## Monday, August 08, 2016

### Eight basic laws of physics, and one that isn't

**by Paul Braterman**

Michael Gove (remember him?), when England's Secretary of State for Education, told teachers

"What [students] need is a rooting in the basic scientific principles, Newton's Laws of thermodynamics and Boyle's law."

Never have I seen so many major errors expressed in Newton via Wikipedia in so few words. But the wise learn from everyone, [1] so let us see what we can learn here from Gove.

From the top: Newton's laws. Gove most probably meant Newton's Laws of Motion, but he may also have been thinking of Newton's Law (note singular) of Gravity. It was by combining all four of these that Newton explained the hitherto mysterious phenomena of lunar and planetary motion, and related these to the motion of falling bodies on Earth; an intellectual achievement not equalled until Einstein's General Theory of Relativity.

*Above, L, Isaac Newton, 1689. Below, R, Michael Gove, 2013 *

In Newton's physics, 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 a 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. And, very importantly, 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.

*Left, Solar system (schematic, not to scale), showing orbits of inner planets*

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.

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 separate objects.

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. If, for instance, we could move the Earth to twice its present distance from the Sun, the Sun's gravitational pull on it would drop to a quarter of its present value.

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 this exactly matches the amount of acceleration needed to hold the moon in its orbit going round the Earth 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 that if two things are in thermal equilibrium with a third thing, they must be in thermal equilibrium with each other. Otherwise, we could transform heat into work by making it go round in circles.)

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. [2] 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 the turbine of a nuclear power station. 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.

*Above, L, the rotor of a turbine is a device for converting heat energy into electrical energy, in accord with the First Law. But the Second Law (see below) places a limit on how efficiently we can do this. Below, R, dye becoming more, not less, spread out over time, in accord with the Second Law*

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 while retaining 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.[3]

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 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. 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 equally 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?

In the end, it comes down to statistics. There are more ways of being spread out than there are of being restricted. There are more ways of moving dye molecules from high to low concentration regions than there are of moving them back again, simply because there *are* more dye molecules in the former than there are in the latter. There is an excellent video illustration of this effect, using sheep, by the Princeton-based educator Aatish Bhatia.

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 substances, 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.

*R, a fluyt, typical ocean-going vesselof Newton's time. Below, L, the *Great Western*, first trans-Atlantic steamship, designed by Isidore Kingdom Brunel, on its maiden voyage*

So 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. Neither the science, nor its social and economic context.

That's bad enough. But the kind of ignorance involved in describing Boyle's Law as a "basic scientific principle" is even more damaging.

(Disclosure: I taught Boyle's Law for over 40 years, and it gets three index entries in my book, *From Stars to Stalagmites*.)

Bottom line: Boyle's Law is *not* basic. It is a secondary consequence of the Kinetic Theory of Gases, which *is* basic. The difference is enormous, and matters. Anyone who thinks that Boyle's Law is a principle doesn't know what a principle is. (So a leading Westminster politician doesn't know what a principle is? That figures.)

Mathematically, the Law is simply stated, which may be why Mr Gove thinks it is basic: volume is inversely proportional to pressure, which gives you a nice simple equation, as in the graph on the right:

*P x V = a constant*

that even a Cabinet Minister can understand. But on its own, it is of no educational value whatsoever. It only acquires value if you put it in its context, but this appeal to context implies a perspective on education beyond his comprehension.

Now to what *is* basic; the fundamental processes that make gases behave as Boyle discovered. His Law states that if you double the pressure on a sample of gas, you will halve the volume. He thought this was because the molecules of gas repel each other, so it takes more pressure to push them closer together, and Newton even put this idea on a mathematical footing, by suggesting an inverse square law for repulsion, rather like his Inverse Square Law for gravitational attraction. They were wrong.

The Law is now explained using the Kinetic Theory of Gases. This describes a gas as shown on the left; as a whole lot of molecules, of such small volume compared to their container that we can think of them as points, each wandering around doing their own thing, and, from time to time, bouncing off the walls. It is the impact of these bounces that gives rise to pressure. If you push the same number of molecules (at the same temperature) into half the volume, each area of wall will get twice as many bounces per second, and so will experience twice the pressure. Pressure x volume remains constant; hence Boyle's Law.

Actually, Boyle's Law isn't even true. Simple kinetic theory neglects the fact that gas molecules attract each other a little, making the pressure less than what the theory tells you it ought to be. And if we compress the gas into a very small volume, we can no longer ignore the volume taken up by the actual molecules themselves.

So what does teaching Boyle's Law achieve? Firstly, a bit of elementary algebra that gives clear answers, and that can be used to bully students if, as so often happens, they meet it in science before they have been adequately prepared in their maths classes. This, I suspect, is the aspect that Gove finds particularly appealing. Secondly, some rather nice experiments involving balancing weights on top of sealed-off syringes. Thirdly, insight into how to use a mathematical model and, at a more advanced level, how to allow for the fact that real gases do not exactly meet its assumptions. Fourthly, a good example of how the practice of science depends on the technology of the society that produces it. In this case, seventeenth century improvements in glassmaking made it possible to construct tubes of uniform cross-section, which are needed to compare volumes of gas accurately. Fifthly … but that's enough to be going on with. Further elaboration would, ironically, lead us on to introductory thermodynamics. Ironically, given the interview that started this discussion. The one thing it does *not* achieve is the inculcation of a fundamental principle.

There are mistakes like thinking that Shakespeare, not Marlowe, wrote *Edward II*. There are mistakes like thinking that Shakespeare wrote *War and Peace*. And finally, there are mistakes like thinking that Shakespeare wrote *War and Peace*, that this is basic to our understanding of literature, and that English teachers need to make sure that their pupils know this. Then Education Secretary Gove's remarks about science teaching fall into this last category. Such ignorance of basic science (and education) at the highest levels of government is laughable. But it is not funny.

1] Ben Zoma, *Mishnah* *Chapters of the Fathers*, 4a. "Chapters of the Fathers" may also be interpreted to mean "Fundamental Principles".

2] It is often said that Einstein's famous equation,

*E = mc ^{2}*

means that we can turn mass into energy. That puts it back to front. The equation is really telling us that energy itself has mass.

3] There are lots of situations (steam condensing to make water, living things growing, or indeed urine becoming more concentrated in the kidney) where a system becomes less spread out, but this change is always accompanied by something in the surrounds, usually heat energy, becoming more spread out to compensate.

*Newton as painted by Godfrey Keller, via Wikipedia. Gove image via Daily Telegraph (Gove connoisseurs may find the link amusing. Solar system image from NASA. Steam turbine blade Siemens via Wikipedia. Dye diffusing in water from Royal Society of Chemistry. Fluyt imge from Pirate King website. *Great Western *on maiden voyage, 1938, by unknown artist, via Wikipedia. *Boyle's Law curve from Krishnavedala repllot of Boyle's own data, via Wikipedia. *Kinetic theory image via Chinese University of Hong Kong*

Posted by Paul Braterman at 12:45 AM | Permalink