Newton, thermodynamics, Boyle’s Law, and the basics; a lesson for Michael Gove

On Monday, the Education Secretary said “What [students] need is a rooting in the basic scientific principles, Newton’s laws of thermodynamics and Boyle’s law.” [Times interview, reported here]. He has been widely criticized for this (e.g. here and here), but it’s still worth discussing exactly why what he said is so appallingly wrong, on at least four separate counts. In the unlikely event that Mr. Gove ever reads this, he may learn something. Muddling up the laws of motion with the laws of thermodynamics is bad enough. Muddling up an almost incidental observation, like Boyle’s Law, is even worse, especially when this muddle comes from someone in charge of our educational system [well, not mine actually; I’m glad to say I live in Scotland], and in the very act of his telling teachers and examiners what is, and what is not, important.

Okay, from the top. Newton’s laws; Gove probably meant (if he meant anything) Newton’s laws of motion, but he may also have been thinking of Newton’s law (note singular) of gravity. The laws of motion are three in number:

1) If no force is acting on it, a body will carry on moving at the same speed in a straight line.

2) If force is acting on it, the body will undergo acceleration, according to the equation

 Force = mass x acceleration

3) Action and reaction are equal and opposite

So what does all this mean? In particular, what do scientists mean by “acceleration”? Acceleration is rate of change of velocity. Velocity is not quite the same thing as speed; it is speed in a particular direction. So the first law just says that if there’s no force, there’ll be no acceleration, no change in velocity, and the body will carry on moving in the same direction at the same speed. Notice, by the way, that if a body changes direction, that is a kind of acceleration, even if it keeps on going at the same speed. For example, if something is going round in circles, there must be a force (sometimes, confusingly, called centrifugal force) that keeps it accelerating inwards, and stops it from going straight off at a tangent.

Then what about the heavenly bodies, which travel in curves, pretty close to circles although Kepler’s more accurate measurement had already shown by Newton’s time that the curves are actually ellipses? The moon, for example. The moon goes round the earth, without flying off at a tangent. So the earth must be exerting a force on the moon.

And finally, the third law. If the earth is tugging on the moon, then the moon is tugging equally hard on the earth. We say that the moon goes round the earth, but it is more accurate to say that earth and moon both rotate around their common centre of gravity.

Notice that all of this describes the motion of single bodies. Thermodynamics, as we shall see, only comes into play when we have very large numbers of individual bodies.

The other thing that Gove might have meant is Newton’s inverse square law of gravity, which tells us just how fast gravity decreases with distance.

Now here is the really beautiful bit. We can measure (Galileo already had measured) how fast falling bodies here on earth accelerate under gravity. Knowing how far we are from the centre of the earth, and how far away the moon is, we can work out from the inverse square law how strong the earth’s gravity is at that distance, and then, from Newton’s second law, how fast the moon ought to be accelerating towards the earth. And when we do this calculation, we find that that exactly matches the amount of acceleration needed to hold the moon in its orbit going round the earth just once every lunar month. (Any decent present-day physics student should be able to do this calculation in minutes. For Newton to do it for the first time involved some rather more impressive intellectual feats, such as clarifying the concepts of force, speed, velocity and acceleration, formulating the laws I’ve referred to, and inventing calculus.)

But what about the laws of thermodynamics? These weren’t discovered until the 19^th century, the century of the steam engine. People usually talk about the three laws of thermodynamics, although there is actually another one called the Zero^th Law, because people only really noticed they had been assuming it long after they had formulated the others. (This very boring law says roughly that if two things are at the same temperature as – in physics-speak, at thermal equilibrium with – a third thing, they must be at the same temperature as each other. Otherwise, we couldn’t have the concept of “same temperature”.)

The First Law of thermodynamics is, simply, the conservation of energy. That’s all kinds of energy added up together, including for example heat energy, light energy, electrical energy, and the “kinetic energy” that things have because they’re moving. One very important example of the conservation of energy is what happens inside a heat engine, be it an old-fashioned steam engine, an internal combustion engine, or a power-generating turbine. Here, heat is converted into other forms of energy, such as mechanical or electrical. This is all far beyond anything Newton could have imagined. Newton wrote in terms of force, rather than energy, and he had been dead for over a century before people realized that the different forms of energy include heat.

There are many ways of expressing the Second Law, usually involving rather technical language, but the basic idea is always the same; things tend to get more spread out over time, and won’t get less spread out unless you do some work to make them. (One common formulation is that things tend to get more disordered over time, but I don’t like that one, because I’m not quite sure how you define the amount of disorder, whereas there are exact mathematical methods for describing how spread out things are.) For example, let a drop of food dye fall into a glass full of water. Wait, and you will see the dye spread through the water. Keep on waiting, and you will never see it separating out again as a separate drop. You can force it to, if you can make a very fine filter that lets the water through but retains the dye, but it always takes work to do this. To be precise, you would be working against osmotic pressure, something your kidneys are doing all the time as they concentrate your urine.

This sounds a long way from steam engines, but it isn’t. Usable energy (electrical or kinetic, say) is much less spread out than heat energy, and so the Second Law limits how efficiently heat can ever be converted into more useful forms.

The Second Law of thermodynamics also involves a radical, and very surprising, departure from Newton’s scheme of things. Newton’s world is timeless. Things happen over time, but you would see the same kinds of things if you ran the video backwards. We can use Newton’s physics to describe the motion of planets, but it could equally well describe these motions if they were all exactly reversed.

Now we have a paradox, to which I have yet to see a good solution, although I have seen many brave tries. Every single event taking place in the dye/water mixture can be described in terms of interactions between particles, and every such interaction can, as in Newton’s physics, be as well described going forwards or backwards. To use the technical term, each individual interaction is reversible. But the overall process is irreversible; you can’t go back again. You cannot unscramble eggs. Why not?

The Third Law is more complicated, and was not formulated until the early 20^th century. It enables us to compare the spread-out-ness of heat energy in different chemical materials, and hence to predict which way chemical reactions tend to go. We can excuse Gove for not knowing about the Third Law, but the first two, as C. P. Snow pointed out a generation ago, should be part of the furniture of any educated mind.

If you don’t immediately realize that Newton’s laws and the laws of thermodynamics belong to different stages of technology, the age of sail as opposed to the age of steam, and to different levels of scientific understanding, the individual and macroscopic as opposed to the statistical and submicroscopic, then you don’t know what you’re talking about. Gove’s blunder has been compared to confusing Shakespeare with Dickens. It is far, far worse than that. It is – I am at a loss for an adequate simile. All I can say is that it is as bad as confusing Newton’s laws with the laws of thermodynamics, and I can’t say worse than that.

I will write on why Boyle’s Law is not basic tomorrow.