Model, Physics, Science

Understanding Radiation via Antennas

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).

lambda class shuttle from star wars
Not that type of lambda. Image Credit: Marshal Banana on Flickr

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.

animated gif showing oscillating magnetic and electric fields orthogonal to direction of travel
Here wavelength is labeled with “λ”, the electric field is red and labelled with “E” and the magnetic field is blue and labelled with “B”. “B” is the standard symbol for magnetic fields, for reasons I have never understood. Image Credit: Lookang on Wikimedia Commons.

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

picture of house with old fashioned aerial antenna
Image Credit: B137 on Wikimedia Commons

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.

image of the VLA radio telescopes
Fun fact: these dishes together make up a very large radio telescope, unimaginatively called the “Very Large Array”. Image Credit: Hajor on Wikimedia Commons

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.


[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. ^

Ethics, Philosophy

Utilitarianism: An Overview

What is a utilitarian?

To answer that question, you have to think about another, namely: “what makes an action right?”

Is it the outcome? The intent? What is a good intent or a good outcome?

Kantian deontologists have pithy slogans like: ” I ought never to act except in such a way that I could also will that my maxim should become a universal law” or “an action is morally right if done for duty and in accordance to duty.

Virtue ethicists have a rich philosophical tradition that dates back (in Western philosophy) to Plato and Aristotle.

And utilitarians have math.

Utilitarianism is a subset of consequentialism. Consequentialism is the belief that only the effects of an action matter. This belief lends itself equally well to selfish and universal ethical systems.

When choosing between two actions, selfish consequentialist (philosophers and ethicists would call such a person an egoist) would say that the morally superior action is the one that brings them the most happiness.

Utilitarians would say that the morally superior option is the one that brings the most ______ to the world/universe/multiverse, where ______ is whatever measure of goodness they’ve chosen. The fact that the world/universe/multiverse is the object of optimization is where the math comes in. It’s often pretty hard to add up any measure of goodness over a set as large as a world/universe/multiverse.

It’s also hard to define goodness in abstract without lapsing into tautology (“how does it represent goodness?” – “well it’s obvious, it’s the best thing!”). Instead of looking at in abstract, it’s helpful to look at utilitarian systems in action.

What quality people choose as their ethical barometer/best measure of the goodness of the world tells you a lot about what they value. Here’s four common ones. As you read them, consider both what implicit values they encode and which ones call out to you.

QALY Utilitarianism

QALY Utilitarianism is most commonly seen in discussions around medical ethics, where QALYs are frequently used to determine the optimal allocation of resources. One QALY represents one year of reasonably healthy and happy life. Any conditions which reduce someone’s enjoyment of life results in those years so blighted being weighed as less than one full QALY.

For example, a year living with asthma is worth 0.9 QALYs. A year with severe seizures is worth 0.7 QALYs.

Let’s say we have a treatment for asthma that cost $1000 and another for epilepsy that costs $1000. If we only have $1000, we should treat the epilepsy (this leads to an increase of 0.3 QALYs, more than the 0.1 QALYs we’d get for treating asthma).

If we have more money, we should treat epilepsy until we run out of epileptic patients, then use the remaining money for asthma.

Things become more complicated if the treatments cost different amounts of money. If it is only $100 to treat asthma, then we should instead prioritize treating asthma, because $1000 of treatment buys us 1 QALY, instead of only 0.3.

Note that QALY utilitarianism (and utilitarianism in general) doesn’t tell us what is right per se. It only gives us a relative ranking of actions. One of those actions may produce the most utility. But that doesn’t necessarily mean that the only right thing to do is constantly pursue the actions that produce the very most utility.

QALY utilitarianism remains most useful in medical science, where researchers have spent a lot of time figuring out the QALY values for many potential conditions. Used with a set of accurate QALY tables, it becomes a powerful way to ensure cost effectiveness in healthcare. QALY utilitarianism is less useful when we lack these tables and therefore remains sparsely used for non-healthcare related decisions.

Hedonistic Utilitarianism

Hedonistic utilitarianism is much more general than QALY utilitarianism, in part because its value function is relatively easy to calculate.

It is almost a tautology to claim that people wish to seek out pleasure and avoid pain. If we see someone happy about an activity we think of us painful, it’s much more likely that we’re incorrectly assessing how pleasurable/painful they find it than it is that they also find the activity painful.

Given how common pleasure-seeking/pain-avoiding is, it’s unsurprising that pleasure has been associated with The [moral] Good and pain with The [moral] Bad at least since the time of Plato and Socrates.

It’s also unsurprising that pleasure and pain can form the basis of utilitarian value functions. This is Hedonistic Utilitarianism and it judges actions based on the amount of net pleasure they cause across all people.

Weighing net pleasure across all people gives us some wiggle room. Repeatedly taking heroin is apparently really, really pleasurable. But it may lead to less pleasure overall if you quickly die from a heroin overdose, leaving behind a bereaved family and preventing all the other pleasure you could have had in your life.

So the hedonistic utilitarianism value function probably doesn’t assign the highest rating to getting everyone in the world blissed out on the most powerful drugs available.

But even ignoring constant drug use, or other descents into purely hedonistic pleasures, hedonistic utilitarianism often frustrates people who hold a higher value on actions that may produce less direct pleasure, but lead to them feeling more satisfied and contented overall. These people are left with two options: they can argue for ever more complicated definitions of pleasure and pain, taking into account the hedonic treadmill and hedonistic paradox, or they can pick another value function.

Preference Utilitarianism

Preference utilitarianism is simple on the surface. Its value function is supposed to track how closely people’s preferences are fulfilled. But there are three big problems with this simple framing.

First, which preferences? I may have the avowed preference to study for a test tomorrow, but once I sit down to study my preference may be revealed to be procrastinating all night. Which preference is more important? Some preference utilitarians say that the true preference is the action you’d pick in hindsight if you were perfectly rational. Others drop the “truly rational” part, but still talk about preferences in terms of what you’d most want in hindsight. Another camp gives credence to the highest level preference over all the others. If I prefer in the moment to procrastinate but would prefer to prefer to want to study, then the meta-preference is the one that counts. And yet another group of people give the most weighting to revealed preferences ­– what you’d actually do in the situation.

It’s basically a personal judgement call as to which of these groups you fall into, a decision which your own interactions with your preferences will heavily shape.

The second problem is even thornier. What do we do when preferences collide? Say my friend and I go out to a restaurant. She may prefer that we each pay for our own meals. I may prefer that she pays for both of our meals. There is no way to satisfy both of our preferences at the same time. Is the most moral outcome assuaging whomever holds their preferences the most strongly? Won’t that just incentivize everyone to hold their preferences as strongly as humanly possible and never cooperate? If enough people hold a preference that a person or a group of people should die, does it provide more utility to kill them than to let them continue living?

One more problem: what do we do with beings that cannot hold preferences? Animals, small children, foetuses, and people in vegetative states are commonly cited as holding no preferences. Does this mean that others may do whatever they want with them? Does it always produce more utility for me to kill any animal I desire to kill, given it has no preferences to balance mine?

All of these questions remain inconclusively answered, leaving each preference utilitarian to decide for herself where she stands on them.

Rule Utilitarianism

The three previous forms of utilitarianism are broadly grouped together (along with many others) under act utilitarianism. But there is another way and a whole other class of value functions. Meet rule utilitarianism.

Rule utilitarians do not compare actions and outcomes directly when calculating utility. Instead they come up with a general set of rules which they believe promotes the most utility generally and judge actions according to how well they satisfy these rules.

Rule utilitarianism is similar to Kantian deontology, but it still has a distinctly consequentialist flavour. It is true that both of these systems result (if followed perfectly) in someone rigidly following a set of rules without making any exceptions. The difference, however, is in the attitude of the individual. Whereas Kant would call an action good only if done for the right reasons, rule utilitarians call actions that follow their rules good regardless of the motivation.

The rules that arise can also look different from Kantian deontology, depending on the beliefs of the person coming up with the rules. If she’s a neo-reactionary who believes that only autocratic states can lead to the common good, she’ll come up with a very different set of rules than Immanuel Kant did.

First Order Utilitarianism?

All of the systems described here are what I’ve taken to calling first order utilitarianism. They only explicitly consider the direct effects of actions, not any follow-on effects that may happen years down the road. Second-order utilitarianism is a topic for another day.

Other Value Functions?

This is just a survey of some of the possible value functions a utilitarian can have. If you’re interested in utilitarianism in principle but feel like all of these value functions are lacking, I encourage you to see what other ones exist out there.

I’m going to be following this post up with a post on precedent utilitarianism, which solved this problem for me.

Epistemic Status: Ethics