April 1st, making it useful for the purposes of checking my prediction), while Éric Grenier’s model has him at 50.6% approval.

Both of these are within all three probability intervals I offered. In addition, Trudeau was polling higher in March than he was in February, further evidence that the scandals in February (and the abandonment of electoral reform) haven’t hurt his popularity.

I continue to believe that the erosion of political norms around scandals during Steven Harper’s time in office has played a large role in Trudeau’s enduring popularity.

# On Low-Income Voters and Self-Interest

Neil McDonald’s new column points out that Trump’s low-income supporters voted against their own economic self-interest. This presents a fine opportunity for Mr. McDonald to lecture those voters about how bad Trump’s policies will be for them, as if they couldn’t have figured it out themselves.

I say: some of Trump’s supporters voted against their own self-interest? So what? Hillary Clinton’s well-off supporters, from Sam Altman, to many of my friends in the Bay Area did as well.

Back in Canada, I have even more examples of people who voted against their self-interest. They include myself, Mr. McDonald (in all likelihood), a bevy of well off technologists and programmers, and a bunch of highly educated students who expect to start high-paying jobs before the next election.

Just like Trump’s lower-income voters, we knew what we were getting into. We understood that we were voting for higher taxes for people like us. We voted for higher taxes because we like the things taxes buy – infrastructure, social services, and science funding, to name a few.

I have no doubt Mr. McDonald would understand this. But when it comes to low-income voters putting their aspirations for their country above their self-interest, he’s flabbergasted.

Americans are raised to believe that anything is possible in America if you are pure of heart and willing to work hard, which is nonsense, and that anyone can become president, which is even more foolish, and that free markets always make the right decision, which is nuts.

They are told that rugged individualism is the American way, which it isn’t, and that government is never the solution, which it sometimes most definitely is.

Mr. McDonald forgot to wonder if the people voting for Trump might desperately want these things to be true. What if the people he’s talking about really wanted everything he listed to be true and saw voting for Trump as their best chance to make them reality? What if they understood what they might lose and chose to vote anyway? Why should he believe they’re less likely to evaluate the consequence of a vote than he is? If any of these are true, are these voters still sheep led astray by right-wing politicians? Or are the politicians just responding to a real demand from their constituents?

These are the sorts of questions I’d like to see journalists who want to write about people – especially low-income people – voting against their economic self-interest grapple with.

It’s certainly unlikely that Mr. Trump will be able to deliver everything his supporters hope he will or everything he’s promised. That makes him a liar, or more charitably, overambitious. It doesn’t make his followers worthy of scorn for the simple act of voting for the type of society they wanted.

I would like to note that I view many of Trump’s policies as wrong-headed and profoundly lacking in compassion. I have no objections to someone scorning Trump voters because those voters seem to prefer fear to compassion and division to equity. I simply object to the hypocrisy of journalists mocking low-income Republicans for the same actions for which they lionize well-off Democrats (replace with Conservatives and Liberals if you’re in Canada and it still holds).

Why should people vote for their economic self-interest anyway? Sure, studies show that money totally can buy happiness, but it’s not the only thing that can. You can also become happy by living in a place that embodies your values. What left-wing think pieces criticizing the poor for voting against their interests miss is that this is true no matter how much money you make.

Here’s one theory of political consensus: if everyone votes for the policies that will be most to their own economic benefit, we’ll end up with compromise policies that tend to economically benefit everyone reasonably well. Here’s a different take: if everyone votes for the type of country they want to live in, we’ll end up with a country that fits everyone’s preferences reasonably well.

If you look at the exit poll data, it looks like people are pursuing a mix of these two strategies. Hillary Clinton won among people making less than \$50,000 per year and Donald Trump won among people making more. While this may look like people are mainly voting in their economic interest, all of these margins were remarkably thin and notably much smaller than they were in the last election cycle. This could be indicative of more and more people voting aspirationally, rather than economically.

One interesting tidbit for Mr. McDonald though – if you look at the exit poll data, it turns out low income voters are the ones least likely to vote against their own self-interest.