Why The World Is Warming

(Work in Progress)

Since the industrial revolution, the mean temperature of our planet’s surface has increased by 1.1°C. This heating is projected to continue at an increasing pace. That is very, very bad for a number of reasons, including:

1. The air becomes too hot for humans and other life. Heatwaves threaten to directly kill millions of people in susceptible regions like South Asia.
2. Hotter water evaporates faster from the sea, raining down in more frequent and intense storms and floods which wipe away topsoil. Meanwhile, soil moisture also evaporates faster, leading to droughts.
3. The ocean thermally expands from its own increased heat and grows further as it receives melt water from vanishing polar and mountain ice, swallowing coastal populations as it rises.

Most people know that the root cause of this heating is the release of ‘greenhouse gases’ into the atmosphere from the burning of fossilised hydrocarbons (e.g. coal, petroleum, methane gas) for fuel. However, I reckon that most people’s scientific understanding of the causes of global warming does not extend much further than that—even among those who are correctly concerned about its consequences. I feel justified in thinking this because it was certainly true of me!

It was only when I started to get curious about the details of global warming that I realised how little I actually understood. One unanswered question would lead me to think of another, and step by step I built up an intuitive understanding of what was going on. My purpose here is to take you on that journey with me (well, a sped-up version without confusion and dead ends) so that when you’re done reading you’ll feel like it’s obvious.

Let’s start with a seemingly odd question.

Why isn’t the planet melting?

No, seriously, think about it.

The planet is being continuously cooked by the Sun. We may as well be roasting in an oven that someone forgot to turn off. Logically, then, without some way of cooling off, things should get hotter and hotter without limit until the oceans become a seafood hotpot and eventually everything solid melts in a the-floor-is-lava style apocalypse.

You and I and everything else on Earth can cool down by conducting our heat into the surrounding air, of course, which then convects away. But the atmosphere doesn’t go on forever. The planet itself is surrounded by the near-perfect vacuum of outer space–there is nothing up there for the atmosphere to conduct its own heat away to! Yet, obviously, the planet isn’t melting. So the question becomes: how does it release its heat?

The answer turns out to be that it leaves exactly the same way it got here: as light!

In order to understand how that’s possible, though, we need to answer a more basic question.

What the heck is light?

First, a rant. I promise this is relevant.

Physics is full of horrible jargon. Of all its many confusing words, though, I believe the worst offender may be the humble label chosen for the second derivative of position with respect to time: acceleration. For starters, in no other discipline can I think of a concept so fundamental being saddled with a word that takes up five whole syllables. It would be like if mathematicians talked about ‘countingdoohickeys’ instead of numbers.

Perhaps more importantly, it carries a meaning in ordinary language that is crucially different to its meaning in physics. When we say that something is ‘accelerating’, we ordinarily just mean that it is getting faster. By contrast, if something is slowing down, we will ordinarily say that it is ‘decelerating’. If something is changing its direction of movement, we will say that it is ‘turning’, ‘spinning’, or ‘orbiting’, depending on context. In physics parlance, though, all of these things are accelerations, because acceleration refers to any change in the speed or direction of movement–including coming to a complete stop! To avoid confusion, let us use a simple word without unwanted connotations to refer to this all-encompassing sense of acceleration as any change in velocity: velshift.

In order to accelerate—er, I mean, velshift something, you need to apply a force to it. In fact, that’s how force is defined: something that causes a certain mass to velshift by a certain amount. In normal life, it seems you have to touch something in order to apply a force to it (unless you happen to be telekinetic). However, forces can be exerted over distance through what physicists call fields. Think of two magnets repelling or attracting one another. They are able to do so because they ‘touch’ through their overlapping influences on the volume of the invisible electromagnetic field between them. Actually, it turns out that all forces are exerted through fields (and hence they are the origin of all velshifts). Even when you are pressing against something with your skin, on an atomic level the force is mediated by the electromagnetic repulsion between your skin’s atoms and the atoms of the thing you are pressing against–not so dissimilar from tiny magnets!

The way the electromagnetic force field works is a bit complicated, to say the least. Fortunately for our purposes, there is only one thing about it which we absolutely need to understand.

Whenever an electron velshifts, it produces a ripple in the electric field which, when the ripple reaches another electron, forces the other electron to velshift the same way. For example, if an electron velshifts to the left, then it will send out a ripple–which is really to say an outwardly expanding 3-dimensional sphere–of right-pointing force in the electric field, which if felt by other electrons will push them right, too.

If an electron is continuously velshifting, such as by vibrating (essentially wiggling back and forth), then it will therefore produce not just a ripple but a continuous wave in the electric field, which will force other electrons to feel the same continuous velshift–they will start to wiggle too.

Since heat fundamentally refers to the velshifting of atoms within matter, and velshifting atoms contain velshifting electrons, all matter naturally converts its heat into outgoing EM waves over time. Even within matter of a uniform temperature, though, individual electrons will be velshifting with different frequencies. Therefore, the EM waves emitted will be distributed across a range of frequencies. However, they will not be evenly distributed, and the peak of the frequency distribution will be higher the higher the temperature of the emitting matter. The total amount of energy emitted this way will be proportional to the fourth power of the temperature. So, if an object doubles in temperature, it will release energy as EM waves sixteen times faster.

Our Sun, whose surface is 5600°C, therefore emits a huge amount of EM waves. Some of this radiation reaches Earth and makes the Earth’s atoms wiggle (heat up). We have evolved specialised sensory organs to detect and distinguish the peak frequencies of this solar radiation. We call these organs ‘eyes’ and the radiation ‘light’. Really, though, there’s no reason to restrict the word ‘light’ to just those frequencies we evolved to see. In fact, I think much becomes clearer when we understand that all EM waves are light, just light that is mostly invisible to us. That’s because it allows us to carry over valuable intuitions and language we’ve built from interacting with visible light. For example, human bodies emit thermal electromagnetic radiation, too. But I think it would be more intuitive to say that our heat makes us glow, albeit vastly dimmer and only in invisible infrared ‘colours’, in exactly the same way that the Sun’s heat makes it glow.

And now we are able to answer our first question: as the Sun’s thermal light is absorbed by the Earth as heat, by the same principle the Earth starts glowing with thermal light of its own, thereby releasing the energy back into space.

Because the intensity of the Earth’s glow increases with (the fourth power of) its temperature, it must eventually reach a point where the amount of light it is emitting into space is exactly equal to the amount it is absorbing from the Sun. At this point, which we call thermal equilibrium, the temperature will be stable.

Since we know the amount of energy that we receive from the Sun per unit time, and we know how much energy will be thermally radiated from the Earth’s surface at each possible temperature, we can very easily calculate what the temperature of the Earth’s surface should be at this thermal equilibrium. Plugging in the numbers, the result turns out to be… −18°C. Needless to say, this is not what we experience.

We’re now left with the opposite question from the one we started with.

Why isn’t the planet freezing?

It turns out that, in a certain sense, the above calculation was entirely correct. If you were floating in space, and you pointed a temperature gun (infrared thermometer) at the Earth, it really would read around −18°C, on average. Meanwhile, the Earth’s mean surface temperature–the increase of which is what we mean when we talk about global warming–is about 15°C, a full 33° hotter. So, what gives?

Let’s consider a single visible photon of light coming to us from the Sun. It will have no trouble passing through the atmosphere. It may be scattered (which is why the sky is visible), but it is unlikely to be absorbed by atmospheric molecules. Once it reaches the surface, it might be reflected back into space (which is why you can see the Earth’s surface from space), but otherwise it will simply be absorbed as heat, as it wiggles the electrons of an atom. This thermal energy will then no doubt be conducted to other atoms, and eventually re-emitted as light again, but this time as lower-frequency infrared. However, although the atmosphere does not absorb visible light, it does contain molecules which absorb infrared light. Therefore, infrared light from the surface is quickly absorbed as heat. After being absorbed, the heat is almost immediately conducted to other molecules, and then almost as quickly re-radiated by them as infrared light–but in a random direction, so just as likely down as back up. This process repeats many times, with the energy slowly making its way up towards space in a very, very long random path.

This energy only escapes once it reaches an altitude of, on average, about 5000 metres, where the atmosphere above is thin enough that the infrared light will (on average) reach the vacuum of space without being absorbed again. This is known as the Effective Altitude of Emission or, more colloquially, the Top-of-Atmosphere–in truth the atmosphere extends far beyond this but there aren’t many infrared absorbing molecules up there. In any case, would you like to have a guess at what the average air temperature at the Effective Altitude of Emission is? It’s −18°C. As the concentration of infrared absorbing gases in the atmosphere increases, energy needs to reach higher and higher altitudes before it can escape, and thus the Effective Altitude of Emission increases. This means that the energy stays on Earth for longer. Another way of thinking about it is that, since the atmosphere gets colder with altitude at a fixed rate of about 6.5°C per 1000 metres (known as the atmospheric lapse rate), if the atmosphere is reaching −18°C at a higher altitude, this implies the surface has gotten hotter. If the Effective Altitude of Emission were to be raised by just 500 metres, then that would result in more than three degrees of warming. This is the greenhouse effect.

If one took all of the greenhouse gases out of the atmosphere, the Effective Altitude of Emission would fall to 0m, and so the mean surface temperature would be −18°C. The greenhouse effect is essential to life on earth.

How are greenhouse gases possible?

Why do some gases let most light through but block specific frequencies?

Imagine you are pushing someone on a swing. You give them an initial push, and they swing forward. As they gain height, they slow down, stop for an instant, and then start swinging back to you as their gravitational potential is released. But you wait until they are about to start swinging away from you again before you make your second push. Why? Because pushing them whilst they are swinging toward you would take energy out of the system. You always want to push when your force and the restoring force of gravity are pushing in the same direction.

If you push the swing for long enough, you could note down an exact frequency that is optimal for maximising the height of the swing. If you want to get the swing to go higher–enter a higher energy state–you need to push with the same frequency. If you push with any other frequency, then it doesn’t matter how hard you push, you will not add energy to the system in the long run as half of your pushes will be slowing the swing down.

Essentially, molecular bonds in a polar molecule are like the swing. The restoring force is the electromagnetic force between the two atoms. Light pushes the electrons in these atoms back and forth, however because there is a charge imbalance it pushes one atom more strongly than the other, causing the bond to bend. Infrared light does this at just the right frequency that this bending is amplified over time, and the light is thereby absorbed.

In fact, any gas molecule with three or more atoms is guaranteed to have polar vibrational states and therefore to absorb infrared light as heat.

Putting it all together

The world is warming because the Sun’s energy is overstaying its welcome as the distance in space and time between first absorption and final re-emission increases.

To see it for yourself: in the simulation, sunlight streams down from above and warms the ground. The ground glows infrared upward. The greenhouse gas molecules (green) catch some of that outgoing infrared and re-emit it in a random direction; the non-greenhouse molecules (faint grey) just bounce around, indifferent.

Hold the smokestack’s button to release CO₂. Click the tree to absorb some. Watch what happens to the average altitude of emission—the dashed red line—and to the ground temperature.

(More to come.)